相关论文: Density in Approximation Theory

Model checking and testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, when an…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

We consider the problem of finding the best harmonic or analytic approximant to a given function. We discuss when the best approximant is unique, and what regularity properties the best approximant inherits from the original function. All…

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…

The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…

We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…

I describe the foundation of a Density Functional Theory approach to include pairing correlations, which was applied to a variety of systems ranging from dilute fermions, to neutron stars and finite nuclei. Ground state properties as well…

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory…

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by…

The density functional theory is extended to account for self-bound systems. To this end the Hohenberg-Kohn theorem is formulated for the intrinsic density and a Kohn-Sham like procedure for an $N$--body system is derived using the…

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…

We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation greatly varies. This problem occurs in epidemiology, for example, where different diseases may share similar…

Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…

Exact conditions have long been used to guide the construction of density functional approximations. But hundreds of empirical-based approximations tailored for chemistry are in use, many of which neglect these conditions in their design.…

The many-body problem can in general not be solved exactly, and one of the most prominent approximations is to build perturbation expansions. A huge variety of expansions is possible, which differ by the quantity to be expanded, the…

The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in…