Sylvie Hamel 848 de la Gauchetière Est Montréal, Québec H2L 2N2 General informations. Sex: Female Nationality: Canadian Languages: French, english Web address: http://www.lacim.uqam.ca/ hamel E-mail: sylvie@cs.mcgill.ca Status. I m now a postdoctoral fellow at McGill s Computer Science Department. Refereed publications and communications. - Algorithmic and computational biology - Approximate string matching: One paper in the International Journal of Foundations of Computer Science [2] and two communications: [5] and [6]. - Weighted distances between trees: One paper in preparation. - Language and automata theory - Cascade decomposition of automata: One paper accepted in Theoretical Computer Science [1] and one communication [4]. - Algebraic Combinatoric - Macdonald s polynomials: One paper in Discrete Mathematics [3] and four communications: [7], [8], [9] and [10]. Teaching and students supervision. -01/02-04/02: Lecturer; mathematics for computer scientist, UQAM -09/01-12/01: Lecturer; linear algebra, UQAM -05/01-09/01: Coordinator of a computational biology training, UQAM -09/00-12/00: Lecturer; linear algebra, UQAM -09/94-12/99: Teaching assistant; calculus, analysis, algebra, UQAM -07/98-08/98: Teaching assistant; algebraic topology and convex polytope, George Washington University -09/97-05/98: Teaching assistant, probability and stochastic processes, MIT. Administrative activities. 1998-2001 Representative on the Ph.D. program committee. 1996-1997 Representative on the Master program committee. 1
1 Academic 2002 - Postdoctoral fellow, McGill University. 1998-2002 Ph.D. in mathematics of computer science, Université du Québec à Montréal 1997-1998 Ph.D. student( ), Massachusetts Institute of Technology 1996-1997 M.Sc. in Mathematics, Université du Québec à Montréal 1993-1996 B.Sc. in Mathematics, Université du Québec à Montréal (*) The change of university is strictly due to personal reasons, not professional ones. Ph.D. Thesis S. Hamel, Algorithmes vectoriels et bioinformatique, Université du Québec à Montréal, 2002. Master Thesis S. Hamel, Représentations bigraduées et polynômes de Macdonald, Université du Québec à Montréal, 1997. 2 Scholarship 09/02-09/04 NSERC Postdoctoral fellowship, McGill. 09/01-04/02 ISM, Ph.D. Université du Québec à Montréal 01/01-12/01 FCAR, Ph.D. Université du Québec à Montréal 09/98-12/00 NSERC, Ph.D. Université du Québec à Montréal 09/97-08/98 FCAR, Ph.D. Massachusetts Institute of Technology 09/96-08/97 NSERC, M.Sc. Université du Québec à Montréal 05/95-09/95 NSERC summer scholarship, B.Sc. Université du Québec à Montréal 09/94-08/95 Marie-Thérèse scholarship, B.Sc. Université du Québec à Montréal 05/94-09/94 NSERC summer scholarship, B.Sc. Université du Québec à Montréal 09/93-08/96 Canada scholarship, B.Sc. Université du Québec à Montréal 3 Experience 3.1 Lecturer, UQAM - 01/02-04/02 Mathematics for computer scientist: Logic. Set theory. Definitions and representations of relations, functions and graphs. Introduction to complexity analysis. Inductive proof. - 09/01-12/01 Linear algebra: Algebraic operations on matrices; applications to directed graphs and Markov processes. Algorithms for the resolution of linear systems, for inverting matrices. Determinant. Vector Space. - 09/00-12/00 Linear Algebra. 3.2 Students supervision, UQAM - 05/01-09/01 Coordinator of a computational biology training for students in biochemistry: preparation of the teaching material and training projects, and supervision of the students. The training was divided in two parts. The first, more theoretical, consisted of lectures on topics in computational biology (databank, global and local alignments of two sequences, multiple 2
alignments, folding algorithms, phylogeny and gene predictions) followed by computer lab sessions. For the second part of the training students had to work on specific projects and write a report. 3.3 Research training, UQAM - 05/96-08/97 Algorithmic and Algebraic Combinatorics: Development of algorithms for specific problems related to symmetric functions. Director: François Bergeron. - 05/95-08/95 Algebraic Combinatorics: Construction of basis for certain polynomial s spaces. Director: François Bergeron. - 05/94-08/94 Automata Theory: Studies of temporal constraints of certain processes, with real time abstraction. Director: Anne Bergeron. 3.4 Teaching Assistant UQAM - 09/94-12/99 Various courses: Basic programming, mathematics for computer scientists, calculus, complex analysis, algebra. Georges Washington University - 07/98-08/98 Closed manifolds and convex polytopes for a summer school for women in mathematics: Summer Program for Women in Mathematics. Massachusetts Institute of Technology - 09/97-05/98 Probability and stochastic processes. 4 Research Interests 4.1 Automata Theory Vector algorithms related to an automaton. Given a deterministic finite automaton, and an input sequence e 1... e m, we are interested in output sequence r 1... r m of visited states. Since executing one transition is usually considered to be a constant time operation, the output sequence can clearly be obtained in O(m) time. We have constructed faster parallel algorithms using bit-vector operations. This approach, first considered in special cases, by Myers (Myers, G., A Fast Bit-Vector Algorithm for Approximate String Matching Based on Dynamic Programming, Journal of the ACM, 46-3, pp. 395 415, 1999), uses bit-vectors to code both the input and output sequence of an automaton, and computes the output with a bounded number of bit-wise operations on the input. Our work (with A. Bergeron) [6], generalizes this approach through the introduction of the notion of solvable automata, for which we prove the existence of bit-vector algorithms. More precisely, we show that the vector algorithm associated to a solvable automaton can be deduced from the transition table. This algorithm has O(d Σ ) time complexity, where d is the number of states of the automaton and Σ the size of the input alphabet. Following these ideas, I m now studying the generalization of solvability for other properties of the syntactic monoid to show how they are related to the existence of vector algorithms. 3
Cascade decompositions of automata. A vector algorithm is an algorithm that applies a bounded number of vector operations to an input vector, regardless of the length of this input. The main drawback of vector operations is that they are applied component wise. In order to tackle more complex problems, we need memory sensitive operations. The theoretical limit seems to be set by Krohn-Rhodes cascade decomposition theorem (Algebraic Theory of Machines, Transactions of the American Mathematical Society, 116, 1965, pp.450 464). In [1] and [4], we investigated the links between the existence of vector algorithms and the cascade decompositions of counter-free automata. The main problem with that method is that the vector algorithm, derived from the cascade, is often time consuming. I m now studying other automata decompositions to find efficient vector algorithms for specific sub-classes of the class of counter-free automata. 4.2 Computational biology and algorithmic Approximate string matching problem. Together with A. Bergeron, we have shown that there exist a vector algorithm solving the approximate string matching problem, in the case where the distance used is a generalized edit distance [2], [5]. This result generalizes a result of G. Myers (A Fast Bit-Vector Algorithm for Approximate String Matching Based on Dynamic Programming, Journal of the ACM, 46-3, pp. 395 415, 1999) by extending it to more general distances which are more adaptable to biological imperatives. For example, it allows to take into consideration the chemical properties of the element to be aligned. On the other hand, the biologists often prefer a similarity notion (not function of the distance) to compare sequences. The best known algorithms, in that case, are those of Smith-Watermen for local alignment and of Needlemen-Wunsch for global alignment. It has been shown that, under certain conditions, the two methods (distance and similarity) are equivalent. I m now studying the generalization of our techniques to construct vector algorithms for the Needlemen-Wunsch and Smith-Waterman problems. Trees and RNA secondary structure. I m also working on how to adapt our bit-vector approach to the study of distances between trees, to speed up known algorithms. This is the subject of a paper in preparation [4], [5]. 4.3 Algebraic Combinatorics Macdonald s polynomials The study of Macdonald s polynomials is related, through a conjecture of A. Garsia and M. Haiman (Some natural bigrated modules and q, t-kostka coefficients, Electronic Journal of Combinatorics, 3, No.2: Foata Festschrift, 1996, 60pp.), to the study of spaces obtained as the linear span of all partial derivatives of some Vandermonde determinants. I have studied, together with F. Bergeron, certain intersections of these modules and described explicit basis for these intersections in [3] and [7]. It has been shown recently that these modules are of dimension n!. This had been a conjecture for the past 10 years and it has been shown using algebraic geometry tools. The interest of the explicit description of the intersection that we have considered is that it contributes to a recursive elementary approach for the proof of the n! dimension of the module considered. It is also the kernel of several conjectures that are still open. 4
5 Publications and communications 5.1 Journal articles 1. A. Bergeron and S. Hamel, From cascade decomposition to bit-vector algorithms submitted to Theoretical Computer Science (TCS), 15 pages. 2. A. Bergeron and S. Hamel, Vector Algorithms for Approximate String Matching, International Journal of Foundations of Computer Science (IJFCS), 13-1, 2002, pp. 53 66. 3. F. Bergeron and S. Hamel, Intersections of modules related to Macdonald s polynomials, Discrete Mathematics, 217, 2000, pp. 51 64. 5.2 Refereed contributions (other than journals) International conferences with proceedings 4. A. Bergeron and S. Hamel, Cascade Decompositions are Bit-Vector Algorithms, to appear in Lecture Note in Computer Science, International Conference on Automata theory and its Applications 01, 14 pages. 5. A. Bergeron and S. Hamel, A Vector Algorithm for Approximate String Matching with Arbitrary Weighted Distances, Currents in Computational Molecular Biology, Les publications CRM, 2001, pp. 1-2. 6. A. Bergeron and S. Hamel, Fast Implementation of Automata Computations, Lecture Notes in Computer Science 2088, International Conference on Automata theory and its Applications 00, 2001, 10 pages. 7. F. Bergeron and S. Hamel, Intersections de modules liés aux polynômes de Macdonald, Proceedings oh the 9th Formal Power Series and Algebraic Combinatorics conference, Vienne, juillet 1997, pp. 73-83. Conferences without proceedings 8. S. Hamel, Characters of some Intersections of Modules related to Macdonald s Polynomials, Workshop of Algebraic Combinatorics, CRM, Montréal, June 9-20, 1997. 9. S. Hamel, Étude d intersections de modules liés aux polynômes de Macdonald, Colloque des Sciences Mathématiques du Québec, Montréal, 1997. 10. S. Hamel, Expérimentations liés aux polynômes de Macdonald, Colloque des Sciences Mathématiques du Québec, Lévis, 1995. 5.3 Non-refereed contributions Communications - S. Hamel, Automata Computations, Vector Algorithms and Approximate String Matching, University of California San Diego, July 2001. - S. Hamel, Intersections of some modules of polynomials in two set of variables, Combinatoric Seminar, Georges Washington University, July 1998. - S. Hamel, A study of some S n -modules related to Macdonald s polynomials, SPAW (Simple Person s Applied Math Seminar), MIT, March 1998. 5
- S. Hamel, Espaces de polynômes harmoniques et combinatoire algébrique, Premier Colloque des Étudiants Avancés du Québec, Montréal, March 1997. - S. Hamel (with F. Bergeron), Petite introduction aux intersections de S n -modules liées aux polynômes de Macdonald, Séminaire de combinatoire et d informatique théorique, LaCIM, UQAM, February 1996. - S. Hamel, Des graphes et des jeux, Canadian Undergraduate Mathematics Conference, Winnipeg, 1994. Series of conferences S. Hamel, Introduction to Symmetric Functions, Macdonald s polynomials and S n -modules, MIT, 1998: 1. Partitions, Ferrer diagrams, standard tableaux. 2. Some bases for the ring of symmetric functions. 3. Description of S n -modules related to Macdonald s polynomials. 4. Intersections of S n -modules. 6