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UPA Model
In the analysis of social networks, the uniform-preferential-attachment model, or UPA model is a variation of the Barabási–Albert model in which the preferential attachment is perceived as having a double nature. New nodes joining the network may either attach themselves with high-degree nodes or with most recently added nodes. This behaviour can be noticed in some examples of social networks, such as the citation network of scientific publications.Pachon, Angelica; Sacerdote, Laura; Yang, Shuyi. ''Scale-free behavior of networks with the copresence of preferential and uniform attachment rules''. Mathematics Department “G. Peano”, University of Torino, 2017. Model description For an UPA network with nodes \, we define for an arriving node v_ a subset of nodes \ with w \in \mathbb N. This subset is called a ''window'', which represents the ''w'' last nodes inserted into the network. A new node may link itself either with a node from the window subset, with probability ''p'', o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics. Social networks and the analysis of them is an inherently interdisciplinary academic field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing the dynamics of triads and "web of group affiliations". Jacob Moreno is credited with developing the first sociograms in the 1930s to study interpersonal relationships. These approaches were mathematically for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barabási–Albert Model
The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the World Wide Web, citation networks, and some social networks are thought to be approximately scale-free and certainly contain few nodes (called hubs) with unusually high degree as compared to the other nodes of the network. The BA model tries to explain the existence of such nodes in real networks. The algorithm is named for its inventors Albert-László Barabási and Réka Albert. Concepts Many observed networks (at least approximately) fall into the class of scale-free networks, meaning that they have power-law (or scale-free) degree distributions, while random graph models such as the Erdős–Rényi (ER) model and the Watts–Strogatz (WS) model do not exhibit power laws. The Barabási–Albert model is one of several proposed models that generate scale-free networks. It i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Citation Analysis
Citation analysis is the examination of the frequency, patterns, and graphs of citations in documents. It uses the directed graph of citations — links from one document to another document — to reveal properties of the documents. A typical aim would be to identify the most important documents in a collection. A classic example is that of the citations between academic articles and books. For another example, judges of law support their judgements by referring back to judgements made in earlier cases (see citation analysis in a legal context). An additional example is provided by patents which contain prior art, citation of earlier patents relevant to the current claim. Documents can be associated with many other features in addition to citations, such as authors, publishers, journals as well as their actual texts. The general analysis of collections of documents is known as bibliometrics and citation analysis is a key part of that field. For example, bibliographi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic eruptions, human judgments of stimulus intensity and many other quantit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Distribution
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. Definition The degree of a node in a network (sometimes referred to incorrectly as the connectivity) is the number of connections or edges the node has to other nodes. If a network is directed, meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of outgoing edges. The degree distribution ''P''(''k'') of a network is then defined to be the fraction of nodes in the network with degree ''k''. Thus if there are ''n'' nodes in total in a network and ''n''''k'' of them have degree ''k'', we have P(k) = \frac. The same information is also sometimes presented in the form of a ''cumulative degree distribution'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral : \Beta(z_1,z_2) = \int_0^1 t^(1-t)^\,dt for complex number inputs z_1, z_2 such that \Re(z_1), \Re(z_2)>0. The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol is a Greek capital beta. Properties The beta function is symmetric, meaning that \Beta(z_1,z_2) = \Beta(z_2,z_1) for all inputs z_1 and z_2.Davis (1972) 6.2.2 p.258 A key property of the beta function is its close relationship to the gamma function: : \Beta(z_1,z_2)=\frac. A proof is given below in . The beta function is also closely related to binomial coefficients. When (or , by symmetry) is a positive integer, it follows from the definition of the gamma function thatDavis (1972) 6.2.1 p.258 : \Beta(m,n) =\dfrac = \frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azuma's Inequality
In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose \ is a martingale (or super-martingale) and :, X_k - X_, \leq c_k, \, almost surely. Then for all positive integers ''N'' and all positive reals ''\epsilon'', :\text(X_N - X_0 \geq \epsilon) \leq \exp\left ( \right). And symmetrically (when ''X''''k'' is a sub-martingale): :\text(X_N - X_0 \leq -\epsilon) \leq \exp\left ( \right). If ''X'' is a martingale, using both inequalities above and applying the union bound allows one to obtain a two-sided bound: :\text(, X_N - X_0, \geq \epsilon) \leq 2\exp\left ( \right). Proof The proof shares similar idea of the proof for the general form of Azuma's inequality listed below. Actually, this can be viewed as a direct corollary of the general form of Azuma's inequality. A general form of Azuma's inequality Limitation of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reddit
Reddit (; stylized in all lowercase as reddit) is an American social news news aggregator, aggregation, Review site#Rating site, content rating, and Internet forum, discussion website. Registered users (commonly referred to as "Redditors") submit content to the site such as links, text posts, images, and videos, which are then #AnchorVote, voted up or down by other members. Posts are organized by subject into user-created boards called "communities" or "subreddits". Submissions with more upvotes appear towards the top of their subreddit and, if they receive enough upvotes, ultimately on the site's front page. Reddit administrators moderate the communities. Moderation is also conducted by community-specific moderators, who are not Reddit employees. As of March 2022, Reddit ranks as the 9th-List of most visited websites, most-visited website in the world and 6th most-visited website in the U.S., according to Semrush. About 42–49.3% of its user base comes from the United States, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Models
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject. Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. The following was said by John von Neumann. There is also an increasing attention to scientific modelling in fields such as science education, philosophy of science, sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
