All Seminars
| Title: Inference of gene regulatory networks by feature selection |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: David Correa Martins of Universidade Federal de ABC |
| Contact: Alexis Aposporidis, aapospo@emory.edu |
| Date: 2011-04-25 at 4:00PM |
| Venue: W302 |
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| Abstract: Gene Regulatory Networks (GRN) can be viewed as a gene interaction network where the level of expression of each gene is related to how vigorously that gene will be transcribed into RNA. The cell control is the result of a multivariate activity of genes, and the understanding of such activity is crucial for therapeutic purposes and development of new drugs. In this context, since the available data is usually noisy and scarce (only dozens of samples with thousands of gene expression values), the inference of GRNs is one of the big challenges in bioinformatics. GRNs can be modeled as graphs where the vertices represent genes and the edges represent dependencies between genes. There are many categories of GRN modeling, such as Bayesian Networks, Boolean Networks (and its stochastic version: Probabilistic Boolean Networks), differential equations and others. This presentation will give an overview of GRNs and some problems about inference by feature selection approaches. Works in progress on this topic will be briefly discussed. |
| Title: Lifting the j-invariant |
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| Seminar: Algebra and Number Theory |
| Speaker: Luis R. Finotti of University of Tennessee, Knoxville |
| Contact: Zachary A. Kent, kent@mathcs.emory.edu |
| Date: 2011-04-19 at 3:00PM |
| Venue: W306 |
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| Abstract: The coordinates of the j-invariant of the canonical lifting of an ordinary elliptic curve are functions on the j invariant of the latter curve. Mazur asked about the nature of these functions and Tate asked about the possibility to extend them to supersingular values. After describing methods to deal with Witt vectors in an efficient way, we will show that only the first three coordinates can be extend to supersingular values and give precise descriptions for the first four coordinates. |
| Title: Decoding Network Structure by Matrix Functions |
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| Colloquium: N/A |
| Speaker: Ernesto Estrada of University of Strathclyde |
| Contact: Michelle Benzi, benzi@mathcs.emory.edu |
| Date: 2011-04-19 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The aim of this talk is to illustrate the necessity of introducing concepts and invariants beyond those of 'small-worldness' (SW) and 'scale-freeness' (SF) that pervade current network analysis. I will present three challenging examples from the real-world analysis of networks. The first is related to the identification of essential proteins in a protein-protein interaction map. The second deals with the identification of communities in rather homogeneous networks like an international trade network. The third one focuses on the discrimination of human brains after suffering strokes from healthy ones. The solution to these three problems are presented on the basis of matrix functions, such as the exponential adjacency matrix. Other extensions are also mentioned. They are presented by introducing the concepts of subgraph centrality and communicability in networks and are compared with the use of simple measures based of SW and SF concepts, such as the use of degree, average path length or betweenness centrality. |
| Title: The maximum size of a Sidon set contained in a sparse random set of integers [Part 2] |
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| Seminar: Combinatorics |
| Speaker: Sangjune Lee of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-04-15 at 4:00PM |
| Venue: W306 |
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| Abstract: This is a continuation of the seminar last week on the maximum size of Sidon sets in sparse random sets of integers. This is joint work with Yoshiharu Kohayakawa and Vojtech R\"odl. [Please note: This is part of the Combinatorics Seminar, an official course offered in the department this term. The time and place are the assigned ones for this course.] |
| Title: 3-dimensional hyperbolic manifolds as discretized configuration spaces of simple graphs |
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| Defense: Honors Thesis |
| Speaker: Michelle Chu of Emory University |
| Contact: Aaron Abrams, |
| Date: 2011-04-13 at 2:00PM |
| Venue: MSC E406 |
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| Abstract: |
| Title: Characteristic Properties of Mobius Transformations and Quasiconformal Mappings |
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| Defense: Honors Thesis |
| Speaker: Daniel Orner of Emory University |
| Contact: Shanshuang Yang, syang@mathcs.emory.edu |
| Date: 2011-04-13 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: |
| Title: Weierstrass points on the Drinfeld modular Curve $X_0(\mathfrak{p})$ |
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| Seminar: Algebra and Number Theory |
| Speaker: Christelle Vincent of University of Wisconsin at Madison |
| Contact: Zachary A Kent, kent@mathcs.emory.edu |
| Date: 2011-04-12 at 2:15PM |
| Venue: MSC E406 |
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| Abstract: For $q$ a power of a prime, consider the ring $\mathbb{F}_q[T]$. Due to the many similarities between $\mathbb{F}_q[T]$ and the ring of integers $\mathbb{Z}$, we can define for $\mathbb{F}_q[T]$ objects that are analogous to elliptic curves, modular forms, and modular curves. In particular, for $\mathfrak{p}$ a prime ideal in $\mathbb{F}_q[T]$, we can define the Drinfeld modular curve $X_0(\mathfrak{p})$, and study the reduction modulo $\mathfrak{p}$ of its Weierstrass points, as is done in the classical case by Rohrlich, and Ahlgren and Ono. In this talk we will present some partial results in this direction, defining all necessary objects as we go. |
| Title: Quasiisometric rigidity of some negatively curved solvable Lie groups |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Xiangdong Xie of Georgia Southern University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-04-12 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We show that, for a class of negatively curved solvable Lie groups, every quasiisometry between them is an almost isometry, that is, it preserves the distance up to an additive constant. We prove this by studying the quasiconformal analysis on the ideal boundary. |
| Title: Multilevel Methods for Ill-Posed Problems |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Lothar Reichel of Kent State University |
| Contact: Michelle Benzi, benzi@mathcs.emory.edu |
| Date: 2011-04-08 at 12:50PM |
| Venue: W306 |
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| Abstract: Multilevel methods for the solution of well-posed problems, such as certain boundary value problems for partial differential equations and Fredholm integral equations of the second kind, are popular and their properties are well understood. Much less is known about the behavior of multilevel methods for the solution of linear ill-posed problems, such as Fredholm integral equations of the first kind with a right-hand side that is contaminated by error. We discuss properties of cascadic multilevel methods for the latter kind of problems. |
| Title: The maximum size of a Sidon set contained in a sparse random set of integers |
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| Seminar: Combinatorics |
| Speaker: Sangjune Lee of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-04-08 at 4:00PM |
| Venue: W306 |
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| Abstract: A set $A$ of integers is a \textit{Sidon set} if all the sums~$a_1+a_2$, with~$a_1\leq a_2$ and~$a_1$,~$a_2\in A$, are distinct. In the 1940s, Chowla, Erd\H{o}s and Tur\'an showed that the maximum possible size of a Sidon set contained in $[n]=\{0,1,\dots,n-1\}$ is $\sqrt{n}(1+o(1))$. We study Sidon sets contained in sparse random sets of integers, replacing the `dense environment'~$[n]$ by a sparse, random subset~$R$ of~$[n]$.\\ \\ Let~$R=[n]_m$ be a uniformly chosen, random $m$-element subset of~$[n]$. Let~$F([n]_m)=\max\{|S|\colon S\subset[n]_m\hbox{ Sidon}\}$. An abridged version of our results states as follows. Fix a constant~$0\leq a\leq1$ and suppose~$m=m(n)=(1+o(1))n^a$. Then there is a constant $b=b(a)$ for which~$F([n]_m)=n^{b+o(1)}$ almost surely. The function~$b=b(a)$ is a continuous, piecewise linear function of~$a$, not differentiable at two points:~$a=1/3$ and~$a=2/3$; between those two points, the function~$b=b(a)$ is constant. \\ \\ This is joint work with Yoshiharu Kohayakawa and Vojtech R\"odl. |