Related papers: A sparse approximation of the Lieb functional with…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
We study when local reduced density operators, viewed as quantum marginals, can be assembled into a global quantum state with a prescribed Markov structure. The starting point is a canonical logarithmic construction $T(\mathcal R)$, the…
We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamics are ballistic in a rather strong sense; namely, the…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
The goal of this note is to prove a analogue of the Littewood-Paley decomposition for densities of operators and to use it in the context of Lieb-Thirring inequalities.
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…
We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of…
We report a series of calculations testing the predictions of the Tran-Blaha functional for the electronic structure and magnetic properties of condensed systems. We find a general improvement in the properties of semiconducting and…
Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential…
The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a non-empirical tightening of that bound in both universal and electron-number-dependent form. The test functional is PBE. Regarding both…
The $L^1$ optimal transport density $\mu^*$ is the unique $L^\infty$ solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of the $L^1$ -transport energy functional E. In the present…
The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
This paper considers solving the unconstrained $\ell_q$-norm ($0\leq q<1$) regularized least squares ($\ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via…
The local-density approximation (LDA), together with the half-occupation (transition state) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
Current metrological bounds typically assume full control over all particles that are involved in the protocol. Relaxing this assumption we study metrological performance when only limited control is available. As an example, we measure a…
We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as for instance in some problems of optimal transport or density estimation. We show that the…
The Electron Localization Function (ELF) by Becke and Edgecombe [J. Chem. Phys. {\bf 92}, 5397 (1990)] is routinely adopted as a descriptor of atomic shells and covalent bonds. Since the ELF and its related quantities find useful…