DOCSLIB.ORG

Sébastien Roch

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Sébastien Roch S´ebastienRoch - Vita - October 27, 2020 1 S´ebastien Roch Department of Mathematics University of Wisconsin{Madison 480 Lincoln Dr., Madison, WI 53706 [email protected] Employment Professor (with tenure), Department of Mathematics, UW{Madison (2016-) - Other affiliations: Affiliate Faculty, Department of Statistics, UW{Madison; Member, Insti- tute for Foundations of Data Science (NSF TRIPODS Phase II) Associate Professor (with tenure), Department of Mathematics, UW{Madison (2013-) Tenure-track Assistant Professor, Department of Mathematics, UW{Madison (2012-2013) Tenure-track Assistant Professor, Department of Mathematics, UCLA (2009-2012) - Other affiliations: Core Member, UCLA Interdepartmental Program in Bioinformatics Post-Doctoral Researcher, Microsoft Research New England, Cambridge, MA (2008-2009) Post-Doctoral Researcher, Microsoft Research, Theory Group, Redmond, WA (2007-2008) Education Ph.D., Statistics, UC Berkeley (2007) M.Sc.A., Applied Mathematics, Polytechnique de Montr´eal,Canada (2003) B.Eng., Engineering Physics, Polytechnique de Montr´eal,Canada (2002) Dipl^omed'Ing´enieur[Bachelor of Engineering], Ecole Polytechnique, France (2001) Honors Vilas Associates Award (2019-2021) Best Paper Award at RECOMB 2018 2018 Simons Fellow in Mathematics Honorable Mention { 2018 Marcus W. Feldman Prize in Theoretical Population Biology NSF CAREER Award (2012-2017) Kavli Fellow, National Academy of Sciences (2014, 2017) Invited Address, AMS Central Fall Sectional Meeting (2015) Alfred P. Sloan Research Fellowship (2012-2014) S´ebastienRoch - Vita - October 27, 2020 2 Funding Current NSF grant DMS-2023239 (2020-2025), \TRIPODS: Institute for Foundations of Data Sci- ence," co-PI, $4,583,262 (overall institute budget: $12.5 million) Vilas Associates Award (2019-2021) NSF grant DMS-1916378 (2019-2022), \Scalable Statistical Inference in Small-World Net- works," PI, $299,999 NSF grant DMS-1902892 (2019-2022), \Scalable Model-Based Reconstruction of Network Evolution," co-PI, $724,239 NSF grant CCF-1740707 (2017-2021), \TRIPODS: Institute for Foundations of Data Sci- ence," co-PI, $1,499,523 Past NSF grant DMS-1614242 (2016-2020), \Probability Questions in Phylogenetics," PI, $194,000 Simons Fellowship (2018-2019) SQuaRE on \Mathematical modeling of adaptive biological networks," American Institute of Mathematics (AIM), jointly with Karen Alim, Eleni Katifori, Marcus Roper (2015-2016) NSF grant DMS-1149312 (2012-2017), \CAREER: Phylogenomics - New Computational Methods through Stochastic Modeling and Analysis," PI, $444,405 Alfred P. Sloan Research Fellowship (2012-2014) NSF grant DMS-1007144 (2010-2013), \Probabilistic Techniques in Mathematical Phyloge- netics," PI, $171,000 Academic Visits Fall 2018-Spring 2019: Wisconsin Institute of Discovery, Madison, WI Spring 2017: Research member, MSRI, Berkeley Spring 2014: Long-term visitor, Simons Institute for the Theory of Computing, UC Berkeley Fall 2011: Program organizer, Institute for Pure and Applied Mathematics (IPAM), UCLA Fall 2009: Visiting scholar, Institute for Pure and Applied Mathematics (IPAM), UCLA September 2007: Visitor, Phylogenetics Programme, Isaac Newton Institute, Cambridge, UK Summer 2006: Intern, Microsoft Research, Redmond, WA Summer 2005: Visitor, Program for Evolutionary Dynamics, Harvard Summer 2004: Visitor, Computer Science and Artificial Intelligence Laboratory (CSAIL), MIT S´ebastienRoch - Vita - October 27, 2020 3 Professional Activities Boards Governing Board and Site Committee, Institute for Foundations of Data Science (TRIPODS Phase II), University of Washington/UW{Madison/UCSC/UChicago (2020-) Executive Committee, Institute for Foundations of Data Science (TRIPODS Phase I), UW{ Madison (2017-2020) Associate Editor, Annals of Applied Probability (2013-2018) Organizational Work Scientific Committee, 41st Midwest Probability Colloquium, Northwestern University (Oc- tober 2019) Co-organizer, Special Session on \Recent Trends in the Mathematics of Data," AMS Fall Central Sectional Meeting, UW{Madison (September 2019) Organizer, Invited Session on \Biomedical Applications of Stochastic Processes," 41st Con- ference on Stochastic Processes and their Applications (SPA) (July 2019) Organizing committee, Summer School on \Fundamentals of Data Analysis," Institute for Foundations of Data Science, UW{Madison (July 2018) Co-organizer, Special session on \Probability Theory," AMS Central Fall Sectional Meeting (October 2015) Co-organizer, Workshop on \Multiple Sequence Alignment," IPAM (January 2015) Co-organizer, Second reunion workshop on \High-Throughput Genomics," Lake Arrowhead, IPAM (June 2014) Co-organizer, First reunion workshop on \High-Throughput Genomics," Lake Arrowhead, IPAM (June 2013) Organizing committee, Long program on \Mathematical Approaches in High-Throughput Genomics," IPAM (Fall 2011) Chair, Workshop on \Evolutionary Genomics," IPAM (November 2011) Co-organizer, Tutorials on \High-Throughput Genomics," IPAM (September 2011) Co-organizer, Special session on \Probability and Related Fields," AMS Western Fall Sec- tional Meeting (October 2010) Co-organizer, Computational Aspects of Biological Information Workshop, Microsoft Re- search (December 2007) Organizer, Session on \Bioinformatics," INFORMS Annual Meeting (October 2008) Program Committees S´ebastienRoch - Vita - October 27, 2020 4 Great Lakes Bioinformatics Conference (GLBIO), 2019 Workshop on Algorithms in Bioinformatics (WABI), 2019 Annual International Conference on Intelligent Systems for Molecular Biology/European Conference on Computational Biology (ISMB/ECCB), 2013-2016 ACM-SIAM Symposium on Discrete Algorithms (SODA), 2009 Reviewer Journals: Algorithms for Molecular Biology, American Mathematical Monthly, Annals of Ap- plied Probability, Annals of Combinatorics, Annals of Probability, Annals of Statistics, Ap- plied Mathematics Letters, Bioinformatics, Biometrika, Computational Biology and Chem- istry, Electronic Communications in Probability, Electronic Journal in Probability, Genome Biology and Evolution, IEEE/ACM Transactions on Computational Biology and Bioinfor- matics, IEEE Transactions on Automatic Control, Journal of Applied Probability, Journal of Classification, Journal of Computer and System Sciences, Journal of Mathematical Biology, Journal of Theoretical Biology, Molecular Biology and Evolution, Nature Communications, PLOS ONE, PLOS Computational Biology, Random Structures and Algorithms, Science, SIAM Journal on Applied Algebra and Geometry, SIAM Journal on Computing, SIAM Jour- nal on Discrete Mathematics, Soft Computing, Systematic Biology, Theoretical Population Biology. Conferences: ACM Conference on Electronic Commerce (EC), ACM-SIAM Symposium on Discrete Algorithms (SODA), ACM Symposium on Theory of Computing (STOC), Algo- rithmic Learning Theory (ALT), Conference on Learning Theory (COLT), IEEE Sympo- sium on Foundations of Computer Science (FOCS), Great Lakes Bioinformatics Conference (GLBIO), International Conference on Intelligent Systems for Molecular Biology (ISMB), Innovations in Theoretical Computer Science (ITCS), Pacific Symposium on Biocomputing (PSB), International Workshop on Randomized Techniques in Computation (RANDOM), Annual International Conference on Research in Computational Molecular Biology (RE- COMB), Workshop on Algorithms in Bioinformatics (WABI). University/Departmental Committees UW{Madison: served on Awards Committee, Budget Committee, Cluster Hire Search Com- mittee Chair, Colloquium Committee, Early Undergraduate Program Committee, Faculty Affairs Committee, Faculty Senate, Fundraising/Newsletter Committee, Graduate Admis- sions Committee, Graduate Program Committee, Hiring Committee, L&S Data Science Ma- jor Working Group, Data Science Major Program Committee, Salary Committee, Statistics Liaison, Undergraduate Advising Committee UCLA: served on Analysis Qualifying Exam Committee, Bioinformatics Interdepartmen- tal Program, Graduate Studies Committee, Graduate Admissions Committee, Mathemat- ics/Economics Interdepartmental Program, Program in Computing Committee, Staff Search Committee, UCLA Systems and Integrative Biology (SIB) Training Program S´ebastienRoch - Vita - October 27, 2020 5 Courses Taught UW{Madison Fall 2020: MATH 833 { Topics in the Theory of Probability (Graduate) Fall 2020: MATH 535 { Mathematical Methods in Data Science (Undergraduate) Spring 2020: MATH 535 { Mathematical Methods in Data Science (Undergraduate) Fall 2019: MATH 431 { Introduction to the Theory of Probability (Undergraduate) Fall 2019: 2×MATH 431 { Introduction to the Theory of Probability (Undergraduate) Spring 2018: MATH 734 { Theory of Probability II (Graduate) Fall 2017: MATH 833 { Topics in the Theory of Probability (Graduate) Fall 2017: MATH 431 { Introduction to the Theory of Probability (Undergraduate) Fall 2016: 2×MATH 632 { Introduction to Stochastic Processes (Undergraduate) Spring 2016: 2×MATH 632 { Introduction to Stochastic Processes (Undergraduate) Fall 2015: MATH 632 { Introduction to Stochastic Processes (Undergraduate) Spring 2015: MATH 632 { Introduction to Stochastic Processes (Undergraduate) Fall 2014: MATH 833 { Topics in the Theory of Probability (Graduate) Fall 2014: MATH 632 { Introduction to Stochastic Processes (Undergraduate) Fall 2013: MATH 331 { Introduction to Probability and Markov Chain modelling (Under- graduate) Fall 2013: MATH 632 { Introduction to Stochastic Processes (Undergraduate) Fall 2013: MATH 733 { Theory of Probability I (Graduate) Fall 2012: MATH 213 { Calculus and Introduction to Differential Equations
Load more

Recommended publications
  • Of the American Mathematical Society August 2017 Volume 64, Number 7
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves
    [Show full text]
  • Downloads Over 8,000)
    Volume 47 • Issue 1 IMS Bulletin January/February 2018 National Academy new member The US National Academy of Medicine (NAM) has announced the election of 70 reg- CONTENTS ular members and 10 international members. Among them is Nicholas Patrick Jewell, 1 National Academy of University of California, Berkeley. Medicine elects Jewell Election to the Academy is considered one of the highest honors in the fields of 2 Members’ news: Nick Horton, health and medicine, recognizing individuals who have made major contributions to Eric Kolaczyk, Hongzhe Li, the advancement of the medical sciences, health care, and public health. A diversity Runze Li, Douglas Simpson, of talent among NAM’s membership is Greg Lawler, Mike Jordan, Mir assured by its Articles of Organization, Masoom Ali which stipulate that at least one-quarter 3 Journal news: EJP, ECP, Prob of the membership is selected from fields Surveys; OECD guidelines outside the health professions, for exam- 4 Takis Konstantopoulos: new ple, from law, engineering, social sciences, column and the humanities—and statistics. The newly elected members bring 6 Recent papers: Electronic Journal of Probability; Electronic NAM’s total membership to 2,127 and Communications in Probability the number of international members to 172. 11 Special Invited Lecturers; IMS Fellow Nicholas P. Jewell is New Textbook Professor of Biostatistics and Statistics 12 Obituary: Ron Getoor at the University of California, Berkeley. 13 IMS Awards Since arriving at Berkeley in 1981, he has held various academic and administrative 15 Student Puzzle Corner 19; New Researcher Award positions, most notably serving as Vice Provost from 1994 to 2000.
    [Show full text]
  • "Real Analysis in Computer Science" (Fall 2013) Final Program Report Elchanan Mossel and Luca Trevisan (Organizers) Ba
    "Real Analysis in Computer Science" (Fall 2013) Final Program Report Elchanan Mossel and Luca Trevisan (Organizers) Background Sophisticated tools in Real Analysis have played an increasingly central role in a number of areas in theoretical computer science over the past thirty years. As a first example, the discrete Fourier expansion can be used to analyze combinatorial problems of a discrete nature using the language and techniques of real analysis. Such Fourier analysis techniques have played a key role since the 1980s in the development of computational learning theory (PAC learning) and property testing, and, in complexity theory, they have led to circuit lower bounds and to probabilistically checkable proof (PCP) constructions and hardness of approximation results. More modern mathematical tools developed to study Banach space properties of Gaussian processes in the 1960s and 70s (in particular, the idea of hypercontractivity from functional analysis) were introduced in computer science by Kahn, Kalai and Linial in 1988. This circle of ideas played a key role in subsequent developments in coding theory, metric embeddings of graphs, and hardness of approximation of optimization problems. Finally, concepts from Gaussian geometry and Gaussian isoperimetric theory have played an implicit role in the analysis of semi-definite programs, starting with the work of Goemans and Williamson in 1995. A rigorous theory connecting optimization problems, semi-definite programs and hardness of approximation to Gaussian geometry and isoperimetry was established in the “Unique Games” framework introduced by Khot in 2002, and was further developed via the non-linear invariance principle of Mossel, O’Donnell and Oleszkiewicz (2005) and the geometry of Gaussian space.
    [Show full text]
  • Information Theory and Concentration Phenomena
    IMA Workshops April 13-17, 2015 Information Theory and Concentration Phenomena ORGANIZERS SPEAKERS Sergey Bobkov, University of Minnesota, Twin Cities Andrew Barron, Yale University Michel Ledoux, Université de Toulouse (Paul Ronen Eldan, University of Washington Sabatier) Larry Goldstein, University of Southern California Joel Tropp, California Institute of Technology Oliver Johnson, University of Bristol Bo’az Klartag, Tel Aviv University Holger Kösters, Universität Bielefeld Concentration phenomena have come to play Victoria Kostina, California Institute of a significant role in probability, statistics, and Technology Rafal Latala, University of Warsaw computer science. Ideas from information theory Katalin Marton, Hungarian Academy of and geometry can be used to establish new Sciences (MTA) types of concentration inequalities. At the same Elizabeth Meckes, Case Western time, concentration results can lead to a deeper Reserve University understanding of information theory and geometry. Emanuel Milman, Technion-Israel Institute of Technology Although these principles are well established, there Andrea Montanari, Stanford University have been many striking advances in recent years. Elchanan Mossel, University of Researchers have made significant progress on California, Berkeley subadditivity of quantum information, quantitative Roberto Oliveira, Institute of Pure and entropy power inequalities, and concentration Applied Mathematics (IMPA) properties for random variables that have many Grigorios Paouris, Texas A & M University symmetries
    [Show full text]
  • Presentation of the Austrian Mathematical Society - E-Mail: [email protected] La Rochelle University Lasie, Avenue Michel Crépeau B
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Features S E European A Problem for the 21st/22nd Century M M Mathematical Euler, Stirling and Wallis E S Society History Grothendieck: The Myth of a Break December 2019 Issue 114 Society ISSN 1027-488X The Austrian Mathematical Society Yerevan, venue of the EMS Executive Committee Meeting New books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. Todd Fisher (Brigham Young University, Provo, USA) and Boris Hasselblatt (Tufts University, Medford, USA) Hyperbolic Flows (Zürich Lectures in Advanced Mathematics) ISBN 978-3-03719-200-9. 2019. 737 pages. Softcover. 17 x 24 cm. 78.00 Euro The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consulta- tion with experts is often needed to find them. This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments.
    [Show full text]
  • Mathematics People
    NEWS Mathematics People Mann Receives Speh Awarded Duszenko Award Noether Lectureship Kathryn Mann of Cornell University Birgit Speh of Cornell University has has been awarded the 2019 Kamil been named the 2020 Noether Lec- Duszenko Award for her work in turer by the Association for Women topology, geometry, geometric group in Mathematics (AWM) and the AMS. theory, dynamics, and other areas She will deliver the prize lectures at of mathematics. Her work involves the 2020 Joint Mathematics Meet- actions of infinite groups on mani- ings. folds and the moduli spaces of such Speh is known for her work on the actions: character varieties, spaces of representation theory of reductive Kathryn Mann flat bundles or foliations, and spaces Birgit Speh Lie groups and its relationship to of left-invariant orders on groups. automorphic forms and the coho- Some of her work involves the relationship between the mology of arithmetic groups. Her research has explored algebraic and topological structure of diffeomorphism and connections between unitary representations, automorphic homeomorphism groups, the large-scale geometry of such forms, and the geometry of locally symmetric spaces. In groups (e.g. subgroup distortion and dynamical conse- recent work Speh has studied restrictions of representations quences of this), and rigidity phenomena for group actions, of reductive groups to noncompact reductive subgroups. often arising from some geometric structure. Mann received This work on “symmetry breaking” has led, in joint work her PhD from the University of Chicago in 2014 under with Kobayashi, to proofs of conjectures of Gross–Prasad the supervision of Benson Farb. She has held positions at for some pairs of orthogonal groups.
    [Show full text]
  • January 2019 Volume 66 · Issue 01
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) Notices ofof the American MathematicalMathematical Society January 2019 Volume 66, Number 1 The cover art is from the JMM Sampler, page 84. AT THE AMS BOOTH, JMM 2019 ISSN 0002-9920 (print) ISSN 1088-9477 (online) Notices of the American Mathematical Society January 2019 Volume 66, Number 1 © Pomona College © Pomona Talk to Erica about the AMS membership magazine, pick up a free Notices travel mug*, and enjoy a piece of cake. facebook.com/amermathsoc @amermathsoc A WORD FROM... Erica Flapan, Notices Editor in Chief I would like to introduce myself as the new Editor in Chief of the Notices and share my plans with readers. The Notices is an interesting and engaging magazine that is read by mathematicians all over the world. As members of the AMS, we should all be proud to have the Notices as our magazine of record. Personally, I have enjoyed reading the Notices for over 30 years, and I appreciate the opportunity that the AMS has given me to shape the magazine for the next three years. I hope that under my leadership even more people will look forward to reading it each month as much as I do. Above all, I would like the focus of the Notices to be on expository articles about pure and applied mathematics broadly defined. I would like the authors, topics, and writing styles of these articles to be diverse in every sense except for their desire to explain the mathematics that they love in a clear and engaging way.
    [Show full text]
  • 2018-06-108.Pdf
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Feature S E European Tensor Product and Semi-Stability M M Mathematical Interviews E S Society Peter Sarnak Gigliola Staffilani June 2018 Obituary Robert A. Minlos Issue 108 ISSN 1027-488X Prague, venue of the EMS Council Meeting, 23–24 June 2018 New books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. Bogdan Nica (McGill University, Montreal, Canada) A Brief Introduction to Spectral Graph Theory (EMS Textbooks in Mathematics) ISBN 978-3-03719-188-0. 2018. 168 pages. Hardcover. 16.5 x 23.5 cm. 38.00 Euro Spectral graph theory starts by associating matrices to graphs – notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions.
    [Show full text]
  • Distributed Corruption Detection in Networks
    THEORY OF COMPUTING, Volume 16 (986), 2020, pp. 1–23 www.theoryofcomputing.org Distributed Corruption Detection in Networks Noga Alon∗ Elchanan Mossely Robin Pemantlez Received November 29, 2015; Revised April 18, 2019, March 9, 2020; Published March 31, 2020 Abstract: We consider the problem of distributed corruption detection in networks. In this model each node of a directed graph is either truthful or corrupt. Each node reports the type (truthful or corrupt) of each of its outneighbors. If it is truthful, it reports the truth, whereas if it is corrupt, it reports adversarially. This model, first considered by Preparata, Metze and Chien in 1967, motivated by the desire to identify the faulty components of a digital system by having the other components checking them, became known as the PMC model. The main known results for this model characterize networks in which all corrupt (that is, faulty) nodes can be identified, when there is a known upper bound on their number. We are interested in networks in which a large fraction of the nodes can be classified. It is known that in the PMC model, in order to identify all corrupt nodes when their number is t, all in-degrees have to be at least t. In contrast, we show that in d regular-graphs with strong expansion properties, a 1 − O(1=d) fraction of the corrupt nodes, and a 1 − O(1=d) fraction of the truthful nodes can be identified, whenever there is a majority of truthful nodes. We also observe that if the graph is very far from being a good expander, namely, if the deletion ∗Research supported in part by NSF grant DMS-1855464, ISF grant 281/17, BSF grant 2018267 and the Simons Foundation.
    [Show full text]
  • Recursive Reconstruction on Periodic Trees
    University of Pennsylvania ScholarlyCommons Statistics Papers Wharton Faculty Research 8-1998 Recursive Reconstruction on Periodic Trees Elchanan Mossel University of Pennsylvania Follow this and additional works at: https://repository.upenn.edu/statistics_papers Part of the Statistics and Probability Commons Recommended Citation Mossel, E. (1998). Recursive Reconstruction on Periodic Trees. Random Structures & Algorithms, 13 (1), 81-97. http://dx.doi.org/10.1002/(SICI)1098-2418(199808)13:1<81::AID-RSA5>3.0.CO;2-O This paper is posted at ScholarlyCommons. https://repository.upenn.edu/statistics_papers/435 For more information, please contact [email protected]. Recursive Reconstruction on Periodic Trees Abstract A periodic tree Tn consists of full n-level copies of a finite tree T. The tree Tn is labeled by random bits. The root label is chosen randomly, and the probability of two adjacent vertices to have the same label is 1−ϵ. This model simulates noisy propagation of a bit from the root, and has significance both in communication theory and in biology. Our aim is to find an algorithm which decides for ve ery set of values of the boundary bits of T, if the root is more probable to be 0 or 1. We want to use this algorithm recursively to reconstruct the value of the root of Tn with a probability bounded away from ½ for all n. In this paper we find for all T, the values of ϵ for which such a reconstruction is possible. We then compare the ϵ values for recursive and nonrecursive algorithms. Finally, we discuss some problems concerning generalizations of this model.
    [Show full text]
  • Distributed Corruption Detection in Networks
    THEORY OF COMPUTING, Volume 16 (1), 2020, pp. 1–23 www.theoryofcomputing.org Distributed Corruption Detection in Networks Noga Alon∗ Elchanan Mossel† Robin Pemantle‡ Received November 29, 2015; Revised April 18, 2019, March 9, 2020; Published March 30, 2020 Abstract: We consider the problem of distributed corruption detection in networks. In this model each node of a directed graph is either truthful or corrupt. Each node reports the type (truthful or corrupt) of each of its outneighbors. If it is truthful, it reports the truth, whereas if it is corrupt, it reports adversarially. This model, first considered by Preparata, Metze and Chien in 1967, motivated by the desire to identify the faulty components of a digital system by having the other components checking them, became known as the PMC model. The main known results for this model characterize networks in which all corrupt (that is, faulty) nodes can be identified, when there is a known upper bound on their number. We are interested in networks in which a large fraction of the nodes can be classified. It is known that in the PMC model, in order to identify all corrupt nodes when their number is t, all in-degrees have to be at least t. In contrast, we show that in d regular-graphs with strong expansion properties, a 1 − O(1=d) fraction of the corrupt nodes, and a 1 − O(1=d) fraction of the truthful nodes can be identified, whenever there is a majority of truthful nodes. We also observe that if the graph is very far from being a good expander, namely, if the deletion ∗Research supported in part by NSF grant DMS-1855464, ISF grant 281/17, BSF grant 2018267 and the Simons Foundation.
    [Show full text]
  • Evolutionary Trees and the Ising Model on the Bethe Lattice: a Proof of Steel’S Conjecture
    University of Pennsylvania ScholarlyCommons Statistics Papers Wharton Faculty Research 2-2011 Evolutionary Trees and the Ising Model on the Bethe Lattice: A Proof of Steel’s Conjecture Constantinos Daskalakis Elchanan Mossel University of Pennsylvania Sébastien Roch Follow this and additional works at: https://repository.upenn.edu/statistics_papers Part of the Biostatistics Commons Recommended Citation Daskalakis, C., Mossel, E., & Roch, S. (2011). Evolutionary Trees and the Ising Model on the Bethe Lattice: A Proof of Steel’s Conjecture. Probability Theory and Related Fields, 149 (1), 149-189. http://dx.doi.org/ 10.1007/s00440-009-0246-2 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/statistics_papers/530 For more information, please contact [email protected]. Evolutionary Trees and the Ising Model on the Bethe Lattice: A Proof of Steel’s Conjecture Abstract A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree. It is well known that in order to reconstruct a tree on n leaves, sample sequences of length Ω(log n) are needed. It was conjectured by Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of the tree is less than p∗=(√2−1)/23/2 , then the tree can be recovered from sequences of length O(log n). The value p* is given by the transition point for the extremality of the free Gibbs measure for the Ising model on the binary tree.
    [Show full text]