Related papers: Maximal $d$-spectra via Priestley duality
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
Vertex bisection is a graph partitioning problem in which the aim is to find a partition into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. We are interested in giving…
In recent years, a great deal of emphasis has been placed on achieving the diffraction limit with large aperture telescopes. For a well matched focal-plane instrument, the diffraction limit provides the highest possible angular resolution…
What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a…
The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "minimal" representative of the homotopy class that is well…
We emulate the Rademacher functions on any non-commutative compact group requiring the resulting system to have pairwise disjoint spectra.
In a recent paper of Akhunzhanov and Shatskov the two-dimensional Dirichlet spectrum with respect to Euclidean norm was defined. We consider an analogous definition for arbitrary norms on $\mathbb{R}^2$ and prove that, for each such norm,…
The $\alpha$-spectral radius of a connected graph $G$ is the spectral radius of $A_\alpha$-matrix of $G$. In this paper, we discuss the methods for comparing $\alpha$-spectral radius of graphs. As applications, we characterize the graphs…
This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…
While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…
For pointed compact metric spaces $(X,d)$, we address the biduality problem as to when the space of Lipschitz functions $\mathrm{Lip}_0(X,d)$ is isometrically isomorphic to the bidual of the space of little Lipschitz functions…
We study the free energy of mean-field multi-species spin glasses with convex covariance function. For such models with $D$ species, the Parisi formula is known to be valid, and expresses the limit free energy as a supremum over monotone…
This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…
In this paper we analyze the spectral gap of a weighted graph which is the difference between the smallest positive and largest negative eigenvalue of its adjacency matrix. Such a graph can represent e.g. a chemical organic molecule. Our…
We present here a variational method for maximizing the bandgap in a one-dimensional system where the potential is subject to given constraints. Two specific examples are studied in detail. In the first, we show that if the potential is…
We provide a self-contained exposition of the well-known multifractal formalism for self-similar measures satisfying the strong separation condition. At the heart of our method lies a pair of quasiconvex optimization problems which encode…
It is an interesting, maybe surprising, fact that different dense subspaces of even "nice" topological spaces can have different densities. So, our aim here is to investigate the set of densities of all dense subspaces of a topological…
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic…
A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first…
We study regular graphs whose distance-$2$ graph or distance-$1$-or-$2$ graph is strongly regular. We provide a characterization of such graphs $\Gamma$ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the…