Related papers: Optimal measures for p-frame energies on spheres
We study energy minimization for pair potentials among periodic sets in Euclidean spaces. We derive some sufficient conditions under which a point lattice locally minimizes the energy associated to a large class of potential functions. This…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
We study the problem of minimizing the energy function $M^p(m,n) := \min \sum_{1\le i<j\le m} |\langle v_i, v_j\rangle|^p$, where $v_i$ are unit vectors in $F^n$, $F=\mathbb R$ or $\mathbb C$, $m,n,p>0$ are integers and $p$ is even. This…
The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and…
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
We study approaches for compressing the empirical measure in the context of finite dimensional reproducing kernel Hilbert spaces (RKHSs). In this context, the empirical measure is contained within a natural convex set and can be…
We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…
Knot and link energies can be computed from sets of closed curves in three dimensional space, and each type of knot or link has a minimum energy associated with it. Here, we consider embeddings of links that locally or globally minimize the…
In this paper we prove the existence of an optimal set for the minimization of the $k$-th variational eigenvalue of the $p$-Laplacian among $p$-quasi open sets of fixed measure included in a box of finite measure. An analogous existence…
Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions, and compare them to corresponding results for monomer packings. We…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
We construct good $p$-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type $p$-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen $p$-energy forms in…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…
In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in…
The null space condition for $\ell_1$ minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via $\ell_1$…