Amaq News Agency (Arabic: وكالة أعماق الإخبارية, romanized: Wakālat Aʻmāq al-Ikhbārīyah) is a news outlet linked to the Islamic State (IS). Amaq is often the "first point of publication for claims of responsibility" for terrorist attacks in Western countries by the Islamic State. In March 2019, Amaq News Agency was designated as a foreign terrorist organization by the United States Department of State. == History == Among the founders of Amaq was Syrian journalist Baraa Kadek, who joined IS in late 2013, Abu Muhammad al-Furqan, and seven others who originally worked for Halab News Network. According to The New York Times, it has a direct connection with IS, from which it "gets tips". Its name was taken from Amik Valley in Hatay Province, which is mentioned in a hadith as the site of an "apocalyptic victory over non-believers". Amaq News Agency was first noticed by SITE during the Siege of Kobanî (Syria) in 2014, when its updates were shared among IS fighters. It became more widely known after it began reporting claims of responsibility for terrorist attacks in Western countries, such as the 2015 San Bernardino attack, for which IS officially claimed responsibility the next day. An Amaq cameraman shot the first footage of the capture of Palmyra in 2015. Amaq launched an official mobile app in 2015 and has warned against unofficial versions that reportedly have been used to spy on its users. It also uses a Telegram account. It had a WordPress-based blog, but it was removed without explanation in April 2016. On 12 June 2016, IS claimed responsibility for the Pulse nightclub shooting through Amaq, without prior knowledge of the attack. The shooter, Omar Mateen had later pledged allegiance to IS via a phone call with emergency services. On 31 May 2017, a Facebook post announced Amaq's founder, Baraa Kadek AKA Rayan Meshaal, had been killed with his daughter by an American airstrike on Mayadin. The post was reportedly made by his younger brother. Reuters could not immediately verify this account. On 27 July 2017, the US confirmed that Kadek had been killed by a coalition airstrike near Mayadin between 25 and 27 May 2017. In June 2017, German police arrested a 23-year-old Syrian man identified only as Mohammed G., accusing him of communicating with the alleged perpetrator of the 2016 Malmö Muslim community centre arson in order to report to Amaq. On 21 March 2019, the U.S. Department of State officially deemed Amaq an alias of IS, and thus a Foreign Terrorist Organization. On 22 March 2024, the Islamic State claimed responsibility for the Crocus City Hall attack through Amaq, U.S. officials confirmed the claim shortly after. A day after the attack, Amaq published a video of the attack, filmed by one of the attackers. It showed the attackers shooting victims and slitting the throat of another, while the filming attacker praises Allah and speaks against infidels. == Character == Amaq publishes a stream of short news reports, both text and video, on the mobile app Telegram. The reports take on the trappings of mainstream journalism, with "Breaking News" headings, and embedded reporters at the scenes of IS battles. The reports try to appear neutral, toning down the jihadist language and sectarian slurs IS uses in its official releases. Charlie Winter of the Transcultural Conflict and Violence Initiative at Georgia State University, and Rita Katz of SITE Intelligence Group in Washington say Amaq functions much like the state-owned news agency of IS, though the group does not acknowledge it as such. Katz said it behaves "like a state media". Amaq appears to have been allowed to develop by IS as a way to have a news outlet that is controlled by the group but is somewhat removed from it, giving IS more of the appearance of legitimacy. == Reliability == According to Rukmini Callimachi in The New York Times: "Despite a widespread view that the Islamic State opportunistically claims attacks with which it has little genuine connection, its track record—minus a handful of exceptions—suggests a more rigorous protocol. At times, the Islamic State has got details wrong, or inflated casualty figures, but the gist of its claims is typically correct." According to Callimachi, the group considers itself responsible for acts carried out by people who were inspired by its propaganda, as well as acts carried out by its own personnel and in some instances, had claimed attacks before the identities of the killers were known. Graeme Wood writing in The Atlantic in October 2017, wrote "The idea that the Islamic State simply scans the news in search of mass killings, then sends out press releases in hope of stealing glory, is false. Amaq may learn details of the attacks from mainstream media ... but its claim of credit typically flows from an Amaq-specific source." An October 2017 article in The Hill, points to two false claims made in the summer of 2017, the Resorts World Manila attack and a false claim that bombs had been planted at Charles de Gaulle Airport in Paris. Also, a claimed IS connection to the 2017 Las Vegas shooting proved to be false. According to Rita Katz on the SITE Intelligence Group website, calling a terrorist a "soldier of the caliphate (warrior from the caliphate)" in a statement issued by Amaq, was the usual way in which IS indicated that it inspired an attack. Centrally coordinated attacks were usually described as "executed by a detachment belonging to the Islamic State", and were often announced by both Amaq and by IS' central media command. == Online presence == In November 2019, Belgian police said they had carried out a successful cyberattack on Amaq, thus leaving IS without an operational communication channel. However, Amaq has since regained online presence, primarily on dark web platforms to make it harder for law enforcement to take them down without physical access to the server hosting the specific platform.
AdTruth
AdTruth is a software product and the digital media division of 41st Parameter, a company headquartered in Scottsdale, Arizona, with regional offices in San Jose, California; London, England; and Munich, Germany. AdTruth allows marketers to recognize and reach target audiences across online devices. AdTruth software identifies users for targeting, tracking, performance tracking across digital media, including mobile and desktop, by analysing patterns in large numbers of advertisements served over the internet, rather than through the use of cookies. == History == AdTruth was founded in 2011 by Ori Eisen of 41st Parameter, to repurpose the company's fraud detection and prevention technology, for use within the advertising industry to accurately target intended audiences, particularly in mobile. Eisen was joined by James Lamberti in the role of vice president and general manager. In 2012 41st Parameter raised $13 million in Series D financing from Norwest Venture Partners, Kleiner Perkins Caufield & Byers, Jafco Ventures and Georgian Partners, bringing total funding to about $35 million. In May 2012, AdTruth hosted a meeting of digital media executives to discuss Apple’s UDID deprecation, with the intent of developing a device-neutral replacement standard. AdTruth joined the World Wide Web Consortium's Tracking Protection Working Group, which provides guidance for implementing and adhering to Do Not Track policies. AdTruth also worked with privacy firm Truste to create a privacy compliant Do Not Track-style mechanism for mobile. In 2013, the company Experian purchased 41st Parameter, acquiring AdTruth as part of the deal. == Product == AdTruth software helps marketers track, target and retarget consumers using more than 100 parameters, including milliseconds in differences in the internal clock setting, to recognize a particular device anonymously. AdTruth's technology uses non-UDID information to identify a wide range of devices for cookieless ad targeting. Its technology currently has about a 90 percent accuracy rate on iOS, higher on Android and desktop. AdTruth also has mobile web to app bridging capabilities as well as DeviceInsight technology, enabling marketers to identify users across mobile web and app content. 41st Parameter's patented AdTruth technology is being used by MdotM, in response to the deprecation of the UDID that included tracking and targeting capabilities. == Competitors == AdTruth's main competitor is BlueCava, which deploys a similar device-fingerprinting technology.
Fitness approximation
Fitness approximation aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation. Fitness approximation in evolutionary optimization can be seen as a sub-area of data-driven evolutionary optimization. == Approximate models in function optimization == === Motivation === In many real-world optimization problems including engineering problems, the number of fitness function evaluations needed to obtain a good solution dominates the optimization cost. In order to obtain efficient optimization algorithms, it is crucial to use prior information gained during the optimization process. Conceptually, a natural approach to utilizing the known prior information is building a model of the fitness function to assist in the selection of candidate solutions for evaluation. A variety of techniques for constructing such a model, often also referred to as surrogates, metamodels or approximation models – for computationally expensive optimization problems have been considered. === Approaches === Common approaches to constructing approximate models based on learning and interpolation from known fitness values of a small population include: Low-degree polynomials and regression models Fourier surrogate modeling Artificial neural networks including Multilayer perceptrons Radial basis function network Support vector machines Due to the limited number of training samples and high dimensionality encountered in engineering design optimization, constructing a globally valid approximate model remains difficult. As a result, evolutionary algorithms using such approximate fitness functions may converge to local optima. Therefore, it can be beneficial to selectively use the original fitness function together with the approximate model.
Variational autoencoder
In machine learning, a variational autoencoder (VAE) is an artificial neural network architecture introduced by Diederik P. Kingma and Max Welling in 2013. It is part of the families of probabilistic graphical models and variational Bayesian methods. In addition to being seen as an autoencoder neural network architecture, variational autoencoders can also be studied within the mathematical formulation of variational Bayesian methods, connecting a neural encoder network to its decoder through a probabilistic latent space (for example, as a multivariate Gaussian distribution) that corresponds to the parameters of a variational distribution. Thus, the encoder maps each point (such as an image) from a large complex dataset into a distribution within the latent space, rather than to a single point in that space. The decoder has the opposite function, which is to map from the latent space to the input space, again according to a distribution (although in practice, noise is rarely added during the decoding stage). By mapping a point to a distribution instead of a single point, the network can avoid overfitting the training data. Both networks are typically trained together with the usage of the reparameterization trick, although the variance of the noise model can be learned separately. Although this type of model was initially designed for unsupervised learning, its effectiveness has been proven for semi-supervised learning and supervised learning. == Overview of architecture and operation == A variational autoencoder is a generative model with a prior and noise distribution respectively. Usually such models are trained using the expectation-maximization meta-algorithm (e.g. probabilistic PCA, (spike & slab) sparse coding). Such a scheme optimizes a lower bound of the data likelihood, which is usually computationally intractable, and in doing so requires the discovery of q-distributions, or variational posteriors. These q-distributions are normally parameterized for each individual data point in a separate optimization process. However, variational autoencoders use a neural network as an amortized approach to jointly optimize across data points. In that way, the same parameters are reused for multiple data points, which can result in massive memory savings. The first neural network takes as input the data points themselves, and outputs parameters for the variational distribution. As it maps from a known input space to the low-dimensional latent space, it is called the encoder. The decoder is the second neural network of this model. It is a function that maps from the latent space to the input space, e.g. as the means of the noise distribution. It is possible to use another neural network that maps to the variance, however this can be omitted for simplicity. In such a case, the variance can be optimized with gradient descent. To optimize this model, one needs to know two terms: the "reconstruction error", and the Kullback–Leibler divergence (KL-D). Both terms are derived from the free energy expression of the probabilistic model, and therefore differ depending on the noise distribution and the assumed prior of the data, here referred to as p-distribution. For example, a standard VAE task such as IMAGENET is typically assumed to have a gaussianly distributed noise; however, tasks such as binarized MNIST require a Bernoulli noise. The KL-D from the free energy expression maximizes the probability mass of the q-distribution that overlaps with the p-distribution, which unfortunately can result in mode-seeking behaviour. The "reconstruction" term is the remainder of the free energy expression, and requires a sampling approximation to compute its expectation value. More recent approaches replace Kullback–Leibler divergence (KL-D) with various statistical distances, see "Statistical distance VAE variants" below. == Formulation == From the point of view of probabilistic modeling, one wants to maximize the likelihood of the data x {\displaystyle x} by their chosen parameterized probability distribution p θ ( x ) = p ( x | θ ) {\displaystyle p_{\theta }(x)=p(x|\theta )} . This distribution is usually chosen to be a Gaussian N ( x | μ , σ ) {\displaystyle N(x|\mu ,\sigma )} which is parameterized by μ {\displaystyle \mu } and σ {\displaystyle \sigma } respectively, and as a member of the exponential family it is easy to work with as a noise distribution. Simple distributions are easy enough to maximize, however distributions where a prior is assumed over the latents z {\displaystyle z} results in intractable integrals. Let us find p θ ( x ) {\displaystyle p_{\theta }(x)} via marginalizing over z {\displaystyle z} . p θ ( x ) = ∫ z p θ ( x , z ) d z , {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }({x,z})\,dz,} where p θ ( x , z ) {\displaystyle p_{\theta }({x,z})} represents the joint distribution under p θ {\displaystyle p_{\theta }} of the observable data x {\displaystyle x} and its latent representation or encoding z {\displaystyle z} . According to the chain rule, the equation can be rewritten as p θ ( x ) = ∫ z p θ ( x | z ) p θ ( z ) d z {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }({x|z})p_{\theta }(z)\,dz} In the vanilla variational autoencoder, z {\displaystyle z} is usually taken to be a finite-dimensional vector of real numbers, and p θ ( x | z ) {\displaystyle p_{\theta }({x|z})} to be a Gaussian distribution. Then p θ ( x ) {\displaystyle p_{\theta }(x)} is a mixture of Gaussian distributions. It is now possible to define the set of the relationships between the input data and its latent representation as Prior p θ ( z ) {\displaystyle p_{\theta }(z)} Likelihood p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} Posterior p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} Unfortunately, the computation of p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} is expensive and in most cases intractable. To speed up the calculus to make it feasible, it is necessary to introduce a further function to approximate the posterior distribution as q ϕ ( z | x ) ≈ p θ ( z | x ) {\displaystyle q_{\phi }({z|x})\approx p_{\theta }({z|x})} with ϕ {\displaystyle \phi } defined as the set of real values that parametrize q {\displaystyle q} . This is sometimes called amortized inference, since by "investing" in finding a good q ϕ {\displaystyle q_{\phi }} , one can later infer z {\displaystyle z} from x {\displaystyle x} quickly without doing any integrals. In this way, the problem is to find a good probabilistic autoencoder, in which the conditional likelihood distribution p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is computed by the probabilistic decoder, and the approximated posterior distribution q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is computed by the probabilistic encoder. Parametrize the encoder as E ϕ {\displaystyle E_{\phi }} , and the decoder as D θ {\displaystyle D_{\theta }} . == Evidence lower bound (ELBO) == Like many deep learning approaches that use gradient-based optimization, VAEs require a differentiable loss function to update the network weights through backpropagation. For variational autoencoders, the idea is to jointly optimize the generative model parameters θ {\displaystyle \theta } to reduce the reconstruction error between the input and the output, and ϕ {\displaystyle \phi } to make q ϕ ( z | x ) {\displaystyle q_{\phi }({z|x})} as close as possible to p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} . As reconstruction loss, mean squared error and cross entropy are often used. The Kullback–Leibler divergence D K L ( q ϕ ( z | x ) ∥ p θ ( z | x ) ) {\displaystyle D_{KL}(q_{\phi }({z|x})\parallel p_{\theta }({z|x}))} can be used as a loss function to squeeze q ϕ ( z | x ) {\displaystyle q_{\phi }({z|x})} under p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} . This divergence loss expands to D K L ( q ϕ ( z | x ) ∥ p θ ( z | x ) ) = E z ∼ q ϕ ( ⋅ | x ) [ ln q ϕ ( z | x ) p θ ( z | x ) ] = E z ∼ q ϕ ( ⋅ | x ) [ ln q ϕ ( z | x ) p θ ( x ) p θ ( x , z ) ] = ln p θ ( x ) + E z ∼ q ϕ ( ⋅ | x ) [ ln q ϕ ( z | x ) p θ ( x , z ) ] . {\displaystyle {\begin{aligned}D_{KL}(q_{\phi }({z|x})\parallel p_{\theta }({z|x}))&=\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {q_{\phi }(z|x)}{p_{\theta }(z|x)}}\right]\\&=\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {q_{\phi }({z|x})p_{\theta }(x)}{p_{\theta }(x,z)}}\right]\\&=\ln p_{\theta }(x)+\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {q_{\phi }({z|x})}{p_{\theta }(x,z)}}\right].\end{aligned}}} Now, define the evidence lower bound (ELBO): L θ , ϕ ( x ) := E z ∼ q ϕ ( ⋅ | x ) [ ln p θ ( x , z ) q ϕ ( z | x ) ] = ln p θ ( x ) − D K L ( q ϕ ( ⋅ | x ) ∥ p θ ( ⋅ | x ) ) {\displaystyle L_{\theta ,\phi }(x):=\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {p_{\theta }(x,z)}{q_{\phi }({z|x})}}\right]=\ln p_{\theta }(x)-D_{KL}(q_{\phi }({\cdot |x})\parallel p_{\theta }({\cdot |x}))} Maximizing the ELBO θ ∗ , ϕ ∗ = argmax θ , ϕ L θ , ϕ ( x ) {\dis
Implicit blockmodeling
Implicit blockmodeling is an approach in blockmodeling, similar to a valued and homogeneity blockmodeling, where initially an additional normalization is used and then while specifying the parameter of the relevant link is replaced by the block maximum. This approach was first proposed by Batagelj and Ferligoj in 2000, and developed by Aleš Žiberna in 2007/08. Comparing with homogeneity, the implicit blockmodeling will perform similarly with max-regular equivalence, but slightly worse in other settings. It will perform worse than valued and homogeneity blockmodeling with a pre-specified blockmodel.
Racter
Racter is an artificial intelligence program that generates English language prose at random. It was published by Mindscape for IBM PC compatibles in 1984, then for the Apple II, Mac, and Amiga. An expanded version of the software, not the one released through Mindscape, was used to generate the text for the published book The Policeman's Beard Is Half Constructed. == History == Racter, short for raconteur, was written by William Chamberlain and Thomas Etter. Racter's initial creation was the short story Soft Ions, which appeared in the October 1981 issue of Omni (magazine). The publication's editors bought the story in January 1980, before it had even been written. In exchange for the rights, the editors offered financial support to Chamberlain and Etter so the two could refine Racter. In 1983, Racter produced a book called The Policeman's Beard Is Half Constructed (ISBN 0-446-38051-2). The program originally was written for an OSI which only supported file names at most six characters long, causing the name to be shorted to Racter and it was later adapted to run on a CP/M machine where it was written in "compiled ASIC on a Z80 microcomputer with 64K of RAM." This version, the program that allegedly wrote the book, was not released to the general public. The sophistication claimed for the program was likely exaggerated, as could be seen by investigation of the template system of text generation. In 1984, Mindscape released an interactive version of Racter, developed by Inrac Corporation, for IBM PC compatibles, and it was ported to the Apple II, Mac, and Amiga. The published Racter was similar to a chatterbot. The BASIC program that was released by Mindscape was far less sophisticated than anything that could have written the fairly sophisticated prose of The Policeman's Beard. The commercial version of Racter could be likened to a computerized version of Mad Libs, the game in which you fill in the blanks in advance and then plug them into a text template to produce a surrealistic tale. The commercial program attempted to parse text inputs, identifying significant nouns and verbs, which it would then regurgitate to create "conversations", plugging the input from the user into phrase templates which it then combined, along with modules that conjugated English verbs. By contrast, the text in The Policeman's Beard, apart from being edited from a large amount of output, would have been the product of Chamberlain's own specialized templates and modules, which were not included in the commercial release of the program. == Reception == The Boston Phoenix called the story Soft Ions "schematic nonsense. But the scheme is obvious enough and the nonsense accessible enough to an attentive reader that one can almost believe Chamberlain when he predicts that before long Racter will be ready to write for the pulp-reading public." PC Magazine described some of Policeman's Beard's scenes as "surprising for their frankness" and "reflective". It concluded that the book was "whimsical and wise and sometimes fun". Computer Gaming World described Racter as "a diversion into another dimension that might best be seen before paying the price of a ticket. (Try before you buy!)" A 1985 review of the program in The New York Times notes that, "As computers move ever closer to artificial intelligence, Racter is on the edge of artificial insanity." It also states that Racter's "always-changing sentences are grammatically correct, often funny and, for a computer, sometimes profound." The article includes examples showing interaction with Racter, most often Racter asking the user questions. == Reviews == Jeux & Stratégie #47
Analogical modeling
Analogical modeling (AM) is a formal theory of exemplar based analogical reasoning, proposed by Royal Skousen, professor of Linguistics and English language at Brigham Young University in Provo, Utah. It is applicable to language modeling and other categorization tasks. Analogical modeling is related to connectionism and nearest neighbor approaches, in that it is data-based rather than abstraction-based; but it is distinguished by its ability to cope with imperfect datasets (such as caused by simulated short term memory limits) and to base predictions on all relevant segments of the dataset, whether near or far. In language modeling, AM has successfully predicted empirically valid forms for which no theoretical explanation was known (see the discussion of Finnish morphology in Skousen et al. 2002). == Implementation == === Overview === An exemplar-based model consists of a general-purpose modeling engine and a problem-specific dataset. Within the dataset, each exemplar (a case to be reasoned from, or an informative past experience) appears as a feature vector: a row of values for the set of parameters that define the problem. For example, in a spelling-to-sound task, the feature vector might consist of the letters of a word. Each exemplar in the dataset is stored with an outcome, such as a phoneme or phone to be generated. When the model is presented with a novel situation (in the form of an outcome-less feature vector), the engine algorithmically sorts the dataset to find exemplars that helpfully resemble it, and selects one, whose outcome is the model's prediction. The particulars of the algorithm distinguish one exemplar-based modeling system from another. In AM, we think of the feature values as characterizing a context, and the outcome as a behavior that occurs within that context. Accordingly, the novel situation is known as the given context. Given the known features of the context, the AM engine systematically generates all contexts that include it (all of its supracontexts), and extracts from the dataset the exemplars that belong to each. The engine then discards those supracontexts whose outcomes are inconsistent (this measure of consistency will be discussed further below), leaving an analogical set of supracontexts, and probabilistically selects an exemplar from the analogical set with a bias toward those in large supracontexts. This multilevel search exponentially magnifies the likelihood of a behavior's being predicted as it occurs reliably in settings that specifically resemble the given context. === Analogical modeling in detail === AM performs the same process for each case it is asked to evaluate. The given context, consisting of n variables, is used as a template to generate 2 n {\displaystyle 2^{n}} supracontexts. Each supracontext is a set of exemplars in which one or more variables have the same values that they do in the given context, and the other variables are ignored. In effect, each is a view of the data, created by filtering for some criteria of similarity to the given context, and the total set of supracontexts exhausts all such views. Alternatively, each supracontext is a theory of the task or a proposed rule whose predictive power needs to be evaluated. It is important to note that the supracontexts are not equal peers one with another; they are arranged by their distance from the given context, forming a hierarchy. If a supracontext specifies all of the variables that another one does and more, it is a subcontext of that other one, and it lies closer to the given context. (The hierarchy is not strictly branching; each supracontext can itself be a subcontext of several others, and can have several subcontexts.) This hierarchy becomes significant in the next step of the algorithm. The engine now chooses the analogical set from among the supracontexts. A supracontext may contain exemplars that only exhibit one behavior; it is deterministically homogeneous and is included. It is a view of the data that displays regularity, or a relevant theory that has never yet been disproven. A supracontext may exhibit several behaviors, but contain no exemplars that occur in any more specific supracontext (that is, in any of its subcontexts); in this case it is non-deterministically homogeneous and is included. Here there is no great evidence that a systematic behavior occurs, but also no counterargument. Finally, a supracontext may be heterogeneous, meaning that it exhibits behaviors that are found in a subcontext (closer to the given context), and also behaviors that are not. Where the ambiguous behavior of the nondeterministically homogeneous supracontext was accepted, this is rejected because the intervening subcontext demonstrates that there is a better theory to be found. The heterogeneous supracontext is therefore excluded. This guarantees that we see an increase in meaningfully consistent behavior in the analogical set as we approach the given context. With the analogical set chosen, each appearance of an exemplar (for a given exemplar may appear in several of the analogical supracontexts) is given a pointer to every other appearance of an exemplar within its supracontexts. One of these pointers is then selected at random and followed, and the exemplar to which it points provides the outcome. This gives each supracontext an importance proportional to the square of its size, and makes each exemplar likely to be selected in direct proportion to the sum of the sizes of all analogically consistent supracontexts in which it appears. Then, of course, the probability of predicting a particular outcome is proportional to the summed probabilities of all the exemplars that support it. (Skousen 2002, in Skousen et al. 2002, pp. 11–25, and Skousen 2003, both passim) === Formulas === Given a context with n {\displaystyle n} elements: total number of pairings: n 2 {\displaystyle n^{2}} number of agreements for outcome i: n i 2 {\displaystyle n_{i}^{2}} number of disagreements for outcome i: n i ( n − n i ) {\displaystyle n_{i}(n-n_{i})} total number of agreements: ∑ n i 2 {\displaystyle \sum {n_{i}^{2}}} total number of disagreements: ∑ n i ( n − n i ) = n 2 − ∑ n i 2 {\displaystyle \sum {n_{i}(n-n_{i})}=n^{2}-\sum {n_{i}^{2}}} === Example === This terminology is best understood through an example. In the example used in the second chapter of Skousen (1989), each context consists of three variables with potential values 0-3 Variable 1: 0,1,2,3 Variable 2: 0,1,2,3 Variable 3: 0,1,2,3 The two outcomes for the dataset are e and r, and the exemplars are: 3 1 0 e 0 3 2 r 2 1 0 r 2 1 2 r 3 1 1 r We define a network of pointers like so: The solid lines represent pointers between exemplars with matching outcomes; the dotted lines represent pointers between exemplars with non-matching outcomes. The statistics for this example are as follows: n = 5 {\displaystyle n=5} n r = 4 {\displaystyle n_{r}=4} n e = 1 {\displaystyle n_{e}=1} total number of pairings: n 2 = 25 {\displaystyle n^{2}=25} number of agreements for outcome r: n r 2 = 16 {\displaystyle n_{r}^{2}=16} number of agreements for outcome e: n e 2 = 1 {\displaystyle n_{e}^{2}=1} number of disagreements for outcome r: n r ( n − n r ) = 4 {\displaystyle n_{r}(n-n_{r})=4} number of disagreements for outcome e: n e ( n − n e ) = 4 {\displaystyle n_{e}(n-n_{e})=4} total number of agreements: n r 2 + n e 2 = 17 {\displaystyle n_{r}^{2}+n_{e}^{2}=17} total number of disagreements: n r ( n − n r ) + n e ( n − n e ) = n 2 − ( n r 2 + n e 2 ) = 8 {\displaystyle n_{r}(n-n_{r})+n_{e}(n-n_{e})=n^{2}-(n_{r}^{2}+n_{e}^{2})=8} uncertainty or fraction of disagreement: 8 / 25 = .32 {\displaystyle 8/25=.32} Behavior can only be predicted for a given context; in this example, let us predict the outcome for the context "3 1 2". To do this, we first find all of the contexts containing the given context; these contexts are called supracontexts. We find the supracontexts by systematically eliminating the variables in the given context; with m variables, there will generally be 2 m {\displaystyle 2^{m}} supracontexts. The following table lists each of the sub- and supracontexts; x means "not x", and - means "anything". These contexts are shown in the venn diagram below: The next step is to determine which exemplars belong to which contexts in order to determine which of the contexts are homogeneous. The table below shows each of the subcontexts, their behavior in terms of the given exemplars, and the number of disagreements within the behavior: Analyzing the subcontexts in the table above, we see that there is only 1 subcontext with any disagreements: "3 1 2", which in the dataset consists of "3 1 0 e" and "3 1 1 r". There are 2 disagreements in this subcontext; 1 pointing from each of the exemplars to the other (see the pointer network pictured above). Therefore, only supracontexts containing this subcontext will contain any disagreements. We use a simple rule to identify the homogeneous supraco