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John Harer, Supervisor
, 2014
"... We work on constructing mathematical models of gene regulatory networks for periodic processes, such as the cell cycle in budding yeast, using biological data sets and applying or developing analysis methods in the areas of mathematics, statistics, and computer science. We identify genes with perio ..."
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We work on constructing mathematical models of gene regulatory networks for periodic processes, such as the cell cycle in budding yeast, using biological data sets and applying or developing analysis methods in the areas of mathematics, statistics, and computer science. We identify genes with periodic expression and then the interactions between periodic genes, which defines the structure of the network. This network is then translated into a mathematical model, using Ordinary Differential Equations (ODEs), to describe these entities and their interactions. The models currently describe gene regulatory interactions, but we are expanding to capture other events, such as phosphorylation and ubiquitination. To model the behavior, we must then find appropriate parameters for the mathematical model that allow its dynamics to approximate the biological data. This pipeline for model construction is not focused on a specific algorithm or data set for each step, but instead on leveraging several sources of data and analysis from several algorithms. For example, we are incorporating data from multiple time series
Euler characteristics of moduli spaces of curves
, 2008
"... Let M n g be the moduli space of npointed Riemann surfaces of genus g. Denote by M n g the DeligneMumford compactification of M n g. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M n g for any g and n such that n> 2 − 2g. ..."
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Cited by 207 (2 self)
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Let M n g be the moduli space of npointed Riemann surfaces of genus g. Denote by M n g the DeligneMumford compactification of M n g. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M n g for any g and n such that n> 2 − 2g.
3Dimensional Image Segmentation with Morse Complexes
, 2006
"... This paper describes an algorithm for segmenting threedimensional image datasets as well as its partial implementation optimized for cubic lattice datasets. The algorithm, developed by Herbert Edelsbrunner and John Harer, treats the dataset as a discretely sampled continuous function on a 3manifol ..."
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This paper describes an algorithm for segmenting threedimensional image datasets as well as its partial implementation optimized for cubic lattice datasets. The algorithm, developed by Herbert Edelsbrunner and John Harer, treats the dataset as a discretely sampled continuous function on a 3
The PreHistory Of Operads
, 1996
"... ae ae ae ae ae ae ae ae B B B B B B B B B B \Theta \Theta \Theta \Theta \Theta \Theta \Theta \Theta \Theta Z Z Z Z Z Z Z Z (ab)(cd) a(b(cd)) ((ab)c)d a((bc)d) (a(bc))d While I continued this work as a student in Oxford, Frank Adams visited and discussed his work with Mac Lane on PACTs and PROPs. Wi ..."
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Cited by 6 (0 self)
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of inserting parentheses in a meaningful way in a word of n letters. For n = 5, here is a portrait I copy (literally) from Masahico Saito. From a slighly different perspective, the 6fold cyclic symmetry is more manifest, as in this portrait I learned from John Harer a very few years ago. (It also appears
Computing Persistent Homology
 Discrete Comput. Geom
"... We show that the persistent homology of a filtered d dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enabl ..."
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Cited by 149 (21 self)
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We show that the persistent homology of a filtered d dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This results generalizes and extends the previously known algorithm that was restricted to subcomplexes of S and Z2 coefficients. Finally, our study implies the lack of a simple classification over nonfields. Instead, we give an algorithm for computing individual persistent homology groups over an arbitrary PIDs in any dimension.
Liaison and Rel. Top.
"... Abstract. Here we discuss some open problems about moduli spaces of curves from an algebrogeometric point of view. In particular, we focus on Arbarello stratification and we show that its top dimentional stratum is affine. The moduli spaceMg,n of stable npointed genus g curves is by now a widely e ..."
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on standard algebrogeometric techniques. Indeed, the only essential result borrowed from geometric topology is a vanishing theorem due to John Harer. Namely, the fact that Hk(Mg,n) vanishes for k> 4g − 4 + n if n> 0 and for k> 4g − 5 if n = 0 was deduced in [9] from the construction of a (4g − 4 + n
A REMARK ON THE HOMOTOPICAL DIMENSION OF SOME MODULI SPACES OF STABLE RIEMANN SURFACES
, 2007
"... Abstract. Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most k rational components. These bounds would follow from co ..."
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Cited by 4 (1 self)
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Abstract. Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most k rational components. These bounds would follow from
Results 1  10
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