Concept
Symmetric polynomial
Related publications (100)
From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem
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In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based ...
2024From Kernel Methods to Neural Networks: A Unifying Variational Formulation
The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...
New York2023A Determinantal Identity for the Permanent of a Rank 2 Matrix
We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...
TAYLOR & FRANCIS INC2022Finite free convolutions of polynomials
We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...
SPRINGER HEIDELBERG2022Binary Perceptron: Efficient Algorithms Can Find Solutions in a RareWell-Connected Cluster
It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically to succeed in fin ...
ASSOC COMPUTING MACHINERY2022