4 Search Results for "Roch, Jean-Louis"


Document
Inferring Diploid 3D Chromatin Structures from Hi-C Data

Authors: Alexandra Gesine Cauer, Gürkan Yardımcı, Jean-Philippe Vert, Nelle Varoquaux, and William Stafford Noble

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)


Abstract
The 3D organization of the genome plays a key role in many cellular processes, such as gene regulation, differentiation, and replication. Assays like Hi-C measure DNA-DNA contacts in a high-throughput fashion, and inferring accurate 3D models of chromosomes can yield insights hidden in the raw data. For example, structural inference can account for noise in the data, disambiguate the distinct structures of homologous chromosomes, orient genomic regions relative to nuclear landmarks, and serve as a framework for integrating other data types. Although many methods exist to infer the 3D structure of haploid genomes, inferring a diploid structure from Hi-C data is still an open problem. Indeed, the diploid case is very challenging, because Hi-C data typically does not distinguish between homologous chromosomes. We propose a method to infer 3D diploid genomes from Hi-C data. We demonstrate the accuracy of the method on simulated data, and we also use the method to infer 3D structures for mouse chromosome X, confirming that the active homolog exhibits a bipartite structure, whereas the active homolog does not.

Cite as

Alexandra Gesine Cauer, Gürkan Yardımcı, Jean-Philippe Vert, Nelle Varoquaux, and William Stafford Noble. Inferring Diploid 3D Chromatin Structures from Hi-C Data. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{cauer_et_al:LIPIcs.WABI.2019.11,
  author =	{Cauer, Alexandra Gesine and Yard{\i}mc{\i}, G\"{u}rkan and Vert, Jean-Philippe and Varoquaux, Nelle and Noble, William Stafford},
  title =	{{Inferring Diploid 3D Chromatin Structures from Hi-C Data}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.11},
  URN =		{urn:nbn:de:0030-drops-110418},
  doi =		{10.4230/LIPIcs.WABI.2019.11},
  annote =	{Keywords: Genome 3D architecture, chromatin structure, Hi-C, 3D modeling}
}
Document
Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms

Authors: Rong Ge and Tengyu Ma

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to n^{\lfloor p/2 \rceil} for a p-th order tensor. Previously no efficient algorithm can decompose 3rd order tensors when the rank is super-linear in the dimension. Using ideas from sum-of-squares hierarchy, we give the first quasi-polynomial time algorithm that can decompose a random 3rd order tensor decomposition when the rank is as large as n^{3/2}/poly log n. We also give a polynomial time algorithm for certifying the injective norm of random low rank tensors. Our tensor decomposition algorithm exploits the relationship between injective norm and the tensor components. The proof relies on interesting tools for decoupling random variables to prove better matrix concentration bounds.

Cite as

Rong Ge and Tengyu Ma. Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 829-849, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{ge_et_al:LIPIcs.APPROX-RANDOM.2015.829,
  author =	{Ge, Rong and Ma, Tengyu},
  title =	{{Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{829--849},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.829},
  URN =		{urn:nbn:de:0030-drops-53394},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.829},
  annote =	{Keywords: sum of squares, overcomplete tensor decomposition}
}
Document
Welfare Maximization with Friends-of-Friends Network Externalities

Authors: Sayan Bhattacharya, Wolfgang Dvorák, Monika Henzinger, and Martin Starnberger

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)


Abstract
Online social networks allow the collection of large amounts of data about the influence between users connected by a friendship-like relationship. When distributing items among agents forming a social network, this information allows us to exploit network externalities that each agent receives from his neighbors that get the same item. In this paper we consider Friends-of-Friends (2-hop) network externalities, i.e., externalities that not only depend on the neighbors that get the same item but also on neighbors of neighbors. For these externalities we study a setting where multiple different items are assigned to unit-demand agents. Specifically, we study the problem of welfare maximization under different types of externality functions. Let n be the number of agents and m be the number of items. Our contributions are the following: (1) We show that welfare maximization is APX-hard; we show that even for step functions with 2-hop (and also with 1-hop) externalities it is NP-hard to approximate social welfare better than (1-1/e). (2) On the positive side we present (i) an O(sqrt n)-approximation algorithm for general concave externality functions, (ii) an O(\log m)-approximation algorithm for linear externality functions, and (iii) an (1-1/e)\frac{1}{6}-approximation algorithm for 2-hop step function externalities. We also improve the result from [6] for 1-hop step function externalities by giving a (1-1/e)/2-approximation algorithm.

Cite as

Sayan Bhattacharya, Wolfgang Dvorák, Monika Henzinger, and Martin Starnberger. Welfare Maximization with Friends-of-Friends Network Externalities. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 90-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{bhattacharya_et_al:LIPIcs.STACS.2015.90,
  author =	{Bhattacharya, Sayan and Dvor\'{a}k, Wolfgang and Henzinger, Monika and Starnberger, Martin},
  title =	{{Welfare Maximization with Friends-of-Friends Network Externalities}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{90--102},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.90},
  URN =		{urn:nbn:de:0030-drops-49066},
  doi =		{10.4230/LIPIcs.STACS.2015.90},
  annote =	{Keywords: network externalities, welfare maximization, approximation algorithms}
}
Document
Adaptive Triangular System Solving

Authors: Jean-Guillaume Dumas, Clément Pernet, and Jean-Louis Roch

Published in: Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006)


Abstract
Large-scale applications and software systems are getting increasingly complex. To deal with this complexity, those systems must manage themselves in accordance with high-level guidance from humans. Adaptive and hybrid algorithms enable this self-management of resources and structured inputs. In this talk, we first propose a classification of the different notions of adaptivity. For us, an algorithm is adaptive (or a poly-algorithm) when there is a choice at a high level between at least two distinct algorithms, each of which could solve the same problem. The choice is strategic, not tactical. It is motivated by an increase of the performance of the execution, depending on both input/output data and computing resources. Then we propose a new adaptive algorithm for the exact simultaneous resolution of several triangular systems over finite fields. The resolution of such systems is e.g. one of the two main operations in block Gaussian elimination. For solving triangular systems over finite fields, the block algorithm reduces to matrix multiplication and achieves the best known algebraic complexity. Exact matrix multiplication, together with matrix factorizations, over finite fields can now be performed at the speed of the highly optimized numerical BLAS routines. This has been established by the FFLAS and FFPACK libraries. In this talk we propose several practicable variants solving these systems: a pure recursive version, a reduction to the numerical dtrsm routine and a delaying of the modulus operation. Then a cascading scheme is proposed to merge these variants into an adaptive sequential algorithm. We then propose a parallelization of this resolution. The adaptive sequential algorithm is not the best parallel algorithm since its recursion induces a dependancy. A better parallel algorithm would be to first invert the matrix and then to multiply this inverse by the right hand side. Unfortunately the latter requires more total operations than the adaptive algorithm. We thus propose a coupling of the sequential algorithm and of the parallel one in order to get the best performances on any number of processors. The resulting cascading is then an adaptation to resources. This shows that the same process has been used both for adaptation to data and to resources. We thus propose a generic framework for the automatic adaptation of algorithms using recursive cascading.

Cite as

Jean-Guillaume Dumas, Clément Pernet, and Jean-Louis Roch. Adaptive Triangular System Solving. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{dumas_et_al:DagSemProc.06271.3,
  author =	{Dumas, Jean-Guillaume and Pernet, Cl\'{e}ment and Roch, Jean-Louis},
  title =	{{Adaptive Triangular System Solving}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.3},
  URN =		{urn:nbn:de:0030-drops-7704},
  doi =		{10.4230/DagSemProc.06271.3},
  annote =	{Keywords: Adaptive and hybrid algorithms; triangular system solving; parallel and sequential degenerations}
}
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