相关论文: A Kruskal-Katona type result and applications

The phenomenon of shadowing of nuclear structure functions at small values of Bjorken-$x$ is analyzed. First, multiple scattering is discussed as the underlying physical mechanism. In this context three different but related approaches are…

In this work we focus on the problem of colorization for image compression. Since color information occupies a large proportion of the total storage size of an image, a method that can predict accurate color from its grayscale version can…

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\u{\i} cone compression-expansion type methodologies and Schauder-type ones. In particular we…

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…

A novel covariant formalism for the treatment of the transfer and Compton scattering of partially polarized light is presented. This was initially developed to aid in the computation of relativistic corrections to the polarization generated…

An abstract simplicial complex is said to be $d$-representable if it records the intersection pattern of a collection of convex sets in $\mathbb{R}^d$. In this paper, we show that $d$-representability of a simplicial complex is equivalent…

Cluster analysis has become one of the most exercised research areas over the past few decades in computer science. As a consequence, numerous clustering algorithms have already been developed to find appropriate partitions of a set of…

The $k$-subset sum problem over finite fields is a classical NP-complete problem.Motivated by coding theory applications, a more complex problem is the higher $m$-th moment $k$-subset sum problem over finite fields. We show that there is a…

This paper considers the minimization problem of relaxed submodular functions. For a positive integer $k$, a set function is called $k$-distant submodular if the submodular inequality holds for every pair whose symmetric difference is at…

In this short note, we review several one-dimensional problems such as those involving linear Schroedinger equation, variable-coefficient Helmholtz equation, Zakharov-Shabat system and Kubelka-Munk equations. We show that they all can be…

We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit…

We give an effective criterion for the identifiability of additive decompositions of homogeneous forms of degree $d$ in a fixed number of variables. Asymptotically for large $d$ it has the same order of the Kruskal's criterion adapted to…

We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely…

We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…

In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first principal result -- the lifting theorem for multitensors --…

Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…

We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…

A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a…

Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the…