Related papers: Maximum Entropy Property of Discrete-time Stable S…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes…
This paper analyzes the stability of optimal policies in the long-run stochastic control framework with an averaged risk-sensitive criterion for discrete-time MDPs on finite state-action space. In particular, we study the robustness of…
Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth…
In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
Transformers are designed for discrete tokens, yet many real-world signals are continuous processes observed through noisy sampling. Discrete tokenizations (raw values, patches, finite differences) can be brittle in low signal-to-noise…
Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…
The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…
The predictability of discrete-time processes is studied in a deterministic setting. A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies. For such processes, the prediction error…
We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we…
We study the entropy rate of pattern sequences of stochastic processes, and its relationship to the entropy rate of the original process. We give a complete characterization of this relationship for i.i.d. processes over arbitrary…