## Fall 2005 – Spring 2006 - Colloquium Abstracts

**Tuesday, Nov 8, 2005**

3:00pm, 211 Little Hall

**Dr. Alain Arneodo**, *Laboratoire Joiliot Curie et Laboratoire de Physique, Ecole Normale Superieure de Lyon, France
*DNA in chromatin: what can we learn from a multi-scale wavelet analysis of DNA sequences?

Understanding how chromatin is spatially and dynamically organized in the nucleus of eukaryotic cells and how this affects genome functions is one of the main challenges of cell biology. Recent technical progress in live cell imaging have confirmed that the structure and dynamics of chromatin play an essential role in regulating many biological processes, such as gene activity, DNA replication, recombination and DNA damage repair. The emerging view is that genomes are compartmentalized into subchromosal structural domains that are likely to be fundamental functional units that coordinate the spatial organization and timing of replication and transcription. A remarkable property of these subchromosal foci is that they are likely to be stable structures that persist throughout the cell cycle and subsequent cell generations. As regards to this probable clonal inheritance, one may wonder to which extent one may learn about the higher order structure and dynamics of chromatin directly from the primary DNA sequence and its functional landmarks. In the first part of this talk, we use the space-scale decomposition provided by the continuous wavelet transform (WT) to characterize the scale invariance properties of genomic sequences. We show the existence of long-range correlations (LRC) over distances up to 20-30 kb as the signature of the nucleosomal structure of the 30 nm chromatin fiber. The investigation of the thermodynamic properties of naked DNA shows that the competing effect of entropy and sequence dependent structural disorder favors the formation of loops, larger the LRC, smaller the loop size. This result suggests that the observed LRC may have been encoded during evolution to predispose eukaryotic DNA to interact with histones to form the nucleosomes. In a second part, we explore the large-scale compositional heterogeneity of several large (tens of mega-bases) contigs within human chromosomes through the optics of the WT microscope. We show that the GC content displays relaxational nonlinear oscillations with two main frequencies corresponding to 100 kb and 400 kb which are well recognized characteristic sizes of chromatin loops and loop domains involved in the hierarchical folding of the chromatin fiber. These frequencies are also remarkably similar to the size of mammalian replicons and replicon clusters. When further investigating deviations from intrastrand equimolarities between A and T and between G and C, we corroborate the existence of these two fundamental frequencies as the footprints of the replication and/or transcription mutation bias and we show that the observed nonlinear oscillations enlighten a remarkable cooperative organization of gene location and orientation.

Dr. Arneodo is Director of Research at the CNRS (Centre National de la Recherche Scientifique in France) and has published extensively in the physics literature, including over 200 peer-reviewed papers. He has trained 19 Doctors of Science. Dr. Arneodo is a fellow of the Soci t Francaise de Physique.

**Thursday, Dec 15, 2005**

3:00pm, 421 Neville Hall

**Ben Morin**, *Dept. of Mathematics and Statistics, University of Maine
*An Interspecies Competition Model with Multiscale Interpretations, or What the heck did Ben do last summer?

A method for simulating and analyzing the competition between similar species is presented here by first adapting a Gause type model that allows four fitting parameters. From this deterministic model we derive conditions for the existence and stability of several equilibria, including multiple coexistence equilibria. An agent-based simulation was then created to model the biology of the species on the scale of individual interaction. Changes in the growth scale parameters for the deterministic model were then considered in order to try to replicate the behavior of the agent-based biology. This is done in an attempt to rationalize the growth scale parameters as a tool to capture all possible behaviors. In an effort to observe the dynamics on a different spatial scale, we implemented a spatially structured stochastic simulation with parameters chosen to reflect the different outcomes of the agent-based model. This second simulation tracked, on a larger scale, the interaction between groups or colonies of the species of interest. This talk will focus on the analysis and proofs given in the paper concerning the possible outcomes.

**Friday, Apr 21, 2006**

2:10pm, 421 Neville Hall

**Justin Bronder**, *Dept. of Mathematics and Statistics, University of Maine
*Implementation of the AKS primality test

In August of 2002, three Indian computer scientists, Manindra Agrawal, Neeraj Kayal and Nitin Saxena, released a paper simply titled ‘PRIMES is in P’. Within a scant number of pages, they were able to clearly demonstrate a deterministic polynomial time primality test.

This talk will focus upon presentation of the AKS Primality Test Algorithm that is derived from their new characterization of prime numbers. I will save the proof of this characterization for my upcoming defense, instead providing in this talk a discussion of algorithmic complexity using “Soft-O” notation to prove that the algorithm runs in polynomial time.

We also discuss the challenges of implementing this algorithm to run across a high-performance computing cluster of Xserve G5′s.

**Friday, Apr 28, 2006**

11:15am, 108 Neville Hall

**Ben Morin**, *Dept. of Mathematics and Statistics, University of Maine
*The effect of static and dynamic spatially structured disturbances on a locally dispersing population model

Thesis defense; Advisor: David Hiebeler

Pair approximation equations have been in use now for several years as a method to enhance the level of spatial information captured by mathematical models. David Hiebeler, as well as others (Levin, Rand, Ellner), has been exploring the use of the pair approximation as a way to get better estimates of a system’s behavior than previous methods (i.e. mean field approximations). His previous work has involved looking at the pair approximations for basic contact processes set on homogeneous landscapes, with near and far dispersal, heterogeneous landscapes, and spatially correlated disturbances on the population level.

This thesis will explore the combined effect of two of Dr. Hiebeler’s previous works, that of heterogeneous landscapes and spatially correlated population disturbances. The question of the effect of the simultaneous interactions is so far left open, and this work is an attempt to investigate this synergy. Specifically I will look at the effect of having both the landscape (static) and population level (dynamic) disturbances on the same spatial scale.

**Friday, Apr 28, 2006**

2:10pm, 101 Neville Hall

**Dr. Jian Han**, *Senior Research Biostatistician, Global Biometric Sciences, Bristol-Myers Squibb
*Statistician’s Role in Pharmaceutical Industry — A Snapshot at Bristol-Myers Squibb

I will start with an introduction to BMS, one of the top pharmaceutical companies in US. I will focus on what are the challenges faced not only by BMS but also by all other drug development companies: strategy in pipeline, choice of major disease areas, R&D expenses, and success rate. Next, I will briefly summarize the functional roles of biostatistician in the drug development at BMS,from early drug discovery to phase III or later trials. Some practical statistical issues that we often deal with will be discussed. Finally, I will explain, by using a real example, on what are the major steps in the design of the clinical trial and what are the common key statistical issues that are usually required to be pre-specified.

Jian Han is a former student of University of Maine, Department of Mathematics and Statistics. He has a Master’s degree from our department and a Ph.D .in Biostatistics from Southern Methodist University, Dallas, Texas.

**Friday, Apr 28, 2006**

3:10pm, 421 Neville Hall

**Justin Bronder**, *Dept. of Mathematics and Statistics, University of Maine
*On the AKS primality test

Thesis defense; Advisor: Andrew Knightly

In August of 2002, three Indian computer scientists, Manindra Agrawal, Neeraj Kayal and Nitin Saxena, released a paper simply titled ‘PRIMES is in P’. Within a scant number of pages, they were able to clearly demonstrate a deterministic polynomial time primality test.

Following up on my previous presentation, I will now demonstrate the correctness of the AKS characterization of prime numbers. I also utilize the recent comments of Lenstra, Pomerance, and Granville which improve on a number of areas of the proof.

**Monday, May 1, 2006**

3:00pm, 421 Neville Hall

**Dr. Ian McKeague**, *Department of Biostatistics, Columbia University
*Binary decision trees and split point estimation

This talk discusses the problem of estimating split points (or thresholds) in semiparametric regression models. The aim is to find an effective way of condensing information in the nonparametric part of the model into a small number of estimable parameters. A binary decision tree is used as a working model, with the jump representing a point at which the regression function changes abruptly between two levels. We find the asymptotic distribution of estimators of best-fitting parameters under an arbitrary misspecification of the working model. The estimators converge at cube-root rate to a non-normal continuous limit distribution. This is in marked contrast to change point estimators which converge at rate n to jump processes under the (exuberantly optimistic) assumption that the change point model is correctly specified. The approach is illustrated with two examples. The first concerns a nonparametric regression model for estimating a phosphorus threshold at which biological imbalance occurs, and the second concerns a proportional hazards model for the onset age of schizophrenia. This is joint work with Moulinath Banerjee.