9 papers
Strictly Interlaced Spectral Data for the Weighted Matching Polynomial of a Graph
Shaun Fallat, Johnna Parenteau
Interlacing of the real roots of a weighted matching polynomial for a graph and that of a vertex-deleted subgraph is classical and well-known. In the context of strict interlac…
Determinant Bounds for -Locally Positive Semidefinite Matrices
Shaun Fallat, Samir Mondal, Hristo Sendov
In this framework, the extremal case corresponds to the tightest nontrivial relaxation in this hierarchy, in which every proper principal submatrix is constrained to be positive se…
The Strong Spectral Property and the Jacobian Method for Weighted Laplacian Matrices
Minerva Catral, Shaun Fallat, Himanshu Gupta +1
Strong matrix properties, roughly speaking, refer to generic conditions on a matrix such that its spectral perturbation and pattern perturbation interact nicely to cover a neighbor…
Semigroup automorphisms of total positivity
Projesh Nath Choudhury, Shaun Fallat, Chi-Kwong Li
Totally positive (TP) and totally nonnegative (TN) matrices connect to analysis, mechanics, and to dual canonical bases in reductive groups, by well-known works of Schoenberg, Gant…
Linear Preservers of Real Matrix Classes Admitting a Real Logarithm
Shaun Fallat, Samir Mondal
In real Lie theory, matrices that admit a real logarithm reside in the identity component of the general linear group , wit…
Distance-based Learning of Hypertrees
Shaun Fallat, Kamyar Khodamoradi, David Kirkpatrick +3
We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hyper…