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In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation.
This is a timeline of quantum computing.
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
In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.
A small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other. Due to this, most neighboring nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes grows proportionally to the logarithm of the number of nodes N in the network, that is:
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.
In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions.
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.
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into sets of nodes such that each set of nodes is densely connected internally. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to.
Mark Newman is an English–American physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contributions to the fields of complex networks and complex systems, for which he was awarded the 2014 Lagrange Prize.
Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Modularity is often used in optimization methods for detecting community structure in networks. Biological networks, including animal brains, exhibit a high degree of modularity. However, modularity maximization is not statistically consistent, and finds communities in its own null model, i.e. fully random graphs, and therefore it cannot be used to find statistically significant community structures in empirical networks. Furthermore, it has been shown that modularity suffers a resolution limit and, therefore, it is unable to detect small communities.
The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y.
Cristopher David Moore, known as Cris Moore, is an American computer scientist, mathematician, and physicist. He is resident faculty at the Santa Fe Institute, and was formerly a full professor at the University of New Mexico.
Scientific collaboration network is a social network where nodes are scientists and links are co-authorships as the latter is one of the most well documented forms of scientific collaboration. It is an undirected, scale-free network where the degree distribution follows a power law with an exponential cutoff – most authors are sparsely connected while a few authors are intensively connected. The network has an assortative nature – hubs tend to link to other hubs and low-degree nodes tend to link to low-degree nodes. Assortativity is not structural, meaning that it is not a consequence of the degree distribution, but it is generated by some process that governs the network’s evolution.
The Erdős–Rényi Prize of the Network Science Society is named for Paul Erdős and Alfréd Rényi. This international prize is awarded annually in a special ceremony at the International Conference on Network Science to an outstanding early-career researcher in the field of network science.
Quantum machine learning is the integration of quantum algorithms within machine learning programs.
The Louvain method for community detection is a method to extract non-overlapping communities from large networks created by Blondel et al. from the University of Louvain. The method is a greedy optimization method that appears to run in time where is the number of nodes in the network.
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized by being connected with one another with particular edge densities. For example, edges may be more common within communities than between communities. Its mathematical formulation has been firstly introduced in 1983 in the field of social network by Paul W. Holland et al. The stochastic block model is important in statistics, machine learning, and network science, where it serves as a useful benchmark for the task of recovering community structure in graph data.
The International School and Conference on Network Science, also called NetSci, is an annual conference focusing on networks. It is organized yearly since 2006 by the Network Science Society. Physicists are especially prominently represented among the participants, though people from other backgrounds attend as well. The study of networks expanded at the end of the twentieth century, with increasing citation of some seminal papers.
References
- ↑ Curriculum vitae, retrieved 2016-06-30.
- ↑ Aaron Clauset at the Mathematics Genealogy Project
- 1 2 Cummings, Dominic (2 January 2020). "'Two hands are a lot' — we're hiring data scientists, project managers, policy experts, assorted weirdos…". Dominic Cummings's Blog. Retrieved 4 January 2021.
- 1 2 Gibney, Elizabeth (7 January 2020). "Government call for science 'weirdos' prompts caution from researchers". Nature. doi:10.1038/d41586-020-00012-9.
- 1 2 Vaughan, Adam (7 January 2020). "Dominic Cummings wants 'weirdos' to help run the UK. Will it work?". New Scientist. Retrieved 4 January 2021.
- ↑ "Erdős–Rényi prize for young scientists". Network Science Society. Retrieved 4 June 2016.
- ↑ "realitytvworld".
