Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the probability of events that are more extreme than any previously observed. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of hydrology to estimate the probability of an unusually large flooding event, such as the 100-year flood. Similarly, for the design of a breakwater, a coastal engineer would seek to estimate the 50-year wave and design the structure accordingly.
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.
Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes and the ties, edges, or links that connect them. Examples of social structures commonly visualized through social network analysis include social media networks, memes spread, information circulation, friendship and acquaintance networks, business networks, knowledge networks, difficult working relationships, social networks, collaboration graphs, kinship, disease transmission, and sexual relationships. These networks are often visualized through sociograms in which nodes are represented as points and ties are represented as lines. These visualizations provide a means of qualitatively assessing networks by varying the visual representation of their nodes and edges to reflect attributes of interest.
Opinion leadership is leadership by an active media user who interprets the meaning of media messages or content for lower-end media users. Typically the opinion leader is held in high esteem by those who accept their opinions. Opinion leadership comes from the theory of two-step flow of communication propounded by Paul Lazarsfeld and Elihu Katz. Significant developers of the theory have been Robert K. Merton, C. Wright Mills and Bernard Berelson. This theory is one of several models that try to explain the diffusion of innovations, ideas, or commercial products
A fundamental problem in distributed computing and multi-agent systems is to achieve overall system reliability in the presence of a number of faulty processes. This often requires coordinating processes to reach consensus, or agree on some data value that is needed during computation. Example applications of consensus include agreeing on what transactions to commit to a database in which order, state machine replication, and atomic broadcasts. Real-world applications often requiring consensus include cloud computing, clock synchronization, PageRank, opinion formation, smart power grids, state estimation, control of UAVs, load balancing, blockchain, and others.
Phylogenetic comparative methods (PCMs) use information on the historical relationships of lineages (phylogenies) to test evolutionary hypotheses. The comparative method has a long history in evolutionary biology; indeed, Charles Darwin used differences and similarities between species as a major source of evidence in The Origin of Species. However, the fact that closely related lineages share many traits and trait combinations as a result of the process of descent with modification means that lineages are not independent. This realization inspired the development of explicitly phylogenetic comparative methods. Initially, these methods were primarily developed to control for phylogenetic history when testing for adaptation; however, in recent years the use of the term has broadened to include any use of phylogenies in statistical tests. Although most studies that employ PCMs focus on extant organisms, many methods can also be applied to extinct taxa and can incorporate information from the fossil record.
A weighted network is a network where the ties among nodes have weights assigned to them. A network is a system whose elements are somehow connected. The elements of a system are represented as nodes and the connections among interacting elements are known as ties, edges, arcs, or links. The nodes might be neurons, individuals, groups, organisations, airports, or even countries, whereas ties can take the form of friendship, communication, collaboration, alliance, flow, or trade, to name a few.
Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units, based on specific patterns, which form a distinctive structure through interconnectivity. It is primarily used in statistics, machine learning and network science.
Aleš Žiberna is a Slovene statistician, whose specialty is network analysis. His specific research interests include blockmodeling, multivariate analysis and computer intensive methods.
Blockmodel in blockmodeling is defined as a multitude of structures, which are obtained with:
In generalized blockmodeling, the blockmodeling is done by "the translation of an equivalence type into a set of permitted block types", which differs from the conventional blockmodeling, which is using the indirect approach. It's a special instance of the direct blockmodeling approach.
Patrick Doreian is an American mathematician and social scientist, whose specialty is network analysis. His specific research interests include blockmodeling, social structure and network processeses.
Deterministic blockmodeling is approach in blockmodeling, that does not assume probabilistic model, and instead relies on the exact or approximate algorithms, which are used to find blockmodel(s). This approach typical minimizes some inconsistency, that can accure with the ideal block structure.. Such analysis is focused on clustering (grouping) of the network, that is obtained with minimizing an objective function, which measures discrepancy from the ideal block structure.
Generalized blockmodeling of valued networks is an approach of the generalized blockmodeling, dealing with valued networks.
In mathematics applied to analysis of social structures, homogeneity blockmodeling is an approach in blockmodeling, which is best suited for a preliminary or main approach to valued networks, when a prior knowledge about these networks is not available. This is due to the fact, that homogeneity blockmodeling emphasizes the similarity of link (tie) strengths within the blocks over the pattern of links. In this approach, tie (link) values are assumed to be equal (homogenous) within blocks.
Blockmodeling linked networks is an approach in blockmodeling in analysing the linked networks. Such approach is based on the generalized multilevel blockmodeling approach. The main objective of this approach is to achieve clustering of the nodes from all involved sets, while at the same time using all available information. At the same time, all one-mode and two-node networks, that are connected, are blockmodeled, which results in obtaining only one clustering, using nodes from each sets. Each cluster ideally contains only nodes from one set, which also allows the modeling of the links among clusters from different sets. This approach was introduced by Aleš Žiberna in 2014.
Linked network in statistics is a network, which is composed of one-node networks, where the nodes from different one-node networks are connected through two-node networks. This means, that "linked networks are collections of networks defined on different sets of nodes", where all sets of nodes must be connected to each other.
In a social network analysis, a positive or a negative 'friendship' can be established between two nodes in a network; this results in a signed network. As social interaction between people can be positive or negative, so can be links between the nodes.
Exploratory blockmodeling is an (inductive) approach in blockmodeling regarding the specification of an ideal blockmodel. This approach, also known as hypotheses-generating, is the simplest approach, as it "merely involves the definition of the block types permitted as well as of the number of clusters." With this approach, researcher usually defines the best possible blockmodel, which then represent the base for the anaylsis of the whole network.
Confirmatory blockmodeling is a deductive approach in blockmodeling, where a blockmodel is prespecify before the analysis, and then the analysis is fit to this model. When only a part of analysis is prespecify, it is called partially confirmatory blockmodeling.
