Related papers: Nonanalyticity of the optimized effective potentia…
A number of important modern applications in optimal control can be formulated as open loop control problems in which the underlying dynamical systems are subject to random inputs. These so-called ensemble control problems require the…
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering…
Optimizing a set of functions simultaneously by leveraging their similarity is called multi-task optimization. Current black-box multi-task algorithms only solve a finite set of tasks, even when the tasks originate from a continuous space.…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…
Obvious strategyproofness (OSP) is an appealing concept as it allows to maintain incentive compatibility even in the presence of agents that are not fully rational, e.g., those who struggle with contingent reasoning [Li, 2015]. However, it…
We present a density difference based analysis for a range of orbital--dependent Kohn--Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio…
We propose a simplification of the Optimized Effective Potential (OEP) applied to the Self Interaction Correction (SIC) scheme of Density Functional Theory (DFT). The new scheme fulfills several key formal properties and turns out to be…
We study the {\it quasi-classical limit} of a quantum system composed of finitely many non-relativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding…
The design of algorithms or protocols that are able to align the goals of the planner with the selfish interests of the agents involved in these protocols is of paramount importance in almost every decentralized setting (such as, computer…
We develop an efficient $hp$-finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular arcs. The operators derived from this basis are banded and…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
We compute the effective potential for $\phi^4$ theory with a squeezed coherent state type of construct for the ground state. The method essentially consists in optimising the basis at zero and finite temperatures. The gap equation becomes…
We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We show that, under those deformations, the logarithm of the…
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \begin{eqnarray*} -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u+m|u|^{p-2}u=f(u), &…
Bond-order potentials (BOPs) provide a local and physically transparent description of the interatomic interaction. Here we describe the efficient implementation of analytic BOPs in the BOPfox program and library. We discuss the integration…
This work explores the implications of the exclusivity principle (EP) in the context of quantum and postquantum correlations. We first establish a key technical result demonstrating that given the set of correlations for a complementary…
We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…