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This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
This paper addresses the issue of building a part-based representation of a dataset of images. More precisely, we look for a non-negative, sparse decomposition of the images on a reduced set of atoms, in order to unveil a morphological and…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…
Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces…
Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
While mutual information effectively quantifies dependence between two variables, it does not by itself reveal the complex, fine-grained interactions among variables, i.e., how multiple sources contribute redundantly, uniquely, or…
We consider semidiscrete finite differences schemes for the periodic Scr\"odinger equation in dimension one. We analyze whether the space-time integrability properties observed by Bourgain in the continuous case are satisfied at the…
We propose fully data-driven variational methods, termed successive jump and mode decomposition (SJMD) and its multivariate extension, successive multivariate jump and mode decomposition (SMJMD), for successively decomposing nonstationary…
We consider the "partial information decomposition" (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique…
It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann…
In this note we prove that the local martingale part of a convex function f of a d-dimensional semimartingale X = M + A can be written in terms of an It^o stochastic integral \int H(X)dM, where H(x) is some particular measurable choice of…
The free-particle propagator, a key operator in various algorithms for simulating the time evolution of the Schr\"odinger equation, is studied. A multiscale approximation of this propagator is constructed, representing the semigroup…
In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of…
Full waveform inversion (FWI) enables us to obtain high-resolution velocity models of the subsurface. However, estimating the associated uncertainties in the process is not trivial. Commonly, uncertainty estimation is performed within the…
Conceptually, partial information decomposition (PID) is concerned with separating the information contributions several sources hold about a certain target by decomposing the corresponding joint mutual information into contributions such…
Probablistic solutions of the so called Schr\"{o}dinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input-output statistics data for a…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…