Related papers: Certifying the Potential Energy Landscape
In this paper we show that approximation can help reduce the space used for self-stabilization. In the classic \emph{state model}, where the nodes of a network communicate by reading the states of their neighbors, an important measure of…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some…
We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective…
In this paper, we simulate sample paths of a class of symmetric $\alpha$-stable processes using their series expression. We will develop a result in the approximation of shot-noise series. And finally, we will get a convergence rate for the…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
The self-consistent random-phase approximation (SCRPA) is reexamined within a multilevel-pairing model with double degeneracy. It is shown that the expressions for occupation numbers used in the original version of SCRPA violate the…
Motivated by group-project distribution, we introduce and study stable matching under the constraint of applicants needing to share a location to be matched with the same institute, which we call the Location-Restricted Stable Matching…
Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
By means of molecular dynamics simulations, we study the stationary points of the potential energy in a Lennard-Jones liquid, giving a purely geometric characterization of the energy landscape of the system. We find a linear relation…
This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are…
The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks…
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving…
Sum-of-norms clustering is a clustering formulation based on convex optimization that automatically induces hierarchy. Multiple algorithms have been proposed to solve the optimization problem: subgradient descent by Hocking et al., ADMM and…