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Braunstein–Ghosh–Severini Entropy
In network theory, the Braunstein–Ghosh–Severini entropy (BGS entropy) of a network is the von Neumann entropy of a density matrix given by a normalized Laplacian matrix of the network. This definition of entropy does not have a clear thermodynamical interpretation. The BGS entropy has been used in the context of quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v .... Notes and references {{DEFAULTSORT:Braunstein-Ghosh-Severini entropy Quantum mechanical entropy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Theory
In mathematics, computer science, and network science, network theory is a part of graph theory. It defines networks as Graph (discrete mathematics), graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or directed graph, asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience. Applications of network theory include Logistics, logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.; see List of network theory topics for more examples. Euler's solution of the Seven Bridges of Königsberg, Seven Bridges of Königsberg problem is c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Combinatorics
''Annals of Combinatorics'' is a quarterly peer-reviewed scientific journal covering research in combinatorics. It was established in 1997 by William Chen and is published by Birkhäuser. The journal publishes articles in combinatorics and related areas with a focus on algebraic combinatorics, analytic combinatorics, graph theory, and matroid theory. Until December 2019, the journal was edited by George Andrews, William Chen, and Peter Paule. The current editors-in-chief are Frédérique Bassino, Kolja Knauer, and Matjaž Konvalinka. Abstracting and indexing The journal is abstracted and indexed in *MathSciNet, *Science Citation Index Expanded, *Scopus, and *ZbMATH Open. According to the ''Journal Citation Reports'', the journal has a 2022 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Entropy
In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system. It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics, and it is the quantum counterpart of the Shannon entropy from classical information theory. For a quantum-mechanical system described by a density matrix , the von Neumann entropy is S = - \operatorname(\rho \ln \rho), where \operatorname denotes the trace and \operatorname denotes the matrix version of the natural logarithm. If the density matrix is written in a basis of its eigenvectors , 1\rangle, , 2\rangle, , 3\rangle, \dots as \rho = \sum_j \eta_j \left, j \right\rang \left\lang j \ , then the von Neumann entropy is merely S = -\sum_j \eta_j \ln \eta_j . In this form, ''S'' can be seen as the Shannon entropy of the eigenvalues, reinterpreted as probabilities. The von Neumann entropy and quantities based upon i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Matrix
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states. These arise in quantum mechanics in two different situations: # when the preparation of a system can randomly produce different pure states, and thus one must deal with the statistics of possible preparations, and # when one wants to describe a physical system that is entangled with another, without describing their combined state. This case is typical for a system interacting with some environment (e.g. decoherence). In this case, the density matrix of an entangled system differs from that of an ensemble of pure states that, combined, would give the same statistical results upon measurement. Density matrices are thus crucial tools in areas of quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplacian Matrix
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating the negative continuous Laplacian obtained by the finite difference method. The Laplacian matrix relates to many functional graph properties. Kirchhoff's theorem can be used to calculate the number of spanning trees for a given graph. The sparsest cut of a graph can be approximated through the Fiedler vector — the eigenvector corresponding to the second smallest eigenvalue of the graph Laplacian — as established by Cheeger's inequality. The spectral decomposition of the Laplacian matrix allows the construction of low-dimensional embeddings that appear in many machine learning applications and determines a spectral layo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang. Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the Electromagnetism, electromagnetic interaction, the Strong interaction, strong force, and the Weak interaction, weak force; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
