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Time-varying Network
A temporal network, also known as a time-varying network, is a network whose links are active only at certain points in time. Each link carries information on when it is active, along with other possible characteristics such as a weight. Time-varying networks are of particular relevance to spreading processes, like the spread of information and disease, since each link is a contact opportunity and the time ordering of contacts is included. Examples of time-varying networks include communication networks where each link is relatively short or instantaneous, such as phone calls or e-mails.J.-P. Eckmann, E. Moses, and D. Sergi. Entropy of dialogues creates coherent structures in e-mail traffic" ''Proc. Natl. Acad. Sci. USA'' 2004; 101:14333–14337. https://www.weizmann.ac.il/complex/EMoses/pdf/EntropyDialogues.pdf Information spreads over both networks, and some computer viruses spread over the second. Networks of physical proximity, encoding who encounters whom and when, can be re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Intransitivity
In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. That is, we can find three values a, b, and c where the transitive condition does not hold. Antitransitivity is a Mathematical jargon#stronger, stronger property which describes a relation where, for any three values, the transitivity condition never holds. Some authors use the term to refer to antitransitivity. Intransitivity A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C. A relation is if it is not transitive. Assuming the relation is named R, it is intransitive if: \lnot\left(\forall a, b, c: a R b \land b R c \implies a R c\right). This statement is equivalent to \exists a,b,c : a R b \land b R c \land \lnot(a R c). For example, the inequality relation, \neq, is intransitive. This can be demonstrated by replacing R with \neq and choosing a=1, b=2, and c=1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scale-free Network
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction ''P''(''k'') of nodes in the network having ''k'' connections to other nodes goes for large values of ''k'' as : P(k) \ \sim \ k^\boldsymbol where \gamma is a parameter whose value is typically in the range 2<\gamma<3 (wherein the second moment ( scale parameter) of is infinite but the first moment is finite), although occasionally it may lie outside these bounds. The name "scale-free" could be explained by the fact that some moments of the degree distribution are not defined, so that the network does not have a characteristic scale or "size". and the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Exponential Random Graph Models
Exponential family random graph models (ERGMs) are a set of statistical models used to study the structure and patterns within networks, such as those in social, organizational, or scientific contexts. They analyze how connections ( edges) form between individuals or entities ( nodes) by modeling the likelihood of network features, like clustering or centrality, across diverse examples including knowledge networks, organizational networks, colleague networks, social media networks, networks of scientific collaboration, and more. Part of the exponential family of distributions, ERGMs help researchers understand and predict network behavior in fields ranging from sociology to data science. Background Many metrics exist to describe the structural features of an observed network such as the density, centrality, or assortativity. However, these metrics describe the observed network which is only one instance of a large number of possible alternative networks. This set of alternative netw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dynamic Network Analysis
Dynamic network analysis (DNA) is an emergent scientific field that brings together traditional social network analysis (SNA), link analysis (LA), social simulation and multi-agent systems (MAS) within network science and network theory. Dynamic networks are a function of time (modeled as a subset of the real numbers) to a set of graphs; for each time point there is a graph. This is akin to the definition of dynamical systems, in which the function is from time to an ambient space, where instead of ambient space time is translated to relationships between pairs of vertices. Overview There are two aspects of this field. The first is the statistical analysis of DNA data. The second is the utilization of simulation to address issues of network dynamics. DNA networks vary from traditional social networks in that they are larger, dynamic, multi-mode, multi-plex networks, and may contain varying levels of uncertainty. The main difference of DNA to SNA is that DNA takes interactio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Directed Percolation
In statistical physics, directed percolation (DP) refers to a class of models that mimic filtering of fluids through porous materials along a given direction, due to the effect of gravity. Varying the microscopic connectivity of the pores, these models display a phase transition from a macroscopically permeable (percolating) to an impermeable (non-percolating) state. Directed percolation is also used as a simple model for epidemic spreading with a transition between survival and extinction of the disease depending on the infection rate. More generally, the term directed percolation stands for a universality class of continuous phase transitions which are characterized by the same type of collective behavior on large scales. Directed percolation is probably the simplest universality class of transitions out of thermal equilibrium. Lattice models One of the simplest realizations of DP is bond directed percolation. This model is a directed variant of percolation, ordinary (isotr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Epidemic Model
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc. History The modelling of infectious diseases is a tool that has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. The first scientist who systematically tried to quantify causes of death was John Graunt in his book ''Natural and Political Observations made upon the Bills of Mortality'', in 1662. The bills he studied were listings of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mean
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. The ''arithmetic mean'', also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the '' sample mean'' (\bar) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x. Outside probability and statistics, a wide rang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Poisson Process
In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of Point (geometry), points randomly located on a Space (mathematics), mathematical space with the essential feature that the points occur independently of one another. The process's name derives from the fact that the number of points in any given finite region follows a Poisson distribution. The process and the distribution are named after French mathematician Siméon Denis Poisson. The process itself was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and actuarial science. This point process is used as a mathematical model for seemingly random processes in numerous disciplines including astronomy,G. J. Babu and E. D. Feigelson. Spatial point processes in astronomy. ''Journal of st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
