Related papers: Computational Bounds For Photonic Design
The correct numerical calculation of the resonance characteristics and, principally, the quality factor $Q$ of contemporary photonic and plasmonic resonant systems is of utmost importance, since $Q$ defines the bandwidth and affects…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…
This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…
Grothendieck constants $K_G(d)$ bound the advantage of $d$-dimensional strategies over $1$-dimensional ones in a specific optimisation task. They have applications ranging from approximation algorithms to quantum nonlocality. However, apart…
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
The locally repairable code (LRC) studied in this paper is an $[n,k]$ linear code of which the value at each coordinate can be recovered by a linear combination of at most $r$ other coordinates. The central problem in this work is to…
Dielectric structures composed of many inclusions that manipulate light in ways the bulk materials cannot are commonly seen in the field of metamaterials. In these structures, each inclusion depends on a set of parameters such as location…
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical…
The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances…
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bounds we derive via the linear programming (LP) techniques of…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
We develop a branch-and-bound algorithm for the integer D-optimality problem, a central problem in statistical design theory, based on two convex relaxations, employing variable-bound tightening and fast local-search procedures, testing our…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
The paper is devoted to optimization of resonances associated with 1-D wave equations in inhomogeneous media. The medium's structure is represented by a nonnegative function B. The problem is to design for a given $\alpha \in \R$ a medium…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
The realization of lossless metasurfaces with true chirality crucially requires the fabrication of three-dimensional structures, constraining their feasibility for experiments and hampering practical implementations. Even though the…