The Experts below are selected from a list of 20508 Experts worldwide ranked by ideXlab platform
J.j. Halliwell - One of the best experts on this subject based on the ideXlab platform.
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Information-Theoretic Measure of uncertainty due to quantum and thermal fluctuations.
Physical review. D Particles and fields, 1993Co-Authors: Arlen Anderson, J.j. HalliwellAbstract:We study an information-Theoretic Measure of uncertainty for quantum systems. It is the Shannon information I of the phase-space probability distribution , where |z> are coherent states and ρ is the density matrix. As shown by Lieb I ≥ 1, and this bound represents a strengthened version of the uncertainty principle. For a harmonic oscillator in a thermal state, I coincides with von Neumann entropy, −Tr(ρlnρ), in the high-temperature regime, but unlike entropy, it is nonzero (and equal to the Lieb bound) at zero temperature. It therefore supplies a nontrivial Measure of uncertainty due to both quantum and thermal fluctuations
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information Theoretic Measure of uncertainty due to quantum and thermal fluctuations
Physical Review D, 1993Co-Authors: Arlen Anderson, J.j. HalliwellAbstract:We study an information-Theoretic Measure of uncertainty for quantum systems. It is the Shannon information I of the phase-space probability distribution 〈z\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}z〉, where \ensuremath{\Vert}z〉 are coherent states and \ensuremath{\rho} is the density matrix. As shown by Lieb I\ensuremath{\ge}1, and this bound represents a strengthened version of the uncertainty principle. For a harmonic oscillator in a thermal state, I coincides with von Neumann entropy, -Tr(\ensuremath{\rho}ln\ensuremath{\rho}), in the high-temperature regime, but unlike entropy, it is nonzero (and equal to the Lieb bound) at zero temperature. It therefore supplies a nontrivial Measure of uncertainty due to both quantum and thermal fluctuations. We study I as a function of time for a class of nonequilibrium quantum systems consisting of a distinguished system coupled to a heat bath. We derive an evolution equation for I. For the harmonic oscillator, in the Fokker-Planck regime, we show that I increases monotonically, if the width of the coherent states is chosen to be the same as the width of the harmonic oscillator ground state. For other choices of the width, and for more general Hamiltonians, I settles down to a monotonic increase in the long run, but may suffer an initial decrease for certain initial states that undergo ``reassembly'' (the opposite of quantum spreading). Our main result is to prove, for linear systems, that I at each moment of time has a lower bound ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$, over all possible initial states.This bound is a generalization of the uncertainty principle to include thermal fluctuations in nonequilibrium systems, and represents the least amount of uncertainty the system must suffer after evolution in the presence of an environment for time t. ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ is an envelope, equal for each time t, to the time evolution of I for a certain initial state, which we calculate to be a nonminimal Gaussian. ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ coincides with the Lieb bound in the absence of an environment, and is related to von Neumann entropy in the long-time limit. The form of ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ indicates that the thermal fluctuations become comparable with the quantum fluctuations on a time scale equal to the decoherence time scale, in agreement with earlier work of Hu and Zhang. Our results are also related to those of Zurek, Habib, and Paz, who looked for the set of initial states generating the least amount of von Neumann entropy after a fixed period of nonunitary evolution.
Tomaso Aste - One of the best experts on this subject based on the ideXlab platform.
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Information-Theoretic Measures for nonlinear causality detection: application to social media sentiment and cryptocurrency prices.
Royal Society open science, 2020Co-Authors: Z. Keskin, Tomaso AsteAbstract:Information transfer between time series is calculated using the asymmetric information-Theoretic Measure known as transfer entropy. Geweke’s autoregressive formulation of Granger causality is used...
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Information-Theoretic Measures for non-linear causality detection: application to social media sentiment and cryptocurrency prices.
arXiv: Data Analysis Statistics and Probability, 2019Co-Authors: Z. Keskin, Tomaso AsteAbstract:Information transfer between time series is calculated by using the asymmetric information-Theoretic Measure known as transfer entropy. Geweke's autoregressive formulation of Granger causality is used to find linear transfer entropy, and Schreiber's general, non-parametric, information-Theoretic formulation is used to detect non-linear transfer entropy. We first validate these Measures against synthetic data. Then we apply these Measures to detect causality between social sentiment and cryptocurrency prices. We perform significance tests by comparing the information transfer against a null hypothesis, determined via shuffled time series, and calculate the Z-score. We also investigate different approaches for partitioning in nonparametric density estimation which can improve the significance of results. Using these techniques on sentiment and price data over a 48-month period to August 2018, for four major cryptocurrencies, namely bitcoin (BTC), ripple (XRP), litecoin (LTC) and ethereum (ETH), we detect significant information transfer, on hourly timescales, in directions of both sentiment to price and of price to sentiment. We report the scale of non-linear causality to be an order of magnitude greater than linear causality.
Mikhail Prokopenko - One of the best experts on this subject based on the ideXlab platform.
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transfer entropy and transient limits of computation
Scientific Reports, 2015Co-Authors: Mikhail Prokopenko, Joseph T LizierAbstract:Transfer entropy is a recently introduced information-Theoretic Measure quantifying directed statistical coherence between spatiotemporal processes, and is widely used in diverse fields ranging from finance to neuroscience. However, its relationships to fundamental limits of computation, such as Landauer's limit, remain unknown. Here we show that in order to increase transfer entropy (predictability) by one bit, heat flow must match or exceed Landauer's limit. Importantly, we generalise Landauer's limit to bi-directional information dynamics for non-equilibrium processes, revealing that the limit applies to prediction, in addition to retrodiction (information erasure). Furthermore, the results are related to negentropy, and to Bremermann's limit and the Bekenstein bound, producing, perhaps surprisingly, lower bounds on the computational deceleration and information loss incurred during an increase in predictability about the process. The identified relationships set new computational limits in terms of fundamental physical quantities, and establish transfer entropy as a central Measure connecting information theory, thermodynamics and theory of computation.
John Goutsias - One of the best experts on this subject based on the ideXlab platform.
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ranking genomic features using an information Theoretic Measure of epigenetic discordance
BMC Bioinformatics, 2019Co-Authors: Garrett W Jenkinson, Jordi Abante, Michael A Koldobskiy, Andrew P Feinberg, John GoutsiasAbstract:Background Establishment and maintenance of DNA methylation throughout the genome is an important epigenetic mechanism that regulates gene expression whose disruption has been implicated in human diseases like cancer. It is therefore crucial to know which genes, or other genomic features of interest, exhibit significant discordance in DNA methylation between two phenotypes. We have previously proposed an approach for ranking genes based on methylation discordance within their promoter regions, determined by centering a window of fixed size at their transcription start sites. However, we cannot use this method to identify statistically significant genomic features and handle features of variable length and with missing data.
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ranking genomic features using an information Theoretic Measure of epigenetic discordance
BMC Bioinformatics, 2019Co-Authors: Jordi Abante, Michael A Koldobskiy, Andrew P Feinberg, Garrett Jenkinson, John GoutsiasAbstract:Establishment and maintenance of DNA methylation throughout the genome is an important epigenetic mechanism that regulates gene expression whose disruption has been implicated in human diseases like cancer. It is therefore crucial to know which genes, or other genomic features of interest, exhibit significant discordance in DNA methylation between two phenotypes. We have previously proposed an approach for ranking genes based on methylation discordance within their promoter regions, determined by centering a window of fixed size at their transcription start sites. However, we cannot use this method to identify statistically significant genomic features and handle features of variable length and with missing data. We present a new approach for computing the statistical significance of methylation discordance within genomic features of interest in single and multiple test/reference studies. We base the proposed method on a well-articulated hypothesis testing problem that produces p- and q-values for each genomic feature, which we then use to identify and rank features based on the statistical significance of their epigenetic dysregulation. We employ the information-Theoretic concept of mutual information to derive a novel test statistic, which we can evaluate by computing Jensen-Shannon distances between the probability distributions of methylation in a test and a reference sample. We design the proposed methodology to simultaneously handle biological, statistical, and technical variability in the data, as well as variable feature lengths and missing data, thus enabling its wide-spread use on any list of genomic features. This is accomplished by estimating, from reference data, the null distribution of the test statistic as a function of feature length using generalized additive regression models. Differential assessment, using normal/cancer data from healthy fetal tissue and pediatric high-grade glioma patients, illustrates the potential of our approach to greatly facilitate the exploratory phases of clinically and biologically relevant methylation studies. The proposed approach provides the first computational tool for statistically testing and ranking genomic features of interest based on observed DNA methylation discordance in comparative studies that accounts, in a rigorous manner, for biological, statistical, and technical variability in methylation data, as well as for variability in feature length and for missing data.
Arlen Anderson - One of the best experts on this subject based on the ideXlab platform.
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Information-Theoretic Measure of uncertainty due to quantum and thermal fluctuations.
Physical review. D Particles and fields, 1993Co-Authors: Arlen Anderson, J.j. HalliwellAbstract:We study an information-Theoretic Measure of uncertainty for quantum systems. It is the Shannon information I of the phase-space probability distribution , where |z> are coherent states and ρ is the density matrix. As shown by Lieb I ≥ 1, and this bound represents a strengthened version of the uncertainty principle. For a harmonic oscillator in a thermal state, I coincides with von Neumann entropy, −Tr(ρlnρ), in the high-temperature regime, but unlike entropy, it is nonzero (and equal to the Lieb bound) at zero temperature. It therefore supplies a nontrivial Measure of uncertainty due to both quantum and thermal fluctuations
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information Theoretic Measure of uncertainty due to quantum and thermal fluctuations
Physical Review D, 1993Co-Authors: Arlen Anderson, J.j. HalliwellAbstract:We study an information-Theoretic Measure of uncertainty for quantum systems. It is the Shannon information I of the phase-space probability distribution 〈z\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}z〉, where \ensuremath{\Vert}z〉 are coherent states and \ensuremath{\rho} is the density matrix. As shown by Lieb I\ensuremath{\ge}1, and this bound represents a strengthened version of the uncertainty principle. For a harmonic oscillator in a thermal state, I coincides with von Neumann entropy, -Tr(\ensuremath{\rho}ln\ensuremath{\rho}), in the high-temperature regime, but unlike entropy, it is nonzero (and equal to the Lieb bound) at zero temperature. It therefore supplies a nontrivial Measure of uncertainty due to both quantum and thermal fluctuations. We study I as a function of time for a class of nonequilibrium quantum systems consisting of a distinguished system coupled to a heat bath. We derive an evolution equation for I. For the harmonic oscillator, in the Fokker-Planck regime, we show that I increases monotonically, if the width of the coherent states is chosen to be the same as the width of the harmonic oscillator ground state. For other choices of the width, and for more general Hamiltonians, I settles down to a monotonic increase in the long run, but may suffer an initial decrease for certain initial states that undergo ``reassembly'' (the opposite of quantum spreading). Our main result is to prove, for linear systems, that I at each moment of time has a lower bound ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$, over all possible initial states.This bound is a generalization of the uncertainty principle to include thermal fluctuations in nonequilibrium systems, and represents the least amount of uncertainty the system must suffer after evolution in the presence of an environment for time t. ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ is an envelope, equal for each time t, to the time evolution of I for a certain initial state, which we calculate to be a nonminimal Gaussian. ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ coincides with the Lieb bound in the absence of an environment, and is related to von Neumann entropy in the long-time limit. The form of ${\mathit{I}}_{\mathit{t}}^{\mathrm{min}}$ indicates that the thermal fluctuations become comparable with the quantum fluctuations on a time scale equal to the decoherence time scale, in agreement with earlier work of Hu and Zhang. Our results are also related to those of Zurek, Habib, and Paz, who looked for the set of initial states generating the least amount of von Neumann entropy after a fixed period of nonunitary evolution.
