English
Related papers

Related papers: On the Information Dimension of Stochastic Process…

200 papers

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…

Computational Physics · Physics 2013-06-28 M. Schmuck , M. Pradas , S. Kalliadasis , G. A. Pavliotis

To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been…

Molecular Networks · Quantitative Biology 2015-08-28 Hector Zenil , Narsis A. Kiani , Jesper Tegnér

When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic…

Soft Condensed Matter · Physics 2020-04-16 Anna Frishman , Pierre Ronceray

The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various…

Nuclear Theory · Physics 2015-06-26 G. A. Lalazissis , S. E. Massen , C. P. Panos , S. S. Dimitrova

The quadratic decaying property of the information rate function states that given a fixed conditional distribution $p_{\mathsf{Y}|\mathsf{X}}$, the mutual information between the (finite) discrete random variables $\mathsf{X}$ and…

Information Theory · Computer Science 2023-05-15 Michael X. Cao , Marco Tomamichel

For a Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE's) time discretization numerical schemes usually destroy the property of…

Numerical Analysis · Mathematics 2019-02-20 Markos Katsoulakis , Yannis Pantazis , Luc Rey-Bellet

This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…

Information Theory · Computer Science 2016-11-15 Victoria Kostina , Sergio Verdú

This paper investigates the rate-distortion function, under a squared error distortion $D$, for an $n$-dimensional random vector uniformly distributed on an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion function…

Information Theory · Computer Science 2024-01-10 Alex Dytso , Martina Cardone

Kolmogorov argued that the concept of information exists also in problems with no underlying stochastic model (as Shannon's information representation) for instance, the information contained in an algorithm or in the genome. He introduced…

Discrete Mathematics · Computer Science 2008-07-01 Joel Ratsaby

The amount of information generated by a discrete time stochastic processes in a single step can be quantified by the entropy rate. We investigate the differences between two discrete time walk models, the discrete time quantum walk and the…

Quantum Physics · Physics 2014-03-04 Bálint Kollár , Mátyás Koniorczyk

While an important topic in practice, the estimation of the number of non-noise components in blind source separation has received little attention in the literature. Recently, two bootstrap-based techniques for estimating the dimension…

Statistics Theory · Mathematics 2024-04-12 Joni Virta , Klaus Nordhausen

Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…

Quantum Physics · Physics 2025-09-26 Álvaro Yángüez , Thomas A. Hahn , Jan Kochanowski

The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…

Machine Learning · Statistics 2026-01-16 Hamish Flynn

In some practical learning tasks, such as traffic video analysis, the number of available training samples is restricted by different factors, such as limited communication bandwidth and computation power. Determinantal Point Process (DPP)…

Machine Learning · Computer Science 2023-08-17 Xiwen Chen , Huayu Li , Rahul Amin , Abolfazl Razi

As shown by M\'edard, the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input $X$ with power $P$ and by upper-bounding the conditional entropy $h(X|Y,\hat{H})$…

Information Theory · Computer Science 2016-11-15 Adriano Pastore , Tobias Koch , Javier Rodríguez Fonollosa

We review connections between the cumulant generating function of full counting statistics of particle number and the R\'enyi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on…

Mesoscale and Nanoscale Physics · Physics 2019-02-05 Yasuhiro Utsumi

In lossy image compression, the objective is to achieve minimal signal distortion while compressing images to a specified bit rate. The increasing demand for visual analysis applications, particularly in classification tasks, has emphasized…

Multimedia · Computer Science 2024-05-07 Yuefeng Zhang

Transfer Entropy and Directed Information are information-theoretic measures of the directional dependency between stochastic processes. Following the definitions of Schreiber and Massey in discrete time, we define and evaluate these…

Probability · Mathematics 2016-04-08 Nigel J. Newton

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the…

Information Theory · Computer Science 2011-05-03 Milan S. Derpich , Jan Østergaard

With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction…

Information Theory · Computer Science 2022-01-19 Jie Han , Tao Guo , Qiaoqiao Zhou , Wei Han , Bo Bai , Gong Zhang