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SEPTEMBER 2005 |
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Ergodic Theory Seminar | |
Topic: | Algebraic actions of discrete nilpotent groups |
Presenter: | Klaus Schmidt, University of Vienna |
Date: | Thursday, September 8, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: | In a recent paper Deninger found an entropy formula for certain actions of discrete nilpotent groups by automorphisms of compact abelian groups in terms of Kadison-Fuglede determinants. This talk discusses this formula and other dynamical properties of these actions. |
PACM Colloquium | |
Topic: | Collective Motion in Engineered and Natural Multi-Agent Systems |
Presenter: | Naomi Leonard, Mechanical & Aerospace Engineering, Princeton University |
Date: | Monday, September 19, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: | The collective control of mobile, multi-agent systems is motivated by a range of engineering applications that require the coordination of a group of individually controlled systems. A closely related problem focuses on the role of feedback and interconnection in the collective motion of animal groups. Tools from control and dynamical systems can be used to study both engineered and natural mobile networks in a systematic and scalable way. One goal is to prove stability and robustness of designed patterns or emergent behaviors. In this talk I will describe recent collaborative work on models for collective motion based on a planar group of self-propelled particles with steering control. We extend phase models of coupled oscillators to include spatial dynamics and use these models to stabilize and control collective motion patterns. The patterns can be parametrized, in part, by the extent of oscillator synchrony. I will conclude the talk with some discussion of open problems in the area of cooperative control. |
Operations Research and Financial Engineering Seminar | |
Topic: | Semiparametric methods for gene-environment case-control studies |
Presenter: | Raymond Carroll, Texas A&M University |
Date: | Tuesday, September 20, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
Abstract: | We consider case-control studies of gene and environment interactions using prospective logistic regression models. In a typical case-control study, neither the intercept of the logistic regression nor the population probability of disease can be identified. However, in many cases it is reasonable to assume that genotype and environment are independent in the population, possibly conditional on covariates to account for population stratification. In such as case, we show that the intercept and population probability of disease are identified. We develop a semiparametric likelihood approach for this problem, showing that it leads to more efficient estimates of gene-environment interaction parameters than the standard approach. In addition, if the probability of disease is known in the population, we show efficiency gains for estimating gene-environment interactions, again in contrast to the standard approach. Multiple extensions are discussed, including to missing genotype data, haplotype data, and measurement error in genotypes or environmental variables. Applications to two important data sets are discussed. This is joint work with Nilanjan Chatterjee (National Cancer Institute). |
Statistical Mechanics Seminar | |
Topic: | Microscopic models and mesoscopic free energies |
Presenter: | Joel Lebowitz, Rutgers University |
Date: | Wednesday, September 28, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: | I will describe the statistical mechanical derivation of mesoscopic free energy functionals for systems interacting via both short range and long range (Kac) potentials. These functionals are useful for describing the spatial structure of components in various types of phase transitions. I will then consider the phenomenological Cahn Hilliard free energy functional and derive criteria for stability of droplets of the minority phase just inside the coexistence region. |
Department Colloquium | |
Topic: | TBA |
Presenter: | Zeev Rudnick, Tel Aviv |
Date: | Wednesday, September 28, Time: 4:30 p.m., Location: Fine Hall 314 |
OCTOBER 2005 |
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PACM Colloquium | |
Topic: | TBA |
Presenter: | Mung Chiang, Electrical Engineering, Princeton University |
Date: | Monday, October 3, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Statistical Mechanics Seminar | |
Topic: | Is entropy production local in an infinite classical system? |
Presenter: | David Ruelle, IHES France |
Date: | Wednesday, October 5, Time: 2:00 p.m., Location: Jadwin 343 |
PACM Colloquium | |
Topic: | Low-order models for control of fluids |
Presenter: | Clancy Rowley, Mechanical & Aerospace Engineering, Princeton University |
Date: | Monday, October 10, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: | The ability to effectively control a fluid would enable many exciting technological advances, including the design of quieter, more efficient aircraft. Most of the flow control strategies tried so far have been largely ad hoc, and have not used many of the available tools from control theory and dynamical systems, which can guide controller design as well as placement of sensors and actuators. These tools require knowledge of a model of the system in terms of a system of differential equations, and the equations governing a fluid, though known, are too complex for these tools to apply. This talk addresses model reduction techniques, which are used to simplify existing models, to obtain low-order models tractable enough to be used for analysis and control, while retaining the essential physics. These techniques provide a bridge between complex problems and the mathematical tools useful for their analysis. Specifically, the talk will focus on recent developments of two techniques, Proper Orthogonal Decomposition (POD) and balanced truncation. Each of these techniques has strengths and weaknesses, and we show how ideas from both techniques may be combined, to exploit their strengths. We illustrate the methods by obtaining reduced-order models for a compressible flow past a cavity, and an incompressible channel flow. |
PACM Colloquium | |
Topic: | Algebraic topology and the statistics of natural images |
Presenter: | Gunnar Carlsson, Mathematics, Stanford University |
Date: | Monday, October 17, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: | Natural images taken with a digital camera can be viewed as vectors in a high-dimensional vector space whose dimension is the number of pixels. To understand the set of natural images within this vector space is a very interesting problem, but as stated it is very difficult and likely intractable. A. Lee, D. Mumford, and K. Pedersen have created a data set consisting of small (3 by 3) patches, and one can then ask questions about this set. We (V. de Silva, T. Ishkanov, and myself) have used algebraic topological techniques to obtain information about this set, and I will discuss this application of topological methods in this talk. I will also discuss potential applications in compression and in the neuroscience of vision. |
Department Colloquium | |
Topic: | TBA |
Presenter: | Assaf Naor, Microsoft Research |
Date: | Wednesday, October 19, Time: 4:30 p.m., Location: Fine Hall 314 |
PACM Colloquium | |
Topic: | Sparse recovery |
Presenter: | Terence Tao, Mathematics, University of California, Los Angeles |
Date: | Monday, October 24, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: | Suppose one is given a small number of (possibly noisy) linear measurements of a signal. If the number of measurements is less than the number of degrees of freedom of the signal, then one of course cannot reconstruct the signal from the measurements in general. But if one makes the additional hypothesis that the signal is sparse, or at least compressible, then it does become possible to recover the signal accurately, stably, and quickly. The key is decoherence: the measurement basis has to be very "skew" with respect to the sparsity basis. We will survey a number of recent theoretical developments of this idea by several groups and in several contexts (Fourier reconstruction, linear codes, statistical selection.) |
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