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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
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Posts
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portfolio
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publications
On the degree-chromatic polynomial of a tree
Published in International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), 2012
We prove Humpert-Martin’s conjecture on the degree chromatic polynomial of a tree.
Recommended citation: Diego Cifuentes (2012). "On the degree-chromatic polynomial of a tree." DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), Nagoya, Japan. https://dmtcs.episciences.org/3020
Bringing cross-layer MIMO to today’s wireless LANs
Published in ACM SIGCOMM, 2013
Recommended citation: Swarun Kumar, Diego Cifuentes, Shyamnath Gollakota, and Dina Katabi (2013). "Bringing cross-layer MIMO to today’s wireless LANs." Proceedings of the ACM SIGCOMM, Hong Kong, China. https://doi.org/10.1145/2534169.2486034
An efficient tree decomposition method for permanents and mixed discriminants
Published in Linear Algebra and its Applications, 2016
A novel algorithm to compute permanents, mixed discriminants and hyperdeterminants of structured matrices and multidimensional arrays.
Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "An efficient tree decomposition method for permanents and mixed discriminants." Linear Algebra and its Applications. 493:45-81. http://dx.doi.org/10.1016/j.laa.2015.12.004
Exploiting chordal structure in polynomials ideals: A Gröbner bases approach
Published in SIAM J. Discrete Math., 2016
We begin the study of how to exploit chordal structure in computational algebraic geometry, and in particular, for solving polynomial systems.
Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "Exploiting chordal structure in polynomials ideals: A Gröbner bases approach." SIAM J. Discrete Math.. 30(3):1534-1570. http://dx.doi.org/10.1137/151002666
Chordal networks of polynomial ideals
Published in SIAM J. Appl. Algebra Geometry, 2017
We introduce a novel representation of structured polynomial ideals: chordal networks.
Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "Chordal networks of polynomial ideals." SIAM J. Appl. Algebra Geometry. 1(1):73-170. http://dx.doi.org/10.1137/16M106995X
Sampling algebraic varieties for sum of squares programs
Published in SIAM J. Optimization, 2017
A new SOS-based method for optimizing polynomials over algebraic varieties.
Recommended citation: Diego Cifuentes, Pablo Parrilo (2017). "Sampling algebraic varieties for sum of squares programs." SIAM J. Optimization. 27(4):2381-2404. https://doi.org/10.1137/15M1052548
On the local stability of semidefinite relaxations
Published in preprint, 2017
SDP relaxations provide a tractable alternative for polynomial optimization problems. We study sufficient conditions for stability of these relaxations.
Recommended citation: Diego Cifuentes, Sameer Agarwal, Pablo Parrilo, Rekha Thomas (2017). "On the local stability of semidefinite relaxations." arXiv:1710.04287. https://arxiv.org/abs/1710.04287
Sums of squares in Macaulay2
Published in J. Software Algebra Geom., 2018
Introducing a Macaulay2 package for sums of squares problems.
Recommended citation: Diego Cifuentes, Thomas Kahle, Pablo Parrilo (2020). "Sums of squares in Macaulay2." J. Software Algebra Geom. 10(1):17--24 https://doi.org/10.2140/jsag.2020.10.17
On the Complexity of Toric Ideals
Published in preprint, 2019
We investigate the complexity of problems such as normal forms, Gröbner basis and Graver basis
Recommended citation: Diego Cifuentes, Shmuel Onn (2019). "On the Complexity of Toric Ideals." arXiv:1902.01484. https://arxiv.org/abs/1902.01484
On the Burer-Monteiro method for general semidefinite programs
Published in preprint, 2019
We prove global guarantees for the Burer-Monteiro method in general SDPs
Recommended citation: Diego Cifuentes (2021). "On the Burer-Monteiro method for general semidefinite programs." Optimization Letters, https://doi.org/10.1007/s11590-021-01705-4 https://doi.org/10.1007/s11590-021-01705-4
A convex relaxation to compute the nearest structured rank deficient matrix
Published in preprint, 2019
We propose a novel SDP relaxation for computing rank deficient matrices in an affine subspace
Recommended citation: Diego Cifuentes (2019). "A convex relaxation to compute the nearest structured rank deficient matrix." arXiv:1904.09661. https://arxiv.org/abs/1904.09661
Polynomial time guarantees for the Burer-Monteiro method
Published in preprint, 2019
We prove that the Burer-Monteiro method can solve SDPs in polynomial time
Recommended citation: Diego Cifuentes, Ankur Moitra (2019). "Polynomial time guarantees for the Burer-Monteiro method." arXiv:1904.07147. https://arxiv.org/abs/1912.01745
The geometry of SDP exactness in quadratic optimization
Published in Mathematical Programming, 2020
We study the set of objective functions for which SDP relaxations are exact.
Recommended citation: Diego Cifuentes, Corey Harris, Bernd Sturmfels (2020). "The geometry of SDP exactness in quadratic optimization." Mathematical Programming. 182:399-428. https://doi.org/10.1007/s10107-019-01399-8
Voronoi Cells of Varieties
Published in J. Symbolic Computation, 2020
We study the Voronoi decomposition determined by a real algebraic variety.
Recommended citation: Diego Cifuentes, Kristian Ranestad, Bernd Sturmfels, Madeleine Weinstein (2020). "Voronoi Cells of Varieties." J. Symbolic Computation, Special Issue on MEGA 2019. https://doi.org/10.1016/j.jsc.2020.07.009
Efficient sampling from shallow Gaussian quantum-optical circuits with local interactions
Published in preprint, 2020
We prove that a classical computer can efficiently sample from a quantum GBS system given by a shallow, local circuit.
Recommended citation: Haoyu Qi, Diego Cifuentes, Kamil Brádler, Robert Israel, Timjan Kalajdzievski, Nicolás Quesada (2020). "Efficient sampling from shallow Gaussian quantum-optical circuits with local interactions." arXiv:2009.11824. https://arxiv.org/abs/2009.11824
software
Sparse permanents
Matlab, 2016
Download: “zip”, “tar.gz”. Github: sparse-permanents
talks
Chordal structure in polynomial systems
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Chordal structure in polynomial systems
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Chordal structure in polynomial systems
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Sampling varieties for SOS optimization
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Sampling varieties for SOS optimization
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Sampling varieties for SOS optimization
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Chordal networks of polynomial ideals
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Sampling varieties for SOS optimization
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The nearest point to a variety
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On the stability of semidefinite relaxations
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Graphical structure in polynomial ideals
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teaching
Instructor - Colombian Math Olimpiads
Math olympiads, Universidad Antonio Nariño, 2010
Instructor of Algebra, Combinatorics and Geometry at the Colombian Math Olympiads during 2010–2012.
TA of MATE 2230 - Complex variable calculus and numerical analysis
Undergraduate course, Universidad de los Andes, 2010
Mathematical concepts for electrical engineering, such as calculus of complex variable, partial differential equations and numerical methods.
TA of MATE 1105 - Linear Algebra 1
Undergraduate course, Universidad de los Andes, 2011
A first course in linear algebra.
TA of 6.042 - Math for Computer Science
Undergraduate course, MIT EECS, 2014
Elementary discrete mathematics for computer science and engineering. Emphasis on mathematical definitions and proofs as well as on applicable methods.
TA of 6.251 - Introduction to Mathematical Programming
Graduate course, MIT EECS, 2014
Introduction to linear optimization and its extensions, emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems.
TA of 6.256 - Algebraic Techniques and Semidefinite Optimization
Graduate course, MIT EECS, 2016
Research-oriented course, focused on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities, with particular emphasis on the connections with semidefinite optimization.
TA of 6.438 - Algorithms for Inference
Graduate course, MIT EECS, 2017
Graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations.
TA of 18.022 - Vector Calculus (honors)
Undergraduate course, MIT Math, 2018
Calculus of several variables. The honors section puts more focus on mathematical concepts.
TA of 18.200 - Principles of Discrete Applied Mathematics
Undergraduate course, MIT Math, 2019
Topics in discrete applied mathematics, such as probability, information theory, coding theory, generating functions, and linear programming. This is a communication intensive subject.
Instructor of 18.200A - Principles of Discrete Applied Mathematics
Undergraduate course, MIT Math, 2019
Topics in discrete applied mathematics, such as probability, information theory, coding theory, generating functions, and linear programming.
Instructor of 18.031 - System functions and the Laplace transform
Undergraduate course, MIT Math, 2020
Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering.
Instructor of 18.200A - Principles of Discrete Applied Mathematics
Undergraduate course, MIT Math, 2020
Topics in discrete applied mathematics, such as probability, information theory, coding theory, generating functions, and linear programming.