Related papers: Optimal measures for p-frame energies on spheres
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
We devise and explore an iterative optimization procedure for controlling particle populations in particle-in-cell (PIC) codes via merging and splitting of computational macro-particles. Our approach, is to compute an optimal representation…
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…
We present a detailed study of the performance and reliability of design procedures based on energy minimization. The analysis is carried out for model proteins where exact results can be obtained through exhaustive enumeration. The…
We study the sphere packing problem in Euclidean space where we impose additional constraints on the separations of the center points. We prove that any sphere packing in dimension $48$, with spheres of radii $r$, such that no two centers…
In this paper we address a series of open questions about the construction of spatially coupled measurement matrices in compressed sensing. For hardware implementations one is forced to depart from the limiting regime of parameters in which…
We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the pairwise distances are bounded below, and that every closed…
We use linear programming techniques to find points of absolute minimum over the unit sphere $S^{d}$ in $\mathbb R^{d+1}$ of the total potential of a point configuration $\omega_N\subset S^{d}$ which is a spherical $(2m-1)$-design contained…
We provide a general framework for the optimal design of surface energies on networks. We prove sharp bounds for the homogenization of discrete systems describing mixtures of ferromagnetic interactions by constructing optimal…
We derive upper bounds for the potential energy of spherical designs of cardinality close to the Delsarte-Goethals-Seidel bound. These bounds are obtained by linear programming with the use of the Hermite interpolating polynomial of the…
We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the…
Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…
The spectral $p$-norm and nuclear $p$-norm of matrices and tensors appear in various applications albeit both are NP-hard to compute. The former sets a foundation of $\ell_p$-sphere constrained polynomial optimization problems and the…
We investigate the nonlocal energy corresponding to the $p$-oscillation of the unit normal vector for hypersurfaces, or the unit tangent vector for curves. The energy satisfies geometric inequalities with optimal constants $c(n,p)$ and…
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool is a local evaluation of the approximated gradients together with sparsity of the resulting…