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in astrophysics and planetary science, spectral slope, also called spectral gradient, is a measure of dependence of the reflectance on the wavelength. in digital signal processing, it is a measure of how quickly the spectrum of an audio sound tails off towards the high frequencies, calculated using a linear regression. = = spectral slope in astrophysics and planetary science = = the visible and infrared spectrum of the reflected sunlight is used to infer physical and chemical properties of the surface of a body. some objects are brighter ( reflect more ) in longer wavelengths ( red ). consequently, in visible light they will appear redder than objects showing no dependence of reflectance on the wavelength. the diagram illustrates three slopes : a red slope, the reflectance is increasing with the wavelengths flat spectrum ( in black ) and a blue slope, the reflectance actually diminishing with the wavelengths the slope ( spectral gradient ) is defined as : s = r f 1 − r f 0 λ 1 − λ 0 { \ displaystyle s = { \ frac { r _ { f _ { 1 } } - r _ { f _ { 0 } } } { \ lambda _ { 1 } - \ lambda _ { 0 } } } } where r f 0, r f 1 { \ displaystyle r _ { f _ { 0 } }, r _ { f _ { 1 } } } is the reflectance measured with filters f0, f1 having the central wavelengths λ0 and λ1, respectively. the slope is typically expressed in percentage increase of reflectance ( i. e. reflexivity ) per unit of wavelength : % / 100 nm ( or % / 1000 a ) the slope is mostly used in near infrared part of the spectrum while colour indices are commonly used in the visible part of the spectrum. the trans - neptunian object sedna is a typical example of a body showing a steep red slope ( 20 % / 100 nm ) while orcus'spectrum appears flat in near infra - red. = = spectral slope in audio = = the spectral " slope " of many natural audio signals ( their tendency to have less energy at high frequencies ) has been known for many years, and the fact that this slope is related to the nature of the sound source. one way to quantify this is by applying linear regression to the fourier magnitude spectrum of the signal, which produces a single number indicating the slope of the line - of - best - fit through the spectral data. alternative ways to characterise a sound signal's distribution of energy vs	Spectral slope	wikipedia
is by applying linear regression to the fourier magnitude spectrum of the signal, which produces a single number indicating the slope of the line - of - best - fit through the spectral data. alternative ways to characterise a sound signal's distribution of energy vs. frequency include spectral rolloff, spectral centroid. = = animals that can sense spectral slope = = the dung beetle can see the spectral gradient of the sky and polarised light, and they used this to navigate. desert ants cataglyphis use the polarization and spectral skylight gradients to navigate. = = see also = = roll - off = = references = =	Spectral slope	wikipedia
in machine learning and computer vision, m - theory is a learning framework inspired by feed - forward processing in the ventral stream of visual cortex and originally developed for recognition and classification of objects in visual scenes. m - theory was later applied to other areas, such as speech recognition. on certain image recognition tasks, algorithms based on a specific instantiation of m - theory, hmax, achieved human - level performance. the core principle of m - theory is extracting representations invariant under various transformations of images ( translation, scale, 2d and 3d rotation and others ). in contrast with other approaches using invariant representations, in m - theory they are not hardcoded into the algorithms, but learned. m - theory also shares some principles with compressed sensing. the theory proposes multilayered hierarchical learning architecture, similar to that of visual cortex. = = intuition = = = = = invariant representations = = = a great challenge in visual recognition tasks is that the same object can be seen in a variety of conditions. it can be seen from different distances, different viewpoints, under different lighting, partially occluded, etc. in addition, for particular classes objects, such as faces, highly complex specific transformations may be relevant, such as changing facial expressions. for learning to recognize images, it is greatly beneficial to factor out these variations. it results in much simpler classification problem and, consequently, in great reduction of sample complexity of the model. a simple computational experiment illustrates this idea. two instances of a classifier were trained to distinguish images of planes from those of cars. for training and testing of the first instance, images with arbitrary viewpoints were used. another instance received only images seen from a particular viewpoint, which was equivalent to training and testing the system on invariant representation of the images. one can see that the second classifier performed quite well even after receiving a single example from each category, while performance of the first classifier was close to random guess even after seeing 20 examples. invariant representations has been incorporated into several learning architectures, such as neocognitrons. most of these architectures, however, provided invariance through custom - designed features or properties of architecture itself. while it helps to take into account some sorts of transformations, such as translations, it is very nontrivial to accommodate for other sorts of transformations, such as 3d rotations and changing facial expressions. m - theory provides a framework of how such transformations can be learned. in addition to higher flexibility, this theory also suggests how human brain may have similar capabilities. =	M-theory (learning framework)	wikipedia
accommodate for other sorts of transformations, such as 3d rotations and changing facial expressions. m - theory provides a framework of how such transformations can be learned. in addition to higher flexibility, this theory also suggests how human brain may have similar capabilities. = = = templates = = = another core idea of m - theory is close in spirit to ideas from the field of compressed sensing. an implication from johnson – lindenstrauss lemma says that a particular number of images can be embedded into a low - dimensional feature space with the same distances between images by using random projections. this result suggests that dot product between the observed image and some other image stored in memory, called template, can be used as a feature helping to distinguish the image from other images. the template need not to be anyhow related to the image, it could be chosen randomly. = = = combining templates and invariant representations = = = the two ideas outlined in previous sections can be brought together to construct a framework for learning invariant representations. the key observation is how dot product between image i { \ displaystyle i } and a template t { \ displaystyle t } behaves when image is transformed ( by such transformations as translations, rotations, scales, etc. ). if transformation g { \ displaystyle g } is a member of a unitary group of transformations, then the following holds : ⟨ g i, t ⟩ = ⟨ i, g − 1 t ⟩ ( 1 ) { \ displaystyle \ langle gi, t \ rangle = \ langle i, g ^ { - 1 } t \ rangle \ qquad ( 1 ) } in other words, the dot product of transformed image and a template is equal to the dot product of original image and inversely transformed template. for instance, for image rotated by 90 degrees, the inversely transformed template would be rotated by −90 degrees. consider the set of dot products of an image i { \ displaystyle i } to all possible transformations of template : { ⟨ i, g ′ t ⟩ g ′ ∈ g } { \ displaystyle \ lbrace \ langle i, g ^ { \ prime } t \ rangle \ mid g ^ { \ prime } \ in g \ rbrace }. if one applies a transformation g { \ displaystyle g } to i { \ displaystyle i }, the set would become { ⟨ g i, g ′ t ⟩ g ′ ∈ g } { \ displaystyle \ lbrace \ langle gi, g ^ { \ prime	M-theory (learning framework)	wikipedia
\ displaystyle g } to i { \ displaystyle i }, the set would become { ⟨ g i, g ′ t ⟩ g ′ ∈ g } { \ displaystyle \ lbrace \ langle gi, g ^ { \ prime } t \ rangle \ mid g ^ { \ prime } \ in g \ rbrace }. but because of the property ( 1 ), this is equal to { ⟨ i, g − 1 g ′ t ⟩ g ′ ∈ g } { \ displaystyle \ lbrace \ langle i, g ^ { - 1 } g ^ { \ prime } t \ rangle \ mid g ^ { \ prime } \ in g \ rbrace }. the set { g − 1 g ′ g ′ ∈ g } { \ displaystyle \ lbrace g ^ { - 1 } g ^ { \ prime } \ mid g ^ { \ prime } \ in g \ rbrace } is equal to just the set of all elements in g { \ displaystyle g }. to see this, note that every g − 1 g ′ { \ displaystyle g ^ { - 1 } g ^ { \ prime } } is in g { \ displaystyle g } due to the closure property of groups, and for every g ′ ′ { \ displaystyle g ^ { \ prime \ prime } } in g there exist its prototype g ′ { \ displaystyle g ^ { \ prime } } such as g ′ ′ = g − 1 g ′ { \ displaystyle g ^ { \ prime \ prime } = g ^ { - 1 } g ^ { \ prime } } ( namely, g ′ = g g ′ ′ { \ displaystyle g ^ { \ prime } = gg ^ { \ prime \ prime } } ). thus, { ⟨ i, g − 1 g ′ t ⟩ g ′ ∈ g } = { ⟨ i, g ′ ′ t ⟩ g ′ ′ ∈ g } { \ displaystyle \ lbrace \ langle i, g ^ { - 1 } g ^ { \ prime } t \ rangle \ mid g ^ { \ prime } \ in g \ rbrace = \ lbrace \ langle i, g ^ { \ prime \ prime } t \ rangle \ mid g ^ { \ prime \ prime } \ in g \ rbrace }. one can see that the set of dot products remains the same despite that a transformation was applied to the image! this set by itself may serve as a	M-theory (learning framework)	wikipedia
rangle \ mid g ^ { \ prime \ prime } \ in g \ rbrace }. one can see that the set of dot products remains the same despite that a transformation was applied to the image! this set by itself may serve as a ( very cumbersome ) invariant representation of an image. more practical representations can be derived from it. in the introductory section, it was claimed that m - theory allows to learn invariant representations. this is because templates and their transformed versions can be learned from visual experience – by exposing the system to sequences of transformations of objects. it is plausible that similar visual experiences occur in early period of human life, for instance when infants twiddle toys in their hands. because templates may be totally unrelated to images that the system later will try to classify, memories of these visual experiences may serve as a basis for recognizing many different kinds of objects in later life. however, as it is shown later, for some kinds of transformations, specific templates are needed. = = theoretical aspects = = = = = from orbits to distribution measures = = = to implement the ideas described in previous sections, one need to know how to derive a computationally efficient invariant representation of an image. such unique representation for each image can be characterized as it appears by a set of one - dimensional probability distributions ( empirical distributions of the dot - products between image and a set of templates stored during unsupervised learning ). these probability distributions in their turn can be described by either histograms or a set of statistical moments of it, as it will be shown below. orbit o i { \ displaystyle o _ { i } } is a set of images g i { \ displaystyle gi } generated from a single image i { \ displaystyle i } under the action of the group g, g ∈ g { \ displaystyle g, \ forall g \ in g }. in other words, images of an object and of its transformations correspond to an orbit o i { \ displaystyle o _ { i } }. if two orbits have a point in common they are identical everywhere, i. e. an orbit is an invariant and unique representation of an image. so, two images are called equivalent when they belong to the same orbit : i i ′ { \ displaystyle i \ sim i ^ { \ prime } } if g ∈ g { \ displaystyle \ exists g \ in g } such that i ′ = g i { \ displaystyle i ^ { \ prime }	M-theory (learning framework)	wikipedia
i ′ { \ displaystyle i \ sim i ^ { \ prime } } if g ∈ g { \ displaystyle \ exists g \ in g } such that i ′ = g i { \ displaystyle i ^ { \ prime } = gi }. conversely, two orbits are different if none of the images in one orbit coincide with any image in the other. a natural question arises : how can one compare two orbits? there are several possible approaches. one of them employs the fact that intuitively two empirical orbits are the same irrespective of the ordering of their points. thus, one can consider a probability distribution p i { \ displaystyle p _ { i } } induced by the group's action on images i { \ displaystyle i } ( g i { \ displaystyle gi } can be seen as a realization of a random variable ). this probability distribution p i { \ displaystyle p _ { i } } can be almost uniquely characterized by k { \ displaystyle k } one - dimensional probability distributions p ⟨ i, t k ⟩ { \ displaystyle p _ { \ langle i, t ^ { k } \ rangle } } induced by the ( one - dimensional ) results of projections ⟨ i, t k ⟩ { \ displaystyle \ langle i, t ^ { k } \ rangle }, where t k, k = 1, …, k { \ displaystyle t ^ { k }, k = 1, \ ldots, k } are a set of templates ( randomly chosen images ) ( based on the cramer – wold theorem and concentration of measures ). consider n { \ displaystyle n } images x n ∈ x { \ displaystyle x _ { n } \ in x }. let k ≥ 2 c ε 2 log n δ { \ displaystyle k \ geq { \ frac { 2 } { c \ varepsilon ^ { 2 } } } \ log { \ frac { n } { \ delta } } }, where c { \ displaystyle c } is a universal constant. then \| d ( p i, p i ′ ) − d k ( p i, p i ′ ) \| ≤ ε, { \ displaystyle \| d ( p _ { i }, p _ { i } ^ { \ prime } ) - dk ( p _ { i }, p _ { i } ^ { \ prime } ) \| \ leq \ varepsilon, } with probability 1 −	M-theory (learning framework)	wikipedia
i }, p _ { i } ^ { \ prime } ) - dk ( p _ { i }, p _ { i } ^ { \ prime } ) \| \ leq \ varepsilon, } with probability 1 − δ 2 { \ displaystyle 1 - \ delta ^ { 2 } }, for all i, i ′ { \ displaystyle i, i ^ { \ prime } } ∈ { \ displaystyle \ in } x n { \ displaystyle x _ { n } }. this result ( informally ) says that an approximately invariant and unique representation of an image i { \ displaystyle i } can be obtained from the estimates of k { \ displaystyle k } 1 - d probability distributions p ⟨ i, t k ⟩ { \ displaystyle p _ { \ langle i, t ^ { k } \ rangle } } for k = 1, …, k { \ displaystyle k = 1, \ ldots, k }. the number k { \ displaystyle k } of projections needed to discriminate n { \ displaystyle n } orbits, induced by n { \ displaystyle n } images, up to precision ε { \ displaystyle \ varepsilon } ( and with confidence 1 − δ 2 { \ displaystyle 1 - \ delta ^ { 2 } } ) is k ≥ 2 c ε 2 log n δ { \ displaystyle k \ geq { \ frac { 2 } { c \ varepsilon ^ { 2 } } } \ log { \ frac { n } { \ delta } } }, where c { \ displaystyle c } is a universal constant. to classify an image, the following " recipe " can be used : memorize a set of images / objects called templates ; memorize observed transformations for each template ; compute dot products of its transformations with image ; compute histogram of the resulting values, called signature of the image ; compare the obtained histogram with signatures stored in memory. estimates of such one - dimensional probability density functions ( pdfs ) p ⟨ i, t k ⟩ { \ displaystyle p _ { \ langle i, t ^ { k } \ rangle } } can be written in terms of histograms as μ n k ( i ) = 1 / \| g \| i = 1 \| g \| η n ( ⟨ i, g i t k ⟩ ) { \ displaystyle \ mu _ { n } ^ { k } ( i ) = 1	M-theory (learning framework)	wikipedia
μ n k ( i ) = 1 / \| g \| i = 1 \| g \| η n ( ⟨ i, g i t k ⟩ ) { \ displaystyle \ mu _ { n } ^ { k } ( i ) = 1 / \ left \| g \ right \| \ sum _ { i = 1 } ^ { \ left \| g \ right \| } \ eta _ { n } ( \ langle i, g _ { i } t ^ { k } \ rangle ) }, where η n, n = 1, …, n { \ displaystyle \ eta _ { n }, n = 1, \ ldots, n } is a set of nonlinear functions. these 1 - d probability distributions can be characterized with n - bin histograms or set of statistical moments. for example, hmax represents an architecture in which pooling is done with a max operation. = = = non - compact groups of transformations = = = in the " recipe " for image classification, groups of transformations are approximated with finite number of transformations. such approximation is possible only when the group is compact. such groups as all translations and all scalings of the image are not compact, as they allow arbitrarily big transformations. however, they are locally compact. for locally compact groups, invariance is achievable within certain range of transformations. assume that g 0 { \ displaystyle g _ { 0 } } is a subset of transformations from g { \ displaystyle g } for which the transformed patterns exist in memory. for an image i { \ displaystyle i } and template t k { \ displaystyle t _ { k } }, assume that ⟨ i, g − 1 t k ⟩ { \ displaystyle \ langle i, g ^ { - 1 } t _ { k } \ rangle } is equal to zero everywhere except some subset of g 0 { \ displaystyle g _ { 0 } }. this subset is called support of ⟨ i, g − 1 t k ⟩ { \ displaystyle \ langle i, g ^ { - 1 } t _ { k } \ rangle } and denoted as supp ( ⟨ i, g − 1 t k ⟩ ) { \ displaystyle \ operatorname { supp } ( \ langle i, g ^ { - 1 } t _ { k } \ rangle ) }. it can be proven that if for a transformation g ′ { \ displaystyle g ^ { \ prime } }, support	M-theory (learning framework)	wikipedia
supp } ( \ langle i, g ^ { - 1 } t _ { k } \ rangle ) }. it can be proven that if for a transformation g ′ { \ displaystyle g ^ { \ prime } }, support set will also lie within g ′ g 0 { \ displaystyle g ^ { \ prime } g _ { 0 } }, then signature of i { \ displaystyle i } is invariant with respect to g ′ { \ displaystyle g ^ { \ prime } }. this theorem determines the range of transformations for which invariance is guaranteed to hold. one can see that the smaller is supp ( ⟨ i, g − 1 t k ⟩ ) { \ displaystyle \ operatorname { supp } ( \ langle i, g ^ { - 1 } t _ { k } \ rangle ) }, the larger is the range of transformations for which invariance is guaranteed to hold. it means that for a group that is only locally compact, not all templates would work equally well anymore. preferable templates are those with a reasonably small supp ( ⟨ g i, t k ⟩ ) { \ displaystyle \ operatorname { supp } ( \ langle gi, t _ { k } \ rangle ) } for a generic image. this property is called localization : templates are sensitive only to images within a small range of transformations. although minimizing supp ( ⟨ g i, t k ⟩ ) { \ displaystyle \ operatorname { supp } ( \ langle gi, t _ { k } \ rangle ) } is not absolutely necessary for the system to work, it improves approximation of invariance. requiring localization simultaneously for translation and scale yields a very specific kind of templates : gabor functions. the desirability of custom templates for non - compact group is in conflict with the principle of learning invariant representations. however, for certain kinds of regularly encountered image transformations, templates might be the result of evolutionary adaptations. neurobiological data suggests that there is gabor - like tuning in the first layer of visual cortex. the optimality of gabor templates for translations and scales is a possible explanation of this phenomenon. = = = non - group transformations = = = many interesting transformations of images do not form groups. for instance, transformations of images associated with 3d rotation of corresponding 3d object do not form a group, because it is impossible to define an inverse transformation ( two objects may looks the	M-theory (learning framework)	wikipedia
group transformations = = = many interesting transformations of images do not form groups. for instance, transformations of images associated with 3d rotation of corresponding 3d object do not form a group, because it is impossible to define an inverse transformation ( two objects may looks the same from one angle but different from another angle ). however, approximate invariance is still achievable even for non - group transformations, if localization condition for templates holds and transformation can be locally linearized. as it was said in the previous section, for specific case of translations and scaling, localization condition can be satisfied by use of generic gabor templates. however, for general case ( non - group ) transformation, localization condition can be satisfied only for specific class of objects. more specifically, in order to satisfy the condition, templates must be similar to the objects one would like to recognize. for instance, if one would like to build a system to recognize 3d rotated faces, one need to use other 3d rotated faces as templates. this may explain the existence of such specialized modules in the brain as one responsible for face recognition. even with custom templates, a noise - like encoding of images and templates is necessary for localization. it can be naturally achieved if the non - group transformation is processed on any layer other than the first in hierarchical recognition architecture. = = = hierarchical architectures = = = the previous section suggests one motivation for hierarchical image recognition architectures. however, they have other benefits as well. firstly, hierarchical architectures best accomplish the goal of ‘ parsing ’ a complex visual scene with many objects consisting of many parts, whose relative position may greatly vary. in this case, different elements of the system must react to different objects and parts. in hierarchical architectures, representations of parts at different levels of embedding hierarchy can be stored at different layers of hierarchy. secondly, hierarchical architectures which have invariant representations for parts of objects may facilitate learning of complex compositional concepts. this facilitation may happen through reusing of learned representations of parts that were constructed before in process of learning of other concepts. as a result, sample complexity of learning compositional concepts may be greatly reduced. finally, hierarchical architectures have better tolerance to clutter. clutter problem arises when the target object is in front of a non - uniform background, which functions as a distractor for the visual task. hierarchical architecture provides signatures for parts of target objects, which do not include parts of background and are not affected by background variations. in hierarchical architecture	M-theory (learning framework)	wikipedia
object is in front of a non - uniform background, which functions as a distractor for the visual task. hierarchical architecture provides signatures for parts of target objects, which do not include parts of background and are not affected by background variations. in hierarchical architectures, one layer is not necessarily invariant to all transformations that are handled by the hierarchy as a whole. some transformations may pass through that layer to upper layers, as in the case of non - group transformations described in the previous section. for other transformations, an element of the layer may produce invariant representations only within small range of transformations. for instance, elements of the lower layers in hierarchy have small visual field and thus can handle only a small range of translation. for such transformations, the layer should provide covariant rather than invariant, signatures. the property of covariance can be written as distr ( ⟨ μ l ( g i ), μ l ( t ) ⟩ ) = distr ( ⟨ μ l ( i ), μ l ( g − 1 t ) ⟩ ) { \ displaystyle \ operatorname { distr } ( \ langle \ mu _ { l } ( gi ), \ mu _ { l } ( t ) \ rangle ) = \ operatorname { distr } ( \ langle \ mu _ { l } ( i ), \ mu _ { l } ( g ^ { - 1 } t ) \ rangle ) }, where l { \ displaystyle l } is a layer, μ l ( i ) { \ displaystyle \ mu _ { l } ( i ) } is the signature of image on that layer, and distr { \ displaystyle \ operatorname { distr } } stands for " distribution of values of the expression for all g ∈ g { \ displaystyle g \ in g } ". = = relation to biology = = m - theory is based on a quantitative theory of the ventral stream of visual cortex. understanding how visual cortex works in object recognition is still a challenging task for neuroscience. humans and primates are able to memorize and recognize objects after seeing just couple of examples unlike any state - of - the art machine vision systems that usually require a lot of data in order to recognize objects. prior to the use of visual neuroscience in computer vision has been limited to early vision for deriving stereo algorithms ( e. g., ) and to justify the use of dog ( derivative - of - gaussian ) filters and more recently of gabor filters. no	M-theory (learning framework)	wikipedia
of visual neuroscience in computer vision has been limited to early vision for deriving stereo algorithms ( e. g., ) and to justify the use of dog ( derivative - of - gaussian ) filters and more recently of gabor filters. no real attention has been given to biologically plausible features of higher complexity. while mainstream computer vision has always been inspired and challenged by human vision, it seems to have never advanced past the very first stages of processing in the simple cells in v1 and v2. although some of the systems inspired – to various degrees – by neuroscience, have been tested on at least some natural images, neurobiological models of object recognition in cortex have not yet been extended to deal with real - world image databases. m - theory learning framework employs a novel hypothesis about the main computational function of the ventral stream : the representation of new objects / images in terms of a signature, which is invariant to transformations learned during visual experience. this allows recognition from very few labeled examples – in the limit, just one. neuroscience suggests that natural functionals for a neuron to compute is a high - dimensional dot product between an " image patch " and another image patch ( called template ) which is stored in terms of synaptic weights ( synapses per neuron ). the standard computational model of a neuron is based on a dot product and a threshold. another important feature of the visual cortex is that it consists of simple and complex cells. this idea was originally proposed by hubel and wiesel. m - theory employs this idea. simple cells compute dot products of an image and transformations of templates ⟨ i, g i t k ⟩ { \ displaystyle \ langle i, g _ { i } t ^ { k } \ rangle } for i = 1, …, \| g \| { \ displaystyle i = 1, \ ldots, \| g \| } ( \| g \| { \ displaystyle \| g \| } is a number of simple cells ). complex cells are responsible for pooling and computing empirical histograms or statistical moments of it. the following formula for constructing histogram can be computed by neurons : 1 \| g \| i = 1 \| g \| σ ( ⟨ i, g i t k ⟩ + n δ ), { \ displaystyle { \ frac { 1 } { \| g \| } } \ sum _ { i = 1 } ^ { \| g \| } \ sigma ( \ langle i, g _ { i } t ^ {	M-theory (learning framework)	wikipedia
δ ), { \ displaystyle { \ frac { 1 } { \| g \| } } \ sum _ { i = 1 } ^ { \| g \| } \ sigma ( \ langle i, g _ { i } t ^ { k } \ rangle + n \ delta ), } where σ { \ displaystyle \ sigma } is a smooth version of step function, δ { \ displaystyle \ delta } is the width of a histogram bin, and n { \ displaystyle n } is the number of the bin. = = applications = = = = = applications to computer vision = = = in authors applied m - theory to unconstrained face recognition in natural photographs. unlike the dar ( detection, alignment, and recognition ) method, which handles clutter by detecting objects and cropping closely around them so that very little background remains, this approach accomplishes detection and alignment implicitly by storing transformations of training images ( templates ) rather than explicitly detecting and aligning or cropping faces at test time. this system is built according to the principles of a recent theory of invariance in hierarchical networks and can evade the clutter problem generally problematic for feedforward systems. the resulting end - to - end system achieves a drastic improvement in the state of the art on this end - to - end task, reaching the same level of performance as the best systems operating on aligned, closely cropped images ( no outside training data ). it also performs well on two newer datasets, similar to lfw, but more difficult : significantly jittered ( misaligned ) version of lfw and sufr - w ( for example, the model's accuracy in the lfw " unaligned & no outside data used " category is 87. 55±1. 41 % compared to state - of - the - art apem ( adaptive probabilistic elastic matching ) : 81. 70±1. 78 % ). the theory was also applied to a range of recognition tasks : from invariant single object recognition in clutter to multiclass categorization problems on publicly available data sets ( caltech5, caltech101, mit - cbcl ) and complex ( street ) scene understanding tasks that requires the recognition of both shape - based as well as texture - based objects ( on streetscenes data set ). the approach performs really well : it has the capability of learning from only a few training examples and was shown to outperform several more complex state -	M-theory (learning framework)	wikipedia
both shape - based as well as texture - based objects ( on streetscenes data set ). the approach performs really well : it has the capability of learning from only a few training examples and was shown to outperform several more complex state - of - the - art systems constellation models, the hierarchical svm - based face - detection system. a key element in the approach is a new set of scale and position - tolerant feature detectors, which are biologically plausible and agree quantitatively with the tuning properties of cells along the ventral stream of visual cortex. these features are adaptive to the training set, though we also show that a universal feature set, learned from a set of natural images unrelated to any categorization task, likewise achieves good performance. = = = applications to speech recognition = = = this theory can also be extended for the speech recognition domain. as an example, in an extension of a theory for unsupervised learning of invariant visual representations to the auditory domain and empirically evaluated its validity for voiced speech sound classification was proposed. authors empirically demonstrated that a single - layer, phone - level representation, extracted from base speech features, improves segment classification accuracy and decreases the number of training examples in comparison with standard spectral and cepstral features for an acoustic classification task on timit dataset. = = references = =	M-theory (learning framework)	wikipedia
a floating airport is an airport built and situated on a very large floating structure ( vlfs ) located many miles out at sea utilizing a flotation type of device or devices such as pneumatic stabilized platform ( psp ) technology. as the population increases and land becomes more expensive and scarce, very large floating structures ( vlfs ) such as floating airports could help solve land use, pollution and aircraft noise issues. = = early history = = the first discussion of a floating airport was for trans - atlantic flights. at that time a passenger aircraft capable of making the trip could be built, but because of the massive need for fuel for the flight, it had a limited payload. an article appeared in the january 1930 issue of popular mechanics in which a model of a floating airport located in the atlantic was proposed. to make safe flight possible with the aviation technology of that time, it called for eight such airports in the atlantic. but unlike future floating airport ideas which were free floating, this 1930 concept had a floating airport platform, but with stabilizer legs which prevent the flight deck from pitching and rolling, similar in concept to some of today's off shore oil rigs. the cost of establishing eight such floating airports in 1930 was estimated at approximately usd $ 12, 000, 000 equivalent to $ 174, 257, 000 in 2023. the idea of floating airports received fresh attention in 1935 when the famous french aviation pilot and builder bleriot gave one of his last interviews in which he made the case for installing some mid - atlantic ; he called them seadromes as a solution to economical trans - atlantic passenger flights. in 1943, a floating pontoon flight deck, 272 feet wide and 1, 810 feet long was constructed by the seabees at allen harbor using a total of 10, 291 pontoons. it was towed to a cove in narragansett bay, where 140 takeoffs, landings and refuellings were successful in both smooth and rough waters. the pontoon airfield was noted to have advantages over aircraft carriers in lack of requirement for arresting gear for landings, and these could be executed at shorter time intervals. tests showed that damage from four 100 - pound bombs exploding on the floating deck did not interfere with flight operations and could be easily repaired. = = description = = in theory, issues and problems of land - based airports could be minimized by locating airports several miles off the coast. takeoffs and landings would be over water, not over populated areas, thereby eliminating noise pollution and reducing risks of aircraft	Floating airport	wikipedia
description = = in theory, issues and problems of land - based airports could be minimized by locating airports several miles off the coast. takeoffs and landings would be over water, not over populated areas, thereby eliminating noise pollution and reducing risks of aircraft crashes to the land - locked population. since little of the ocean's surface is currently being used for human activity, growth and alterations in configuration would be relatively easy to achieve with minimal impact to the environment or to local residents who would utilize the airport. water taxis or other high speed surface vessels would be a part of an offshore mass transit system that could connect the floating airport to coastal communities and minimize traffic issues. a floating structure, such as a floating airport, is theorized to have less impact on the environment than the land - based alternative. it would not require much, if any, dredging or moving of mountains or clearing of green space and the floating structure provides a reef - like environment conducive to marine life. in theory, wave energy could be harnessed, using the structure to convert waves into energy to help sustain the energy needs of the airport. = = modern floating airport projects = = in 2000, the japanese ministry of land, infrastructure, and transport sponsored the construction of mega - float, a 1000 - metre floating runway in tokyo bay. after conducting several real aircraft landings, the ministry concluded that floating runways'hydro - elastic response would not affect aircraft operations, including precision instrument approaches in a protected waterway such as a large bay. the structure has been dismantled and is no longer in use. the pneumatic stabilized platform ( psp ) was proposed as a means for constructing a new floating airport for san diego in the pacific ocean, at least three miles off the tip of point loma. however, this proposed design was rejected in october 2003 due to very high cost, the difficulty in accessing such an airport, the difficulty in transporting jet fuel, electricity, water, and gas to the structure, failure to address security concerns such as a bomb blast, inadequate room for high - speed exits and taxiways, and environmental concerns. achmad yani international airport, the first floating airport in the world started construction on 17 june 2014, and was completed in 2018. however, only the passenger terminal and apron are floating. = = see also = = lily and clover aerospace architecture mobile offshore base = = references = = = = external links = = center for contemporary conflict - " the atlantis garrison : a comprehensive, cost effective cargo and port security strategy " by dr.	Floating airport	wikipedia
. = = see also = = lily and clover aerospace architecture mobile offshore base = = references = = = = external links = = center for contemporary conflict - " the atlantis garrison : a comprehensive, cost effective cargo and port security strategy " by dr. michael j. hillyard ( psp / floating airport technology could be used for cost effective cargo & port security ) september 1996 - " floating airports : wave of the future " november 18, 1999 by michael mccabe, sf chronicle staff writer " planes would land on floating runways built on s. f. bay " centre national de la recherche scientifique " floatport : a floating solution to the san diego airport's environmental problems " auteur ( s ) / author ( s ) blood h. ; innis d., float inc., san diego ca, etats - unis san diego union tribune - signonsandiego. com " floating airport proposal resurfaces " jim bell - ecological designer " airport : thinking outside the box " 9 / 26 / 2005 usatoday. com " today in the sky : will san diego build an airport in the ocean? " by ben mutzabaugh san diego citybeat, " the sinking of the san diego floating airport proposal " by d. a. kolodenko	Floating airport	wikipedia
homeric psychology is a field of study with regards to the psychology of ancient greek culture no later than mycenaean greece, around 1700 – 1200 bce, during the homeric epic poems ( specifically the illiad and the odyssey ). the first scholar to present a theory was bruno snell in his 1953 german book. he argued that an ancient greek person did not have a sense of self, and the greek culture later " self - realized " or " discovered " what he considered the " modern intellect ". eric robertson dodds in 1951 wrote how ancient greek thought may have been irrational, relative to his. he posited that the greeks may have known that a person did things, but the reason was attributed to divine externalities, such as gods and demons. julian jaynes, in 1976, stipulated that greek consciousness emerged from the use of special words related to cognition. some of his claims were empirically supported in a 2021 study by psychohistorian boban dedovic. it compared the word counts of mental language between 34 versions of the iliad and odyssey. = = references = =	Homeric psychology	wikipedia
in quantum electrodynamics ( qed ), the schwinger limit is a scale above which the electromagnetic field is expected to become nonlinear. the limit was first derived in one of qed's earliest theoretical successes by fritz sauter in 1931 and discussed further by werner heisenberg and his student hans heinrich euler. the limit, however, is commonly named in the literature for julian schwinger, who derived the leading nonlinear corrections to the fields and calculated the rate of electron – positron pair production in a strong electric field. the limit is typically reported as a maximum electric field or magnetic field before nonlinearity for the vacuum of e c = m e 2 c 3 q e 1. 32 × 10 18 v / m { \ displaystyle e _ { \ text { c } } = { \ frac { m _ { \ text { e } } ^ { 2 } c ^ { 3 } } { q _ { \ text { e } } \ hbar } } \ simeq 1. 32 \ times 10 ^ { 18 } \, \ mathrm { v } / \ mathrm { m } } b c = m e 2 c 2 q e 4. 41 × 10 9 t, { \ displaystyle b _ { \ text { c } } = { \ frac { m _ { \ text { e } } ^ { 2 } c ^ { 2 } } { q _ { \ text { e } } \ hbar } } \ simeq 4. 41 \ times 10 ^ { 9 } \, \ mathrm { t }, } where me is the mass of the electron, c is the speed of light in vacuum, qe is the elementary charge, and ħ is the reduced planck constant. these are enormous field strengths. such an electric field is capable of accelerating a proton from rest to the maximum energy attained by protons at the large hadron collider in only approximately 5 micrometers. the magnetic field is associated with birefringence of the vacuum and is exceeded on magnetars. in vacuum, the classical maxwell's equations are perfectly linear differential equations. this implies – by the superposition principle – that the sum of any two solutions to maxwell's equations is another solution to maxwell's equations. for example, two intersecting beams of light should simply add together their electric fields and pass right through each other. thus maxwell's equations predict the impossibility of any but trivial	Schwinger limit	wikipedia
to maxwell's equations is another solution to maxwell's equations. for example, two intersecting beams of light should simply add together their electric fields and pass right through each other. thus maxwell's equations predict the impossibility of any but trivial elastic photon – photon scattering. in qed, however, non - elastic photon – photon scattering becomes possible when the combined energy is large enough to create virtual electron – positron pairs spontaneously, illustrated by the feynman diagram in the adjacent figure. this creates nonlinear effects that are approximately described by euler and heisenberg's nonlinear variant of maxwell's equations. a single plane wave is insufficient to cause nonlinear effects, even in qed. the basic reason for this is that a single plane wave of a given energy may always be viewed in a different reference frame, where it has less energy ( the same is the case for a single photon ). a single wave or photon does not have a center - of - momentum frame where its energy must be at minimal value. however, two waves or two photons not traveling in the same direction always have a minimum combined energy in their center - of - momentum frame, and it is this energy and the electric field strengths associated with it, which determine particle – antiparticle creation, and associated scattering phenomena. photon – photon scattering and other effects of nonlinear optics in vacuum is an active area of experimental research, with current or planned technology beginning to approach the schwinger limit. it has already been observed through inelastic channels in slac experiment 144. however, the direct effects in elastic scattering have not been observed. as of 2012, the best constraint on the elastic photon – photon scattering cross section belonged to pvlas, which reported an upper limit far above the level predicted by the standard model. proposals were made to measure elastic light - by - light scattering using the strong electromagnetic fields of the hadrons collided at the lhc. in 2019, the atlas experiment at the lhc announced the first definitive observation of photon – photon scattering, observed in lead ion collisions that produced fields as large as 1025 v / m, well in excess of the schwinger limit. observation of a cross section larger or smaller than that predicted by the standard model could signify new physics such as axions, the search of which is the primary goal of pvlas and several similar experiments. atlas observed more events than expected, potentially evidence that the cross section is larger than predicted by the standard model, but the excess is not yet statistical	Schwinger limit	wikipedia
such as axions, the search of which is the primary goal of pvlas and several similar experiments. atlas observed more events than expected, potentially evidence that the cross section is larger than predicted by the standard model, but the excess is not yet statistically significant. the planned, funded eli – ultra high field facility, which will study light at the intensity frontier, is likely to remain well below the schwinger limit although it may still be possible to observe some nonlinear optical effects. the station of extreme light ( sel ) is another laser facility under construction which should be powerful enough to observe the effect. such an experiment, in which ultra - intense light causes pair production, has been described in the popular media as creating a " hernia " in spacetime. = = see also = = julian schwinger schwinger effect sokolov – ternov effect vacuum polarization = = references = =	Schwinger limit	wikipedia
the subset sum problem ( ssp ) is a decision problem in computer science. in its most general formulation, there is a multiset s { \ displaystyle s } of integers and a target - sum t { \ displaystyle t }, and the question is to decide whether any subset of the integers sum to precisely t { \ displaystyle t }. the problem is known to be np - complete. moreover, some restricted variants of it are np - complete too, for example : the variant in which all inputs are positive. the variant in which inputs may be positive or negative, and t = 0 { \ displaystyle t = 0 }. for example, given the set { − 7, − 3, − 2, 9000, 5, 8 } { \ displaystyle \ { - 7, - 3, - 2, 9000, 5, 8 \ } }, the answer is yes because the subset { − 3, − 2, 5 } { \ displaystyle \ { - 3, - 2, 5 \ } } sums to zero. the variant in which all inputs are positive, and the target sum is exactly half the sum of all inputs, i. e., t = 1 2 ( a 1 + + a n ) { \ displaystyle t = { \ frac { 1 } { 2 } } ( a _ { 1 } + \ dots + a _ { n } ) }. this special case of ssp is known as the partition problem. ssp can also be regarded as an optimization problem : find a subset whose sum is at most t, and subject to that, as close as possible to t. it is np - hard, but there are several algorithms that can solve it reasonably quickly in practice. ssp is a special case of the knapsack problem and of the multiple subset sum problem. = = computational hardness = = the run - time complexity of ssp depends on two parameters : n - the number of input integers. if n is a small fixed number, then an exhaustive search for the solution is practical. l - the precision of the problem, stated as the number of binary place values that it takes to state the problem. if l is a small fixed number, then there are dynamic programming algorithms that can solve it exactly. as both n and l grow large, ssp is np - hard. the complexity of the best known algorithms is exponential in the smaller of the two parameters n and l. the problem is np - hard even when all input	Subset sum problem	wikipedia
can solve it exactly. as both n and l grow large, ssp is np - hard. the complexity of the best known algorithms is exponential in the smaller of the two parameters n and l. the problem is np - hard even when all input integers are positive ( and the target - sum t is a part of the input ). this can be proved by a direct reduction from 3sat. it can also be proved by reduction from 3 - dimensional matching ( 3dm ) : we are given an instance of 3dm, where the vertex sets are w, x, y. each set has n vertices. there are m edges, where each edge contains exactly one vertex from each of w, x, y. denote l : = ceiling ( log2 ( m + 1 ) ), so that l is larger than the number of bits required to represent the number of edges. we construct an instance of ssp with m positive integers. the integers are described by their binary representation. each input integer can be represented by 3nl bits, divided into 3n zones of l bits. each zone corresponds to a vertex. for each edge ( w, x, y ) in the 3dm instance, there is an integer in the ssp instance, in which exactly three bits are " 1 " : the least - significant bits in the zones of the vertices w, x, and y. for example, if n = 10 and l = 3, and w = ( 0,..., 9 ), x = ( 10,..., 19 ), y = ( 20,..., 29 ), then the edge ( 0, 10, 20 ) is represented by the number ( 20 + 230 + 260 ). the target sum t in the ssp instance is set to an integer with " 1 " in the least - significant bit of every zone, that is, ( 20 + 21 +... + 23n - 1 ). if the 3dm instance has a perfect matching, then summing the corresponding integers in the ssp instance yields exactly t. conversely, if the ssp instance has a subset with sum exactly t, then, since the zones are sufficiently large so that there are no " carries " from one zone to the next, the sum must correspond to a perfect matching in the 3dm instance. the following variants are also known to be np - hard : the input integers can be both positive and negative, and the target - sum t = 0. this can be proved by reduction from	Subset sum problem	wikipedia
must correspond to a perfect matching in the 3dm instance. the following variants are also known to be np - hard : the input integers can be both positive and negative, and the target - sum t = 0. this can be proved by reduction from the variant with positive integers. denote that variant by subsetsumpositive and the current variant by subsetsumzero. given an instance ( s, t ) of subsetsumpositive, construct an instance of subsetsumzero by adding a single element with value −t. given a solution to the subsetsumpositive instance, adding the −t yields a solution to the subsetsumzero instance. conversely, given a solution to the subsetsumzero instance, it must contain the −t ( since all integers in s are positive ), so to get a sum of zero, it must also contain a subset of s with a sum of + t, which is a solution of the subsetsumpositive instance. the input integers are positive, and t = sum ( s ) / 2. this can also be proved by reduction from the general variant ; see partition problem. the analogous counting problem # ssp, which asks to enumerate the number of subsets summing to the target, is # p - complete. = = exponential time algorithms = = there are several ways to solve ssp in time exponential in n. = = = inclusion – exclusion = = = the most naive algorithm would be to cycle through all subsets of n numbers and, for every one of them, check if the subset sums to the right number. the running time is of order o ( 2 n ⋅ n ) { \ displaystyle o ( 2 ^ { n } \ cdot n ) }, since there are 2 n { \ displaystyle 2 ^ { n } } subsets and, to check each subset, we need to sum at most n elements. the algorithm can be implemented by depth - first search of a binary tree : each level in the tree corresponds to an input number ; the left branch corresponds to excluding the number from the set, and the right branch corresponds to including the number ( hence the name inclusion - exclusion ). the memory required is o ( n ) { \ displaystyle o ( n ) }. the run - time can be improved by several heuristics : process the input numbers in descending order. if the integers included in a given node exceed the sum of the best subset found so far, the node is pruned.	Subset sum problem	wikipedia
}. the run - time can be improved by several heuristics : process the input numbers in descending order. if the integers included in a given node exceed the sum of the best subset found so far, the node is pruned. if the integers included in a given node, plus all remaining integers, are less than the sum of the best subset found so far, the node is pruned. = = = horowitz and sahni = = = in 1974, horowitz and sahni published a faster exponential - time algorithm, which runs in time o ( 2 n / 2 ⋅ ( n / 2 ) ) { \ displaystyle o ( 2 ^ { n / 2 } \ cdot ( n / 2 ) ) }, but requires much more space - o ( 2 n / 2 ) { \ displaystyle o ( 2 ^ { n / 2 } ) }. the algorithm splits arbitrarily the n elements into two sets of n / 2 { \ displaystyle n / 2 } each. for each of these two sets, it stores a list of the sums of all 2 n / 2 { \ displaystyle 2 ^ { n / 2 } } possible subsets of its elements. each of these two lists is then sorted. using even the fastest comparison sorting algorithm, mergesort for this step would take time o ( 2 n / 2 n ) { \ displaystyle o ( 2 ^ { n / 2 } n ) }. however, given a sorted list of sums for k { \ displaystyle k } elements, the list can be expanded to two sorted lists with the introduction of a ( k + 1 { \ displaystyle k + 1 } ) th element, and these two sorted lists can be merged in time o ( 2 k ) { \ displaystyle o ( 2 ^ { k } ) }. thus, each list can be generated in sorted form in time o ( 2 n / 2 ) { \ displaystyle o ( 2 ^ { n / 2 } ) }. given the two sorted lists, the algorithm can check if an element of the first array and an element of the second array sum up to t in time o ( 2 n / 2 ) { \ displaystyle o ( 2 ^ { n / 2 } ) }. to do that, the algorithm passes through the first array in decreasing order ( starting at the largest element ) and the second array in increasing order ( starting at the smallest element ). whenever the sum of the current element in the	Subset sum problem	wikipedia
2 } ) }. to do that, the algorithm passes through the first array in decreasing order ( starting at the largest element ) and the second array in increasing order ( starting at the smallest element ). whenever the sum of the current element in the first array and the current element in the second array is more than t, the algorithm moves to the next element in the first array. if it is less than t, the algorithm moves to the next element in the second array. if two elements that sum to t are found, it stops. ( the sub - problem for two elements sum is known as two - sum. ) = = = schroeppel and shamir = = = in 1981, schroeppel and shamir presented an algorithm based on horowitz and sanhi, that requires similar runtime - o ( 2 n / 2 ⋅ ( n / 4 ) ) { \ displaystyle o ( 2 ^ { n / 2 } \ cdot ( n / 4 ) ) }, much less space - o ( 2 n / 4 ) { \ displaystyle o ( 2 ^ { n / 4 } ) }. rather than generating and storing all subsets of n / 2 elements in advance, they partition the elements into 4 sets of n / 4 elements each, and generate subsets of n / 2 element pairs dynamically using a min heap, which yields the above time and space complexities since this can be done in o ( k 2 log ( k ) ) { \ displaystyle o ( k ^ { 2 } \ log ( k ) ) } and space o ( k ) { \ displaystyle o ( k ) } given 4 lists of length k. due to space requirements, the hs algorithm is practical for up to about 50 integers, and the ss algorithm is practical for up to 100 integers. = = = howgrave - graham and joux = = = in 2010, howgrave - graham and joux presented a probabilistic algorithm that runs faster than all previous ones - in time o ( 2 0. 337 n ) { \ displaystyle o ( 2 ^ { 0. 337n } ) } using space o ( 2 0. 256 n ) { \ displaystyle o ( 2 ^ { 0. 256n } ) }. it solves only the decision problem, cannot prove there is no solution for a given sum, and does not return the subset sum closest to t. the techniques of howgrave - graham and joux were subsequently extended bringing the time complexity to o (	Subset sum problem	wikipedia
it solves only the decision problem, cannot prove there is no solution for a given sum, and does not return the subset sum closest to t. the techniques of howgrave - graham and joux were subsequently extended bringing the time complexity to o ( 2 0. 291 n ) { \ displaystyle o ( 2 ^ { 0. 291n } ) }. a more recent generalization lowered the time complexity to o ( 2 0. 283 n ) { \ displaystyle o ( 2 ^ { 0. 283n } ) }. = = pseudo - polynomial time dynamic programming solutions = = ssp can be solved in pseudo - polynomial time using dynamic programming. suppose we have the following sequence of elements in an instance : x 1, …, x n { \ displaystyle x _ { 1 }, \ ldots, x _ { n } } we define a state as a pair ( i, s ) of integers. this state represents the fact that " there is a nonempty subset of x 1, …, x i { \ displaystyle x _ { 1 }, \ ldots, x _ { i } } which sums to s. " each state ( i, s ) has two next states : ( i + 1, s ), implying that x i + 1 { \ displaystyle x _ { i + 1 } } is not included in the subset ; ( i + 1, s + x i + 1 { \ displaystyle x _ { i + 1 } } ), implying that x i + 1 { \ displaystyle x _ { i + 1 } } is included in the subset. starting from the initial state ( 0, 0 ), it is possible to use any graph search algorithm ( e. g. bfs ) to search the state ( n, t ). if the state is found, then by backtracking we can find a subset with a sum of exactly t. the run - time of this algorithm is at most linear in the number of states. the number of states is at most n times the number of different possible sums. let a be the sum of the negative values and b the sum of the positive values ; the number of different possible sums is at most b - a, so the total runtime is in o ( n ( b − a ) ) { \ displaystyle o ( n ( b - a ) ) }. for example, if all input values are positive and bounded by some constant c, then b is at most n c, so the time	Subset sum problem	wikipedia
( n ( b − a ) ) { \ displaystyle o ( n ( b - a ) ) }. for example, if all input values are positive and bounded by some constant c, then b is at most n c, so the time required is o ( n 2 c ) { \ displaystyle o ( n ^ { 2 } c ) }. this solution does not count as polynomial time in complexity theory because b − a { \ displaystyle b - a } is not polynomial in the size of the problem, which is the number of bits used to represent it. this algorithm is polynomial in the values of a and b, which are exponential in their numbers of bits. however, subset sum encoded in unary is in p, since then the size of the encoding is linear in b - a. hence, subset sum is only weakly np - complete. for the case that each x i { \ displaystyle x _ { i } } is positive and bounded by a fixed constant c, in 1999, pisinger found a linear time algorithm having time complexity o ( n c ) { \ displaystyle o ( nc ) } ( note that this is for the version of the problem where the target sum is not necessarily zero, as otherwise the problem would be trivial ). in 2015, koiliaris and xu found a deterministic o ~ ( t n ) { \ displaystyle { \ tilde { o } } ( t { \ sqrt { n } } ) } algorithm for the subset sum problem where t is the sum we need to find. in 2017, bringmann found a randomized o ~ ( t + n ) { \ displaystyle { \ tilde { o } } ( t + n ) } time algorithm. in 2014, curtis and sanches found a simple recursion highly scalable in simd machines having o ( n ( m − x min ) / p ) { \ displaystyle o ( n ( m - x _ { \ min } ) / p ) } time and o ( n + m − x min ) { \ displaystyle o ( n + m - x _ { \ min } ) } space, where p is the number of processing elements, m = min ( s, x i − s ) { \ displaystyle m = \ min ( s, \ sum x _ { i } - s ) } and x min { \ displaystyle x _ { \ min } } is the lowest integer. this is the best theoretical parallel complexity known so far	Subset sum problem	wikipedia
\ displaystyle m = \ min ( s, \ sum x _ { i } - s ) } and x min { \ displaystyle x _ { \ min } } is the lowest integer. this is the best theoretical parallel complexity known so far. a comparison of practical results and the solution of hard instances of the ssp is discussed by curtis and sanches. = = polynomial time approximation algorithms = = suppose all inputs are positive. an approximation algorithm to ssp aims to find a subset of s with a sum of at most t and at least r times the optimal sum, where r is a number in ( 0, 1 ) called the approximation ratio. = = = simple 1 / 2 - approximation = = = the following very simple algorithm has an approximation ratio of 1 / 2 : order the inputs by descending value ; put the next - largest input into the subset, as long as it fits there. when this algorithm terminates, either all inputs are in the subset ( which is obviously optimal ), or there is an input that does not fit. the first such input is smaller than all previous inputs that are in the subset and the sum of inputs in the subset is more than t / 2 otherwise the input also is less than t / 2 and it would fit in the set. such a sum greater than t / 2 is obviously more than opt / 2. = = = fully - polynomial time approximation scheme = = = the following algorithm attains, for every > 0 { \ displaystyle \ epsilon > 0 }, an approximation ratio of ( 1 − ) { \ displaystyle ( 1 - \ epsilon ) }. its run time is polynomial in n and 1 / { \ displaystyle 1 / \ epsilon }. recall that n is the number of inputs and t is the upper bound to the subset sum. initialize a list l to contain one element 0. for each i from 1 to n do let ui be a list containing all elements y in l, and all sums xi + y for all y in l. sort ui in ascending order make l empty let y be the smallest element of ui add y to l for each element z of ui in increasing order do / / trim the list by eliminating numbers close to one another / / and throw out elements greater than the target sum t. if y + ε t / n < z ≤ t then y = z add z to l return the largest element in l. note that without the trimming step ( the inner " for each " loop ), the list	Subset sum problem	wikipedia
the target sum t. if y + ε t / n < z ≤ t then y = z add z to l return the largest element in l. note that without the trimming step ( the inner " for each " loop ), the list l would contain the sums of all 2 n { \ displaystyle 2 ^ { n } } subsets of inputs. the trimming step does two things : it ensures that all sums remaining in l are below t, so they are feasible solutions to the subset - sum problem. it ensures that the list l is " sparse ", that is, the difference between each two consecutive partial - sums is at least t / n { \ displaystyle \ epsilon t / n }. these properties together guarantee that the list l contains no more than n / { \ displaystyle n / \ epsilon } elements ; therefore the run - time is polynomial in n / { \ displaystyle n / \ epsilon }. when the algorithm ends, if the optimal sum is in l, then it is returned and we are done. otherwise, it must have been removed in a previous trimming step. each trimming step introduces an additive error of at most t / n { \ displaystyle \ epsilon t / n }, so n steps together introduce an error of at most t { \ displaystyle \ epsilon t }. therefore, the returned solution is at least opt − t { \ displaystyle { \ text { opt } } - \ epsilon t } which is at least ( 1 − ) opt { \ displaystyle ( 1 - \ epsilon ) { \ text { opt } } }. the above algorithm provides an exact solution to ssp in the case that the input numbers are small ( and non - negative ). if any sum of the numbers can be specified with at most p bits, then solving the problem approximately with = 2 − p { \ displaystyle \ epsilon = 2 ^ { - p } } is equivalent to solving it exactly. then, the polynomial time algorithm for approximate subset sum becomes an exact algorithm with running time polynomial in n and 2 p { \ displaystyle 2 ^ { p } } ( i. e., exponential in p ). kellerer, mansini, pferschy and speranza and kellerer, pferschy and pisinger present other fptases for subset sum. = = see also = = knapsack problem – problem in combinatorial optimization - a generalization of ssp in which each input	Subset sum problem	wikipedia
##eranza and kellerer, pferschy and pisinger present other fptases for subset sum. = = see also = = knapsack problem – problem in combinatorial optimization - a generalization of ssp in which each input item has both a value and a weight. the goal is to maximize the value subject to a bound on the total weight. multiple subset sum problem – mathematical optimization problempages displaying short descriptions of redirect targets - a generalization of ssp in which one should choose several subsets. 3sum – problem in computational complexity theory merkle – hellman knapsack cryptosystem – one of the earliest public key cryptosystems invented by ralph merkle and martin hellman in 1978. the ideas behind it are simpler than those involving rsa, and it has been brokenpages displaying wikidata descriptions as a fallback = = references = = = = further reading = = cormen, thomas h. ; leiserson, charles e. ; rivest, ronald l. ; stein, clifford ( 2001 ) [ 1990 ]. " 35. 5 : the subset - sum problem ". introduction to algorithms ( 2nd ed. ). mit press and mcgraw - hill. isbn 0 - 262 - 03293 - 7. michael r. garey and david s. johnson ( 1979 ). computers and intractability : a guide to the theory of np - completeness. w. h. freeman. isbn 0 - 7167 - 1045 - 5. a3. 2 : sp13, pg. 223. lagarias, j. c. ; odlyzko, a. m. ( 1985 - 01 - 01 ). " solving low - density subset sum problems ". journal of the acm. 32 ( 1 ) : 229 – 246. doi : 10. 1145 / 2455. 2461. issn 0004 - 5411. s2cid 885632. martello, silvano ; toth, paolo ( 1990 ). " 4 subset - sum problem ". knapsack problems : algorithms and computer interpretations. wiley - interscience. pp. 105 – 136. isbn 0 - 471 - 92420 - 2. mr 1086874.	Subset sum problem	wikipedia
the map – territory relation is the relationship between an object and a representation of that object, as in the relation between a geographical territory and a map of it. mistaking the map for the territory is a logical fallacy that occurs when someone confuses the semantics of a term with what it represents. polish - american scientist and philosopher alfred korzybski remarked that " the map is not the territory " and that " the word is not the thing ", encapsulating his view that an abstraction derived from something, or a reaction to it, is not the thing itself. korzybski held that many people do confuse maps with territories, that is, confuse conceptual models of reality with reality itself. these ideas are crucial to general semantics, a system korzybski originated. the relationship has also been expressed in other terms, such as " the model is not the data ", " all models are wrong ", and alan watts's " the menu is not the meal. " the concept is thus quite relevant throughout ontology and applied ontology regardless of any connection to general semantics per se ( or absence thereof ). its avatars are thus encountered in semantics, statistics, logistics, business administration, semiotics, and many other applications. a frequent coda to " all models are wrong " is that " all models are wrong ( but some are useful ), " which emphasizes the proper framing of recognizing map – territory differences — that is, how and why they are important, what to do about them, and how to live with them properly. the point is not that all maps are useless ; rather, the point is simply to maintain critical thinking about the discrepancies : whether or not they are either negligible or significant in each context, how to reduce them ( thus iterating a map, or any other model, to become a better version of itself ), and so on. = = history = = the phrase " a map is not the territory " was first introduced by alfred korzybski in his 1931 paper " a non - aristotelian system and its necessity for rigour in mathematics and physics, " presented at a meeting of the american association for the advancement of science in new orleans, and later reprinted in science and sanity ( 1933 ). korzybski credits mathematician eric temple bell for the related phrase, " the map is not the thing mapped. " in the article, korzybski states that " a map is not the territory it represents, but,	Map–territory relation	wikipedia
( 1933 ). korzybski credits mathematician eric temple bell for the related phrase, " the map is not the thing mapped. " in the article, korzybski states that " a map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. " the concept has been illustrated in various cultural works. belgian surrealist rene magritte explored the idea in his painting the treachery of images, which depicts a pipe with the caption, " ceci n'est pas une pipe " ( " this is not a pipe " ). lewis carroll, in sylvie and bruno concluded ( 1893 ), describes a fictional map with a scale of " a mile to the mile ", which proves impractical. jorge luis borges similarly references a map as large as the territory in his short story " on exactitude in science " ( 1946 ). in his 1964 book understanding media, philosopher marshall mcluhan argued that all media representations, including electronic media, are abstractions or " extensions " of reality. the idea has influenced a number of modern works, including robert m. pirsig's lila : an inquiry into morals and michel houellebecq's novel the map and the territory, the latter of which won the prix goncourt. the concept is also discussed in the work of robert anton wilson and james a. lindsay, who critiques the confusion of conceptual maps with reality in his book dot, dot, dot : infinity plus god equals folly. historian of religion jonathan z. smith named one of the books collecting his essays map is not territory. similarly, a collection of writings by ai pessimist eliezer yudkowsky was named map and territory. = = commentary = = gregory bateson, in his 1972 work steps to an ecology of mind, argued that understanding a territory is inherently limited by the sensory channels used to perceive it. he described the " map " of reality as an imperfect representation : we say the map is different from the territory. but what is the territory? operationally, somebody went out with a retina or a measuring stick and made representations which were then put on paper. what is on the paper map is a representation of what was in the retinal representation of the man who made the map... the territory never gets in at all. always, the process of representation will filter it out so that the mental world is only maps of maps, ad infin	Map–territory relation	wikipedia
what was in the retinal representation of the man who made the map... the territory never gets in at all. always, the process of representation will filter it out so that the mental world is only maps of maps, ad infinitum. bateson further explored this in " the cybernetics of'self': a theory of alcoholism " ( 1971 ), arguing that a map's usefulness lies in its structural analogy to the territory, rather than its literal truthfulness. for example, even a cultural belief in colds being caused by spirits can function effectively as a " map " for public health, analogous to germ theory. philosopher david schmidtz addresses the theme of accuracy in elements of justice ( 2006 ), highlighting how overly detailed models can become impractical, a problem also known as bonini's paradox. poet paul valery summarized this idea : " everything simple is false. everything which is complex is unusable. " the rise of electronic media and jean baudrillard's concept of simulacra further complicates the map - territory distinction. in simulacra and simulation, baudrillard argues that in the modern age, simulations precede and even replace reality : today abstraction is no longer that of the map, the double, the mirror, or the concept. simulation is no longer that of a territory, a referential being or substance. it is the generation by models of a real without origin or reality : a hyperreal. the territory no longer precedes the map, nor does it survive it. it is nevertheless the map that precedes the territory — precession of simulacra — that engenders the territory. = = see also = = = = notes = = = = references = = = = = further reading = = = wuppuluri, shyam ; doria, francisco antonio, eds. ( 2018 ). " the map and the territory ". the frontiers collection. springer nature. doi : 10. 1007 / 978 - 3 - 319 - 72478 - 2. isbn 978 - 3 - 319 - 72477 - 5. issn 1612 - 3018.	Map–territory relation	wikipedia
pocosin is a type of palustrine wetland with deep, acidic, sandy, peat soils. groundwater saturates the soil except during brief seasonal dry spells and during prolonged droughts. pocosin soils are nutrient - deficient ( oligotrophic ), especially in phosphorus. pocosins occur in the southern portions of the atlantic coastal plain of north america, spanning from southeastern virginia, through north carolina, and into south carolina. the majority of pocosins are found in north carolina. the alligator river national wildlife refuge was created in 1984 to help preserve pocosin wetlands. the nearby cedar island national wildlife refuge also protects pocosin habitat. = = characteristics = = pocosins occupy poorly drained higher ground between streams and floodplains. seeps cause the inundation. there are often perched water tables underlying pocosins. shrub vegetation is common in a pocosin ecosystem. pocosins are sometimes called shrub bogs. pond pines ( pinus serotina ) dominate pocosin forests, but loblolly pine ( pinus taeda ) and longleaf pine ( pinus palustris ) are also associated with pocosins. additionally, pocosins are home to rare and threatened plant species including venus flytrap ( dionaea muscipula ) and sweet pitcher plant ( sarracenia rubra ). a distinction is sometimes made between short pocosins, which have shorter trees ( less than 20 feet ( 6. 1 m ) ), deeper peat, and fewer soil nutrients, and tall pocosins, which have taller trees ( greater than 20 feet ( 6. 1 m ) ), shallow peat, and more nutrient - rich soil. where soil saturation is less frequent and peat depths shallower, pocosins transition into pine flatwoods. a loose definition of " pocosin " can include all shrub and forest bogs, as well as stands of atlantic white cedar ( chamaecyparis thyoides ) and loblolly pine on the atlantic coastal plain. pocosins are formed by the accumulation of organic matter, resembling black muck, that is built up over thousands of years. this accumulation of material causes the area to be highly acidic and nutrient - deficient. the thickness of the organic buildup varies depending on one's location within the pocosin. near the edges the buildup can be several inches thick but toward the center it can be up to several feet thick. vegetation on the pocosin varies throughout	Pocosin	wikipedia
of the organic buildup varies depending on one's location within the pocosin. near the edges the buildup can be several inches thick but toward the center it can be up to several feet thick. vegetation on the pocosin varies throughout. at the edges more pond pine is found with an abundance of titi, zenobia ( a shrub unique to pocosins ), and greenbrier vines. closer to the center, thin stunted trees are typically found and fewer shrubs and vines are present. pocosins are important to migratory birds due to the abundance of various types of berries. pocosin ecosystems are fire - adapted ( pyrophytic ). pond pines exhibit serotiny, such that wildfire can create a pond pine seedbed in the soil. wildfires in pocosins tend to be intense, sometimes burning deep into the peat, resulting in small lakes and ponds. wildfires occurring about once a decade tend to cause pond pines to dominate over other trees, and cane ( arundinaria ) rather than shrubs to dominate the understory. more frequent fires result in a pyrophytic shrub understory. annual fires prevent shrub growth and thin the pond pine forest cover, creating a flooded savanna with grass, sedge, and herb groundcover. = = etymology = = the word pocosin has eastern algonquian roots. sources have long attested that the term translates into english as " swamp - on - a - hill, " but evidence for this precise translation is lacking. the city of poquoson, virginia, located in the coastal plain of virginia ( see tidewater region of virginia ) derives its name from this geographic feature. = = references = = = = external links = = detailed ecological description of basin pocosin communities	Pocosin	wikipedia
in applied psychology, investigative psychology attempts to describe the actions of offenders and develop an understanding of crime. this understanding can then help solve crimes and contribute to prosecution and defense procedures. it brings together issues in the retrieval of investigative information, the drawing of inferences about that information and the ways in which police decision making can be supported through various systems derived from scientific research. it should not be confused with profiling which grew out of the experience of police officers offering opinions to their colleagues about the possible characteristics of unknown offenders. = = overview = = investigative psychology grows directly out of empirical research and logical inference to cover the full range of investigative activities not only the preparation of'profiles '. the inference processes at the heart of investigative psychology contrast with the approach used in the federal bureau of investigation which emphasises subjective processes such as " thinking like the criminal ". this field provides a system for the integration of many aspects of psychology into all areas of police investigations and forms of crime. investigative psychology stresses that the results of scientific psychology can contribute to many aspects of civilian and criminal investigation, including the full range of crimes from burglary to terrorism, not just those extreme crimes of violence that have an obvious psychopathic component. = = research = = the contribution to investigations draws on the extent to which an offender displays various tested characteristics. as well as procedures for enhancing the processes by which interviews are carried out or information is put before the courts. one aim of investigative psychology research is determining behaviourally important and empirically supported information regarding the consistency and variability of the behaviour of many different types of offenders, although to date most studies have been of violent crimes there is a growing body of research on burglary and arson. it is also important to establish valid and reliable methods of distinguishing between offenders and between offences. already the use of statistical analysis techniques such as multi dimensional scaling in offender profiling has provided support for a theoretical distinction between homicide offenders as either instrumental ( 43 % of offenders ) or expressive ( 31 % of offenders ) in their use of aggression. the most recent advances have seen the development of a narrative action system model for differentiating criminals'styles of offending, allowing empirically based'modus operandi'to be identified within a broad range of offence types from sexual assault and serial murder to stalking, burglary and robbery. this method of analysis has also expanded upon the original theoretical distinction by identifying sub - themes of aggressive action which can be used to further discriminate amongst offenders ( santilla, hakkanen, canter & elfgren	Investigative psychology	wikipedia
burglary and robbery. this method of analysis has also expanded upon the original theoretical distinction by identifying sub - themes of aggressive action which can be used to further discriminate amongst offenders ( santilla, hakkanen, canter & elfgren, 2003 ). these behavioural themes have also been linked to background characteristics and post - offence behaviour, demonstrating their usefulness to the investigation of serial murder cases. the development and application of these techniques to serial offenders is likely to facilitate an increase in the validity of offender profiling of serial murderers. = = see also = = forensic psychology offender profiling fbi method of profiling = = references = =	Investigative psychology	wikipedia
in linguistics, ellipsis ( from ancient greek ελλειψις ( elleipsis )'omission') or an elliptical construction is the omission from a clause of one or more words that are nevertheless understood in the context of the remaining elements. there are numerous distinct types of ellipsis acknowledged in theoretical syntax. theoretical accounts of ellipsis seek to explain its syntactic and semantic factors, the means by which the elided elements are recovered, and the status of the elided elements. = = background = = varieties of ellipsis have long formed a basis of linguistic theory that addresses basic questions of form – meaning correspondence : in particular, how the usual mechanisms of grasping a meaning from a form may be bypassed or supplanted via elliptical structures. in generative linguistics, the term ellipsis has been applied to a range of syntax in which a perceived interpretation is fuller than that which would be expected based solely on the presence of linguistic forms. one trait that many types and instances of ellipsis have in common is that the appearance of ellipsis is optional. the occurrence of vp - ellipsis, for instance, is often optional, e. g. he will help, and she will ( help ), too. whether or not the second occurrence of the verb help is elided in this sentence is up to the speaker and to communicative aspects of the situational context in which the sentence is uttered. this optionality is a clear indication of ellipsis. at other times, however, ellipsis seems to be obligatory, for instance with cases of comparative deletion, e. g., * more girls were there today than girls were there yesterday. the second occurrence of girls must be omitted in this sentence ( more girls were there today than were there yesterday ). the obligatory occurrence of ellipsis complicates the analysis, since one can argue that obligatory cases are not really instances of ellipsis at all, but rather a null pro - form is involved. these aspects of the theory should be kept in mind when considering the various types and instances of ellipsis enumerated below. = = types = = there are numerous widely acknowledged types of ellipsis. they include, as mentioned and briefly illustrated below : gapping stripping verb phrase ellipsis pseudogapping answer ellipsis sluicing nominal ellipsis comparative deletion null complement anaphora among experts, there is no unanimity that	Ellipsis (linguistics)	wikipedia
include, as mentioned and briefly illustrated below : gapping stripping verb phrase ellipsis pseudogapping answer ellipsis sluicing nominal ellipsis comparative deletion null complement anaphora among experts, there is no unanimity that all of the abovementioned syntaxes form a natural class in the sense of being derived by one and the same mechanism. ellipsis - based accounts have been given for other syntaxes, and some of the above have been analyzed in other ways. most experts would agree, however, that most of the above items are in fact ellipses, so the discussion below takes their status as ellipses largely for granted. the example sentences below employ the convention whereby the elided material is indicated with subscripts and smaller font size. all examples given below come from english though similar patterns arise cross - linguistically, with variation from language to language. = = = gapping = = = gapping occurs in coordinate structures. redundant material that is present in the immediately preceding clause can be " gapped ". this gapped material usually contains a finite verb. canonical cases have a true " gap " insofar as a remnant appears to the left and to the right of the elided material. john can play the guitar, and mary can play the violin. fred took a picture of you, and susan took a picture of me. while canonical cases have medial gaps as in these two sentences, the gap need not be medial, and it can even be discontinuous, e. g. : she persuaded him to do the homework, and he persuaded her to do the homework. should i call you, or should you call me? while these two sentences again each have two remnants, the gapped material is no longer continuous. there are in a sense two gaps in each of the gapped clauses. gapping has been thoroughly studied, and it is therefore reasonably well understood, although the theoretical analyses can vary significantly. = = = stripping = = = stripping is also known as bare argument ellipsis. many linguists take stripping to be a particular manifestation of gapping whereby just one remnant appears in the gapped clause instead of the two ( or more ) that occur in instances of gapping. the fact that stripping is limited to occurring in coordinate structures is the main reason why stripping is integrated into the analysis of gapping : john can play the guitar, and mary can play the guitar, also. sam has attempted problem 1, and he has attempted problem 2 as well.	Ellipsis (linguistics)	wikipedia
to occurring in coordinate structures is the main reason why stripping is integrated into the analysis of gapping : john can play the guitar, and mary can play the guitar, also. sam has attempted problem 1, and he has attempted problem 2 as well. these examples illustrate that stripping is flexible insofar as the remnant in the stripped clause is not limited in function ; it can, for instance, be a subject as in the first sentence or an object as in the second sentence. a particularly frequent type of stripping is not - stripping ( stripping in the presence of not ), e. g. : sam did it, not fred did it. - not - stripping sally is working on monday, she is not working on tuesday. not - stripping's status as a form of ellipsis can be debated, since the non - elliptical versions of these sentences are unacceptable, and the key trait of ellipsis is that both the elliptical and non - elliptical versions are acceptable. = = = verb phrase ellipsis = = = verb phrase ellipsis ( also vp - ellipsis or vpe ) is a particularly frequent form of ellipsis in english. vp - ellipsis elides a non - finite vp. the ellipsis must be introduced by an auxiliary verb or by the particle to. john can play the guitar ; mary can play the guitar, too. he has done it before, which means he will do it again. an aspect of vp - ellipsis that is unlike gapping and stripping is that it can occur forwards or backwards. that is, the ellipsis can precede or follow its antecedent, e. g. : the man who wanted to order the salmon did order the salmon. the man who wanted to order the salmon did order the salmon. of the various ellipsis mechanisms, vp - ellipsis has probably been studied the most and is therefore relatively well - understood. = = = pseudogapping = = = many linguists take pseudogapping to be a particular manifestation of vp - ellipsis ( rather than a variation on gapping ). like vp - ellipsis, pseudogapping is introduced by an auxiliary verb. pseudogapping differs from vp - ellipsis, however, insofar as the elided vp is not entirely gone, but rather one ( or more ) remnants of the vp appear, giving it the outward appearance of gapping. pseudogapping occurs frequently in comparative and contrastive contexts : they have been eating the apples	Ellipsis (linguistics)	wikipedia
as the elided vp is not entirely gone, but rather one ( or more ) remnants of the vp appear, giving it the outward appearance of gapping. pseudogapping occurs frequently in comparative and contrastive contexts : they have been eating the apples more than they have been eating the oranges. i will feed the chickens today if you will feed the chickens tomorrow. pseudogapping is more restricted in distribution than vp - ellipsis. for instance, it can hardly occur backwards, i. e., the ellipsis can hardly precede its antecedent. further examples : would you want to say that to me, or would i want to say that to you? they could read this book more easily than they could read that book. = = = answer ellipsis = = = answer ellipsis involves question - answer pairs. the question focuses on an unknown piece of information, often using an interrogative word ( e. g., who, what, when etc. ). the corresponding answer provides the missing information and in so doing, the redundant information that appeared in the question is elided, e. g. : q : who has been hiding the truth? a : billy has been hiding the truth. q : what have you been trying to accomplish? a : i have been trying to accomplish this damn crossword. the fragment answers in these two sentences are verb arguments ( subject and object nps ). the fragment can also correspond to an adjunct, e. g. : q : when does the circus start? a : the circus starts tomorrow. q : why has the campaign been so crazy? a : the campaign has been so crazy due to the personalities. answer ellipsis occurs in most, if not all, languages, and is a very frequent type of ellipsis that is omnipresent in everyday communication between speakers. = = = sluicing = = = sluicing usually elides everything from a direct or indirect question except the question word. it is a frequent type of ellipsis that appears to occur in most if not all languages. it can operate both forwards and backwards like vp - ellipsis, but unlike gapping, stripping, answer fragments, and pseudogapping, e. g. : john can play something, but i don ’ t know what he can play. i don't know when he will call, but john will definitely call. the sluicing illustrated with these two sentences has occurred in indirect questions. sluicing in	Ellipsis (linguistics)	wikipedia
can play something, but i don ’ t know what he can play. i don't know when he will call, but john will definitely call. the sluicing illustrated with these two sentences has occurred in indirect questions. sluicing in direct questions is illustrated with the following two examples : a : something unusual happened. b : what happened? a : he has been working on the problem. b : how long has he been working on the problem? sluicing has been studied intensely in the past decade and can be viewed as a relatively well - understood ellipsis mechanism, although the theoretical analysis of certain aspects of sluicing remains controversial. = = = nominal ellipsis = = = noun ellipsis ( also n - ellipsis, n'- ellipsis, np - ellipsis, npe, ellipsis in the dp ) occurs when the noun and potentially accompanying modifiers are omitted from a noun phrase. nominal ellipsis occurs with a limited set of determinatives in english ( cardinal and ordinal numbers and possessive determiners ), though it is much freer in other languages. the following examples illustrate nominal ellipsis with cardinal and ordinal numbers : fred did three onerous tasks because susan had done two onerous tasks. the first train and the second train have arrived. the following two sentences illustrate nominal ellipsis with possessive determiners : i heard mary's dog, and you heard bill's dog. if doris tries my chili, i will try hers ( her chili ). = = = comparative deletion = = = comparative deletion occurs in clauses introduced by than in english. the expression that is elided corresponds to a comparative morph such as more or - er in the antecedent clause, e. g. : more people arrived than we expected people would arrive. she ordered more beer than we could drink beer. doris looks more satisfied than doreen looks satisfied. william has friends in more countries than you have friends in countries. comparative deletion is different from many of the other optional ellipsis mechanisms insofar as it is obligatory. the non - elliptical versions of these sentences are unacceptable. the classic escher sentence " more people have been to russia than i have " appears to use comparative deletion, but ends up with a meaningless comparison if the apparent elision is included : " more people have been to russia than i have been to russia ". = = = null complement anaphora	Ellipsis (linguistics)	wikipedia
than i have " appears to use comparative deletion, but ends up with a meaningless comparison if the apparent elision is included : " more people have been to russia than i have been to russia ". = = = null complement anaphora = = = null complement anaphora elides a complete complement, whereby the elided complement is a finite clause, infinitive phrase, or prepositional phrase. the verbal predicates that can license null complement anaphora form a limited set ( e. g., know, approve, refuse, decide ). the elided complement cannot be a noun phrase. q : do you know what happened? a : no, i don't know what happened. q : do you approve of the plan? a : no, i don't approve of the plan. they told bill to help, but he refused to help. they offered two ways to spend the day, but i couldn't decide between them. of the various ellipsis mechanisms, null complement anaphora is the least studied. in this regard, its status as ellipsis is a point of debate, since its behavior is not consistent with the behavior of many of the other ellipsis mechanisms. = = less - studied cases of ellipsis = = further instances of ellipsis that do not ( in a clear way ) qualify as any of the ellipsis types listed above : a : the cat likes bill. b : why does the cat [ particularly ] like bill? what will happen if i miss the deadline? more work on ellipsis may need to be done before all ellipsis mechanisms are fully explained. = = theoretical approaches = = ellipsis is widely studied in theoretical literature, with studies focusing especially on the mental representation of elided material, the conditions which license ellipsis, and the means by which the elided material is recovered. one challenge to theoretical accounts of ellipsis comes from cases where the elided material does not appear to be a constituent. since syntactic operations can only target constituents in standard phrase - structural approaches, accounts within these frameworks must posit additional movement operations to explain such cases. these movement rules raise non - elided material out of a constituent, allowing ellipsis to apply only to the material that is left, thus creating the illusion of ellipsis applying to a non - constituent. some alternative analyses assume more flexible conceptions of syntactic units such as the catena, thus allowing ellip	Ellipsis (linguistics)	wikipedia
##lipsis to apply only to the material that is left, thus creating the illusion of ellipsis applying to a non - constituent. some alternative analyses assume more flexible conceptions of syntactic units such as the catena, thus allowing ellipsis to directly target non - constituents without the need for additional movement rules. = = see also = = anaphora ( linguistics ) anapodoton aposiopesis question under discussion right node raising squiggle operator whiz deletion zeugma and syllepsis = = references = = notes bibliography agel, vilmos, ludwig eichinger, hans - werner eroms, peter hellwig, hans jurgen heringer, and henning lobin ( eds. ) 2003 / 6. dependency and valency : an international handbook of contemporary research. berlin : walter de gruyter. johnson, kyle 2001. what vp ellipsis can do, and what it can't, but not why. in the handbook of contemporary syntactic theory, ed. mark baltin and chris collins, 439 – 479. oxford : blackwell publishers. lappin, shalom 1996. the interpretation of ellipsis. in the handbook of contemporary semantic theory, ed. shalom lappin. oxford : blackwell. lobeck, anne. 1995. ellipsis : functional heads, licensing, and identification. new york : oxford university press. lobeck, anne. 2006. ellipsis in dp. in the blackwell companion to syntax, ed. by martin everaert et al., vol. 2, pp. 145 – 173. oxford : blackwell. merchant, jason. 2001. the syntax of silence : sluicing, islands, and the theory of ellipsis. oxford : oxford university press. osborne, timothy and thomas groß 2012. constructions are catenae : construction grammar meets dependency grammar. cognitive linguistics 23, 1 : 163 – 214. sag, ivan 1976. deletion and logical form. doctoral dissertation, massachusetts institute of technology, cambridge, massachusetts.	Ellipsis (linguistics)	wikipedia
in probability theory and statistics, the half - normal distribution is a special case of the folded normal distribution. let x { \ displaystyle x } follow an ordinary normal distribution, n ( 0, σ 2 ) { \ displaystyle n ( 0, \ sigma ^ { 2 } ) }. then, y = \| x \| { \ displaystyle y = \| x \| } follows a half - normal distribution. thus, the half - normal distribution is a fold at the mean of an ordinary normal distribution with mean zero. = = properties = = using the σ { \ displaystyle \ sigma } parametrization of the normal distribution, the probability density function ( pdf ) of the half - normal is given by f y ( y ; σ ) = 2 σ π exp ( − y 2 2 σ 2 ) y ≥ 0, { \ displaystyle f _ { y } ( y ; \ sigma ) = { \ frac { \ sqrt { 2 } } { \ sigma { \ sqrt { \ pi } } } } \ exp \ left ( - { \ frac { y ^ { 2 } } { 2 \ sigma ^ { 2 } } } \ right ) \ quad y \ geq 0, } where e [ y ] = μ = σ 2 π { \ displaystyle e [ y ] = \ mu = { \ frac { \ sigma { \ sqrt { 2 } } } { \ sqrt { \ pi } } } }. alternatively using a scaled precision ( inverse of the variance ) parametrization ( to avoid issues if σ { \ displaystyle \ sigma } is near zero ), obtained by setting θ = π σ 2 { \ displaystyle \ theta = { \ frac { \ sqrt { \ pi } } { \ sigma { \ sqrt { 2 } } } } }, the probability density function is given by f y ( y ; θ ) = 2 θ π exp ( − y 2 θ 2 π ) y ≥ 0, { \ displaystyle f _ { y } ( y ; \ theta ) = { \ frac { 2 \ theta } { \ pi } } \ exp \ left ( - { \ frac { y ^ { 2 } \ theta ^ { 2 } } { \ pi } } \ right ) \ quad y \ geq 0, } where e [ y ] = μ = 1 θ { \ displaystyle e [ y ] = \ mu = { \ frac { 1 } { \ theta	Modified half-normal distribution	wikipedia
} { \ pi } } \ right ) \ quad y \ geq 0, } where e [ y ] = μ = 1 θ { \ displaystyle e [ y ] = \ mu = { \ frac { 1 } { \ theta } } }. the cumulative distribution function ( cdf ) is given by f y ( y ; σ ) = 0 y 1 σ 2 π exp ( − x 2 2 σ 2 ) d x { \ displaystyle f _ { y } ( y ; \ sigma ) = \ int _ { 0 } ^ { y } { \ frac { 1 } { \ sigma } } { \ sqrt { \ frac { 2 } { \ pi } } } \, \ exp \ left ( - { \ frac { x ^ { 2 } } { 2 \ sigma ^ { 2 } } } \ right ) \, dx } using the change - of - variables z = x / ( 2 σ ) { \ displaystyle z = x / ( { \ sqrt { 2 } } \ sigma ) }, the cdf can be written as f y ( y ; σ ) = 2 π 0 y / ( 2 σ ) exp ( − z 2 ) d z = erf ( y 2 σ ), { \ displaystyle f _ { y } ( y ; \ sigma ) = { \ frac { 2 } { \ sqrt { \ pi } } } \, \ int _ { 0 } ^ { y / ( { \ sqrt { 2 } } \ sigma ) } \ exp \ left ( - z ^ { 2 } \ right ) dz = \ operatorname { erf } \ left ( { \ frac { y } { { \ sqrt { 2 } } \ sigma } } \ right ), } where erf is the error function, a standard function in many mathematical software packages. the quantile function ( or inverse cdf ) is written : q ( f ; σ ) = σ 2 erf − 1 ( f ) { \ displaystyle q ( f ; \ sigma ) = \ sigma { \ sqrt { 2 } } \ operatorname { erf } ^ { - 1 } ( f ) } where 0 ≤ f ≤ 1 { \ displaystyle 0 \ leq f \ leq 1 } and erf − 1 { \ displaystyle \ operatorname { erf } ^ { - 1 } } is the inverse error function the expectation is then given	Modified half-normal distribution	wikipedia
≤ f ≤ 1 { \ displaystyle 0 \ leq f \ leq 1 } and erf − 1 { \ displaystyle \ operatorname { erf } ^ { - 1 } } is the inverse error function the expectation is then given by e [ y ] = σ 2 / π, { \ displaystyle e [ y ] = \ sigma { \ sqrt { 2 / \ pi } }, } the variance is given by var ( y ) = σ 2 ( 1 − 2 π ). { \ displaystyle \ operatorname { var } ( y ) = \ sigma ^ { 2 } \ left ( 1 - { \ frac { 2 } { \ pi } } \ right ). } since this is proportional to the variance σ2 of x, σ can be seen as a scale parameter of the new distribution. the differential entropy of the half - normal distribution is exactly one bit less the differential entropy of a zero - mean normal distribution with the same second moment about 0. this can be understood intuitively since the magnitude operator reduces information by one bit ( if the probability distribution at its input is even ). alternatively, since a half - normal distribution is always positive, the one bit it would take to record whether a standard normal random variable were positive ( say, a 1 ) or negative ( say, a 0 ) is no longer necessary. thus, h ( y ) = 1 2 log 2 ( π e σ 2 2 ) = 1 2 log 2 ( 2 π e σ 2 ) − 1. { \ displaystyle h ( y ) = { \ frac { 1 } { 2 } } \ log _ { 2 } \ left ( { \ frac { \ pi e \ sigma ^ { 2 } } { 2 } } \ right ) = { \ frac { 1 } { 2 } } \ log _ { 2 } \ left ( 2 \ pi e \ sigma ^ { 2 } \ right ) - 1. } = = applications = = the half - normal distribution is commonly utilized as a prior probability distribution for variance parameters in bayesian inference applications. = = parameter estimation = = given numbers { x i } i = 1 n { \ displaystyle \ { x _ { i } \ } _ { i = 1 } ^ { n } } drawn from a half - normal distribution, the unknown parameter σ { \ displaystyle \ sigma } of that distribution can be estimated by the method of maximum likelihood, giving σ ^ = 1 n i = 1 n x i 2	Modified half-normal distribution	wikipedia
{ n } } drawn from a half - normal distribution, the unknown parameter σ { \ displaystyle \ sigma } of that distribution can be estimated by the method of maximum likelihood, giving σ ^ = 1 n i = 1 n x i 2 { \ displaystyle { \ hat { \ sigma } } = { \ sqrt { { \ frac { 1 } { n } } \ sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } } } } the bias is equal to b ≡ e [ ( σ ^ m l e − σ ) ] = − σ 4 n { \ displaystyle b \ equiv \ operatorname { e } { \ bigg [ } \ ; ( { \ hat { \ sigma } } _ { \ mathrm { mle } } - \ sigma ) \ ; { \ bigg ] } = - { \ frac { \ sigma } { 4n } } } which yields the bias - corrected maximum likelihood estimator σ ^ mle ∗ = σ ^ mle − b ^. { \ displaystyle { \ hat { \ sigma \, } } _ { \ text { mle } } ^ { * } = { \ hat { \ sigma \, } } _ { \ text { mle } } - { \ hat { b \, } }. } = = related distributions = = the distribution is a special case of the folded normal distribution with μ = 0. it also coincides with a zero - mean normal distribution truncated from below at zero ( see truncated normal distribution ) if y has a half - normal distribution, then ( y / σ ) 2 has a chi square distribution with 1 degree of freedom, i. e. y / σ has a chi distribution with 1 degree of freedom. the half - normal distribution is a special case of the generalized gamma distribution with d = 1, p = 2, a = 2 σ { \ displaystyle { \ sqrt { 2 } } \ sigma }. if y has a half - normal distribution, y - 2 has a levy distribution the rayleigh distribution is a moment - tilted and scaled generalization of the half - normal distribution. modified half - normal distribution with the pdf on ( 0, ∞ ) { \ displaystyle ( 0, \ infty ) } is given as f ( x ) = 2 β α 2 x α − 1 exp ( − β x 2 + γ x ) ψ ( α 2, γ β ) { \	Modified half-normal distribution	wikipedia
{ \ displaystyle ( 0, \ infty ) } is given as f ( x ) = 2 β α 2 x α − 1 exp ( − β x 2 + γ x ) ψ ( α 2, γ β ) { \ displaystyle f ( x ) = { \ frac { 2 \ beta ^ { \ frac { \ alpha } { 2 } } x ^ { \ alpha - 1 } \ exp ( - \ beta x ^ { 2 } + \ gamma x ) } { \ psi { \ left ( { \ frac { \ alpha } { 2 } }, { \ frac { \ gamma } { \ sqrt { \ beta } } } \ right ) } } } }, where ψ ( α, z ) = 1 ψ 1 ( ( α, 1 2 ) ( 1, 0 ) ; z ) { \ displaystyle \ psi ( \ alpha, z ) = { } _ { 1 } \ psi _ { 1 } \ left ( { \ begin { matrix } \ left ( \ alpha, { \ frac { 1 } { 2 } } \ right ) \ \ ( 1, 0 ) \ end { matrix } } ; z \ right ) } denotes the fox – wright psi function. = = see also = = half - t distribution truncated normal distribution folded normal distribution rectified gaussian distribution = = references = = = = further reading = = leone, f. c. ; nelson, l. s. ; nottingham, r. b. ( 1961 ), " the folded normal distribution ", technometrics, 3 ( 4 ) : 543 – 550, doi : 10. 2307 / 1266560, hdl : 2027 / mdp. 39015095248541, jstor 1266560 = = external links = = half - normal distribution at mathworld ( note that mathworld uses the parameter θ = 1 σ π / 2 { \ displaystyle \ theta = { \ frac { 1 } { \ sigma } } { \ sqrt { \ pi / 2 } } }	Modified half-normal distribution	wikipedia
the terms anthropopithecus ( blainville, 1839 ) and pithecanthropus ( haeckel, 1868 ) are obsolete taxa describing either chimpanzees or archaic humans. both are derived from greek ανθρωπος ( anthropos, " man " ) and πιθηκος ( pithekos, " ape " or " monkey " ), translating to " man - ape " and " ape - man ", respectively. anthropopithecus was originally coined to describe the chimpanzee and is now a junior synonym of pan. it had also been used to describe several other extant and extinct species, among others the fossil java man. very quickly, the latter was re - assigned to pithecanthropus, originally coined to refer to a theoretical " missing link ". pithecanthropus is now classed as homo erectus, thus a junior synonym of homo. = = history = = the genus anthropopithecus was first proposed in 1841 by the french zoologist and anatomist henri - marie ducrotay de blainville ( 1777 – 1850 ) in order to give a genus name to some chimpanzee material that he was studying at the time. after the genus anthropopithecus was established by de blainville in 1839, the british surgeon and naturalist john bland - sutton ( 1855 – 1936 ) proposed the species name anthropopithecus troglodytes in 1883 to designate the common chimpanzee. however, the genus pan had already been attributed to chimpanzees in 1816 by the german naturalist lorenz oken ( 1779 – 1851 ). since any earlier nomenclature prevails over subsequent nomenclatures, the genus anthropopithecus definitely lost its validity in 1895, becoming from that date a junior synonym of the genus pan. in 1879, the french archaeologist and anthropologist gabriel de mortillet ( 1821 – 1898 ) proposed the term anthropopithecus to designate a " missing link ", a hypothetical intermediate between ape and man that lived in the tertiary and that supposedly, following de mortillet's theory, produced eoliths. in his work of 1883 le prehistorique, antiquite de l'homme ( the prehistoric : man's antiquity, below quoted after the 2nd edition, 1885 ), de mortillet writes : nous sommes don	Anthropopithecus	wikipedia
##ths. in his work of 1883 le prehistorique, antiquite de l'homme ( the prehistoric : man's antiquity, below quoted after the 2nd edition, 1885 ), de mortillet writes : nous sommes donc forcement conduits a admettre, par une deduction logique tiree de l ’ observation directe des faits, que les animaux intelligents qui savaient faire du feu et tailler des pierres a l ’ epoque tertiaire, n ’ etaient pas des hommes dans l ’ acception geologique et paleontologique du mot, mais des animaux d ’ un autre genre, des precurseurs de l ’ homme dans l ’ echelle des etres, precurseurs auxquels j ’ ai donne le nom d ’ anthropopithecus. ainsi, par le seul raisonnement, solidement appuye sur des observations precises, nous sommes arrives a decouvrir d ’ une maniere certaine un etre intermediaire entre les anthropoides actuels et l ’ homme. we are therefore forced to admit, as a consequence of a logical deduction drawn from the direct observation of the facts, that intelligent animals who knew how to make fire and cut stones in the tertiary period, were not men in the geological and paleontological sense of the word, but animals of another kind, precursors of man in the chain of beings, precursors to whom i gave the name anthropopithecus. thus, by reasoning alone, firmly supported by precise observations, we have come to discover with certainty a being intermediate between the present anthropoids and man. when in 1905 the french paleontologist, paleoanthropologist and geologist marcellin boule ( 1861 – 1942 ) published a paper demonstrating that the eoliths were in fact geofacts produced by natural phenomena ( freezing, pressure, fire ), the argument proposed by de mortillet fell into disrepute and his definition of the term anthropopithecus was dropped. yet the chimpanzee meaning of the genus persisted throughout the 19th century, even to the point of being a genus name attributed to fossil specimens. for example, a fossil primate discovered in 1878 by the british malacologist william theobald ( 1829 - 1908 ) in	Anthropopithecus	wikipedia
##zee meaning of the genus persisted throughout the 19th century, even to the point of being a genus name attributed to fossil specimens. for example, a fossil primate discovered in 1878 by the british malacologist william theobald ( 1829 - 1908 ) in the pakistani punjab in british india was first named palaeopithecus in 1879 but later renamed anthropopithecus sivalensis, assuming that these remains had to be brought back to the chimpanzee genus as the latter was being understood at the time. a famous example of a fossil anthropopithecus is that of the java man, discovered in 1891 in trinil, nearby the solo river, in east java, by dutch physician and anatomist eugene dubois, who named the discovery with the scientific name anthropopithecus erectus. this dubois paper, written during the last quarter of 1892, was published by the dutch government in 1893. in those early 1890s, the term anthropopithecus was still being used by zoologists as the genus name of chimpanzees, so dubois'anthropopithecus erectus came to mean something like " the upright chimpanzee ", or " the chimpanzee standing up ". however, a year later, in 1893, dubois considered that some anatomical characters proper to humans made necessary the attribution of these remains to a genus different than anthropopithecus and he renamed the specimen of java with the name pithecanthropus erectus ( 1893 paper, published in 1894 ). pithecanthropus is a genus that german biologist ernst haeckel ( 1834 - 1919 ) had created in 1868. years later, in the 20th century, the german physician and paleoanthropologist franz weidenreich ( 1873 - 1948 ) compared in detail the characters of dubois'java man, then named pithecanthropus erectus, with the characters of the peking man, then named sinanthropus pekinensis. weidenreich concluded in 1940 that because of their anatomical similarity with modern humans it was necessary to gather all these specimens of java and china in a single species of the genus homo, the species homo erectus. by that time, the genus anthropopithecus had already been abandoned since 1895 at the earliest. = = in popular culture = = the term anthropopithecus is scientifically obsolete in the present day	Anthropopithecus	wikipedia
erectus. by that time, the genus anthropopithecus had already been abandoned since 1895 at the earliest. = = in popular culture = = the term anthropopithecus is scientifically obsolete in the present day but did become widespread in popular culture, mainly in france and belgium : in his short story gil braltar ( 1887 ), jules verne uses the term anthropopitheque ( anthropopithecus ) to describe the simian aspect of one of his characters, general mckackmale : il dormait bien, le general mac kackmale, sur ses deux oreilles, plus longues que ne le comporte l ’ ordonnance. avec ses bras demesures, ses yeux ronds, enfonces sous de rudes sourcils, sa face encadree d ’ une barbe reche, sa physionomie grimacante, ses gestes d ’ anthropopitheque, le prognathisme extraordinaire de sa machoire, il etait d ’ une laideur remarquable, – meme chez un general anglais. un vrai singe, excellent militaire, d ’ ailleurs, malgre sa tournure simiesque. he slept well, did general mackackmale, with both eyes shut, though longer than was permitted by regulations. with his long arms, his round eyes deeply set under their beetling brows, his face embellished with a stubbly beard, his grimaces, his semi - human gestures, the extraordinary jutting - out of his jaw, he was remarkably ugly, even for an english general. something of a monkey but an excellent soldier nevertheless, in spite of his apelike appearance. in the science - fiction novel la cite des tenebres ( the city of darkness ), written by french journalist and writer leon groc in 1926, the anthropopitheques ( anthropopithecuses ) are a large herd of ape - men having reached a very low degree of civilisation. english author george c foster makes use of both pithecanthropus ( aka java man ) and eoanthropus in his 1930 novel full fathom five. he dates the former, a discoverer that fire can be captured, to 500, 000 years ago, and the latter	Anthropopithecus	wikipedia
pithecanthropus ( aka java man ) and eoanthropus in his 1930 novel full fathom five. he dates the former, a discoverer that fire can be captured, to 500, 000 years ago, and the latter, the first hominid to adopt clothing, to 200, 000 years ago. for the purposes of the story, the conversations of both are rendered in contemporary english. the belgian comics author herge made the term anthropopitheque ( anthropopithecus ) one of the numerous swear words of captain haddock in the comic album series the adventures of tintin. in 2001, french singer brigitte fontaine wrote, sang and recorded the song titled pipeau. in this song, the chorus repeats the term anthropopitheque ( anthropopithecus ). = = see also = = anthropomorpha archaic humans caveman hominini human taxonomy humanzee = = notes and references = = = = = notes = = = = = = references = = = = = further reading = = john de vos, lecture the dubois collection : a new look at an old collection. in winkler prins, c. f. & donovan, s. k. ( eds. ), vii international symposium ‘ cultural heritage in geosciences, mining and metallurgy : libraries - archives - museums ’ : “ museums and their collections ”, leiden ( the netherlands ), 19 – 23 may 2003. scripta geologic, special issue, 4 : 267 - 285, 9 figs. ; leiden, august 2004. = = external links = = l'anthropopitheque ( from the " pole international de la prehistoire ", archived document, in french )	Anthropopithecus	wikipedia
autism spectrum disorder ( asd ) or simply autism is a neurodevelopmental disorder that begins in early childhood, persists throughout adulthood, and is characterized by difficulties in social communication and restricted, repetitive patterns of behavior. there are many conditions comorbid to autism, such as attention deficit hyperactivity disorder, anxiety disorders, and epilepsy. in medicine, comorbidity is the presence of one or more additional conditions co - occurring with the primary one, or the effect of such additional disorders. distinguishing between asd and other diagnoses can be challenging because the traits of asd often overlap with symptoms of other disorders, and the characteristics of asd make traditional diagnostic procedures difficult. autism is associated with several genetic disorders, perhaps due to an overlap in genetic causes. about 10 – 15 % of autism cases have an identifiable mendelian ( single - gene ) condition, chromosome abnormality, or other genetic syndrome, a category referred to as syndromic autism. approximately 8 in 10 people with autism suffer from a mental health problem in their lifetime, in comparison to 1 in 4 of the general population that suffers from a mental health problem in their lifetimes. = = comorbid conditions = = = = = anxiety = = = anxiety disorders are common among children and adults with asd. symptoms are likely affected by age, level of cognitive functioning, degree of social impairment, and asd - specific difficulties. many anxiety disorders, such as social anxiety disorder and generalized anxiety disorder, are not commonly diagnosed in people with asd because such symptoms are better explained by asd itself, and it is often difficult to tell whether symptoms such as compulsive checking are part of asd or a co - occurring anxiety problem. the prevalence of anxiety disorders in children with asd has been reported to be anywhere between 11 % and 84 % ; the wide range is likely due to differences in the ways the studies were conducted. a systematic review summarized available evidence on interventions to reduce anxiety in school children with autism spectrum disorder. of the 24 studies reviewed, 22 used a cognitive behavioral therapy ( cbt ) approach. the review found that cbt was moderately to highly effective at reducing anxiety in school children with autism spectrum disorder, but that effects varied depending on whether they were reported by clinicians, parents or self - reported. treatments involving parents and one - on - one compared to group treatments were more effective. = = = attention deficit hyperactivity disorder = = = the diagnosis manual dsm - iv did not allow the	Conditions comorbid to autism	wikipedia
by clinicians, parents or self - reported. treatments involving parents and one - on - one compared to group treatments were more effective. = = = attention deficit hyperactivity disorder = = = the diagnosis manual dsm - iv did not allow the co - diagnosis of asd and attention deficit hyperactivity disorder ( adhd ). however, following years of clinical research, the dsm - 5 released in 2013 removed this prohibition of co - morbidity. thus, individuals with autism spectrum disorder may also have a diagnosis of adhd, with the modifiers of a predominantly inattentive, hyperactive, combined, or not otherwise specified presentation. clinically significant symptoms of these two conditions commonly co - occur, and children with both sets of symptoms may respond poorly to standard adhd treatments. individuals with autism spectrum disorder may benefit from additional types of medications. the term audhd is sometimes used for those with both autism and adhd. there are also studies suggesting noticeable differences in presenting symptoms by gender which can complicate diagnosis, especially in adulthood. = = = avoidant / restrictive food intake disorder = = = avoidant / restrictive food intake disorder ( arfid ) is a feeding or eating disorder in which individuals significantly limit the volume or variety of foods they consume, causing malnutrition, weight loss, and psychosocial problems. a 2023 review concluded that " there is considerable overlap between arfid and autism, " finding that 8 % to 55 % of children diagnosed with arfid were autistic. unlike eating disorders such as anorexia nervosa and bulimia, body image disturbance is not a root cause. individuals with arfid may have trouble eating due to the sensory characteristics of food ( appearance, smell, texture, or taste ) ; executive function disregulation ; fears of choking or vomiting ; low appetite ; or a combination of these factors. = = = bipolar disorder = = = bipolar disorder, or manic - depression, is itself often claimed to be comorbid with a number of conditions, including autism. autism includes some symptoms commonly found in mood and anxiety disorders. = = = bowel disease = = = gastrointestinal symptoms are a common comorbidity in patients with autism spectrum disorders ( asd ), even though the underlying mechanisms are largely unknown. the most common gastrointestinal symptoms reported by proprietary tool developed and administered by mayer, padua, and tillisch ( 2014 ) are abdominal pain, constipation, dia	Conditions comorbid to autism	wikipedia
( asd ), even though the underlying mechanisms are largely unknown. the most common gastrointestinal symptoms reported by proprietary tool developed and administered by mayer, padua, and tillisch ( 2014 ) are abdominal pain, constipation, diarrhea and bloating, reported in at least 25 percent of participants. carbohydrate digestion and transport is impaired in individuals with autism spectrum disorder, which is thought to be attributed to functional disturbances that cause increased intestinal permeability, deficient enzyme activity of disaccharides, increased secretin - induced pancreatico - biliary secretion, and abnormal fecal flora clostridia taxa. altered gastrointestinal function accompanied by pain may induce feeding issues and increase perceived negative behaviors, including self injury, in individuals with autism. = = = depression = = = major depressive disorder has been shown by several studies to be one of the most common comorbid conditions in those with asd, and is thought to develop and occur more in high - functioning individuals during adolescence, when the individual develops greater insight into their differences from others. in addition, the presentation of depression in asds can depend on the level of cognitive functioning in the individual, with lower functioning children displaying more behavioral issues and higher functioning children displaying more traditional depressive symptoms. a 2019 meta - analysis identified autistic people as being four times more likely to have depression than non - autistic people, with approximately 40 % of autistic adults having depression. = = = developmental coordination disorder ( dyspraxia ) = = = the initial accounts of asperger syndrome and other diagnostic schemes include descriptions of developmental coordination disorder. children with asd may be delayed in acquiring motor skills that require motor dexterity, such as bicycle riding or opening a jar, and may appear awkward or " uncomfortable in their own skin ". they may be poorly coordinated, or have an odd or bouncy gait or posture, poor handwriting, other hand / dexterity impairments, or problems with visual - motor integration, visual - perceptual skills, and conceptual learning. they may show problems with proprioception ( sensation of body position ) on measures of developmental coordination disorder, balance, tandem gait, and finger - thumb apposition. = = = epilepsy = = = asd is also associated with epilepsy, with variations in risk of epilepsy due to age, cognitive level, and type of language disorder. one in four au	Conditions comorbid to autism	wikipedia
finger - thumb apposition. = = = epilepsy = = = asd is also associated with epilepsy, with variations in risk of epilepsy due to age, cognitive level, and type of language disorder. one in four autistic children develops seizures, often starting either in early childhood or adolescence. seizures, caused by abnormal electrical activity in the brain, can produce a temporary loss of consciousness ( a " blackout " ), a body convulsion, unusual movements, or staring spells. sometimes a contributing factor is a lack of sleep or a high fever. an eeg can help confirm the seizure's presence. typically, onset of epilepsy occurs before age five or during puberty, and is more common in females and individuals who also have a comorbid intellectual disability. = = = fetal alcohol spectrum disorder = = = fetal alcohol spectrum disorders ( fasd ) are a group of conditions that can occur in a person who is exposed to alcohol during gestation. behavioral traits of fasd can be similar to those of asd. evidence on the link between fasd and asd is limited. although results from studies are mixed, it is estimated that 2. 6 % of children with an fasd have an asd as well, a rate almost two times higher than that reported in the general us population. however, there is no information on the prevalence of fasd amongst those with asd. = = = fragile x syndrome = = = fragile x syndrome is the most common inherited form of intellectual disability. it was so named because one part of the x chromosome has a defective piece that appears pinched and fragile when under a microscope. fragile x syndrome represents an estimated 1 % to 6 % of all asd cases. = = = gender dysphoria = = = gender dysphoria is a diagnosis given to transgender people who experience discomfort related to their gender identity. autistic people are more likely to experience gender dysphoria. around 20 % of gender identity clinic - assessed individuals reported characteristics of asd. = = = hypermobility spectrum disorder and ehlers – danlos syndromes = = = studies have confirmed a link between hereditary connective tissue disorders such as ehlers - danlos syndromes ( eds ) and hypermobility spectrum disorder ( hsd ) with autism, as a comorbidity and a co - occurrence within the same families. = = = intellectual disability = = = the fraction of autistic individuals who also meet criteria for intellectual disability has been	Conditions comorbid to autism	wikipedia
##bility spectrum disorder ( hsd ) with autism, as a comorbidity and a co - occurrence within the same families. = = = intellectual disability = = = the fraction of autistic individuals who also meet criteria for intellectual disability has been reported as anywhere from 25 % to 70 %. this wide variation illustrates the difficulty of assessing intelligence in autistic individuals. for example, a 2001 british study of 26 autistic children found only about 30 % with intelligence in the normal range ( iq above 70 ), 50 % with a mild to moderate intellectual disability, and about 20 % with a severe to profound intellectual disability ( iq below 35 ). for asd other than autism the association is much weaker : the same study reported typical levels of intelligence in about 94 % of 53 children with pdd - nos. estimates are that 40 – 69 % of individuals with asd have some degree of an intellectual disability, with females more likely to be in severe range of an intellectual disability. learning disabilities are also highly comorbid in individuals with an asd. approximately 25 – 75 % of individuals with an asd also have some degree of learning disability, although the types of learning disability vary depending on the specific strengths and weaknesses of the individual. a 2006 review questioned the common assumption that most children with autism have an intellectual disability. it is possible that the association between an intellectual disability and autism is not because they usually have common causes, but because the presence of both makes it more likely that both will be diagnosed. the cdc states that based on information from 11 reporting states 46 % of people with autism have above 85 iq. = = = mitochondrial diseases = = = the central player in bioenergetics is the mitochondrion. mitochondria produce about 90 % of cellular energy, regulate cellular redox status, produce ros, maintain ca2 + homeostasis, synthesize and degrade high - energy biochemical intermediates, and regulate cell death through activation of the mitochondrial permeability transition pore ( mtptp ). when they fail, less and less energy is generated within the cell. cell injury and even cell death follow. if this process is repeated throughout the body, whole organ systems begin to fail. mitochondrial diseases are a heterogeneous group of disorders that can affect multiple organs with varying severity. symptoms may be acute or chronic with intermittent decompensation. neurological manifestations include encephalopathy, stroke, cognitive regression, seizures, cardiopathies ( cardiac conduction defects	Conditions comorbid to autism	wikipedia
of disorders that can affect multiple organs with varying severity. symptoms may be acute or chronic with intermittent decompensation. neurological manifestations include encephalopathy, stroke, cognitive regression, seizures, cardiopathies ( cardiac conduction defects, hypertensive heart disease, cardiomyopathy, etc... ), diabetes, visual and hearing loss, organ failure, neuropathic pain and peripheral neuropathy. mitochondrial disease is estimated to affect less than 0. 1 % of the general population. approximately 5 % of autistic children meet the criteria for classical mitochondrial dysfunction. it is unclear why this mitochondrial disease occurs, considering that only 23 % of children with both asd and mitochondrial disease present with mitochondrial dna abnormalities. = = = neurofibromatosis type i = = = asd is also associated with neurofibromatosis type i ( nf - 1 ). nf - 1 is a complex multi - system human disorder caused by the mutation of a gene on chromosome 17 that is responsible for production of a protein, called neurofibromin 1, which is needed for normal function in many human cell types. nf - 1 causes tumors along the nervous system which can grow anywhere on the body. nf - 1 is one of the most common genetic disorders and is not limited to any person's race or sex. nf - 1 is an autosomal dominant disorder, which means that mutation or deletion of one copy ( or allele ) of the nf - 1 gene is sufficient for the development of nf - 1, although presentation varies widely and is often different even between relatives affected by nf - 1. = = = neuroinflammation and immune disorders = = = the role of the immune system and neuroinflammation in the development of autism is controversial. until recently, there was scant evidence supporting immune hypotheses, but research into the role of immune response and neuroinflammation may have important clinical and therapeutic implications. the exact role of heightened immune response in the central nervous system ( cns ) of patients with autism is uncertain, but may be a primary factor in triggering and sustaining many of the comorbid conditions associated with autism. recent studies indicate the presence of heightened neuroimmune activity in both the brain tissue and the cerebrospinal fluid of patients with autism, supporting the view that heightened immune response may be an essential factor in the onset of autistic symptoms	Conditions comorbid to autism	wikipedia
studies indicate the presence of heightened neuroimmune activity in both the brain tissue and the cerebrospinal fluid of patients with autism, supporting the view that heightened immune response may be an essential factor in the onset of autistic symptoms. a 2013 review also found evidence of microglial activation and increased cytokine production in postmortem brain samples from people with autism. = = = neuropathies = = = the prevalence of peripheral neuropathies would be significantly increased in asd. peripheral neuropathies may be asymptomatic. peripheral neuropathy is a common manifestation of mitochondrial diseases and polyneuropathies would be relatively common. neuropathies could also be caused by other features of asd. = = = obsessive – compulsive disorder = = = obsessive – compulsive disorder is characterized by recurrent obsessive thoughts or compulsive acts. about 30 % of individuals with autism spectrum disorders also have ocd. = = = obsessive – compulsive personality disorder = = = obsessive – compulsive personality disorder ( ocpd ) is a cluster c personality disorder characterized by a general pattern of excessive concern with orderliness, perfectionism, attention to details, mental and interpersonal control and a need for control over one's environment which interferes with personal flexibility, openness to experience and efficiency as well as interfering with relationships. there are considerable similarities and overlap between autism and ocpd, such as list - making, inflexible adherence to rules and obsessive aspects of routines, though the latter may be distinguished from ocpd especially regarding affective behaviors, bad social skills, difficulties with theory of mind and intense intellectual interests e. g. an ability to recall every aspect of a hobby. = = = psychosis and schizophrenia = = = childhood - onset schizophrenia is preceded by childhood autistic spectrum disorders in almost half of cases, and an increasing number of similarities are being discovered between the two disorders. studies have also found that the presence of psychosis in adulthood is significantly higher in those with autism spectrum disorders, especially those with pdd - nos, than in the general population. this psychosis generally occurs in an unusual way, with most individuals with asd experiencing a highly atypical collection of symptoms. recent studies have also found that the core asd symptoms also generally present in a slightly different way during the childhood of the individuals that will later become	Conditions comorbid to autism	wikipedia
in an unusual way, with most individuals with asd experiencing a highly atypical collection of symptoms. recent studies have also found that the core asd symptoms also generally present in a slightly different way during the childhood of the individuals that will later become psychotic, long before the actual psychosis develops. = = = schizoid personality disorder = = = schizoid personality disorder ( spd ) is a personality disorder characterized by a lack of interest in social relationships, a tendency towards a solitary or sheltered lifestyle, secretiveness, emotional coldness, detachment and apathy. other associated features include stilted speech, a lack of deriving enjoyment from most, if not all, activities, feeling as though one is an " observer " rather than a participant in life, an inability to tolerate emotional expectations of others, apparent indifference when praised or criticised, a degree of asexuality and idiosyncratic moral or political beliefs. symptoms typically start in late childhood or adolescence. several studies have reported an overlap, confusion or comorbidity with asperger syndrome ( which has been combined with autism spectrum disorder and no longer appears as a diagnostic label in the dsm - 5 ). asperger syndrome was at one time called " schizoid disorder of childhood ". eugen bleuler coined the term " autism " to describe withdrawal to an internal fantasy, against which any influence from outside becomes an intolerable disturbance. in a 2012 study of a sample of 54 young adults with asperger syndrome, it was found that 26 % of them also met criteria for spd, the highest comorbidity out of any personality disorder in the sample ( the other comorbidities were 19 % for obsessive – compulsive personality disorder, 13 % for avoidant personality disorder and one female with schizotypal personality disorder ). additionally, twice as many men with asperger syndrome met criteria for spd than women. while 41 % of the whole sample were unemployed with no occupation, this rose to 62 % for the asperger's and spd comorbid group. although the cause for this comorbidity is not yet certain, genetic evidence for a spectrum between cluster a personality disorders / schizophrenia and autism spectrum disorders has been found. tantam suggested that asperger syndrome may confer an increased risk of developing spd. in the same 2012 study, it was noted that the dsm may complicate diagnosis of spd by requiring the exclusion of a pervasive developmental disorder (	Conditions comorbid to autism	wikipedia
tantam suggested that asperger syndrome may confer an increased risk of developing spd. in the same 2012 study, it was noted that the dsm may complicate diagnosis of spd by requiring the exclusion of a pervasive developmental disorder ( pdd ) before establishing a diagnosis of spd. the study found that social interaction, stereotyped behaviours and specific interests were more severe in the individuals with asperger syndrome also fulfilling spd criteria, against the notion that social interaction skills are unimpaired in spd. the authors believe that a substantial subgroup of people with autism spectrum disorder or pdd have clear " schizoid traits " and correspond largely to the " loners " in lorna wing's classification the autism spectrum ( lancet 1997 ), described by sula wolff. = = = self - injury and suicide = = = self - injurious behaviors are relatively common in autistic people, and can include head - banging, self - cutting, self - biting, and hair - pulling. some of these can result in serious injury or death. autistic people are about three times as likely as non - autistic people to engage in self - injury. theories about the cause of self - injurious behavior in children with developmental delay, including autistic children, include : frequency or continuation of self - injurious behavior can be influenced by environmental factors ( e. g., reward in return for halting self - injurious behavior ). this theory does not apply to younger children with autism. there is some evidence that frequency of self - injurious behavior can be reduced by removing or modifying environmental factors that reinforce the behavior. : 10 – 12 higher rates of self - injury are noted in socially isolated autistic people. studies have shown that a lack of socialization skills are related factors to self - injurious behavior for autistic people. self - injury could be a response to modulate pain perception when chronic pain or other health problems that cause pain are present. : 12 – 13 abnormal basal ganglia connectivity may predispose to self - injurious behavior. : 13 risk factors for self - harm and suicidality include circumstances that could affect anyone, such as mental health problems ( e. g., anxiety disorder ) and social problems ( e. g., unemployment and social isolation ), plus factors that affect only autistic people, such as actively trying to behave like a neurotypical person, which	Conditions comorbid to autism	wikipedia
health problems ( e. g., anxiety disorder ) and social problems ( e. g., unemployment and social isolation ), plus factors that affect only autistic people, such as actively trying to behave like a neurotypical person, which is called masking. approximately 8 in 10 people with autism suffer from a mental health problem in their lifetime, in comparison to 1 in 4 of the general population that suffers from a mental health problem in their lifetimes. rates of suicidality vary significantly depending upon what is being measured. this is partly because questionnaires developed for neurotypical subjects are not always valid for autistic people. as of 2023, the suicidal behaviours questionnaire – autism spectrum conditions ( sbq - asc ) is the only test validated for autistic people. according to some estimates, about a quarter of autistic youth and a third of all autistic people have experienced suicidal ideation at some point. rates of suicidal ideation are the same for people formally diagnosed with autism and people who have typical intelligence and are believed to have autism but have not been diagnosed. the suicide rate for verbal autistics is nine times that of the general population. in a 2014 study of late diagnosed autistic adults, 66 % had experienced suicidal ideation ( nine times higher than the general population ) and 35 % had a suicide plan or had made a suicide attempt. although most people who attempt suicide are not autistic, autistic people are about three times as likely as non - autistic people to make a suicide attempt. less than 10 % of autistic youth have attempted suicide, but 15 % to 25 % autistic adults have. the rates of suicide attempts are the same among people formally diagnosed with autism and those who have typical intelligence and are believed to have autism but have not been diagnosed. the suicide risk is lower among cisgender autistic males and autistic people with intellectual disabilities. the rate of suicide results in a global excess mortality among autistic people equal to approximately 2 % of all suicide deaths each year. = = = sensory problems = = = unusual responses to sensory stimuli are more common and prominent in individuals with autism, and sensory abnormalities are commonly recognized as diagnostic criteria in autism spectrum disorder ( asd ), as reported in the dsm - 5 ; although there is no good evidence that sensory symptoms differentiate autism from other developmental disorders. sensory processing disorder is comorbid with asd, with comorbidity rates of 42	Conditions comorbid to autism	wikipedia
disorder ( asd ), as reported in the dsm - 5 ; although there is no good evidence that sensory symptoms differentiate autism from other developmental disorders. sensory processing disorder is comorbid with asd, with comorbidity rates of 42 – 88 %. with or without meeting the standards of spd, about 90 % of asd individuals have some type of atypical sensory experiences, described as both hyper - and hypo - reactivity. the prevalence of reported " unusual sensory behaviors " that affect functioning in everyday life is also higher, ranging from 45 to 95 % depending on factors such as age, iq and the control group used. several studies have reported associated motor problems that include poor muscle tone, poor motor planning, and toe walking ; asd is not associated with severe motor disturbances. many with asd often find it uncomfortable to sit or stand in a way which neurotypical people will find ordinary, and may stand in an awkward position, such as with both feet together, supinating, sitting cross - legged or with one foot on top of the other or simply having an awkward gait. however, despite evidently occurring more often in people with asd, all evidence is anecdotal and unresearched at this point. it has been observed by some psychologists that there is commonality to the way in which these'awkward'positions may manifest. = = = sleep disorders = = = sleep disorders are commonly reported by parents of individuals with asds, including late sleep onset, early morning awakening, and poor sleep maintenance ; sleep disturbances are present in 53 – 78 % of individuals with asd. unlike general pediatric insomnia, which has its roots in behavior, sleep disorders in individuals with asd are comorbid with other neurobiological, medical, and psychiatric issues. if not addressed, severe sleep disorders can exacerbate asd behaviors such as self - injury ; however, there are no food and drug administration - approved pharmacological treatments for pediatric insomnia at this time. studies have found abnormalities in the physiology of melatonin and circadian rhythm in people with autism spectrum disorders ( asd ). some evidence suggests that melatonin supplements improve sleep patterns in children with autism but robust, high - quality studies are overall lacking. = = = strabismus = = = according to several studies, there is a high prevalence of strabismus in autistic individuals, with rates 3 – 10 times that of the general population. = =	Conditions comorbid to autism	wikipedia
studies are overall lacking. = = = strabismus = = = according to several studies, there is a high prevalence of strabismus in autistic individuals, with rates 3 – 10 times that of the general population. = = = tinnitus = = = according to one study, 35 % of people who are autistic would be affected by tinnitus, which is much higher than in the general population. = = = tourette syndrome = = = the prevalence of tourette syndrome among individuals who are autistic is estimated to be 6. 5 %, higher than the 2 % to 3 % prevalence for the general population. several hypotheses for this association have been advanced, including common genetic factors and dopamine, glutamate or serotonin abnormalities. = = = tuberous sclerosis = = = tuberous sclerosis is a rare genetic disorder that causes benign tumors to grow in the brain as well as in other vital organs. it has a consistently strong association with the autism spectrum. one to four percent of autistic people also have tuberous sclerosis. studies have reported that between 25 % and 61 % of individuals with tuberous sclerosis meet the diagnostic criteria for autism with an even higher proportion showing features of a broader pervasive developmental disorder. = = = turner syndrome = = = turner syndrome is an intersex condition wherein a person is born phenotypically female but with only one x chromosome or with x / xx mosaicism instead of xx or xy chromosomes. one study found that 23 % of girls with turner syndrome who were included met criteria for a diagnosis of an autism spectrum disorder and the majority had " significant social communication difficulties. " = = = vitamin deficiencies = = = vitamin deficiencies are more common in autism spectrum disorders than in the general population. vitamin d : vitamin d deficiency was concerned in a german study 78 % of hospitalized autistic population. 52 % of the entire asd group in the study was severely deficient, which is much higher than in the general population. other studies also show a higher rate of vitamin d deficiencies in asds. vitamin b12 : the researchers found that, overall, b12 levels in the brain tissue of autistic children were three times lower than those of the brain tissue of children not affected by asd. this lower - than - normal b12 profile persisted throughout life in the brain tissues of patients with autism. these deficiencies are not visible by conventional blood	Conditions comorbid to autism	wikipedia
##ic children were three times lower than those of the brain tissue of children not affected by asd. this lower - than - normal b12 profile persisted throughout life in the brain tissues of patients with autism. these deficiencies are not visible by conventional blood sampling. as for the classic deficiency of vitamin b12, it would affect up to 40 % of the population, its prevalence has not yet been studied in autism spectrum disorders. vitamin b12 deficiency is one of the most serious. vitamin b9 ( folic acid ) : studies have been conducted regarding folic acid supplementation in autism in children. " the results showed that folic acid supplementation significantly improved certain symptoms of autism such as sociability, verbal / preverbal cognitive language, receptive language, and emotional expression and communication. in addition, this treatment improved the concentrations of folic acid, homocysteine and redox metabolism of standardized glutathione. " vitamin a : vitamin a can induce mitochondrial dysfunction. according to a non - specific study on asd : " vitamin a and its derivatives, retinoids, are micronutrients necessary for the human diet in order to maintain several cellular functions of human development in adulthood as well as during aging... although it is either an essential micronutrient, used in clinical applications, vitamin a has several toxic effects on the redox environment and mitochondrial function. a decline in the quality of life and an increase in the mortality rate among users of vitamin a supplements have been reported. although the exact mechanism by which vitamin a causes its deleterious effects is not yet clear... vitamin a and its derivatives, retinoids, disrupt mitochondrial function by a mechanism that is not fully understood. " zinc : zinc deficiency incidence rates in children aged 0 to 3, 4 to 9 and 10 to 15 years were estimated at 43. 5 %, 28. 1 % and 3. 3 % for boys and at 52. 5 %, 28. 7 % and 3. 5 % among girls. magnesium : incidence rates of magnesium deficiency in children aged 0 to 3, 4 to 9 and 10 to 15 years were estimated at 27 %, 17. 1 % and 4. 2 % for boys and at 22. 9 %, 12. 7 % and 4. 3 % among girls. calcium : incidence rates of calcium deficiency in children aged 0 to 3, 4 to 9 years and 10 to 15 years were estimated at 10. 4 %, 6. 1 % and 0. 4 % for boys and at	Conditions comorbid to autism	wikipedia
. 3 % among girls. calcium : incidence rates of calcium deficiency in children aged 0 to 3, 4 to 9 years and 10 to 15 years were estimated at 10. 4 %, 6. 1 % and 0. 4 % for boys and at 3. 4 %, 1. 7 % and 0. 9 % among girls. it has been found that special diets that are inappropriate for children with asd usually result in excessive amounts of certain nutrients and persistent vitamin deficiencies. = = = other mental disorders = = = phobias and other psychopathological disorders have often been described along with asd but this has not been assessed systematically. = = notes = = = = references = =	Conditions comorbid to autism	wikipedia
a duocentric social network is a type of social network composed of the combined network members of a dyad. the network consists of mutual, overlapping ties between members of the dyad as well as non - mutual ties. while an explicit conceptualization of duocentric social networks appeared for the first time in an academic publication in 2008, the history of the analysis dates back to at least the 1950s and has spanned the fields of psychology, sociology, and health. = = history = = = = = original conception = = = coromina et al. coined the term duocentered networks to describe the analytical technique of combining two individuals ’ ( or egos ) social networks to examine both the shared network members ( or alters ) between a dyad and those that are connected to only one individual. in this original conceptualization, coromina et al. did not consider the relationships between the alters ( i. e., the ties between alters ) to be a necessary component of duocentric network analysis. the impetus for this original conceptualization was a compromise between the two most commonly used social network analytical methods : egocentric and sociocentric network analyses. in an egocentric network analysis, a singular individual, his or her network members, and ( occasionally ), the ties between those alters are the focal point of the analysis. egocentric analyses have been used in a wide range of fields, including physical health, psychopathology, family studies, and intimate relationships. on the other hand, the sociocentric network approach utilizes a bounded group as the unit of analyses, examining all ties between actors in the group. this has been utilized to study health in retirement communities and entire cities ( e. g., the framingham heart study ), as well as in the workplace and classroom settings. sociocentric networks could be used to answer research questions focused on dyads, but the time, cost, and difficulty of collecting network data from all members in a bounded group is often prohibitive. coromina et al. also state that duocentered networks relieve issues of data collection in sociocentric networks. first, it reduces “ respondent inaccuracy ” in reporting network contacts, which will be more prevalent in less well socially connected individuals. because the dyad is selected for a specific network research question, they are more likely to be central members of their networks and better positioned to accurately report on their network contacts. second, the technique reduces “ unit non - response, " which is the failure of an eligible study participant to	Duocentric social network	wikipedia
a specific network research question, they are more likely to be central members of their networks and better positioned to accurately report on their network contacts. second, the technique reduces “ unit non - response, " which is the failure of an eligible study participant to respond or provide enough information to deem the response statistically usable. because the focus of a duocentered network is only two individuals rather than a larger group, it will ostensibly be easier to gather usable information. = = = kennedy et al. ( 2015 ) expansion = = = kennedy et al. maintained this basic framework, but redefined the concept as duocentric networks, and suggested that information on the relatedness of ties in the network should be collected. coromina et al. did not take this approach because of the respondent inaccuracy and unit non - response bias that similarly affect sociocentric analyses. respondent inaccuracy in the context of duocentric networks means that people will inaccurately report the connections between their network members. unit non - response follows from this difficulty ; if people are unable to report connections, certain analyses that rely on these connections may not be possible. = = analysis = = = = = structural measures = = = there are several common structural metrics derived from duocentric social networks : degree centrality : the number of ties that an ego has with other network members. more central egos have a greater number of connections. closeness centrality : an ego has higher closeness centrality as the number of “ steps ” it takes to get to other alters in the network decreases. if an alter is the friend of a friend of one's partner, this will decrease one's closeness centrality as compared to a friend of one's partner ( i. e., one step closer to the ego ). betweenness centrality : if a network is visualized as many separate paths connecting network members to each other through varying number of links, an ego has higher betweenness centrality to the extent that they lie on more paths between alters in a network. higher betweenness centrality indicates that one plays a larger role as an intermediary between network members who may not be directly connected. density : the total number of ties in a network relative to the total number of possible ties in a network. overlap : unique to duocentric networks, overlap measures the number of shared ties between two egos. diversity : similar to density, diversity measures the size of the non - overlapping network members of both egos in the dyad.	Duocentric social network	wikipedia
in a network. overlap : unique to duocentric networks, overlap measures the number of shared ties between two egos. diversity : similar to density, diversity measures the size of the non - overlapping network members of both egos in the dyad. components : a component is a portion of the social network that is disconnected from the rest of the full network. the members in a component are connected either directly or through a maximum of one mutual tie. generally, a greater number of components signals a less well - connected network. isolates : a measure of fragmentation in the network, isolates in a duocentric network are those that are connected to only one ego and to no other network members. = = = compositional measures = = = compositional measures are the characteristics of the individuals who make up the network or other societal norms and structures that may influence the structure and function of a social network. compositional measures include social support, intimate relationship approval from network members, proportion of family or friends in the network, demographic characteristics, and norms. = = = feedback loops = = = although primarily supported in egocentric network analyses, evidence suggest that dyads can influence the composition and structure of the duocentric networks in which they are embedded. for example, bryant, conger & meehan ( 2001 ) found that a wife's marital satisfaction predicted lower discord between husbands and the wife's parents at a later time. = = applications = = = = = application to intimate relationships = = = one of the first studies examining duocentric social networks was elizabeth bott's 1957 finding that the density of spouse's separate networks is positively associated with marital role segregation, a finding now known as the bott hypothesis. while bott did not examine the overlapping network of spouses, her work was among the first to collect network data separately from both members of a dyad, and use that data to predict a dyadic phenomenon. perhaps the most well - studied phenomenon utilizing a duocentric network approach in the context of intimate relationships is network overlap. most of this research points to higher relationship satisfaction as the level of overlap increases. network overlap increases as couples transition to cohabitation, and remarriages tend to have less overlap than first marriages. additionally, one finding suggests that more equal numbers of each partner's family contained in the overlapping network is associated with higher marital satisfaction for heterosexual couples. other structural measures have received relatively less attention in the study of intimate relationships. research shows a positive association between duocentric network size and marital	Duocentric social network	wikipedia
equal numbers of each partner's family contained in the overlapping network is associated with higher marital satisfaction for heterosexual couples. other structural measures have received relatively less attention in the study of intimate relationships. research shows a positive association between duocentric network size and marital satisfaction. additionally, marriages in which both spouses are in their first marriage have larger networks than marriages in which both spouse is remarried. other studies have highlighted non - results, including that social network density is not associated with relationship satisfaction and that density is not associated with marital role segregation ( a refutation of the bott hypothesis ). the link between compositional duocentric network factors and intimate relationships is less well - studied. however, evidence from duocentric analyses suggest that discord with in - laws predicts lower satisfaction, commitment, and stability in marriages over time. additionally, support and approval from the social network tends to be associated with higher commitment and marital satisfaction. = = = application to other fields = = = duocentric social network analyses have been used less often outside the context of intimate relationships. one of the earliest examples examined the frequency with which two people mutually named one another in their respective network reports. the study recruited one person who listed their network members, then those network members were contacted and asked to list their own network members. about 86 % of the time, people named by the original interviewee also named that interviewee on their own list. another study of parents of children with brain tumors found that overlap of non - kin was near 50 %, while overlap for kin was slightly higher. more peripheral overlapping ties ( i. e., those to whom the couple is less close ) was associated with lower rates of mental health disorders. another study examined duocentric networks in sibling pairs aged 7 – 13. monozygotic twins had the most overlap in their peer networks ( 82 % ), followed by same - sex dizygotic twins ( 67 % ), same - sex virtual twins ( e. g., unrelated peers matched on certain characteristics ; 62 % ), friend - friend pairs ( 48 % ), opposite - sex dizygotic twins ( 42 % ), same - sex full siblings ( 39 % ), opposite sex virtual twins ( 37 % ), and opposite - sex full siblings ( 27 % ). genetics, sex ( same - or opposite - sex ), age, and relationship intimacy affected rates of peer overlap. another example used pairs of corporations engaged in a business alliance as the focal unit, and found that the more common partners ( i. e	Duocentric social network	wikipedia
genetics, sex ( same - or opposite - sex ), age, and relationship intimacy affected rates of peer overlap. another example used pairs of corporations engaged in a business alliance as the focal unit, and found that the more common partners ( i. e., overlap ) between the two firms, the less likely their alliance would dissolve. = = variants of duocentric network analyses = = kennedy et al. ( 2015 ) outline the most rigorous duocentric network study as one in which both members of the dyad report the specific individuals contained in their social networks. however, the time and cost of this form of data collection has led researchers to use less stringent techniques to gather information on a dyadic network. = = = global network perceptions = = = rather than asking respondents to list the specific people contained in their social network, researchers occasionally ask for global perceptions of network qualities from both members of a dyad. this methodology limits many structural analyses because the relationships between network members is unknown, unless the structural qualities are addressed at a global level ( e. g., for global perceptions of overlap, see kearns & leonard ( 2004 ) ). therefore, these studies typically highlight how compositional network aspects affect the dyad. for example, in the study of intimate relationship research, this methodology has been used to show how global perceptions of approval from the network vary across relationship stage, closeness to family predicts changes in marital happiness, the degree to which liking one's partner's family predicts relationship dissolution, the effect of network support on relationship satisfaction, and the relationship between time spent with the network and relationship commitment. = = = single ego reporting = = = another variant of the duocentric network approach is to interview only one member of a focal dyad, but require the individual to report on both their own and the other person's social network, or the other individual's relationship to their own network. in many of these studies, respondents report global network perceptions. for example, one study asked respondents to report on the propensity for a respondent's relationship partner to receive support from their own network ( a global measure of support ). support was positively associated with relationship satisfaction. another study asked respondents to report their perception of approval from their relationship partner's family ( another global measure ), which was found to be negatively associated with relationship dissolution. however, some research utilizes specific alter reporting in a single ego methodology. milardo ( 1982 ) asked respondents to report their romantic partner's relationship to each of their own	Duocentric social network	wikipedia
another global measure ), which was found to be negatively associated with relationship dissolution. however, some research utilizes specific alter reporting in a single ego methodology. milardo ( 1982 ) asked respondents to report their romantic partner's relationship to each of their own, specific, network members. this method allowed the researcher to understand how much of the ego's social network overlapped with his or her partner without collecting information from the partner. however, this approach risks the ego inaccurately reporting the relationship between their partner and the individual network members. another study asked homeless youth to list recent sexual partners, other non - sexual partner network members, and the relationships between these alters. the risk of unprotected sex was higher to the degree that sexual partners knew other members of the youth's social network. = = see also = = social network analysis social network social psychology industrial and organizational psychology health psychology sociology intimate relationship = = references = =	Duocentric social network	wikipedia
the cargo system ( also known as the civil - religious hierarchy, fiesta or mayordomia system ) is a collection of secular and religious positions held by men or households in rural indigenous communities throughout central and southern mexico and central america. these revolving offices, or cargos, become the unpaid responsibility of men who are active in civic life. they typically hold a given post for a term of one year, and alternate between civic and religious obligations from year to year. office holders execute most of the tasks of local governments and churches. individuals who hold a cargo are generally obligated to incur the costs of feasting during the fiestas that honor particular saints. where it is practiced, there is generally some expectation of all local men to take part in this cargo system throughout their lives. office holders assume greater responsibilities as they grow in stature in the community. such progression requires substantial financial resources, but eventually an individual who holds a requisite number of posts in service to his community retires and joins a group of elders instrumental in community decision - making, including appointing people to cargos. this expectation of local men to take part in this system is both an economic and a social one, as those who do not contribute are seen as not being deserving of living in the village. it served to create a village system where the old were helped by the young and women helped by men. furthermore, the legal enforcement of village obligations solidified communal ( social ) identity, rather than an identity dependent upon and linked to the national state. the cargo system has also been considered influenced by traditional hispanic customs, as the municipal government provided the tradition of cargas consejiles, where village residents are obligated to serve post terms. during the 19th and 20th centuries, the cargo system was a ladder system in which indigenous men could climb up. the cargo system was mainly defined as a public labor and community service. villages that were impoverished were able to get help easier because taxes were not charged, yet public work was given. it was a system which involved faithful and long term community service. men and women ( husband and wife ) were considered one unit, men needed their wives in order to succeed in their community. women did not claim rights in relation to village government. = = history = = the origins of the cargo system are tied to the efforts of spanish missionaries to convert indigenous peoples of the americas to christianity while at the same time forestalling their cultural hispanicization. after the spanish conquest of mesoamerica in the 16th century, many indians were	Cargo system	wikipedia
the cargo system are tied to the efforts of spanish missionaries to convert indigenous peoples of the americas to christianity while at the same time forestalling their cultural hispanicization. after the spanish conquest of mesoamerica in the 16th century, many indians were forcibly relocated to pueblos, which like spanish villages contained a church as the town center. priests were one of many special interest foreigners who had control over the political and social affairs of indigenous peoples, and they had dominion over many of these pueblos and had the authority to keep other colonists out. the priests were mindful that much of their influence over the indians stemmed from the priests'ability to speak indian languages. despite a 1550 royal edict calling for native peoples to be taught the spanish language, missionaries continued to minister to them in nahuatl and other local languages, thus preserving a major source of indian dependency on the church. the colonial church did not insist on excessive catholicization of existing indigenous practices, so long as there was no clear conflict between the two. because the missionaries were small in number, they increasingly placed religious responsibilities in the hands of trusted members of the villages. the village mayor or alcalde was charged with the responsibility of leading the villagers in a procession to sunday mass. over time, these processions were conducted with greater ceremony, making use of trappings such as crosses, incense, and music. the cargo system was used and transformed by communities within the context of law to eliminate noble exemption privileges. this brought to an end many internal feuds over principales with regards to nobility. noble exemptions were opposed by the common people, who were worried that such exemptions would negatively impact the supply of labour to the point of constant service. it was impossible to become part of the nobility by marrying the daughter of a noble, and was instead pushed by claimants based on heritage. therefore, in practice, the system was not as egalitarian as in the hypothetical sense, because while some men could move to greater positions and into seats of authority, others lacked the prestige to accomplish the same. the dispersal of the ability to accumulate wealth along with prestige also contributed greatly to the transformation of these villages. on occasion drawing on a spanish institution called the cofradias, the priests created a hierarchy of village posts in order to better organize the religious and civil lives of their indians. indigenous people filled these roles, which in theory gave them greater status within the community. these roles, however, also placed economic obligations on their recipients and the clergy used them as a way to exercise control over	Cargo system	wikipedia
the religious and civil lives of their indians. indigenous people filled these roles, which in theory gave them greater status within the community. these roles, however, also placed economic obligations on their recipients and the clergy used them as a way to exercise control over the villagers. villagers were obligated to organize efforts to discharge debts related to cost of food, wafers and wine for the mass and payment of the priests. the cargo system could a serve a manner in which people could elevate their station in society. people who faithfully discharged their duties through a series of mundane tasks could increase their social status which resulted in greater access for job opportunities and loftier positions. in short, community service allowed one to move up in the hierarchy of their society. eventually villagers could reach a high ranking position as members of the principals, who in turn would vote for the communal leader, the gobernadores. the caciques ore pre - hispanic nobles were exempt from the low standing positions, although a person from meager beginnings could ultimately serve to accumulate wealth and power. the cargo system also affected marital life. the man would work in the household of his in - laws. after marriage, the wife would move in with the groom's family in which she served as a domestic servant for her mother - in law. = = see also = = indigenous peoples of the americas potlatch spanish colonization of the americas = = sources = = frank cancian, economics and prestige in a maya community : the religious cargo system in zinacantan. stanford ( calif. ) : stanford university press, 1965, 238 p. chance, john k. ; william b. taylor. cofradias and cargos : an historical perspective on the mesoamerican civil - religious hierarchy. american ethnologist, vol. 12, no. 1. ( feb., 1985 ), pp. 1 – 26. dewalt, billie r. changes in the cargo systems of mesoamerica, anthropological quarterly, vol. 48, no. 2. ( apr., 1975 ), pp. 87 – 105. friedlander, judith. the secularization of the cargo system : an example from postrevolutionary central mexico ( in research reports and notes ). latin american research review, vol. 16, no. 2. ( 1981 ), pp. 132 – 143. guardino, peter. “ community service, liberal law, and local custom in indigenous villages : oaxaca, 1750 - 1850. ” honor, status	Cargo system	wikipedia
research review, vol. 16, no. 2. ( 1981 ), pp. 132 – 143. guardino, peter. “ community service, liberal law, and local custom in indigenous villages : oaxaca, 1750 - 1850. ” honor, status and law in modern latin america, duke university press, 2005, pp. 50 – 57.	Cargo system	wikipedia
burn : the misunderstood science of metabolism is a 2022 book written by herman pontzer in which he discusses metabolism, human health and use of energy in the human body. the book examines research and proposes a constrained approach to total energy expenditure. = = references = =	Burn: The Misunderstood Science of Metabolism	wikipedia
ocean elders is a worldwide group of oceans defenders, dedicated to protecting the ocean, wildlife, and nature itself. the group promotes the expansion of existing marine protected areas and the creation of new ones, allowing marine ecosystems to recover from the effects caused by human activities. the elders oppose the destruction of ecosystems, overfishing, and plastic pollution. the group includes scientists, musicians, business leaders, royalty, and country leaders. = = history = = in 2010, gigi brisson attended the mission blue expedition " where over 100 scientists, business leaders, philanthropists, and entertainment icons came together to support dr. sylvia earle ’ s ted wish. " the following year, brisson founded the group with the goal of unifying scientists with government and entertainment leaders. = = members = = notable members include : gigi brisson, founder and ceo sylvia earle, american marine biologist richard branson, british business magnate jackson browne, american singer - songwriter james cameron, canadian filmmaker rita r. colwell, american microbiologist jean - michel cousteau, french oceanographer wade davis, canadian anthropologist jane goodall, english primatologist gerry lopez, american actor catherine a. novelli, american diplomat frederik paulsen jr, swedish businessman bertrand piccard, swiss balloonist thomas remengesau jr., formerly president of palau david e. shaw, american entrepreneur nainoa thompson, native hawaiian navigator ted turner, american media mogul don walsh, american oceanographer bob weir, american musician sheila watt - cloutier, inuk environmentalist neil young, canadian - american singer - songwriter jose maria figueres, former president of costa rica albert _ ii, prince of monaco richard h. bailey rita r. colwell, american environmental microbiologist and scientific administrator graeme kelleher, former chairman of the great barrier reef marine park authority ( gbrmpa ) sven lindblad, son of lars - eric lindblad queen noor of jordan victor vescovo = = recent activity = = in 2016, members of the group visited cuba as part of a delegation to meet leaders from government, academia and civil society. the goal of the visit was to learn about the measures that have been taken to protect the local marine ecosystems. in 2017, ocean elders wrote to malcolm turnbull ( then prime minister of australia ) with petition to reject the carmichael coal mine, proposed by adani group. the activists argued that the coal mine would have a devastating impact on the great barrier reef. = = references = = = = external links =	Ocean Elders	wikipedia
( then prime minister of australia ) with petition to reject the carmichael coal mine, proposed by adani group. the activists argued that the coal mine would have a devastating impact on the great barrier reef. = = references = = = = external links = = official website	Ocean Elders	wikipedia
a web presence is a location on the world wide web where a person, business, or some other entity is represented ( see also web property and point of presence ). examples of a web presence for a person could be a personal website, a blog, a profile page, a wiki page, or a social media point of presence ( e. g. a linkedin profile, a facebook account, or a twitter account ). examples of a web presence for a business or some other entity could be a corporate website, a microsite, a page on a review site, a wiki page, or a social media point of presence ( e. g., a linkedin company page and / or group, a facebook business / brand / product page, or a twitter account ). every web presence is associated with a unique web address to distinguish one point of presence from another. = = owned vs. unowned = = web presence can either be owned or unowned. owned media exists when a single person or group can control the content that is published on its web presence ( e. g. a corporate website or a personal twitter account ). however, when a single person or group cannot solely control the content, the creator is different from the owner. this is considered unowned media ( see earned media ). a wikipedia page or a yelp page about a person, company, or product would be an example of a known ( or " earned " ) web presence. occasionally, a first form of media known as " paid media " is often included in the discussion of media types : " earned vs. owned vs. paid ". paid media is commonly found in the form of advertisements, but it is not considered a form of web presence. = = management = = web presence management is the process of establishing and maintaining a digital footprint on the web. the three factors that are considered include the following : where a person or business has web presence ; how each web presence represents its enterprise ; and what is published at a point of presence. web presence management is the discipline of determining and governing : the distribution of policy documents which platforms are most appropriate ( e. g. internal vs. external blog, youtube vs. vimeo ) the single inventory of personal or corporate web presence ( e. g. partners or advocates ) where on the web a business and any relatable assets are represented where on the web a business and any relatable assets are impersonated or pirated web properties with the particular entities	Web presence	wikipedia
web presence ( e. g. partners or advocates ) where on the web a business and any relatable assets are represented where on the web a business and any relatable assets are impersonated or pirated web properties with the particular entities they represent who has control over which web properties new web properties which are not in the personal or corporate inventory ( e. g. someone creates a new presence ) authorized and unauthorized changes to the creation ( e. g. branding ) of a web presence a workflow for creating a web property that follows its corporate standards = = = management system = = = the purpose of a web presence management system is to manage the web presence of a person or business. this includes the collection of domain names, websites, social media, and other web pages where he, she, or it is being represented. the tool generally offers the following key functions : new presence discovery, inventory management, change detection, access control, stakeholder coordination, and compliance workflow. a web presence management system is meant to have a broader reach so that it emphasizes where a presence has been established, will be established, must be maintained, or must be remediated. an example of a web presence management system is the brandle presence manager. in order to publish content to the various points of web presence, multiple content management systems and sometimes even social media management systems are often used. the primary focus of most content and social media management systems is limited to their specific web platforms. = = = domain names = = = another aspect of web presence management is managing the collection of domain names registered to the person or business. any entity may register multiple domain names for the same property. as a result, they can link alternative spellings, different top - level domains, aliases, brands, or products to the same website. similarly, negative or derogatory domain names may also be registered. this is done to prevent certain domain names from being used against the person or business. it is common for a larger business to have domain names registered by multiple employees at multiple domain name registrars, possibly a result of organizational or geographical requirements. consequently, a web presence management system can be used to monitor all domain names registered by the business, regardless of the registrars used. = = discovery = = web presence discovery is the process of monitoring the web for a new point of presence about a person or business. web presence discovery is often included in a web presence management system. whether a new domain is registered, a new website is published, or	Web presence	wikipedia
= web presence discovery is the process of monitoring the web for a new point of presence about a person or business. web presence discovery is often included in a web presence management system. whether a new domain is registered, a new website is published, or a new social media account is established, it occurs outside of the person's or business ’ control. as a result, its purpose is to assess a new point of presence and appropriately handle any violations. it is important to note that web presence discovery differs from content listening. the former involves looking for new properties on the web, whereas the latter refers to analyzing content that already exists to hear how a person or business is seen often in near real time. examples of content listening systems include sysomos and radian6, which is now a subsidiary of salesforce. com. = = = brand protection = = = a person or business may choose to watch for a new web presence that might appear to misrepresent or mislead an audience, such as counterfeiters, spoofers, or malicious hackers. one of the early software in the online brand protection marketplace was markmonitor, now part of thomson reuters. this software helped detect rogue domain names and websites. however, the modern day growth of social media has seen a rise in the number of fraudulent brand impersonations. it has become much easier for a new web presence to be created on those platforms, which results in a greater frequency of them today. as a preventive measure, online brand protection providers are now adding social media to their domain and website discovery options. = = = security = = = the widespread growth of social media has also made it easier for unauthorized individuals to impersonate an employee. consequently, social media has now become a recognized threat vector in that it can be used to socially engineer an attack on a business. to counter this, companies are able to use web presence monitoring tools to detect new points of presence on the web and thereby defend against socially engineered attacks. = = = distributed inventory management = = = a web presence monitoring system can be used by a business to associate a new web property with its corporate inventory. it is designed to address autonomous, distributed behaviors. this usually applies to larger businesses whose geographically diverse employees are more prone to creating new points of presence on the web. for example, a retail chain may allow each local store to create and manage their web presence to market to and communicate with their local customer base. similarly, a global business may have teams in each country or region	Web presence	wikipedia
new points of presence on the web. for example, a retail chain may allow each local store to create and manage their web presence to market to and communicate with their local customer base. similarly, a global business may have teams in each country or region who create and manage a web presence to adapt to local languages or cultures. = = monitoring = = web presence monitoring is the process of monitoring a known inventory of web presence to detect any changes that are made. web presence monitoring is often included in a web presence management system and can serve multiple purposes for both larger corporations and certain individuals, such as celebrities. it is important to note that presence monitoring differs from content listening. the former involves monitoring the properties ( e. g. branding ) of a web property in an established inventory, whereas the latter refers to analyzing content that already exists to hear how a person or business is seen often in near real time. additionally, presence monitoring focuses on owned media and content listening on earned media. = = = corporate, brand, and regulatory compliance = = = many companies ensure that certain standards are met for a property on the web that represents their business. for companies in regulated industries, such as finance and healthcare, the company may be required by law to ensure that all publicized content, regardless of platform or technology, follow specific requirements. the widespread growth of social media has seen a rise in the number of fraudulent corporate impersonations. it has become much easier for a new web presence to be created on these platforms, and so these are much more prevalent than they used to be. as a preventive measure, a web presence monitoring system alerts the company when a known property is changed, allowing for the property to be reviewed and amended so that it follows the proper standards.. a web presence monitoring system helps alert the company when a known property is changed, so it can be reviewed and brought back, if necessary, into compliance with the appropriate standards. = = audit = = a web presence audit is performed by an enterprise to determine that all points of presence on the web meet the objectives as well as governance, risk management, and compliance ( grc ) needs. to ensure neutrality, these audits are often conducted as part of an information technology audit by a professional services agency or an internal audit team. however, a less formal web presence audit is often performed by internal members as a routine to meet grc objectives. a web presence audit usually includes web presence discovery and a review of all web - based content in the business ’ inventory of web presence. even though	Web presence	wikipedia
a less formal web presence audit is often performed by internal members as a routine to meet grc objectives. a web presence audit usually includes web presence discovery and a review of all web - based content in the business ’ inventory of web presence. even though web presence monitoring is not performed in a web presence audit, a review of the nature and scope of the company's web presence monitoring policies, procedures, and tools is considered. = = = social media audit = = = due to the emerging challenges introduced by the dynamic nature of social media, a business may choose to perform specific social media audits in greater frequency. a social media audit is similar to a web presence audit, but may also include the purposes of maintaining an accurate inventory of all business social media points of presence. alternatively, the business may choose to employ automated web presence discovery and compliance systems to keep the corporate social media inventory up - to - date and compliant with grc needs. = = web presence vs. web reputation management = = reputation management systems are often associated with web presence management. web presence management is knowing where an individual or business is represented, whereas reputation management is knowing what people are saying about an individual or business. web presence management handles owned media, while reputation management systems with earned media. both systems offer some similar degree of remediation. for web presence management systems, remediation would include finding counterfeit properties that infringe on a brand or trademark. for reputation management systems, remediation would include identifying and eliminating misleading reviews and / or encouraging the contribution of authentic comments. even though a web presence monitoring tool can help identify unowned web properties where people are talking about a person, product, or brand, it is only part of the solution. a reputation management system often includes a content listening system to monitor the stream of messages about a particular subject which may be coming from any point of presence on the web ( e. g. a comment about a product by a customer on her personal twitter account ). for examples of some reputation management companies, click here. = = see also = = = = references = =	Web presence	wikipedia
in mathematics, majorization is a preorder on vectors of real numbers. for two such vectors, x, y ∈ r n { \ displaystyle \ mathbf { x }, \ \ mathbf { y } \ in \ mathbb { r } ^ { n } }, we say that x { \ displaystyle \ mathbf { x } } weakly majorizes ( or dominates ) y { \ displaystyle \ mathbf { y } } from below, commonly denoted x w y, { \ displaystyle \ mathbf { x } \ succ _ { w } \ mathbf { y }, } when i = 1 k x i ↓ ≥ i = 1 k y i ↓ { \ displaystyle \ sum _ { i = 1 } ^ { k } x _ { i } ^ { \ downarrow } \ geq \ sum _ { i = 1 } ^ { k } y _ { i } ^ { \ downarrow } } for all k = 1, …, n { \ displaystyle k = 1, \, \ dots, \, n }, where x i ↓ { \ displaystyle x _ { i } ^ { \ downarrow } } denotes i { \ displaystyle i } th largest entry of x { \ displaystyle x }. if x, y { \ displaystyle \ mathbf { x }, \ mathbf { y } } further satisfy i = 1 n x i = i = 1 n y i { \ displaystyle \ sum _ { i = 1 } ^ { n } x _ { i } = \ sum _ { i = 1 } ^ { n } y _ { i } }, we say that x { \ displaystyle \ mathbf { x } } majorizes ( or dominates ) y { \ displaystyle \ mathbf { y } }, commonly denoted x y { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } }. both weak majorization and majorization are partial orders for vectors whose entries are non - decreasing, but only a preorder for general vectors, since majorization is agnostic to the ordering of the entries in vectors, e. g., the statement ( 1, 2 ) ( 0, 3 ) { \ displaystyle ( 1, 2 ) \ prec ( 0, 3 ) } is simply equivalent to ( 2, 1 ) ( 3, 0 ) { \ displaystyle ( 2	Majorization	wikipedia
( 1, 2 ) ( 0, 3 ) { \ displaystyle ( 1, 2 ) \ prec ( 0, 3 ) } is simply equivalent to ( 2, 1 ) ( 3, 0 ) { \ displaystyle ( 2, 1 ) \ prec ( 3, 0 ) }. specifically, x y ∧ y x { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } \ wedge \ mathbf { y } \ succ \ mathbf { x } } if and only if x, y { \ displaystyle \ mathbf { x }, \ mathbf { y } } are permutations of each other. similarly for w { \ displaystyle \ succ _ { w } }. majorizing also sometimes refers to entrywise ordering, e. g. the real - valued function f majorizes the real - valued function g when f ( x ) ≥ g ( x ) { \ displaystyle f ( x ) \ geq g ( x ) } for all x { \ displaystyle x } in the domain, or other technical definitions, such as majorizing measures in probability theory. = = equivalent conditions = = = = = geometric definition = = = for x, y ∈ r n, { \ displaystyle \ mathbf { x }, \ \ mathbf { y } \ in \ mathbb { r } ^ { n }, } we have x y { \ displaystyle \ mathbf { x } \ prec \ mathbf { y } } if and only if x { \ displaystyle \ mathbf { x } } is in the convex hull of all vectors obtained by permuting the coordinates of y { \ displaystyle \ mathbf { y } }. this is equivalent to saying that x = d y { \ displaystyle \ mathbf { x } = \ mathbf { d } \ mathbf { y } } for some doubly stochastic matrix d { \ displaystyle \ mathbf { d } }. : thm. 2. 1 in particular, x { \ displaystyle \ mathbf { x } } can be written as a convex combination of n { \ displaystyle n } permutations of y { \ displaystyle \ mathbf { y } }. in other words, x { \ displaystyle \ mathbf { x } } is in the permutahedron of y { \ displaystyle \ mathbf { y } }.	Majorization	wikipedia
{ \ displaystyle \ mathbf { y } }. in other words, x { \ displaystyle \ mathbf { x } } is in the permutahedron of y { \ displaystyle \ mathbf { y } }. figure 1 displays the convex hull in 2d for the vector y = ( 3, 1 ) { \ displaystyle \ mathbf { y } = ( 3, \, 1 ) }. notice that the center of the convex hull, which is an interval in this case, is the vector x = ( 2, 2 ) { \ displaystyle \ mathbf { x } = ( 2, \, 2 ) }. this is the " smallest " vector satisfying x y { \ displaystyle \ mathbf { x } \ prec \ mathbf { y } } for this given vector y { \ displaystyle \ mathbf { y } }. figure 2 shows the convex hull in 3d. the center of the convex hull, which is a 2d polygon in this case, is the " smallest " vector x { \ displaystyle \ mathbf { x } } satisfying x y { \ displaystyle \ mathbf { x } \ prec \ mathbf { y } } for this given vector y { \ displaystyle \ mathbf { y } }. = = = other definitions = = = each of the following statements is true if and only if x y { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } }. from x { \ displaystyle \ mathbf { x } } we can produce y { \ displaystyle \ mathbf { y } } by a finite sequence of " robin hood operations " where we replace two elements x i { \ displaystyle x _ { i } } and x j < x i { \ displaystyle x _ { j } < x _ { i } } with x i − ε { \ displaystyle x _ { i } - \ varepsilon } and x j + ε { \ displaystyle x _ { j } + \ varepsilon }, respectively, for some ε ∈ ( 0, x i − x j ) { \ displaystyle \ varepsilon \ in ( 0, x _ { i } - x _ { j } ) }. : 11 for every convex function h : r → r { \ displaystyle h : \ mathbb { r } \ to \ mathbb { r } }, i = 1 d	Majorization	wikipedia
{ i } - x _ { j } ) }. : 11 for every convex function h : r → r { \ displaystyle h : \ mathbb { r } \ to \ mathbb { r } }, i = 1 d h ( x i ) ≥ i = 1 d h ( y i ) { \ displaystyle \ sum _ { i = 1 } ^ { d } h ( x _ { i } ) \ geq \ sum _ { i = 1 } ^ { d } h ( y _ { i } ) }. : thm. 2. 9 in fact, a special case suffices : i x i = i y i { \ displaystyle \ sum _ { i } { x _ { i } } = \ sum _ { i } { y _ { i } } } and, for every t, i = 1 d max ( 0, x i − t ) ≥ i = 1 d max ( 0, y i − t ) { \ displaystyle \ sum _ { i = 1 } ^ { d } \ max ( 0, x _ { i } - t ) \ geq \ sum _ { i = 1 } ^ { d } \ max ( 0, y _ { i } - t ) }. for every t ∈ r { \ displaystyle t \ in \ mathbb { r } }, j = 1 d \| x j − t \| ≥ j = 1 d \| y j − t \| { \ displaystyle \ sum _ { j = 1 } ^ { d } \| x _ { j } - t \| \ geq \ sum _ { j = 1 } ^ { d } \| y _ { j } - t \| }. : exercise 12. 17 each vector x { \ displaystyle \ mathbf { x } } can be plotted as a concave curve by connecting ( 0, 0 ), ( 1, x 1 ↓ ), ( 2, x 1 ↓ + x 2 ↓ ), …, ( n, x 1 ↓ + x 2 ↓ + + x n ↓ ) { \ displaystyle ( 0, 0 ), ( 1, x _ { 1 } ^ { \ downarrow } ), ( 2, x _ { 1 } ^ { \ downarrow } + x _ { 2 } ^ { \ downarrow } ), \ dots, ( n, x _ { 1 } ^ { \ downarrow } + x	Majorization	wikipedia
( 2, x _ { 1 } ^ { \ downarrow } + x _ { 2 } ^ { \ downarrow } ), \ dots, ( n, x _ { 1 } ^ { \ downarrow } + x _ { 2 } ^ { \ downarrow } + \ dots + x _ { n } ^ { \ downarrow } ) }. then x y { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } } is equivalent to the curve of x { \ displaystyle \ mathbf { x } } being higher than that of y { \ displaystyle \ mathbf { y } }. = = examples = = among non - negative vectors with three components, ( 1, 0, 0 ) { \ displaystyle ( 1, 0, 0 ) } and permutations of it majorize all other vectors ( p 1, p 2, p 3 ) { \ displaystyle ( p _ { 1 }, p _ { 2 }, p _ { 3 } ) } such that p 1 + p 2 + p 3 = 1 { \ displaystyle p _ { 1 } + p _ { 2 } + p _ { 3 } = 1 }. for example, ( 1, 0, 0 ) ( 1 / 2, 0, 1 / 2 ) { \ displaystyle ( 1, 0, 0 ) \ succ ( 1 / 2, 0, 1 / 2 ) }. similarly, ( 1 / 3, 1 / 3, 1 / 3 ) { \ displaystyle ( 1 / 3, 1 / 3, 1 / 3 ) } is majorized by all other such vectors, so ( 1 / 2, 0, 1 / 2 ) ( 1 / 3, 1 / 3, 1 / 3 ) { \ displaystyle ( 1 / 2, 0, 1 / 2 ) \ succ ( 1 / 3, 1 / 3, 1 / 3 ) }. this behavior extends to general - length probability vectors : the singleton vector majorizes all other probability vectors, and the uniform distribution is majorized by all probability vectors. = = schur convexity = = a function f : r n → r { \ displaystyle f : \ mathbb { r } ^ { n } \ to \ mathbb { r } } is said to be schur convex when x y { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } } implies f (	Majorization	wikipedia
{ r } ^ { n } \ to \ mathbb { r } } is said to be schur convex when x y { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } } implies f ( x ) ≥ f ( y ) { \ displaystyle f ( \ mathbf { x } ) \ geq f ( \ mathbf { y } ) }. hence, schur - convex functions translate the ordering of vectors to a standard ordering in r { \ displaystyle \ mathbb { r } }. similarly, f ( x ) { \ displaystyle f ( \ mathbf { x } ) } is schur concave when x y { \ displaystyle \ mathbf { x } \ succ \ mathbf { y } } implies f ( x ) ≤ f ( y ). { \ displaystyle f ( \ mathbf { x } ) \ leq f ( \ mathbf { y } ). } an example of a schur - convex function is the max function, max ( x ) = x 1 ↓ { \ displaystyle \ max ( \ mathbf { x } ) = x _ { 1 } ^ { \ downarrow } }. schur convex functions are necessarily symmetric that the entries of it argument can be switched without modifying the value of the function. therefore, linear functions, which are convex, are not schur - convex unless they are symmetric. if a function is symmetric and convex, then it is schur - convex. = = generalizations = = majorization can be generalized to the lorenz ordering, a partial order on distribution functions. for example, a wealth distribution is lorenz - greater than another if its lorenz curve lies below the other. as such, a lorenz - greater wealth distribution has a higher gini coefficient, and has more income disparity. the majorization preorder can be naturally extended to density matrices in the context of quantum information. in particular, ρ ρ ′ { \ displaystyle \ rho \ succ \ rho'} exactly when s p e c [ ρ ] s p e c [ ρ ′ ] { \ displaystyle \ mathrm { spec } [ \ rho ] \ succ \ mathrm { spec } [ \ rho'] } ( where s p e c { \ displaystyle \ mathrm { spec } } denotes the state's spectrum ). similarly, one can say a hermitian operator, h {	Majorization	wikipedia
\ mathrm { spec } [ \ rho'] } ( where s p e c { \ displaystyle \ mathrm { spec } } denotes the state's spectrum ). similarly, one can say a hermitian operator, h { \ displaystyle \ mathbf { h } }, majorizes another, m { \ displaystyle \ mathbf { m } }, if the set of eigenvalues of h { \ displaystyle \ mathbf { h } } majorizes that of m { \ displaystyle \ mathbf { m } }. = = see also = = muirhead's inequality karamata's inequality schur - convex function schur – horn theorem relating diagonal entries of a matrix to its eigenvalues. for positive integer numbers, weak majorization is called dominance order. leximin order = = notes = = = = references = = j. karamata. " sur une inegalite relative aux fonctions convexes. " publ. math. univ. belgrade 1, 145 – 158, 1932. g. h. hardy, j. e. littlewood and g. polya, inequalities, 2nd edition, 1952, cambridge university press, london. inequalities : theory of majorization and its applications albert w. marshall, ingram olkin, barry arnold, second edition. springer series in statistics. springer, new york, 2011. isbn 978 - 0 - 387 - 40087 - 7 a tribute to marshall and olkin's book " inequalities : theory of majorization and its applications " matrix analysis ( 1996 ) rajendra bhatia, springer, isbn 978 - 0 - 387 - 94846 - 1 topics in matrix analysis ( 1994 ) roger a. horn and charles r. johnson, cambridge university press, isbn 978 - 0 - 521 - 46713 - 1 majorization and matrix monotone functions in wireless communications ( 2007 ) eduard jorswieck and holger boche, now publishers, isbn 978 - 1 - 60198 - 040 - 3 the cauchy schwarz master class ( 2004 ) j. michael steele, cambridge university press, isbn 978 - 0 - 521 - 54677 - 5 = = external links = = majorization in mathworld majorization in planetmath = = software = = octave / matlab code to check majorization	Majorization	wikipedia
alethic modality ( from greek αληθεια = truth ) is a linguistic modality that indicates modalities of truth, in particular the modalities of logical necessity, contingency, possibility and impossibility. alethic modality is often associated with epistemic modality in research, and it has been questioned whether this modality should be considered distinct from epistemic modality which denotes the speaker's evaluation or judgment of the truth. the criticism states that there is no real difference between " the truth in the world " ( alethic ) and " the truth in an individual's mind " ( epistemic ). an investigation has not found a single language in which alethic and epistemic modalities would be formally distinguished, for example by the means of a grammatical mood. in such a language, " a circle can't be square ", " can't be " would be expressed by an alethic mood, whereas for " he can't be that wealthy ", " can't be " would be expressed by an epistemic mood. as we can see, this is not a distinction drawn in english grammar. " you can't give these plants too much water. " is a well - known play on the distinction between perhaps alethic and hortatory or injunctive modalities ( it can mean either " it is impossible to give these plants too much water = giving them too much water is harmless " or " you must not give these plants too much water = giving them too much water is harmful " ). the dilemma is fairly easily resolved when listening through paralinguistic cues and particularly suprasegmental cues ( intonation ). so while there may not be a morphologically based alethic mood, this does not seem to preclude the usefulness of distinguishing between these two types of modes. alethic modality might then concern what are considered to be apodictic statements. = = references = =	Alethic modality	wikipedia
the econometric society is an international society of academic economists interested in applying statistical tools in the practice of econometrics. it is an independent organization with no connections to societies of professional mathematicians or statisticians. it was founded on december 29, 1930, at the statler hotel in cleveland, ohio. its first president was irving fisher. as of 2014, there are about 700 elected fellows of the econometric society, making it one of the most prevalent research affiliations. new fellows are elected each year by the current fellows. the sixteen founding members were ragnar frisch, charles f. roos, joseph a. schumpeter, harold hotelling, henry schultz, karl menger, edwin b. wilson, frederick c. mills, william f. ogburn, j. harvey rogers, malcolm c. rorty, carl snyder, walter a. shewhart, øystein ore, ingvar wedervang and norbert wiener. the econometric society sponsors the economics academic journal econometrica and publishes the journals theoretical economics and quantitative economics. = = officers = = the econometric society is led by a president, who serves a one - year term. election as a fellow of the econometric society is considered by much of the economics profession to be an honor. list of presidents of the econometric society list of fellows of the econometric society = = honorary lectures = = the econometric society sponsors several annual awards, in which the honored member delivers a lecture : frisch medal walras – bowley lecture fisher – schultz lecture jacob marschak lecture = = references = = = = external links = = official website	Econometric Society	wikipedia
the epigenetics of plant growth and development refers to the heritable changes in gene expression that occur without alterations to the dna sequence, influencing processes in plants such as seed germination, flowering, and stress responses through mechanisms like dna methylation, histone modification, and chromatin remodeling. plants depend on epigenetic processes ( mechanisms that regulate gene activity and expression without changing the underlying dna sequence ) for proper function. the area of study examines protein interactions with dna and its associated components, including histones and various other modifications such as methylation, which alter the rate or target of transcription. epi - alleles and epi - mutants, much like their genetic counterparts, describe changes in phenotypes due to epigenetic mechanisms. epigenetics in plants has attracted scientific enthusiasm because of its importance in agriculture. = = history = = in the past, macroscopic observations on plants led to a basic understanding of how plants respond to their environments and grow. while these investigations could somewhat correlate cause and effect as a plant develops, they could not truly explain the mechanisms at work without inspection at the molecular level. certain studies provided simplistic models with the groundwork for further exploration and eventual explanation through epigenetics. in 1918, gustav gassner published findings that noted the necessity of a cold phase for proper plant growth. meanwhile, garner and allard examined the importance of the duration of light exposure to plant growth in 1920. gassner's work would shape the conceptualization of vernalization, which involves epigenetic changes in plants after a period of cold that leads to the development of flowering. in a similar manner, garner and allard's efforts would gather an awareness of photoperiodism which involves epigenetic modifications following the duration of nighttime which enable flowering. rudimentary comprehensions set precedent for later molecular evaluation and, eventually, a more complete view of how plants operate. modern epigenetic work depends heavily on bioinformatics to gather large quantities of data relating the function of elements such as intensive looks at dna sequences or patterns in dna modifications. with improved methods, flowering mechanisms including vernalization and photoperiodism, flowering wageningen, and the underlying processes controlling germination, meristematic tissue, and heterosis have been explained through epigenetics. research on plants looks at several species. these species are apparently selected on the basis of either conventional model organisms status, such as arabidopsis with	Epigenetics of plant growth and development	wikipedia
##rmination, meristematic tissue, and heterosis have been explained through epigenetics. research on plants looks at several species. these species are apparently selected on the basis of either conventional model organisms status, such as arabidopsis with its manageability in lab and a known genome, or relevance in agronomy, such as rice, barley or tomatoes. = = epigenetics = = epigenetic modifications regulate gene expression. the transcription of dna into rna and subsequent translation into proteins determines the form and function of all living things. the level of dna transcription generally depends on how accessible dna is to transcription factors. many epigenetic changes occur either on histones, which are normally associated with dna in chromatin, or directly on the dna. for instance, methylation of dna leads to transcriptional silencing by denying access to transcription factors. histone methylation can lead to either silencing or activation as determined by the amino acid marked. meanwhile, histone acetylation typically lessens the hold of histones on dna by reducing positive charge, resulting in facilitation of transcription. = = = polycomb and trithorax group proteins = = = polycomb group ( pcg ) proteins and trithorax groups ( trxg ) proteins act as key regulators of gene expression through histone lysine methylation. pcg proteins repress target genes via histone 3 lysine 27 trimethylation ( h3k27me3 ), whereas trxg proteins activate gene expression via histone 3 lysine 4 trimethylation ( h3k4me3 ). = = = long non - coding rna = = = long non - coding rna can associate with dna in tandem with proteins to alter the rate of gene expression. these rna are upwards of 200 base pairs. they can be transcribed from a standalone sequence or be part of a promoter, intron or other component of dna. long non - coding rna often complement functional regions of dna with overlaps or antisense. to direct transcriptional silencing, a non - coding rna will associate with a polycomb group protein which to tether it to a specific gene for silencing. = = seed dormancy and germination = = germination is the early growth of a plant from a seed. meanwhile, dormancy precedes germination and serves to preserve a seed until conditions are receptive towards growth. the transition from dormancy to germination seems	Epigenetics of plant growth and development	wikipedia
= = germination is the early growth of a plant from a seed. meanwhile, dormancy precedes germination and serves to preserve a seed until conditions are receptive towards growth. the transition from dormancy to germination seems to depend on the removal of factors inhibiting growth. there are many models for germination which may differ between species. the activity of genes such as delay of germination and presence of hormones such as gibberelins have been implicated in dormancy while the exact mechanisms surrounding their action is unknown. = = = deacetylation = = = there are at least eighteen histone deacetylases in arabidopsis. genome - wide association mapping has shown that deacetylation of histones by histone deacetylase 2b negatively affects dormancy. the remodeling of chromatin by histone deacetylase leads to silencing of genes that control plant hormones such as ethylene, abscisic acid, and gibberelin which maintain dormancy. additionally, histone deacetylase a6 and a19 activity contributes to silencing of cytochrome p450 707a and activation of 9 - cis - epoxycarotenoid dioxygenase. both of these actions lead to increased abscisic acid. = = = methylaltion = = = methylation by the methyltransferase kryptonite causes histone h3 lysine 9 dimethylation which recruits the dna methyltransferase chromomethtlase3 in tandem with heterochromatin protein1. this association methylates cytosine for a stable silencing of delay of germination 1 and aba insensitive genes which both contribute to dormancy. = = flowering and related mechanisms = = flowering is a pivotal step in plant development. numerous epigenetic factors contribute to the regulation of flowering genes, known as flowering loci ( fl ). in arabidopsis, flowering locus t is responsible for the production of florigen, which induces turck _ 2008 in the shoot apical meristem, a special set of growth tissues, to establish flowering. homologs of the flowering genes exist in flowering plants, but the exact nature of how the genes respond to each mechanism might differ between species. = = = vernalization = = = vernalization depends on the presence of a long non - coding rna that is termed coldair. the	Epigenetics of plant growth and development	wikipedia

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