Results 1 to 10 of about 1,163,661 (206)
Sum-of-squares geometry processing [PDF]
ACM Transactions on Graphics, 2021 Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra, joined with an ...
Z. Marschner +3 more
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Rounding sum-of-squares relaxations [PDF]
Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2014 We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof system to transform a *combining algorithm* -- an algorithm that maps a distribution over solutions into a ...
Barak, Boaz +2 more
openaire +9 more sources
A Sum-of-Squares and Semidefinite Programming Approach for Maximum Likelihood DOA Estimation [PDF]
Sensors, 2016 Direction of arrival (DOA) estimation using a uniform linear array (ULA) is a classical problem in array signal processing. In this paper, we focus on DOA estimation based on the maximum likelihood (ML) criterion, transform the estimation problem into a ...
Shu Cai, Quan Zhou, Hongbo Zhu
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Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction [PDF]
G3: Genes, Genomes, Genetics, 2017 Genomic prediction is a statistical method to predict phenotypes of polygenic traits using high-throughput genomic data. Most diseases and behaviors in humans and animals are polygenic traits. The majority of agronomic traits in crops are also polygenic.
Shizhong Xu
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Sum of squares lower bounds for refuting any CSP [PDF]
Symposium on the Theory of Computing, 2017 Let P:{0,1}k → {0,1} be a nontrivial k-ary predicate. Consider a random instance of the constraint satisfaction problem (P) on n variables with Δ n constraints, each being P applied to k randomly chosen literals. Provided the constraint density satisfies
Pravesh Kothari +3 more
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Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers
Complexity, 2019 The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to
Fanwei Meng +3 more
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Some new relations between T(a₁,a₂,a₃,a₄,a₅; n) and N(a₁,a₂,a₃,a₄,a₅; n) [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let N(a₁,a₂,a₃,a₄,a₅; n) and T(a₁,a₂,a₃,a₄,a₅; n) count the representations of n as a₁x₁²+a₂x₂²+a₃x₃²+a₄x₄²+a₅x₅² and a₁X₁(X₁+1)/2+a₂X₂(X₂+1)/2+a₃X₃(X₃+1)/2+a₄X₄(X₄+1)/2+a₅X₅(X₅+1)/2, respectively, where a₁,a₂,a₃,a₄,a₅ are positive integers, x₁,x₂,x₃,x₄ ...
Vandna, Mandeep Kaur
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Efficient mean estimation with pure differential privacy via a sum-of-squares exponential mechanism [PDF]
Symposium on the Theory of Computing, 2021 We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution with bounded covariance from Õ(d) independent samples subject to pure differential privacy.
Samuel B. Hopkins +2 more
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Exponential Convergence of Sum-of-Squares Hierarchies for Trigonometric Polynomials [PDF]
SIAM Journal on Optimization, 2022 We consider the unconstrained optimization of multivariate trigonometric polynomials by the sum-of-squares hierarchy of lower bounds. We first show a convergence rate of $O(1/s^2)$ for the relaxation with degree $s$ without any assumption on the ...
F. Bach, Alessandro Rudi
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Safety Index Synthesis via Sum-of-Squares Programming [PDF]
American Control Conference, 2022 Control systems often need to satisfy strict safety requirements. Safety index provides a handy way to evaluate the safety level of the system and derive the resulting safe control policies.
Weiye Zhao +4 more
semanticscholar +1 more source