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This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was…

Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of periodic function and a function vanishing at infinity (in the…

We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory…

This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…

Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…

We associate a deformation of Heisenberg algebra to the suitably normalized Yang $R$-matrix and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras which possess the same representation theory as…

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…

Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…

Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal…

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…

This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…

Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…

This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…

This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

We refine a recently-proposed class of local entropic loss functions by restricting the smoothening regularization to only a subset of weights. The new loss functions are referred to as partial local entropies. They can adapt to the…

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…