Related papers: Maximal entropy in the moment body
Human pose estimation (i.e., locating the body parts / joints of a person) is a fundamental problem in human-computer interaction and multimedia applications. Significant progress has been made based on the development of depth sensors,…
The maximal entropy moment method (MEM) is systematic solution of the challenging problem: generating extended hydrodynamic equations valid for both dense and rarefied gases. However, simulating MEM suffers from a computational expensive…
We introduce a numerically exact real-time evolution scheme for quantum impurities in a macroscopically large bath. The algorithm is few-body revealing, namely it identifies the electronic orbitals that can be made inactive (in a trivial…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…
We discuss how well a given convex body B in a real d-dimensional vector space V can be approximated by a set X for which the membership question: ``given an x in V, does x belong to X?'' can be answered efficiently (in time polynomial in…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular semidefinite relaxation of K-means clustering which…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
The partition of a problem into smaller sub-problems satisfying certain properties is often a key ingredient in the design of divide-and-conquer algorithms. For questions related to location, the partition problem can be modeled, in…
Multi-person pose estimation (MPPE) in natural images is key to the meaningful use of visual data in many fields including movement science, security, and rehabilitation. In this paper we tackle MPPE with a bottom-up approach, starting with…
Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…
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…
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…