The Experts below are selected from a list of 199365 Experts worldwide ranked by ideXlab platform
Stefan Thurner - One of the best experts on this subject based on the ideXlab platform.
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Information geometry of scaling expansions of non-exponentially growing configuration Spaces
'Springer Science and Business Media LLC', 2020Co-Authors: Jan Korbel, Rudolf Hanel, Stefan ThurnerAbstract:Many stochastic complex systems are characterized by the fact that their configuration Space doesn’t grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth of the configuration Space volume in terms of the scaling exponents of the system. These scaling exponents can, in turn, be used to define universality classes that uniquely determine the statistics of a system. Every system belongs to one of these classes. Here we derive the information geometry of scaling expansions of Sample Spaces. In particular, we present the deformed logarithms and the metric in a systematic and coherent way. We observe a phase transition for the curvature. The phase transition can be well measured by the characteristic length r, corresponding to a ball with radius 2r having the same curvature as the statistical manifold. Increasing characteristic length with respect to size of the system is associated with sub-exponential Sample Space growth which is related to strongly constrained and correlated complex systems. Decreasing of the characteristic length corresponds to super-exponential Sample Space growth that occurs for example in systems that develop structure as they evolve. Constant curvature means exponential Sample Space growth that is associated with multinomial statistics, and traditional Boltzmann-Gibbs, or Shannon statistics applies. This allows us to characterize transitions between statistical manifolds corresponding to different families of probability distributions
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classification of complex systems by their Sample Space scaling exponents
New Journal of Physics, 2018Co-Authors: Jan Korbel, Rudolf Hanel, Stefan ThurnerAbstract:The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. Here we propose a scaling expansion of the phaseSpace volume W(N) of a stochastic system. The corresponding expansion coefficients (exponents) define the universality class the system belongs to. Systems within the same universality class share the same statistics and thermodynamics. For sub-exponentially growing systems such expansions have been shown to exist. By using the scaling expansion this classification can be extended to all stochastic systems, including correlated, constraint and super-exponential systems. The extensive entropy of these systems can be easily expressed in terms of these scaling exponents. Systems with super-exponential phaseSpace growth contain important systems, such as magnetic coins that combine combinatorial and structural statistics. We discuss other applications in the statistics of networks, aging, and cascading random walks.
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Sample Space reducing cascading processes produce the full spectrum of scaling exponents
arXiv: Statistical Mechanics, 2017Co-Authors: Bernat Corominasmurtra, Rudolf Hanel, Stefan ThurnerAbstract:Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce power laws with arbitrary exponents. We demonstrate analytically that the frequency distributions of states are power laws with exponents that coincide with the multiplication parameter of the cascading process. In addition, we show that imposing energy conservation in SSR cascades allows us to recover Fermi's classic result on the energy spectrum of cosmic rays, with the universal exponent -2, which is independent of the multiplication parameter of the cascade. Applications of the proposed process include fragmentation processes or directed cascading diffusion on networks, such as rumour or epidemic spreading.
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extreme robustness of scaling in Sample Space reducing processes explains zipf s law in diffusion on directed networks
New Journal of Physics, 2016Co-Authors: Bernat Corominasmurtra, Rudolf Hanel, Stefan ThurnerAbstract:It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their Sample Space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space reducing processes offer an alternative new mechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents were shown to be related to noise levels in the process. Here we show that the emergence of scaling is not limited to the simplest SSRPs, but holds for a huge domain of stochastic processes that are characterised by non-uniform prior distributions. We demonstrate mathematically that in the absence of noise the scaling exponents converge to -1 (Zipf's law) for almost all prior distributions. As a consequence it becomes possible to fully understand targeted diffusion on weighted directed networks and its associated scaling laws in node visit distributions. The presence of cycles can be properly interpreted as playing the same role as noise in SSRPs and, accordingly, determine the scaling exponents. The result that Zipf's law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could be relevant for a series of applications in traffic-, transport- and supply chain management.
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understanding scaling through history dependent processes with collapsing Sample Space
Proceedings of the National Academy of Sciences of the United States of America, 2015Co-Authors: Bernat Corominasmurtra, Rudolf Hanel, Stefan ThurnerAbstract:History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their Sample Space, or their set of possible outcomes, reduces as they age. We demonstrate that these Sample-Space-reducing (SSR) processes necessarily lead to Zipf’s law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x)∼x−λ, where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its Sample Space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from α=2 to ∞. We discuss several applications showing how SSR processes can be used to understand Zipf’s law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes.
Stephan Weiss - One of the best experts on this subject based on the ideXlab platform.
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Sample Space time covariance matrix estimation
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Connor Delaosa, Jennifer Pestana, Nicholas J Goddard, Samuel D Somasundaram, Stephan WeissAbstract:Estimation errors are incurred when calculating the Sample Space-time covariance matrix. We formulate the variance of this estimator when operating on a finite Sample set, compare it to known results, and demonstrate its precision in simulations. The variance of the estimation links directly to previously explored perturbation of the analytic eigenvalues and eigenSpaces of a parahermitian cross-spectral density matrix when estimated from finite data.
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support estimation of a Sample Space time covariance matrix
2019 Sensor Signal Processing for Defence Conference (SSPD), 2019Co-Authors: Connor Delaosa, Jennifer Pestana, Nicholas J Goddard, Samuel D Somasundaram, Stephan WeissAbstract:The ensemble-optimum support for a Sample Space-time covariance matrix can be determined from the ground truth Space-time covariance, and the variance of the estimator. In this paper we provide approximations that permit the estimation of the Sample-optimum support from the estimate itself, given a suitable detection threshold. In simulations, we provide some insight into the (in)sensitivity and dependencies of this threshold.
Rudolf Hanel - One of the best experts on this subject based on the ideXlab platform.
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Information geometry of scaling expansions of non-exponentially growing configuration Spaces
'Springer Science and Business Media LLC', 2020Co-Authors: Jan Korbel, Rudolf Hanel, Stefan ThurnerAbstract:Many stochastic complex systems are characterized by the fact that their configuration Space doesn’t grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth of the configuration Space volume in terms of the scaling exponents of the system. These scaling exponents can, in turn, be used to define universality classes that uniquely determine the statistics of a system. Every system belongs to one of these classes. Here we derive the information geometry of scaling expansions of Sample Spaces. In particular, we present the deformed logarithms and the metric in a systematic and coherent way. We observe a phase transition for the curvature. The phase transition can be well measured by the characteristic length r, corresponding to a ball with radius 2r having the same curvature as the statistical manifold. Increasing characteristic length with respect to size of the system is associated with sub-exponential Sample Space growth which is related to strongly constrained and correlated complex systems. Decreasing of the characteristic length corresponds to super-exponential Sample Space growth that occurs for example in systems that develop structure as they evolve. Constant curvature means exponential Sample Space growth that is associated with multinomial statistics, and traditional Boltzmann-Gibbs, or Shannon statistics applies. This allows us to characterize transitions between statistical manifolds corresponding to different families of probability distributions
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classification of complex systems by their Sample Space scaling exponents
New Journal of Physics, 2018Co-Authors: Jan Korbel, Rudolf Hanel, Stefan ThurnerAbstract:The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. Here we propose a scaling expansion of the phaseSpace volume W(N) of a stochastic system. The corresponding expansion coefficients (exponents) define the universality class the system belongs to. Systems within the same universality class share the same statistics and thermodynamics. For sub-exponentially growing systems such expansions have been shown to exist. By using the scaling expansion this classification can be extended to all stochastic systems, including correlated, constraint and super-exponential systems. The extensive entropy of these systems can be easily expressed in terms of these scaling exponents. Systems with super-exponential phaseSpace growth contain important systems, such as magnetic coins that combine combinatorial and structural statistics. We discuss other applications in the statistics of networks, aging, and cascading random walks.
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Sample Space reducing cascading processes produce the full spectrum of scaling exponents
arXiv: Statistical Mechanics, 2017Co-Authors: Bernat Corominasmurtra, Rudolf Hanel, Stefan ThurnerAbstract:Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is able to produce power laws with arbitrary exponents. We demonstrate analytically that the frequency distributions of states are power laws with exponents that coincide with the multiplication parameter of the cascading process. In addition, we show that imposing energy conservation in SSR cascades allows us to recover Fermi's classic result on the energy spectrum of cosmic rays, with the universal exponent -2, which is independent of the multiplication parameter of the cascade. Applications of the proposed process include fragmentation processes or directed cascading diffusion on networks, such as rumour or epidemic spreading.
-
extreme robustness of scaling in Sample Space reducing processes explains zipf s law in diffusion on directed networks
New Journal of Physics, 2016Co-Authors: Bernat Corominasmurtra, Rudolf Hanel, Stefan ThurnerAbstract:It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their Sample Space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space reducing processes offer an alternative new mechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents were shown to be related to noise levels in the process. Here we show that the emergence of scaling is not limited to the simplest SSRPs, but holds for a huge domain of stochastic processes that are characterised by non-uniform prior distributions. We demonstrate mathematically that in the absence of noise the scaling exponents converge to -1 (Zipf's law) for almost all prior distributions. As a consequence it becomes possible to fully understand targeted diffusion on weighted directed networks and its associated scaling laws in node visit distributions. The presence of cycles can be properly interpreted as playing the same role as noise in SSRPs and, accordingly, determine the scaling exponents. The result that Zipf's law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could be relevant for a series of applications in traffic-, transport- and supply chain management.
-
understanding scaling through history dependent processes with collapsing Sample Space
Proceedings of the National Academy of Sciences of the United States of America, 2015Co-Authors: Bernat Corominasmurtra, Rudolf Hanel, Stefan ThurnerAbstract:History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their Sample Space, or their set of possible outcomes, reduces as they age. We demonstrate that these Sample-Space-reducing (SSR) processes necessarily lead to Zipf’s law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x)∼x−λ, where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its Sample Space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from α=2 to ∞. We discuss several applications showing how SSR processes can be used to understand Zipf’s law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes.
Juan M Morales - One of the best experts on this subject based on the ideXlab platform.
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an efficient robust solution to the two stage stochastic unit commitment problem
IEEE Transactions on Power Systems, 2017Co-Authors: Ignacio Blanco, Juan M MoralesAbstract:This paper provides a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case. The proposed reformulation is based on partitioning the Sample Space of the uncertain factors by clustering the scenarios that approximate their probability distributions. The degree of conservatism of the resulting unit-commitment plan (that is, how close it is to the one provided by a purely robust or stochastic unit-commitment formulation) is controlled by the number of partitions into which the said Sample Space is split. To efficiently solve the proposed reformulation of the unit-commitment problem under uncertainty, we develop two alternative parallelization and decomposition schemes that rely on a column-and-constraint generation procedure. Finally, we analyze the quality of the solutions provided by this reformulation for a case study based on the IEEE 14-node power system and test the effectiveness of the proposed parallelization and decomposition solution approaches on the larger IEEE 3-Area RTS-96 power system.
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an efficient robust solution to the two stage stochastic unit commitment problem
arXiv: Optimization and Control, 2016Co-Authors: Ignacio Blanco, Juan M MoralesAbstract:This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of the uncertainties. The proposed reformulation is based on partitioning the Sample Space of the uncertain factors by clustering the scenarios that approximate their probability distributions. It is, furthermore, very amenable to decomposition and parallelization using a column-and-constraint generation procedure.
Connor Delaosa - One of the best experts on this subject based on the ideXlab platform.
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Sample Space time covariance matrix estimation
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Connor Delaosa, Jennifer Pestana, Nicholas J Goddard, Samuel D Somasundaram, Stephan WeissAbstract:Estimation errors are incurred when calculating the Sample Space-time covariance matrix. We formulate the variance of this estimator when operating on a finite Sample set, compare it to known results, and demonstrate its precision in simulations. The variance of the estimation links directly to previously explored perturbation of the analytic eigenvalues and eigenSpaces of a parahermitian cross-spectral density matrix when estimated from finite data.
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support estimation of a Sample Space time covariance matrix
2019 Sensor Signal Processing for Defence Conference (SSPD), 2019Co-Authors: Connor Delaosa, Jennifer Pestana, Nicholas J Goddard, Samuel D Somasundaram, Stephan WeissAbstract:The ensemble-optimum support for a Sample Space-time covariance matrix can be determined from the ground truth Space-time covariance, and the variance of the estimator. In this paper we provide approximations that permit the estimation of the Sample-optimum support from the estimate itself, given a suitable detection threshold. In simulations, we provide some insight into the (in)sensitivity and dependencies of this threshold.
