Updated: April 11th, 2023 10:13

2021 journal article

LOG-CONCAVE POLYNOMIALS, I: ENTROPY AND A DETERMINISTIC APPROXIMATION ALGORITHM FOR COUNTING BASES OF MATROIDS

*DUKE MATHEMATICAL JOURNAL*, *170*(16), 3459–3504.

Source: Web Of Science

Added: November 29, 2021

2021 article

Log-Concave Polynomials IV: Approximate Exchange, Tight Mixing Times, and Near-Optimal Sampling of Forests

*STOC '21: PROCEEDINGS OF THE 53RD ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING*, pp. 408–420.

author keywords: Counting and Sampling; Near-Linear Time Algorithm; Random Walk; Exchange Property; Discrete Optimization

Source: Web Of Science

Added: July 18, 2022

2021 article

Log-Concave Polynomials in Theory and Applications (Tutorial)

*STOC '21: PROCEEDINGS OF THE 53RD ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING*, pp. 12–12.

author keywords: Log-Concave Polynomials; Matroids; Approximate Counting; Approximate Sampling; High Dimensional Expanders

Source: Web Of Science

Added: July 18, 2022

2021 journal article

Positively hyperbolic varieties, tropicalization, and positroids

*ADVANCES IN MATHEMATICS*, *383*.

author keywords: Stable polynomial; Hyperbolicity; Positroid; Positive Grassmannian; Non-crossing partition; M-convex

Source: Web Of Science

Added: May 24, 2021

2019 journal article

Computing complex and real tropical curves using monodromy

*JOURNAL OF PURE AND APPLIED ALGEBRA*, *223*(12), 5232–5250.

Source: Web Of Science

Added: August 5, 2019

2019 article

Log-Concave Polynomials II: High-Dimensional Walks and an FPRAS for Counting Bases of a Matroid

*PROCEEDINGS OF THE 51ST ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING (STOC '19)*, pp. 1–12.

author keywords: Approximating Counting; Approximate Sampling; High-Dimensional Expanders; Geometry of Polynomials

Source: Web Of Science

Added: April 27, 2020

2019 journal article

Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree

*INTERNATIONAL MATHEMATICS RESEARCH NOTICES*, *2019*(1), 33–54.

Source: Web Of Science

Added: February 4, 2019

2018 article

Log-Concave Polynomials, Entropy, and a Deterministic Approximation Algorithm for Counting Bases of Matroids

*2018 IEEE 59TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS)*, pp. 35–46.

author keywords: matroid; deterministic counting; entropy; log-concave polynomial

Source: Web Of Science

Added: January 21, 2019

2015 conference paper

A small frame and a certificate of its injectivity

*2015 International Conference on Sampling Theory and Applications (SAMPTA)*, 197–200.

Source: NC State University Libraries

Added: August 6, 2018

2015 journal article

An algebraic characterization of injectivity in phase retrieval

*Applied and Computational Harmonic Analysis*, *38*(2), 346–356.

author keywords: Phase retrieval; Algebraic geometry

Source: Crossref

Added: February 24, 2020

2015 journal article

Computing Hermitian determinantal representations of hyperbolic curves

*INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION*, *25*(8), 1327–1336.

author keywords: Hyperbolic polynomials; determinantal representations; interlacing; Hermitian matrices of linear forms

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Hyperbolic polynomials, interlacers, and sums of squares

*Mathematical Programming*, *153*(1), 223–245.

Source: Crossref

Added: December 11, 2020

2015 journal article

Quartic spectrahedra

*MATHEMATICAL PROGRAMMING*, *151*(2), 585–612.

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Determinantal representations of hyperbolic plane curves: An elementary approach

*Journal of Symbolic Computation*, *57*, 48–60.

author keywords: Hyperbolic polynomials; Determinantal representations; Interlacing; Hermitian matrices of linear forms

Source: Crossref

Added: August 28, 2020

2013 journal article

The entropic discriminant

*Advances in Mathematics*, *244*, 678–707.

author keywords: Matroid; Discriminant; Hyperplane arrangement; Ramification locus; Fully real system

Source: Crossref

Added: August 28, 2020

2012 journal article

Real radical initial ideals

*Journal of Algebra*, *352*(1), 392–407.

author keywords: Real algebraic geometry; Tropical geometry; Initial ideals; Semialgebraic sets; Preorders; Quadractic modules

Source: Crossref

Added: December 11, 2020

2012 journal article

The Central Curve in Linear Programming

*Foundations of Computational Mathematics*, *12*(4), 509–540.

author keywords: Linear programming; Central path; Hyperplane arrangement; Interior-point methods; Complementary slackness; Matroid; Tutte polynomial; Hyperbolic polynomial; Gauss map; Degree; Curvature; Total curvature; Projective variety; Grobner basis; Prime ideal

Source: Crossref

Added: August 28, 2020

2011 journal article

Edges of the Barvinok–Novik Orbitope

*Discrete & Computational Geometry*, *46*(3), 479–487.

author keywords: Moment curve; Toeplitz operator; Orbitope; Convex hull of a curve

Source: Crossref

Added: January 5, 2021

2011 journal article

Quartic curves and their bitangents

*Journal of Symbolic Computation*, *46*(6), 712–733.

author keywords: Plane curves; Bitangents; Determinantal representations; Sums of squares; Semidefinite programming; Gale duality

Source: Crossref

Added: August 28, 2020

2009 journal article

Lower bounds for optimal alignments of binary sequences

*Discrete Applied Mathematics*, *157*(15), 3341–3346.

author keywords: Sequence alignment; Parametric analysis; Computational biology

Source: Crossref

Added: January 5, 2021