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In this work we present concentration inequalities for the sum $S_n$ of independent integer-valued not necessary indentically distributed random variables, where each variable has tail function that can be bounded by some power function…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries…
Despite the ubiquity of U-statistics in modern Probability and Statistics, their non-asymptotic analysis in a dependent framework may have been overlooked. In a recent work, a new concentration inequality for U-statistics of order two for…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the…
Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by…
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…
We investigate how the transition from integrability to nonintegrability occurs by changing the parameters of the Hamiltonian of a Heisenberg spin-1/2 chain with defects. Randomly distributed defects may lead to quantum chaos. A similar…
The focal-loss has become a widely used alternative to cross-entropy in class-imbalanced classification problems, particularly in computer vision. Despite its empirical success, a systematic information-theoretic study of the focal-loss…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary…
Chaos is generic in strongly-coupled recurrent networks of model neurons, and thought to be an easily accessible dynamical regime in the brain. While neural chaos is typically seen as an impediment to robust computation, we show how such…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some…
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…