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What is information originating in observation? Until now it has no scientifically conclusive definition. Information is memorized entropy cutting in random observations which processing interactions. Randomness of various interactive…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous,…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Directional-change Intrinsic Time analysis has long revealed scaling laws in market microstructure, but the origin of their stability remains elusive. This article presents evidence that Intrinsic Time can be modeled as a memoryless…
This is a paper in the intersection of time series analysis and complexity theory that presents new results on permutation complexity in general and permutation entropy in particular. In this context, permutation complexity refers to the…
It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…
In this paper, we study a simple correlation-based strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequency-domain samples. We model the output of this "compressive…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
The weak-$\ell^p$ norm can be used to define a measure $s$ of sparsity. When we compute $s$ for the discrete cosine transform coefficients of a signal, the value of $s$ is related to the information content of said signal. We use this value…
In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the…
The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a…
Understanding information transfer among individuals is fundamental to revealing collective dynamics of complex systems. Information transfers are quantified by information-theoretical measures and are often correlated with the concept of…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the…
Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem.…
Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…