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08/10/2022
Computing theta function
Let f: R^n ⟶ R be a positive definite quadratic form and let y ∈ R^n be...
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12/12/2021
A quick estimate for the volume of a polyhedron
Let P be a bounded polyhedron defined as the intersection of the non-neg...
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06/15/2021
When the positive semidefinite relaxation guarantees a solution to a system of real quadratic equations
By solving a positive semidefinite program, one can reduce a system of r...
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03/09/2021
Smoothed counting of 0-1 points in polyhedra
Given a system of linear equations ℓ_i(x)=β_i in an n-vector x of 0-1 va...
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06/16/2020
Testing systems of real quadratic equations for approximate solutions
Consider systems of equations q_i(x)=0, where q_i: R^n ⟶ R, i=1, …, m, ...
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05/22/2020
More on zeros and approximation of the Ising partition function
We consider the problem of computing ∑_x e^f(x), where f(x)=∑_ij a_ijξ_i...
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05/13/2020
A remark on approximating permanents of positive definite matrices
Let A be an n × n positive definite Hermitian matrix with all eigenvalue...
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02/17/2020
Integrating products of quadratic forms
We prove that if q_1, ..., q_m: R^n ⟶ R are quadratic forms in variable...
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07/05/2018
Searching for dense subsets in a graph via the partition function
For a set S of vertices of a graph G, we define its density 0 ≤σ(S) ≤ 1 ...
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06/19/2018
Approximating real-rooted and stable polynomials, with combinatorial applications
Let p(x)=a_0 + a_1 x + ... + a_n x^n be a polynomial with all roots real...
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06/13/2018
Stability and complexity of mixed discriminants
We show that the mixed discriminant of n positive semidefinite n × n rea...
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01/12/2018
Computing permanents of complex diagonally dominant matrices and tensors
We prove that for any λ > 1, fixed in advance, the permanent of an n × n...
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04/10/2002