Results 41 to 50 of about 54,917 (203)

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Positive Semi-Definite and Sum of Squares Biquadratic Polynomials

Mathematics
Hilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic polynomials, and a psd homogeneous quartic polynomial of four variables ...
Chunfeng Cui, Liqun Qi, Yi Xu
doaj   +1 more source

Exposed faces of semidefinitely representable sets

, 2009
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite.
Netzer, Tim, Plaumann, Daniel, Schweighofer, Markus   +2 more
core   +1 more source

Enabling Stochastic Dynamic Games for Robotic Swarms

Advanced Intelligent Systems, EarlyView.
This paper scales stochastic dynamic games to large swarms of robots through selective agent modeling and variable partial belief space planning. We formulate these games using a belief space variant of iterative Linear Quadratic Gaussian (iLQG). We scale to teams of 50 agents through selective modeling based on the estimated influence of agents ...
Kamran Vakil, Alyssa Pierson
wiley   +1 more source

On the Burer-Monteiro method for general semidefinite programs

, 2020
Consider a semidefinite program (SDP) involving an $n\times n$ positive semidefinite matrix $X$. The Burer-Monteiro method uses the substitution $X=Y Y^T$ to obtain a nonconvex optimization problem in terms of an $n\times p$ matrix $Y$.
Cifuentes, Diego
core   +1 more source

Semidefinite descriptions of the convex hull of rotation matrices [PDF]

, 2014
We study the convex hull of $SO(n)$, thought of as the set of $n\times n$ orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of $SO(n)$ is doubly spectrahedral, i.e. both it and its
Parrilo, Pablo A., Saunderson, James, Willsky, Alan S.   +2 more
core   +1 more source

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, EarlyView.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source

Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix [PDF]

, 2013
The positive semidefinite rank of a nonnegative $(m\times n)$-matrix~$S$ is the minimum number~$q$ such that there exist positive semidefinite $(q\times q)$-matrices $A_1,\dots,A_m$, $B_1,\dots,B_n$ such that $S(k,\ell) = \mbox{tr}(A_k^* B_\ell)$.
Dirk, Oliver Theis, Troy Lee
core  

A Deep Learning Framework for Forecasting Medium‐Term Covariance in Multiasset Portfolios

Journal of Forecasting, EarlyView.
ABSTRACT Forecasting the covariance matrix of asset returns is central to portfolio construction, risk management, and asset pricing. However, most existing models struggle at medium‐term horizons, several weeks to months, where shifting market regimes and slower dynamics prevail.
Pedro Reis, Ana Paula Serra, João Gama
wiley   +1 more source

Lining up a positive semi-definite six-point bootstrap

Journal of High Energy Physics
In this work, we initiate a positive semi-definite numerical bootstrap program for multi-point correlators. Considering six-point functions of operators on a line, we reformulate the crossing symmetry equation for a pair of comb-channel expansions as a ...
António Antunes, Sebastian Harris, Apratim Kaviraj, Volker Schomerus   +3 more
doaj   +1 more source