Saugata Basu

Negin Karisani

Discret. Comput. Geom., December, 2024

Efficient Computation of a Semi-Algebraic Basis of the First Homology Group of a Semi-Algebraic Set.

[BibT_eX]

[DOI]

Sarah Percival

Discret. Comput. Geom., September, 2024

Harmonic Persistent Homology.

[BibT_eX]

[DOI]

Nathanael Cox

SIAM J. Appl. Algebra Geom., March, 2024

On the complexity of analyticity in semi-definite optimization.

[BibT_eX]

[DOI]

Ali Mohammad Nezhad

Adv. Appl. Math., 2024

2023

Persistent Homology of Semialgebraic Sets.

[BibT_eX]

[DOI]

Negin Karisani

SIAM J. Appl. Algebra Geom., September, 2023

Quantum Analog of Shannon's Lower Bound Theorem.

[BibT_eX]

[DOI]

CoRR, 2023

Randomized Functions with High Round Complexity.

[BibT_eX]

[DOI]

Hamidreza Amini Khorasgani

Hemanta K. Maji

Hai H. Nguyen

Proceedings of the Theory of Cryptography - 21st International Conference, 2023

2022

On the Central Path of Semidefinite Optimization: Degree and Worst-Case Convergence Rate.

[BibT_eX]

[DOI]

Ali Mohammad Nezhad

SIAM J. Appl. Algebra Geom., 2022

Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets.

[BibT_eX]

[DOI]

Found. Comput. Math., 2022

On the Reeb Spaces of Definable Maps.

[BibT_eX]

[DOI]

Nathanael Cox

Sarah Percival

Discret. Comput. Geom., 2022

Sequents, barcodes, and homology.

[BibT_eX]

[DOI]

Negin Karisani

CoRR, 2022

Geometry of Secure Two-party Computation.

[BibT_eX]

[DOI]

Hamidreza Amini Khorasgani

Hemanta K. Maji

Hai H. Nguyen

Proceedings of the 63rd IEEE Annual Symposium on Foundations of Computer Science, 2022

2021

Hausdorff approximations and volume of tubes of singular algebraic sets.

[BibT_eX]

[DOI]

Antonio Lerario

CoRR, 2021

Inferring COVID-19 Biological Pathways from Clinical Phenotypes via Topological Analysis.

[BibT_eX]

[DOI]

CoRR, 2021

Harmonic Persistent Homology (extended abstract).

[BibT_eX]

[DOI]

Nathanael Cox

Proceedings of the 62nd IEEE Annual Symposium on Foundations of Computer Science, 2021

2020

A Topological Data Analysis Approach on Predicting Phenotypes from Gene Expression Data.

[BibT_eX]

[DOI]

Proceedings of the Algorithms for Computational Biology, 2020

2019

Signal enrichment with strain-level resolution in metagenomes using topological data analysis.

[BibT_eX]

[DOI]

BMC Genom., 2019

2018

Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and Applications.

[BibT_eX]

[DOI]

Anthony Rizzie

Discret. Comput. Geom., 2018

Essential Simplices in Persistent Homology and Subtle Admixture Detection.

[BibT_eX]

[DOI]

Filippo Utro

Proceedings of the 18th International Workshop on Algorithms in Bioinformatics, 2018

2016

Polynomial Partitioning on Varieties of Codimension Two and Point-Hypersurface Incidences in Four Dimensions.

[BibT_eX]

[DOI]

Martín Sombra

Discret. Comput. Geom., 2016

An o-minimal Szemerédi-Trotter theorem.

[BibT_eX]

[DOI]

Orit E. Raz

CoRR, 2016

On the equivariant Betti numbers of symmetric semi-algebraic sets: vanishing, bounds and algorithms.

[BibT_eX]

[DOI]

CoRR, 2016

Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets.

[BibT_eX]

[DOI]

CoRR, 2016

Categorical Complexity.

[BibT_eX]

[DOI]

M. Umut Isik

CoRR, 2016

Characterizing redescriptions using persistent homology to isolate genetic pathways contributing to pathogenesis.

[BibT_eX]

[DOI]

BMC Syst. Biol., 2016

2015

A Complexity Theory of Constructible Functions and Sheaves.

[BibT_eX]

[DOI]

Found. Comput. Math., 2015

On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities.

[BibT_eX]

[DOI]

CoRR, 2015

Topological Signatures for Population Admixture.

[BibT_eX]

[DOI]

Proceedings of the Research in Computational Molecular Biology, 2015

2014

A Baby Step-Giant Step Roadmap Algorithm for General Algebraic Sets.

[BibT_eX]

[DOI]

Found. Comput. Math., 2014

Divide and Conquer Roadmap for Algebraic Sets.

[BibT_eX]

[DOI]

Discret. Comput. Geom., 2014

Polynomial partitioning on varieties and point-hypersurface incidences in four dimensions.

[BibT_eX]

[DOI]

Martín Sombra

CoRR, 2014

Algorithms in Real Algebraic Geometry: A Survey.

[BibT_eX]

[DOI]

CoRR, 2014

2013

A Helly-Type Theorem for Semi-monotone Sets and Monotone Maps.

[BibT_eX]

[DOI]

Andrei Gabrielov

Nicolai N. Vorobjov Jr.

Discret. Comput. Geom., 2013

Bounding the equivariant Betti numbers and computing the generalized Euler-Poincaré characteristic of symmetric semi-algebraic sets.

[BibT_eX]

[DOI]

CoRR, 2013

Spectral Sequences, Exact Couples and Persistent Homology of filtrations.

[BibT_eX]

[DOI]

CoRR, 2013

2012

A Complex Analogue of Toda's Theorem.

[BibT_eX]

[DOI]

Found. Comput. Math., 2012

Refined Bounds on the Number of Connected Components of Sign Conditions on a Variety.

[BibT_eX]

[DOI]

Sal Barone

Discret. Comput. Geom., 2012

2010

Bounding the radii of balls meeting every connected component of semi-algebraic sets.

[BibT_eX]

[DOI]

J. Symb. Comput., 2010

Polynomial Hierarchy, Betti Numbers, and a Real Analogue of Toda's Theorem.

[BibT_eX]

[DOI]

Thierry Zell

Found. Comput. Math., 2010

2009

A bound on the minimum of a real positive polynomial over the standard simplex

[BibT_eX]

[DOI]

Richard Leroy

CoRR, 2009

An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions.

[BibT_eX]

[DOI]

Comb., 2009

2008

Computing the First Betti Number of a Semi-Algebraic Set.

[BibT_eX]

[DOI]

Found. Comput. Math., 2008

Errata for Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time.

[BibT_eX]

[DOI]

Found. Comput. Math., 2008

Computing the Top Betti Numbers of Semialgebraic Sets Defined by Quadratic Inequalities in Polynomial Time.

[BibT_eX]

[DOI]

Found. Comput. Math., 2008

On Projections of Semi-Algebraic Sets Defined by Few Quadratic Inequalities.

[BibT_eX]

[DOI]

Thierry Zell

Discret. Comput. Geom., 2008

A Sharper Estimate on the Betti Numbers of Sets Defined by Quadratic Inequalities.

[BibT_eX]

[DOI]

Michael Kettner

Discret. Comput. Geom., 2008

On the Number of Topological Types Occurring in a Parameterized Family of Arrangements.

[BibT_eX]

[DOI]

Discret. Comput. Geom., 2008

Polynomials that Sign Represent Parity and Descartes' Rule of Signs.

[BibT_eX]

[DOI]

Comput. Complex., 2008

2007

Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials

[BibT_eX]

[DOI]

Dmitrii V. Pasechnik

CoRR, 2007

Algorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open Problems

[BibT_eX]

[DOI]

CoRR, 2007

Combinatorial complexity in O-minimal geometry.

[BibT_eX]

[DOI]

Proceedings of the 39th Annual ACM Symposium on Theory of Computing, 2007

2006

Computing the first few Betti numbers of semi-algebraic sets in single exponential time.

[BibT_eX]

[DOI]

J. Symb. Comput., 2006

Computing the Top Betti Numbers of Semi-algebraic Sets Defined by Quadratic Inequalities in Polynomial Time

[BibT_eX]

[DOI]

CoRR, 2006

An asymptotically tight bound on the number of connected components of realizable sign conditions

[BibT_eX]

[DOI]

CoRR, 2006

Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets

[BibT_eX]

[DOI]

CoRR, 2006

Efficient algorithm for computing the Euler-Poincaré characteristic of a semi-algebraic set defined by few quadratic inequalities.

[BibT_eX]

[DOI]

Comput. Complex., 2006

2005

Computing the euler-poincaré characteristics of sign conditions.

[BibT_eX]

[DOI]

Comput. Complex., 2005

Computing the first Betti number and the connected components of semi-algebraic sets.

[BibT_eX]

[DOI]

Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 2005

Polynomial time algorithm for computing the top Betti numbers of semi-algebraic sets defined by quadratic inequalities.

[BibT_eX]

[DOI]

Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 2005

Computing the Betti Numbers of Arrangements in Practice.

[BibT_eX]

[DOI]

Michael Kettner

Proceedings of the Computer Algebra in Scientific Computing, 8th International Workshop, 2005

2004

On the Realizable Weaving Patterns of Polynomial Curves in R<sup>3</sup>.

[BibT_eX]

[DOI]

Raghavan Dhandapani

Proceedings of the Graph Drawing, 12th International Symposium, 2004

2003

Computing the Betti numbers of arrangements via spectral sequences.

[BibT_eX]

[DOI]

J. Comput. Syst. Sci., 2003

Different Bounds on the Different Betti Numbers of Semi-Algebraic Sets.

[BibT_eX]

[DOI]

Discret. Comput. Geom., 2003

The Combinatorial and Topological Complexity of a Single Cell.

[BibT_eX]

[DOI]

Discret. Comput. Geom., 2003

2002

Computing the betti numbers of arrangements.

[BibT_eX]

[DOI]

Proceedings of the Proceedings on 34th Annual ACM Symposium on Theory of Computing, 2002

1999

New Results on Quantifier Elimination over Real Closed Fields and Applications to Constraint Databases.

[BibT_eX]

[DOI]

J. ACM, 1999

On Bounding the Betti Numbers and Computing the Euler Characteristic of Semi-Algebraic Sets.

[BibT_eX]

[DOI]

Discret. Comput. Geom., 1999

1998

Complexity of Computing Semi-Algebraic Descriptions of the Connected Components of a Semi-Algebraic Set.

[BibT_eX]

[DOI]

Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, 1998

1997

On Computing a Set of Points Meeting Every Cell Defined by a Family of Polynomials on a Variety.

[BibT_eX]

[DOI]

J. Complex., 1997

Uniform Quantifier Elimination and Constraint Query Processing.

[BibT_eX]

[DOI]

Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, 1997

An Improved Algorithm for Quantifier Elimination Over Real Closed Fields.

[BibT_eX]

[DOI]

Proceedings of the 38th Annual Symposium on Foundations of Computer Science, 1997

1996

Algorithms in Semi-Algabraic Geometry.

[BibT_eX]

PhD thesis, 1996

On the Combinatorial and Algebraic Complexity of Quantifier Elimination.

[BibT_eX]

[DOI]

J. ACM, 1996

Computing Roadmaps of Semi-Algebraic Sets (Extended Abstract).

[BibT_eX]

[DOI]

Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, 1996

1994

Design of CAECC-Cellular Automata Based Error Correcting Code.

[BibT_eX]

[DOI]

Dipanwita Roy Chowdhury

Idranil Sen Gupta

Parimal Pal Chaudhuri

IEEE Trans. Computers, 1994

1992

A Novel Scheme for Designing Error Correcting Codes Using Cellular Automata.

[BibT_eX]

[DOI]

Dipanwita Roy Chowdhury