September 2011
Jean-Pierre Fouque (University of California, Santa Barbara)-Calibration of Stock Betas from Skews of Implied Volatilities
Friday, 9/9/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We develop call option price approximations for both the market index and an individual asset using a singular perturbation of a continuous time Capital Asset Pricing Model (CAPM) in a stochastic volatility environment.
These approximations show the role played by the asset's beta parameter as a component of the parameters of the call option price of the asset. They also show how these parameters, in combination with the parameters of the call option price for the market, can be used to extract the beta parameter. Finally, a calibration technique for the beta parameter is derived using the estimated option price parameters of both the asset and market index. The resulting estimator of the beta parameter is not only simple to implement but has the advantage of being forward-looking as it is calibrated from skews of implied volatilities.
For more information, e-mail ma-chair@wpi.edu.
David Vogan (2011 AMS Levi L. Conant Prize Recipient) - "The Character Table of E_8(R)"
Thursday, 9/15/2011 4:00 PM-5:00 PM
Fuller Laboratories, Lower Perreault Hall
ABSTRACT: In 2007, a group of about 20 mathematicians completed the computation of character tables for all the real forms of the exceptional Lie groups, using algorithms introduced by Kazhdan and Lusztig nearly 30 years ago. In the case of the 248-dimensional group called E_8(R), the character table (in a very compressed form) occupies about 50 gigabytes of disk space. I'll talk about several (closely related) questions:
* Since these groups have infinitely many conjugacy classes and infinitely many representations, how can one write a character table in finite terms?
* What assurance is there that these enormous tables are correct?
* How can one extract from them information that a human can understand and find interesting?
As a corollary of these investigations, I will also try to shed some light on the question of whether computers are animated by a demonic malevolence toward humanity.
David Vogan has been a member of the MIT faculty since 1979. He received his PhD from MIT in 1976, under the direction of Bertram Kostant. Most of his work concerns representation theory of Lie groups. He has written papers and books with 13 separate co-authors (an approach he recommends for its effect on Erdös number, for relief of writer's cramp, for looking smarter, and for enjoying mathematics). He is a member of the American Academy of Arts and Sciences.
For more information, e-mail ma-chair@wpi.edu.
Lucian Beznea (Simion Stoilow Institute of Mathematics of the Romanian Academy)-A probabilistic approach to a nonlinear Dirichlet problem
Thursday, 9/22/2011 4:00 PM-5:00 PM
Stratton Hall, 106
ABSTRACT: A Dirichlet problem associated with the operator $\Delta u + u^2$ is solved, using a branching Markov process on the space of finite configurations. We follow the pioneering works of M. Nagasawa, N. Ikeda, S. Watanabe, M.L. Silverstein, and the approach of E.B. Dynkin.
For more information, e-mail ma-chair@wpi.edu.
Mahadevan Ganesh (Colorado School of Mines) - A reduced basis method for multiple electromagnetic scattering
Friday, 9/23/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We consider a parametrized multiple particle wave propagation model in three dimensions. The parameters in the model describe the location, orientation, size, shape, and number of scattering particles as well as properties of the input source field such as the frequency, polarization, and incident direction. For such dynamic parametrized multiple scattering models, the standard discretization procedures are prohibitively expensive due to the computational cost associated with solving the full model for each online parameter choice. In this talk, we discuss an iterative offline/online reduced basis approach for a boundary element method to simulate the multiple particle wave propagation model.
For more information, e-mail ma-chair@wpi.edu.
Luis Carvalho (Boston University)-Bayesian land cover classification for MODIS data
Friday, 9/30/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We discuss a Bayesian inferential approach to land cover classification, according to the IGBP categorization, of a Moderate Resolution Imaging Spectroradiometer (MODIS) dataset collected from a number of validated sites. The dataset comprehends time series with 46 observations per year and per site from 2001 to 2009 of an enhanced vegetation index (EVI) computed from MODIS spectral observations. In order to capture spatial and temporal co-dependencies, we adopt a Potts model prior on the latent IGBP classes. We further model a hierarchical Gaussian likelihood structure that represents expected within-year EVI intensities and aims to explain EVIs for specific site, time of the year, and year through between-year and between-site variances. We develop an efficient Gibbs sampler that allows us to conduct inference on IGBP classifications by obtaining centroid estimates and testing for changes, in time, of land cover classes. Finally, we propose directions for future work involving improved MCMC schemes and an explicit change point model.
For more information, e-mail ma-chair@wpi.edu.
November 2011
Frederi Viens (Purdue University)-The Malliavin calculus: basic properties and new directions
Friday, 11/4/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The Malliavin Calculus is a theory and a set of tools at the intersection of probability and functional analysis, which helps analyze the behavior of models for random evolutions based on white noise (derivative of the Wiener process) and other types of stochastic input. We will provide a short primer on Wiener space and the Malliavin calculus, followed by a presentation of some recently developed tools for estimating the behavior of tails and densities of random variables.
The basic new ingredient is an observation due to Ivan Nourdin and Giovanni Peccati, by which any random variable on Wiener space can be compared to Gaussian random variables via a certain Malliavin calculus operator. Applications to stochastic PDEs will be given. Extensions beyond Gaussian estimates, to the entire so-called Pearson class, will be mentioned, including their connection to a study of the solutions of relevant Stein equations. Lastly, some results and open questions for estimating distributions of vectors on Wiener space will be given.
This talk covers works by H. Airault, R.Eden, P. Malliavin, I. Nourdin, G. Peccati, and the presenter.
For more information, e-mail ma-chair@wpi.edu.
Burt Tilley (WPI)-Geometry-driven charge accumulation in electrokinetic flows between thin, closely spaced laminates
Friday, 11/11/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Fluid flows through anisotropic media are found in a wide variety of geophysical and biological systems. The macroscale behavior of these systems depend on the microstructure, which in turn may depend on local and global physical processes. Classically, geometric restrictions are needed to model these systems on the largest length scale, and we are interested in developing effective models which relax these restrictions. We consider an array of closely spaced, purely dielectric rigid laminates with nonuniform thickness. The laminate thickness and spacing varies on a length scale much longer than the characteristic thickness of the laminates. In the spacing between the laminates, an electrically conducting fluid is driven by an applied electric field through electroosmosis and electrophoresis along with an applied pressure gradient. Debye layers occur at the laminate-fluid interface, which are assumed to be much smaller than the laminate thickness. From a modification of the classical homogenization approach that relies on a physical microscale constraint in place of a geometric constraint, we derive an effective set of equations that describe the fluid pressure, the anion and cation concentrations in the fluid and the electric potential. Anisotropic dispersion effects in the electric field are included, and electroneutrality in the fluid is not imposed. We find that gradients in the laminate spacing can lead to charge accumulation when electroosmosis and the electrophoresis induced from the anisotropic dispersion effects balance. (Co-authors: B. Vernescu and J.D. Plummer, WPI.)
For more information, e-mail ma-chair@wpi.edu.
Mansoor Haider (North Carolina State University)-" Mixture Models for Cartilage Tissue Engineering in Biomaterial Scaffolds Seeded with Chondrocytes"
Friday, 11/18/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Articular cartilage physiology is regulated by a single population of specialized cells called chondrocytes. The chondroyctes are sparsely distributed within the extracellular matrix (ECM) and maintain a state of homeostasis in healthy tissue. ECM degeneration due to osteoarthritis can lead to complete degradation of cartilage surfaces, necessitating total joint replacement. Chondrocytes can be utilized to regenerate cartilage via tissue engineering approaches in which these cells are seeded in biocompatible and degradable biopolymer or hydrogel scaffolds. In such systems, biosynthetic activity of the cells in response to their non-native environment results in regeneration and accumulation of ECM constituents concurrent with degradation of the surrounding scaffold material. In this talk, mixture models are presented for interactions between biosynthesis of ECM constituents and ECM linking in cell-seeded scaffolds. Both ODE-based (temporal) models for evolution of average apparent densities and PDE-based (spatio-temporal) models will be presented for variables including unlinked ECM, linked ECM and scaffold. Of particular interest are model predictions for the evolution of solid phase apparent density, which is correlated with the compressive elastic modulus of the tissue construct. These models provide a quantitative framework for assessing and optimizing the design of engineered cell-scaffold systems and guiding strategies for articular cartilage tissue engineering.
For more information, e-mail ma-chair@wpi.edu.
CIMS Talk - Ansuman Bagchi (Director, Applied Computer Science & Mathematics, Merck & Co.) - Mathematics in the Pharmaceutical Industry
Friday, 11/18/2011 1:00 PM-2:00 PM
Stratton Hall, 203
ABSTRACT: The pharmaceutical industry, in general, has been under intense pressure to produce more drugs through their pipeline under a multitude of external and internal economical pressures, such as increased FDA scrutiny and demand for longer range studies, health-care regulations that are cost/price restrictive, and patent expirations. Significant increases to the research and development expenditures have not yielded results as expected. With a few examples, we will highlight how the industry is planning to adopt a business strategy that complements scientific discovery with process innovation where mathematical modeling and, in general, informatics play a critical role.
Supported by NSF Grant DMS-0753050: Mathematical Problems in Industry (MPI) Workshop
For more information, e-mail ma-chair@wpi.edu.
December 2011
CIMS Talk - Brenda Ramirez (Amgen, Providence, RI) - Techniques for Understanding Measurement System Variation: Gage R&R vs. EMP
Friday, 12/2/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Understanding and minimizing measurement system variation, i.e., gage error, is critical in a manufacturing environment. Many statistical techniques have been developed over the years to quantify and dissect the sources of variation that contribute to measurement error. In this talk, two of these techniques will be discussed. The traditional Gage R&R studies, which are widely promoted in the automotive industry, will be compared with a more comprehensive approach called Evaluating the Measurement Process (EMP).
For more information, e-mail ma-chair@wpi.edu.
Graeme Milton (University of Utah) - H.J. Gay Lecture - Cloaking: Where Science Fiction Meets Science
Friday, 12/2/2011 3:00 PM-4:00 PM
Higgins Laboratories, 218
ABSTRACT: Cloaking involves making an object partly or completely invisible to incoming waves such as sound waves, sea waves or seismic waves, but usually electromagnetic waves such as visible light, microwaves, infrared light, or radio waves. Camouflage and stealth technology achieve partial invisibility, but can one achieve true invisibility from such waves? This lecture will survey some of the wide variety of ideas on cloaking: these include cloaking by plasmonic covers, transformation based cloaking, non Euclidean cloaking, cloaking due to anomalous resonance, cloaking by complementary media, active interior cloaking and active exterior cloaking. Beautiful mathematics is involved.
For more information, e-mail ma-chair@wpi.edu.
Robert Hardt - H.J. Gay Lecture - Some New Uses of Functions with Finite Total Variation
Friday, 12/9/2011 11:00 AM-12:00 PM
Bartlett Center
ABSTRACT: 1) Estimate the length of a continuous curve using drafting dividers.
2) Enhance an image by sharpening edges and smoothing roughness.
3) Find a spanning surface of least area in a very singular space X.
These 3 problems can all be attacked using the notion of the Total Variation (TV) of a function.
For 1) the usual formula for the length of a curve f :[a, b] -+ RN is the definition of TV( f).
For 2) one considers a two-variable function g :[a, b] x [c, d] -+ [0, 1] giving the grayscale intensity of an image in the rectangle [a, b] x [c, d]. Assuming TV(g), suitably defined, is finite, edges and roughness are described using different parts of the derivative of g. The models for image enhancement that we will discuss involve interesting POE's and many open questions.
For 3) we consider functions h whose values are finite sums of point masses in X. Assuming X has a distance function, we find a geometrically reasonable notion of the distance between 2 such sums. Then functions with TV(h) < oo essentially determine the surfaces and give a surprising amount of regularity. Analysis in singular spaces has had wide applications from algebraic geometry to data analysis.
For more information, e-mail ma-chair@wpi.edu.
Howard Elman (University of Maryland)-Efficient Solution Algorithms for Partial Differential Equations with Random Coefficients
Friday, 12/16/2011 2:00 PM-3:00 PM
Stratton Hall, 203
ABSTRACT: We consider new computational methods for solving partial differential equations (PDEs) when components of the problem such as diffusion coefficients are random fields. In recent years, several computational techniques have been developed for such models that offer potential for improved efficiencies compared with traditional Monte-Carlo methods. These include stochastic Galerkin methods, which use an augmented weak formulation of the PDE derived from averaging with respect to expected value, and stochastic collocation methods, which use a set of samples relatively small in cardinality that captures the character of the solution space. We discuss the relative advantages of these two methods and explore their performance. For problems in which the dependence on uncertain parameters is linear, the Galerkin systems can be solved efficiently by multigrid methods so that the overall cost of solution is significantly lower than for collocation. We also discuss refinements of these methodologies to handle nonlinearities. A commonly used model takes the diffusion coefficient to be of log-normal form, which ensures well-posedness but causes the dependence on uncertain parameters to be nonlinear. We show that this difficulty can be alleviated by reformulating the problem in convection-diffusion form. Finally, computation of statistical properties of solutions such as moments requires explicit knowledge of the joint density function associated with the (finite number of) random variables that determine the uncertain coefficients. This is often not available, and instead, computation is enabled under a simplifying and possibly false assumption that the joint density is simply the product of the marginal densities. We discuss the use of kernel density estimation to circumvent this difficulty.
For more information, e-mail ma-chair@wpi.edu.
Arkadi Berezovski (Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Estonia) - Numerical simulation of waves and fronts in inhomogeneous solids
Monday, 12/19/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Numerical simulations of dynamical problems in inhomogeneous solids meet considerable difficulties in the case of existence of moving discontinuities such as phase transition fronts or cracks. The origin of these difficulties is a constitutive deficiency in the thermomechanical description of corresponding irreversible processes, which leads to an uncertainty in jump relations at moving discontinuities. Consequently, the construction of an appropriate numerical algorithm should be complemented by the development of the thermomechanical theory. The thermodynamic representation of finite volume methods, which is formally identical to well-known numerical methods on smooth solutions, gives additional possibilities in the solution of problems with moving discontinuities due to its ability to handle jump relations at discontinuities.
For more information, e-mail ma-chair@wpi.edu.
January 2012
Christopher Godsil (Department of Combinatorics and Optimization, University of Waterloo)-State Transfer on Graphs
Tuesday, 1/3/2012 2:00 PM-3:00 PM
Stratton Hall, 203
ABSTRACT: Let $X$ be a graph with adjacency matrix $A$. Motivated by work in quantum physics, we study the operator $$
H(t) := \exp(itA).
$$
Physically interesting questions concern the entries of the matrix $M(t)$, whose $rs$-entry is the square of the absolute value of the $rs$-entry of $H(t)$. Thus we might ask if, for given vertices $r$ and $s$, there is a time $t$ such that $M(t)_{r,s}=1$. (In this case have what is called perfect state transfer.) Or we might ask if there is a time $t$ such that all entries of $M(t)$ are equal to $1/n$ (instantaneous uniform mixing), or whether the entries if $M(t)$ average over time are equal to $1/n$ (average uniform mixing). I will discuss the recent progress on these and related problems, and show how they lead to interesting problems in graph theory.
For more information, e-mail ma-chair@wpi.edu.
Kun Gou (Ph.D. Candidate, Department of Mathematics, Texas A&M University) - An in-vivo spectral technique for estimation of residual stress of arterial wall by a novel application of intravascular ultrasound technology
Thursday, 1/5/2012 3:00 PM-4:00 PM
Stratton Hall, 203
Abstract: Residual stress is a stress that can exist in a body in the absence of externally applied loads. It is a challenge to recover it in soft tissues both theoretically and experimentally. A mathematical inverse spectral technique is developed to reconstruct the residual stress in the arterial wall in vivo. The technique is theoretically based on a novel use of intravascular ultrasound technology (IVUS), which is part of a long-range project to distinguish vulnerable atherosclerotic plaques from safe ones more accurately. As the IVUS is interrogating inside the artery, it produces small amplitude, high frequency time harmonic vibrations superimposed on the static deformations of the stressed artery. Two categories of boundary value problems are formulated to form Sturm-Liouville problems (SLP). The natural eigenfrequencies of arterial wall gained from IVUS implementation are employed as eigenvalues of the SLP. Via an optimization approach, the algorithms for an inverse spectral technique are established to recover the residual stress.
For more information, e-mail ma-chair@wpi.edu.
Lisa Fauci (Tulane University)-Spiny disks, flexible fibers and waving rings: explorations in phytoplankton fluid dynamics
Friday, 1/20/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Phytoplankton motion in the ocean, at the scale of individual cells, involves the interaction of passive and actuated elastic structures with a surrounding fluid - a common theme in biological fluid dynamics. We present recent modeling results that shed light on the active swimming of dinoflagellates, as well as the passive motion of diatoms in shear flows . These diatoms may form chains or bear spines. In addition to examining how the flexibility and geometry of the diatoms affect their rotational dynamics, we will discuss how laboratory experiments and computational simulations are being calibrated in an effort to characterize the elastic properties of different species of chain-forming diatoms.
For more information, e-mail ma-chair@wpi.edu.
Gabe Cunningham (Northeastern University) - Constructing abstract regular polytopes with external symmetries
Friday, 1/27/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Abstract polytopes are a combinatorial generalization of convex polytopes and tessellations of surfaces. Of particular importance are the regular polytopes, which have the highest degree of internal symmetry. In addition to these internal symmetries, which correspond to reflections and rotations, some regular polytopes have external symmetries such as self-duality. This talk will introduce and motivate the subject of abstract polytopes, and then we will see a group-theoretic method for constructing regular polytopes with specified external symmetries.
For more information, e-mail ma-chair@wpi.edu.
February 2012
Ilie-Radu Mitric (University of Connecticut)-Ruin Models Featuring Interest and Diffusion
Friday, 2/3/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: A number of extensions to the risk theory models are analyzed. Initially, we consider a multi-threshold compound Poisson surplus process with interest earned at a constant rate. Then, we considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk model with interclaim times that are generalized Erlang (n) distributed and claim amounts following a Matrix-Exponential (ME) distribution. Under this scenario, we present a general methodology to analyze the Gerber-Shiu discounted penalty function defined at absolute ruin, as a solution of high-order linear differential equations with non-constant coefficients. Closed-form solutions for the absolute ruin probabilities in the generalized Erlang (2) case complement recent results from literature obtained under the classical risk model.
Lastly, we analyze a multi-layer compound Poisson surplus process perturbed by diffusion and examine the behavior of the Gerber-Shiu discounted penalty function.
For more information, e-mail ma-chair@wpi.edu.
Stephan Sturm (Princeton University)-From Smile Wings to Market Risk Measures
Tuesday, 2/7/2012 11:00 AM-12:00 PM
Stratton Hall, 203
Abstract: The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In particular, we make use of indifference pricing by dynamic convex risk measures, which are given as solutions of backward stochastic differential equations (BSDEs), to establish a link between these two approaches to risk measurement. We derive a characterization of the implied volatility in terms of the solution of a nonlinear PDE and provide a small time-to-maturity expansion. This procedure allows to choose convex risk measures in a conveniently parametrized class, distorted entropic dynamic risk measures, such that the asymptotic volatility skew under indifference pricing can be matched with the market skew. This is joint work with Ronnie Sircar.
For more information, e-mail ma-chair@wpi.edu.
Harsh Jain (Ohio State University)-A non-autonomous delay differential equation model of cancer chemotherapy
Thursday, 2/9/2012 4:15 PM-5:15 PM
Gateway Park, 1002
ABSTRACT: The use of delay differential equations (DDEs) to study biological phenomena has a long history, when the rate of change of model variables depends their previous history. Today, DDEs occupy a central place in models of infectious disease dynamics, epidemiology, ecology and tumor growth. In this talk, I will present a delayed partial differential equation (PDE) model applied to tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy. The tumor is assumed to undergo logistic growth in the absence of therapy. To accurately simulate the action of chemotherapy, an age-structure together with a delay is imposed on proliferating cancer cells, and intracellular signaling pathways relevant to drug action explicitly modeled. The age-structured model results in a 1D hyperbolic PDE, which can be reduced to a nonlinear, non-autonomous DDE by projecting along the characteristics. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined. This has clinical implications since it leads to a lower bound for the amount of therapy required to affect a cure. Finally, I will present a clinical application of the model, by applying it to the treatment of ovarian cancers. Two types of drugs are considered platinum-based chemotherapeutic agents that are the current standard of care for most solid tumors, and small molecule cell death inducers that are currently under development. The model is calibrated versus in vitro experimental results, and is then used to predict optimal doses and administration time scheduling for the treatment of a tumor growing in vivo.
This talk is jointly sponsored by the Departments of Biology & Biotechnology, and Mathematical Sciences
For more information, e-mail ma-chair@wpi.edu.
Jeffrey Chuang (Boston College)-Identifying Hidden Functional Elements in Coding Regions
Thursday, 2/16/2012 4:15 PM-5:15 PM
Gateway Park, 1002
ABSTRACT: It has been increasingly appreciated that protein-coding DNA sequences harbor hidden regulatory sequences in addition to encoding for protein. These may include motifs that act at the DNA level, such as transcription factor binding sites, as well as motifs that act at the RNA level, such as microRNA-RNA binding sites. Detecting unusually overrepresented or conserved motifs has been algorithmically challenging because of interference by constraints at the protein level. I will present methods we have developed to efficiently calculate motifs of unusual conservation or overrepresentation in coding regions. Our studies indicate that hidden regulatory motifs are prevalent throughout eukaryotic and prokaryotic genomes. Additionally, I will present experimental results on whether coding regions can contain larger regulatory sequences. Our zebrafish studies indicate that vertebrate developmental genes contain large numbers of transcriptional enhancers, showing that proteins are malleable enough that even complex secondary functions can evolve in the same location.
This colloquium is jointly sponsored by the Departments of Biology & Biotechnology, and Mathematical Sciences.
For more information, e-mail ma-chair@wpi.edu.
March 2012
Giuliano Lazzaroni (Institut für Mathematik, Universität Würzburg) - On the role of the kinetic energy during unstable propagation in a heterogeneous peeling test
Friday, 3/2/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
Ugur G. Abdulla (Florida Institute of Technology)-Wiener Test at $\infty$ for Elliptic and Parabolic PDEs, and its Measure-Theoretical, Topological, and Probabilistic Consequences
Friday, 3/16/2012 11:00 AM-12:00 PM
Stratton Hall, 203
Wieners celebrated result on the boundary regularity of harmonic functions is one of the most beautiful and delicate results in XX century mathematics. It has shaped the boundary regularity theory for elliptic and parabolic PDEs, and has become a central result in the development of potential theory at the intersection of functional analysis, PDE, and measure theories. This talk describes the new developments which precisely characterize the regularity of the point at $\infty$ for second order elliptic and parabolic PDEs and broadly extend the role of the Wiener test in classical analysis. The Wiener test at $\infty$ arises as a global characterization of uniqueness in boundary value problems for arbitrary unbounded open sets. From a topological point of view, the Wiener test at $\infty$ arises as a thinness criteria at $\infty$ in fine topology. In a probabilistic context, the Wiener test at $\infty$ characterizes asymptotic laws for the characteristic Markov processes whose generator is the given differential operator. The counterpart of the new Wiener test at a finite boundary point leads to uniqueness in the Dirichlet problem for a class of unbounded functions growing at a certain rate near the boundary point; a criteria for the removability of singularities and/or for unique continuation at the finite boundary point. The Wiener criterion at $\infty$ is a largely unexplored issue of great importance in various disciplines, most notably in Nonlinear Potential Theory, Nonlinear Elliptic and Parabolic PDEs, Calculus of Variations, Topology, and in Probability Theory. The talk will end with a description of some open problems in those directions.
For more information, e-mail ma-chair@wpi.edu.
H.J. Gay Lecture - David Jerison (MIT) - Title TBA
Friday, 3/23/2012 11:00 AM-12:00 PM
Bartlett Center
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
TO BE RESCHEDULED, DATE TBD Heiko Enderling (Center of Cancer Systems Biology, Tufts University School of Medicine)-Cancer stem cells in solid tumors
Friday, 3/23/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The cancer stem cell hypothesis postulates that only a subpopulation of cancer cells in a tumor is capable of initiating, sustaining and re-initiating tumors, leaving the bulk of the population being non-stem cancer cells that lack tumor initiation and progression potential. With these two phenotypically distinct populations interacting with each other, the emerging tumor population can exhibit various non-linear growth kinetics. An environmentally independent early dormant state is an inevitable early tumor progression bottleneck for a large range of biologically realistic cell kinetic parameters. When intrinsic cell kinetics combine in unexpected manner, escape to tumor progression occurs as morphologically distinct self-metastatic expansion of multiple self-limited tumor clones.
For more information, e-mail ma-chair@wpi.edu.
April 2012
Marian Bocea (Loyola University)-Title TBA
Friday, 4/6/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
H.J. Gay Lecture - Alfio Quarteroni - Title TBA
Friday, 4/13/2012 11:00 AM-12:00 PM
Atwater Kent Laboratories, 219
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
September 2011
Jean-Pierre Fouque (University of California, Santa Barbara)-Calibration of Stock Betas from Skews of Implied Volatilities
Friday, 9/9/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We develop call option price approximations for both the market index and an individual asset using a singular perturbation of a continuous time Capital Asset Pricing Model (CAPM) in a stochastic volatility environment.
These approximations show the role played by the asset's beta parameter as a component of the parameters of the call option price of the asset. They also show how these parameters, in combination with the parameters of the call option price for the market, can be used to extract the beta parameter. Finally, a calibration technique for the beta parameter is derived using the estimated option price parameters of both the asset and market index. The resulting estimator of the beta parameter is not only simple to implement but has the advantage of being forward-looking as it is calibrated from skews of implied volatilities.
For more information, e-mail ma-chair@wpi.edu.
David Vogan (2011 AMS Levi L. Conant Prize Recipient) - "The Character Table of E_8(R)"
Thursday, 9/15/2011 4:00 PM-5:00 PM
Fuller Laboratories, Lower Perreault Hall
ABSTRACT: In 2007, a group of about 20 mathematicians completed the computation of character tables for all the real forms of the exceptional Lie groups, using algorithms introduced by Kazhdan and Lusztig nearly 30 years ago. In the case of the 248-dimensional group called E_8(R), the character table (in a very compressed form) occupies about 50 gigabytes of disk space. I'll talk about several (closely related) questions:
* Since these groups have infinitely many conjugacy classes and infinitely many representations, how can one write a character table in finite terms?
* What assurance is there that these enormous tables are correct?
* How can one extract from them information that a human can understand and find interesting?
As a corollary of these investigations, I will also try to shed some light on the question of whether computers are animated by a demonic malevolence toward humanity.
David Vogan has been a member of the MIT faculty since 1979. He received his PhD from MIT in 1976, under the direction of Bertram Kostant. Most of his work concerns representation theory of Lie groups. He has written papers and books with 13 separate co-authors (an approach he recommends for its effect on Erdös number, for relief of writer's cramp, for looking smarter, and for enjoying mathematics). He is a member of the American Academy of Arts and Sciences.
For more information, e-mail ma-chair@wpi.edu.
Lucian Beznea (Simion Stoilow Institute of Mathematics of the Romanian Academy)-A probabilistic approach to a nonlinear Dirichlet problem
Thursday, 9/22/2011 4:00 PM-5:00 PM
Stratton Hall, 106
ABSTRACT: A Dirichlet problem associated with the operator $\Delta u + u^2$ is solved, using a branching Markov process on the space of finite configurations. We follow the pioneering works of M. Nagasawa, N. Ikeda, S. Watanabe, M.L. Silverstein, and the approach of E.B. Dynkin.
For more information, e-mail ma-chair@wpi.edu.
Mahadevan Ganesh (Colorado School of Mines) - A reduced basis method for multiple electromagnetic scattering
Friday, 9/23/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We consider a parametrized multiple particle wave propagation model in three dimensions. The parameters in the model describe the location, orientation, size, shape, and number of scattering particles as well as properties of the input source field such as the frequency, polarization, and incident direction. For such dynamic parametrized multiple scattering models, the standard discretization procedures are prohibitively expensive due to the computational cost associated with solving the full model for each online parameter choice. In this talk, we discuss an iterative offline/online reduced basis approach for a boundary element method to simulate the multiple particle wave propagation model.
For more information, e-mail ma-chair@wpi.edu.
Luis Carvalho (Boston University)-Bayesian land cover classification for MODIS data
Friday, 9/30/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We discuss a Bayesian inferential approach to land cover classification, according to the IGBP categorization, of a Moderate Resolution Imaging Spectroradiometer (MODIS) dataset collected from a number of validated sites. The dataset comprehends time series with 46 observations per year and per site from 2001 to 2009 of an enhanced vegetation index (EVI) computed from MODIS spectral observations. In order to capture spatial and temporal co-dependencies, we adopt a Potts model prior on the latent IGBP classes. We further model a hierarchical Gaussian likelihood structure that represents expected within-year EVI intensities and aims to explain EVIs for specific site, time of the year, and year through between-year and between-site variances. We develop an efficient Gibbs sampler that allows us to conduct inference on IGBP classifications by obtaining centroid estimates and testing for changes, in time, of land cover classes. Finally, we propose directions for future work involving improved MCMC schemes and an explicit change point model.
For more information, e-mail ma-chair@wpi.edu.
November 2011
Frederi Viens (Purdue University)-The Malliavin calculus: basic properties and new directions
Friday, 11/4/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The Malliavin Calculus is a theory and a set of tools at the intersection of probability and functional analysis, which helps analyze the behavior of models for random evolutions based on white noise (derivative of the Wiener process) and other types of stochastic input. We will provide a short primer on Wiener space and the Malliavin calculus, followed by a presentation of some recently developed tools for estimating the behavior of tails and densities of random variables.
The basic new ingredient is an observation due to Ivan Nourdin and Giovanni Peccati, by which any random variable on Wiener space can be compared to Gaussian random variables via a certain Malliavin calculus operator. Applications to stochastic PDEs will be given. Extensions beyond Gaussian estimates, to the entire so-called Pearson class, will be mentioned, including their connection to a study of the solutions of relevant Stein equations. Lastly, some results and open questions for estimating distributions of vectors on Wiener space will be given.
This talk covers works by H. Airault, R.Eden, P. Malliavin, I. Nourdin, G. Peccati, and the presenter.
For more information, e-mail ma-chair@wpi.edu.
Burt Tilley (WPI)-Geometry-driven charge accumulation in electrokinetic flows between thin, closely spaced laminates
Friday, 11/11/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Fluid flows through anisotropic media are found in a wide variety of geophysical and biological systems. The macroscale behavior of these systems depend on the microstructure, which in turn may depend on local and global physical processes. Classically, geometric restrictions are needed to model these systems on the largest length scale, and we are interested in developing effective models which relax these restrictions. We consider an array of closely spaced, purely dielectric rigid laminates with nonuniform thickness. The laminate thickness and spacing varies on a length scale much longer than the characteristic thickness of the laminates. In the spacing between the laminates, an electrically conducting fluid is driven by an applied electric field through electroosmosis and electrophoresis along with an applied pressure gradient. Debye layers occur at the laminate-fluid interface, which are assumed to be much smaller than the laminate thickness. From a modification of the classical homogenization approach that relies on a physical microscale constraint in place of a geometric constraint, we derive an effective set of equations that describe the fluid pressure, the anion and cation concentrations in the fluid and the electric potential. Anisotropic dispersion effects in the electric field are included, and electroneutrality in the fluid is not imposed. We find that gradients in the laminate spacing can lead to charge accumulation when electroosmosis and the electrophoresis induced from the anisotropic dispersion effects balance. (Co-authors: B. Vernescu and J.D. Plummer, WPI.)
For more information, e-mail ma-chair@wpi.edu.
Mansoor Haider (North Carolina State University)-" Mixture Models for Cartilage Tissue Engineering in Biomaterial Scaffolds Seeded with Chondrocytes"
Friday, 11/18/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Articular cartilage physiology is regulated by a single population of specialized cells called chondrocytes. The chondroyctes are sparsely distributed within the extracellular matrix (ECM) and maintain a state of homeostasis in healthy tissue. ECM degeneration due to osteoarthritis can lead to complete degradation of cartilage surfaces, necessitating total joint replacement. Chondrocytes can be utilized to regenerate cartilage via tissue engineering approaches in which these cells are seeded in biocompatible and degradable biopolymer or hydrogel scaffolds. In such systems, biosynthetic activity of the cells in response to their non-native environment results in regeneration and accumulation of ECM constituents concurrent with degradation of the surrounding scaffold material. In this talk, mixture models are presented for interactions between biosynthesis of ECM constituents and ECM linking in cell-seeded scaffolds. Both ODE-based (temporal) models for evolution of average apparent densities and PDE-based (spatio-temporal) models will be presented for variables including unlinked ECM, linked ECM and scaffold. Of particular interest are model predictions for the evolution of solid phase apparent density, which is correlated with the compressive elastic modulus of the tissue construct. These models provide a quantitative framework for assessing and optimizing the design of engineered cell-scaffold systems and guiding strategies for articular cartilage tissue engineering.
For more information, e-mail ma-chair@wpi.edu.
CIMS Talk - Ansuman Bagchi (Director, Applied Computer Science & Mathematics, Merck & Co.) - Mathematics in the Pharmaceutical Industry
Friday, 11/18/2011 1:00 PM-2:00 PM
Stratton Hall, 203
ABSTRACT: The pharmaceutical industry, in general, has been under intense pressure to produce more drugs through their pipeline under a multitude of external and internal economical pressures, such as increased FDA scrutiny and demand for longer range studies, health-care regulations that are cost/price restrictive, and patent expirations. Significant increases to the research and development expenditures have not yielded results as expected. With a few examples, we will highlight how the industry is planning to adopt a business strategy that complements scientific discovery with process innovation where mathematical modeling and, in general, informatics play a critical role.
Supported by NSF Grant DMS-0753050: Mathematical Problems in Industry (MPI) Workshop
For more information, e-mail ma-chair@wpi.edu.
December 2011
CIMS Talk - Brenda Ramirez (Amgen, Providence, RI) - Techniques for Understanding Measurement System Variation: Gage R&R vs. EMP
Friday, 12/2/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Understanding and minimizing measurement system variation, i.e., gage error, is critical in a manufacturing environment. Many statistical techniques have been developed over the years to quantify and dissect the sources of variation that contribute to measurement error. In this talk, two of these techniques will be discussed. The traditional Gage R&R studies, which are widely promoted in the automotive industry, will be compared with a more comprehensive approach called Evaluating the Measurement Process (EMP).
For more information, e-mail ma-chair@wpi.edu.
Graeme Milton (University of Utah) - H.J. Gay Lecture - Cloaking: Where Science Fiction Meets Science
Friday, 12/2/2011 3:00 PM-4:00 PM
Higgins Laboratories, 218
ABSTRACT: Cloaking involves making an object partly or completely invisible to incoming waves such as sound waves, sea waves or seismic waves, but usually electromagnetic waves such as visible light, microwaves, infrared light, or radio waves. Camouflage and stealth technology achieve partial invisibility, but can one achieve true invisibility from such waves? This lecture will survey some of the wide variety of ideas on cloaking: these include cloaking by plasmonic covers, transformation based cloaking, non Euclidean cloaking, cloaking due to anomalous resonance, cloaking by complementary media, active interior cloaking and active exterior cloaking. Beautiful mathematics is involved.
For more information, e-mail ma-chair@wpi.edu.
Robert Hardt - H.J. Gay Lecture - Some New Uses of Functions with Finite Total Variation
Friday, 12/9/2011 11:00 AM-12:00 PM
Bartlett Center
ABSTRACT: 1) Estimate the length of a continuous curve using drafting dividers.
2) Enhance an image by sharpening edges and smoothing roughness.
3) Find a spanning surface of least area in a very singular space X.
These 3 problems can all be attacked using the notion of the Total Variation (TV) of a function.
For 1) the usual formula for the length of a curve f :[a, b] -+ RN is the definition of TV( f).
For 2) one considers a two-variable function g :[a, b] x [c, d] -+ [0, 1] giving the grayscale intensity of an image in the rectangle [a, b] x [c, d]. Assuming TV(g), suitably defined, is finite, edges and roughness are described using different parts of the derivative of g. The models for image enhancement that we will discuss involve interesting POE's and many open questions.
For 3) we consider functions h whose values are finite sums of point masses in X. Assuming X has a distance function, we find a geometrically reasonable notion of the distance between 2 such sums. Then functions with TV(h) < oo essentially determine the surfaces and give a surprising amount of regularity. Analysis in singular spaces has had wide applications from algebraic geometry to data analysis.
For more information, e-mail ma-chair@wpi.edu.
Howard Elman (University of Maryland)-Efficient Solution Algorithms for Partial Differential Equations with Random Coefficients
Friday, 12/16/2011 2:00 PM-3:00 PM
Stratton Hall, 203
ABSTRACT: We consider new computational methods for solving partial differential equations (PDEs) when components of the problem such as diffusion coefficients are random fields. In recent years, several computational techniques have been developed for such models that offer potential for improved efficiencies compared with traditional Monte-Carlo methods. These include stochastic Galerkin methods, which use an augmented weak formulation of the PDE derived from averaging with respect to expected value, and stochastic collocation methods, which use a set of samples relatively small in cardinality that captures the character of the solution space. We discuss the relative advantages of these two methods and explore their performance. For problems in which the dependence on uncertain parameters is linear, the Galerkin systems can be solved efficiently by multigrid methods so that the overall cost of solution is significantly lower than for collocation. We also discuss refinements of these methodologies to handle nonlinearities. A commonly used model takes the diffusion coefficient to be of log-normal form, which ensures well-posedness but causes the dependence on uncertain parameters to be nonlinear. We show that this difficulty can be alleviated by reformulating the problem in convection-diffusion form. Finally, computation of statistical properties of solutions such as moments requires explicit knowledge of the joint density function associated with the (finite number of) random variables that determine the uncertain coefficients. This is often not available, and instead, computation is enabled under a simplifying and possibly false assumption that the joint density is simply the product of the marginal densities. We discuss the use of kernel density estimation to circumvent this difficulty.
For more information, e-mail ma-chair@wpi.edu.
Arkadi Berezovski (Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Estonia) - Numerical simulation of waves and fronts in inhomogeneous solids
Monday, 12/19/2011 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Numerical simulations of dynamical problems in inhomogeneous solids meet considerable difficulties in the case of existence of moving discontinuities such as phase transition fronts or cracks. The origin of these difficulties is a constitutive deficiency in the thermomechanical description of corresponding irreversible processes, which leads to an uncertainty in jump relations at moving discontinuities. Consequently, the construction of an appropriate numerical algorithm should be complemented by the development of the thermomechanical theory. The thermodynamic representation of finite volume methods, which is formally identical to well-known numerical methods on smooth solutions, gives additional possibilities in the solution of problems with moving discontinuities due to its ability to handle jump relations at discontinuities.
For more information, e-mail ma-chair@wpi.edu.
January 2012
Christopher Godsil (Department of Combinatorics and Optimization, University of Waterloo)-State Transfer on Graphs
Tuesday, 1/3/2012 2:00 PM-3:00 PM
Stratton Hall, 203
ABSTRACT: Let $X$ be a graph with adjacency matrix $A$. Motivated by work in quantum physics, we study the operator $$
H(t) := \exp(itA).
$$
Physically interesting questions concern the entries of the matrix $M(t)$, whose $rs$-entry is the square of the absolute value of the $rs$-entry of $H(t)$. Thus we might ask if, for given vertices $r$ and $s$, there is a time $t$ such that $M(t)_{r,s}=1$. (In this case have what is called perfect state transfer.) Or we might ask if there is a time $t$ such that all entries of $M(t)$ are equal to $1/n$ (instantaneous uniform mixing), or whether the entries if $M(t)$ average over time are equal to $1/n$ (average uniform mixing). I will discuss the recent progress on these and related problems, and show how they lead to interesting problems in graph theory.
For more information, e-mail ma-chair@wpi.edu.
Kun Gou (Ph.D. Candidate, Department of Mathematics, Texas A&M University) - An in-vivo spectral technique for estimation of residual stress of arterial wall by a novel application of intravascular ultrasound technology
Thursday, 1/5/2012 3:00 PM-4:00 PM
Stratton Hall, 203
Abstract: Residual stress is a stress that can exist in a body in the absence of externally applied loads. It is a challenge to recover it in soft tissues both theoretically and experimentally. A mathematical inverse spectral technique is developed to reconstruct the residual stress in the arterial wall in vivo. The technique is theoretically based on a novel use of intravascular ultrasound technology (IVUS), which is part of a long-range project to distinguish vulnerable atherosclerotic plaques from safe ones more accurately. As the IVUS is interrogating inside the artery, it produces small amplitude, high frequency time harmonic vibrations superimposed on the static deformations of the stressed artery. Two categories of boundary value problems are formulated to form Sturm-Liouville problems (SLP). The natural eigenfrequencies of arterial wall gained from IVUS implementation are employed as eigenvalues of the SLP. Via an optimization approach, the algorithms for an inverse spectral technique are established to recover the residual stress.
For more information, e-mail ma-chair@wpi.edu.
Lisa Fauci (Tulane University)-Spiny disks, flexible fibers and waving rings: explorations in phytoplankton fluid dynamics
Friday, 1/20/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Phytoplankton motion in the ocean, at the scale of individual cells, involves the interaction of passive and actuated elastic structures with a surrounding fluid - a common theme in biological fluid dynamics. We present recent modeling results that shed light on the active swimming of dinoflagellates, as well as the passive motion of diatoms in shear flows . These diatoms may form chains or bear spines. In addition to examining how the flexibility and geometry of the diatoms affect their rotational dynamics, we will discuss how laboratory experiments and computational simulations are being calibrated in an effort to characterize the elastic properties of different species of chain-forming diatoms.
For more information, e-mail ma-chair@wpi.edu.
Gabe Cunningham (Northeastern University) - Constructing abstract regular polytopes with external symmetries
Friday, 1/27/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: Abstract polytopes are a combinatorial generalization of convex polytopes and tessellations of surfaces. Of particular importance are the regular polytopes, which have the highest degree of internal symmetry. In addition to these internal symmetries, which correspond to reflections and rotations, some regular polytopes have external symmetries such as self-duality. This talk will introduce and motivate the subject of abstract polytopes, and then we will see a group-theoretic method for constructing regular polytopes with specified external symmetries.
For more information, e-mail ma-chair@wpi.edu.
February 2012
Ilie-Radu Mitric (University of Connecticut)-Ruin Models Featuring Interest and Diffusion
Friday, 2/3/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: A number of extensions to the risk theory models are analyzed. Initially, we consider a multi-threshold compound Poisson surplus process with interest earned at a constant rate. Then, we considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk model with interclaim times that are generalized Erlang (n) distributed and claim amounts following a Matrix-Exponential (ME) distribution. Under this scenario, we present a general methodology to analyze the Gerber-Shiu discounted penalty function defined at absolute ruin, as a solution of high-order linear differential equations with non-constant coefficients. Closed-form solutions for the absolute ruin probabilities in the generalized Erlang (2) case complement recent results from literature obtained under the classical risk model.
Lastly, we analyze a multi-layer compound Poisson surplus process perturbed by diffusion and examine the behavior of the Gerber-Shiu discounted penalty function.
For more information, e-mail ma-chair@wpi.edu.
Stephan Sturm (Princeton University)-From Smile Wings to Market Risk Measures
Tuesday, 2/7/2012 11:00 AM-12:00 PM
Stratton Hall, 203
Abstract: The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In particular, we make use of indifference pricing by dynamic convex risk measures, which are given as solutions of backward stochastic differential equations (BSDEs), to establish a link between these two approaches to risk measurement. We derive a characterization of the implied volatility in terms of the solution of a nonlinear PDE and provide a small time-to-maturity expansion. This procedure allows to choose convex risk measures in a conveniently parametrized class, distorted entropic dynamic risk measures, such that the asymptotic volatility skew under indifference pricing can be matched with the market skew. This is joint work with Ronnie Sircar.
For more information, e-mail ma-chair@wpi.edu.
Harsh Jain (Ohio State University)-A non-autonomous delay differential equation model of cancer chemotherapy
Thursday, 2/9/2012 4:15 PM-5:15 PM
Gateway Park, 1002
ABSTRACT: The use of delay differential equations (DDEs) to study biological phenomena has a long history, when the rate of change of model variables depends their previous history. Today, DDEs occupy a central place in models of infectious disease dynamics, epidemiology, ecology and tumor growth. In this talk, I will present a delayed partial differential equation (PDE) model applied to tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy. The tumor is assumed to undergo logistic growth in the absence of therapy. To accurately simulate the action of chemotherapy, an age-structure together with a delay is imposed on proliferating cancer cells, and intracellular signaling pathways relevant to drug action explicitly modeled. The age-structured model results in a 1D hyperbolic PDE, which can be reduced to a nonlinear, non-autonomous DDE by projecting along the characteristics. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined. This has clinical implications since it leads to a lower bound for the amount of therapy required to affect a cure. Finally, I will present a clinical application of the model, by applying it to the treatment of ovarian cancers. Two types of drugs are considered platinum-based chemotherapeutic agents that are the current standard of care for most solid tumors, and small molecule cell death inducers that are currently under development. The model is calibrated versus in vitro experimental results, and is then used to predict optimal doses and administration time scheduling for the treatment of a tumor growing in vivo.
This talk is jointly sponsored by the Departments of Biology & Biotechnology, and Mathematical Sciences
For more information, e-mail ma-chair@wpi.edu.
Jeffrey Chuang (Boston College)-Identifying Hidden Functional Elements in Coding Regions
Thursday, 2/16/2012 4:15 PM-5:15 PM
Gateway Park, 1002
ABSTRACT: It has been increasingly appreciated that protein-coding DNA sequences harbor hidden regulatory sequences in addition to encoding for protein. These may include motifs that act at the DNA level, such as transcription factor binding sites, as well as motifs that act at the RNA level, such as microRNA-RNA binding sites. Detecting unusually overrepresented or conserved motifs has been algorithmically challenging because of interference by constraints at the protein level. I will present methods we have developed to efficiently calculate motifs of unusual conservation or overrepresentation in coding regions. Our studies indicate that hidden regulatory motifs are prevalent throughout eukaryotic and prokaryotic genomes. Additionally, I will present experimental results on whether coding regions can contain larger regulatory sequences. Our zebrafish studies indicate that vertebrate developmental genes contain large numbers of transcriptional enhancers, showing that proteins are malleable enough that even complex secondary functions can evolve in the same location.
This colloquium is jointly sponsored by the Departments of Biology & Biotechnology, and Mathematical Sciences.
For more information, e-mail ma-chair@wpi.edu.
March 2012
Giuliano Lazzaroni (Institut für Mathematik, Universität Würzburg) - On the role of the kinetic energy during unstable propagation in a heterogeneous peeling test
Friday, 3/2/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
Ugur G. Abdulla (Florida Institute of Technology)-Wiener Test at $\infty$ for Elliptic and Parabolic PDEs, and its Measure-Theoretical, Topological, and Probabilistic Consequences
Friday, 3/16/2012 11:00 AM-12:00 PM
Stratton Hall, 203
Wieners celebrated result on the boundary regularity of harmonic functions is one of the most beautiful and delicate results in XX century mathematics. It has shaped the boundary regularity theory for elliptic and parabolic PDEs, and has become a central result in the development of potential theory at the intersection of functional analysis, PDE, and measure theories. This talk describes the new developments which precisely characterize the regularity of the point at $\infty$ for second order elliptic and parabolic PDEs and broadly extend the role of the Wiener test in classical analysis. The Wiener test at $\infty$ arises as a global characterization of uniqueness in boundary value problems for arbitrary unbounded open sets. From a topological point of view, the Wiener test at $\infty$ arises as a thinness criteria at $\infty$ in fine topology. In a probabilistic context, the Wiener test at $\infty$ characterizes asymptotic laws for the characteristic Markov processes whose generator is the given differential operator. The counterpart of the new Wiener test at a finite boundary point leads to uniqueness in the Dirichlet problem for a class of unbounded functions growing at a certain rate near the boundary point; a criteria for the removability of singularities and/or for unique continuation at the finite boundary point. The Wiener criterion at $\infty$ is a largely unexplored issue of great importance in various disciplines, most notably in Nonlinear Potential Theory, Nonlinear Elliptic and Parabolic PDEs, Calculus of Variations, Topology, and in Probability Theory. The talk will end with a description of some open problems in those directions.
For more information, e-mail ma-chair@wpi.edu.
H.J. Gay Lecture - David Jerison (MIT) - Title TBA
Friday, 3/23/2012 11:00 AM-12:00 PM
Bartlett Center
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
TO BE RESCHEDULED, DATE TBD Heiko Enderling (Center of Cancer Systems Biology, Tufts University School of Medicine)-Cancer stem cells in solid tumors
Friday, 3/23/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The cancer stem cell hypothesis postulates that only a subpopulation of cancer cells in a tumor is capable of initiating, sustaining and re-initiating tumors, leaving the bulk of the population being non-stem cancer cells that lack tumor initiation and progression potential. With these two phenotypically distinct populations interacting with each other, the emerging tumor population can exhibit various non-linear growth kinetics. An environmentally independent early dormant state is an inevitable early tumor progression bottleneck for a large range of biologically realistic cell kinetic parameters. When intrinsic cell kinetics combine in unexpected manner, escape to tumor progression occurs as morphologically distinct self-metastatic expansion of multiple self-limited tumor clones.
For more information, e-mail ma-chair@wpi.edu.
April 2012
Marian Bocea (Loyola University)-Title TBA
Friday, 4/6/2012 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.
H.J. Gay Lecture - Alfio Quarteroni - Title TBA
Friday, 4/13/2012 11:00 AM-12:00 PM
Atwater Kent Laboratories, 219
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.