Related papers: Spectrally Optimized Pointset Configurations
Consider $n \times n$ matrix $A$ and a set $\Lambda$ consisting of $k \le n$ prescribed complex numbers. Lippert (2010) in a challenging article, studied geometrically the spectral norm distance from $A$ to the set $\Lambda$ and constructed…
The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition operators" defined as continuous superpositions of operators of…
In this paper, we use elementary and simple ideas which are based on the significant applications of the power set ring to rebuild and study the patch topology on the prime spectrum from a completely different and new point of view.…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a…
Weights are geometrical degrees of freedom that allow to generalise Lagrangian finite elements. They are defined through integrals over specific supports, well understood in terms of differential forms and integration, and lie within the…
In this work, we consider a method of searching of the direction of a wireless network development (the places of new access points or base stations etc.) optimized with criteria of coverage of important territories and minimum cost of…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
Photonic graph states are important for measurement- and fusion-based quantum computing, quantum networks, and sensing. They can in principle be generated deterministically by using emitters to create the requisite entanglement. Finding…
In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and…
The spectral extremal problem of planar graphs has aroused a lot of interest over the past three decades. In 1991, Boots and Royle [Geogr. Anal. 23(3) (1991) 276--282] (and Cao and Vince [Linear Algebra Appl. 187 (1993) 251--257]…
We introduce and explore a family of vertex-coloring problems which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of…
We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the $l_1$ norm of its entries --- a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this…
This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…
Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ and $\delta'$ types. Assuming rational independence of edge lengths, necessary and sufficient…
The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…
Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of…
A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. The most popular criteria include the A- and D-criteria. Regular graph designs occur in many…