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Documents authored by Chalkis, Apostolos

Document
DOI: 10.4230/LIPIcs.SoCG.2021.21
Geometric Algorithms for Sampling the Flux Space of Metabolic Networks

Authors: Apostolos Chalkis, Vissarion Fisikopoulos, Elias Tsigaridas, and Haris Zafeiropoulos

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
Systems Biology is a fundamental field and paradigm that introduces a new era in Biology. The crux of its functionality and usefulness relies on metabolic networks that model the reactions occurring inside an organism and provide the means to understand the underlying mechanisms that govern biological systems. Even more, metabolic networks have a broader impact that ranges from resolution of ecosystems to personalized medicine. The analysis of metabolic networks is a computational geometry oriented field as one of the main operations they depend on is sampling uniformly points from polytopes; the latter provides a representation of the steady states of the metabolic networks. However, the polytopes that result from biological data are of very high dimension (to the order of thousands) and in most, if not all, the cases are considerably skinny. Therefore, to perform uniform random sampling efficiently in this setting, we need a novel algorithmic and computational framework specially tailored for the properties of metabolic networks. We present a complete software framework to handle sampling in metabolic networks. Its backbone is a Multiphase Monte Carlo Sampling (MMCS) algorithm that unifies rounding and sampling in one pass, obtaining both upon termination. It exploits an improved variant of the Billiard Walk that enjoys faster arithmetic complexity per step. We demonstrate the efficiency of our approach by performing extensive experiments on various metabolic networks. Notably, sampling on the most complicated human metabolic network accessible today, Recon3D, corresponding to a polytope of dimension 5335, took less than 30 hours. To our knowledge, that is out of reach for existing software.
Cite as

Apostolos Chalkis, Vissarion Fisikopoulos, Elias Tsigaridas, and Haris Zafeiropoulos. Geometric Algorithms for Sampling the Flux Space of Metabolic Networks. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chalkis_et_al:LIPIcs.SoCG.2021.21,
  author =	{Chalkis, Apostolos and Fisikopoulos, Vissarion and Tsigaridas, Elias and Zafeiropoulos, Haris},
  title =	{{Geometric Algorithms for Sampling the Flux Space of Metabolic Networks}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.21},
  URN =		{urn:nbn:de:0030-drops-138201},
  doi =		{10.4230/LIPIcs.SoCG.2021.21},
  annote =	{Keywords: Flux analysis, metabolic networks, convex polytopes, random walks, sampling}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.19
Practical Volume Computation of Structured Convex Bodies, and an Application to Modeling Portfolio Dependencies and Financial Crises

Authors: Ludovic Calès, Apostolos Chalkis, Ioannis Z. Emiris, and Vissarion Fisikopoulos

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
We examine volume computation of general-dimensional polytopes and more general convex bodies, defined as the intersection of a simplex by a family of parallel hyperplanes, and another family of parallel hyperplanes or a family of concentric ellipsoids. Such convex bodies appear in modeling and predicting financial crises. The impact of crises on the economy (labor, income, etc.) makes its detection of prime interest for the public in general and for policy makers in particular. Certain features of dependencies in the markets clearly identify times of turmoil. We describe the relationship between asset characteristics by means of a copula; each characteristic is either a linear or quadratic form of the portfolio components, hence the copula can be constructed by computing volumes of convex bodies. We design and implement practical algorithms in the exact and approximate setting, we experimentally juxtapose them and study the tradeoff of exactness and accuracy for speed. We analyze the following methods in order of increasing generality: rejection sampling relying on uniformly sampling the simplex, which is the fastest approach, but inaccurate for small volumes; exact formulae based on the computation of integrals of probability distribution functions, which are the method of choice for intersections with a single hyperplane; an optimized Lawrence sign decomposition method, since the polytopes at hand are shown to be simple with additional structure; Markov chain Monte Carlo algorithms using random walks based on the hit-and-run paradigm generalized to nonlinear convex bodies and relying on new methods for computing a ball enclosed in the given body, such as a second-order cone program; the latter is experimentally extended to non-convex bodies with very encouraging results. Our C++ software, based on CGAL and Eigen and available on github, is shown to be very effective in up to 100 dimensions. Our results offer novel, effective means of computing portfolio dependencies and an indicator of financial crises, which is shown to correctly identify past crises.
Cite as

Ludovic Calès, Apostolos Chalkis, Ioannis Z. Emiris, and Vissarion Fisikopoulos. Practical Volume Computation of Structured Convex Bodies, and an Application to Modeling Portfolio Dependencies and Financial Crises. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cales_et_al:LIPIcs.SoCG.2018.19,
  author =	{Cal\`{e}s, Ludovic and Chalkis, Apostolos and Emiris, Ioannis Z. and Fisikopoulos, Vissarion},
  title =	{{Practical Volume Computation of Structured Convex Bodies, and an Application to Modeling Portfolio Dependencies and Financial Crises}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.19},
  URN =		{urn:nbn:de:0030-drops-87328},
  doi =		{10.4230/LIPIcs.SoCG.2018.19},
  annote =	{Keywords: Polytope volume, convex body, simplex, sampling, financial portfolio}
}
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