Lefschetz Center for Dynamical Systems Seminar
Abstract: Invariant tori of dynamical systems occur both in the dissipative and in the conservative context. We focus in this talk on the latter, where the tori are intrinsically parametrised by the actions $ I_1, \ldots, I_n $ conjugate to the angles $ \theta_1, \ldots, \theta_n $ on the torus. The distribution of maximal tori in a nearly integrable Hamiltonian system is governed by the invariant tori of co-dimension one. The different Cantor families of maximal tori shrink down to normally elliptic tori and are separated by the web formed by stable and unstable manifolds of normally hyperbolic tori. The lower dimensional invariant tori form Cantor families themselves, and may bifurcate under variation of these parameters.
Brown University Center for Statistical Science Seminar
*Joint Seminar with Community Health
University of Oxford | |
Abstract: I will summarize the considerable evidence that the methodological quality of much medical research is unacceptable. I will highlight aspects of design, analysis and interpretation that cause particular difficulty, and give illustrative examples. I will present evidence of relation between methodological quality and research findings and discuss efforts by journals and others to improve quality (use of statistical reviewers, checklists, guidelines etc.), any evidence of effectiveness of these, and recent efforts to improve the quality of reporting of research, such as the CONSORT statement. I will consider various types of research but will give particular attention to randomized trials.
Center for Fluid Mechanics Seminar
University of Maryland | |
of Heavy Particles with a Horizontal Turbulent Channel Flow | |
Abstract: Particle/wall turbulence interaction is an inportant topic to many natural and industrial processes such as particle deposition in materials processing, pneumatic transport of granular materials, and sediment transport within rivers and marine flows. Although much work has been done on this topic, there are still many aspects of particle/turbulence interaction within the wall bounded region that is only known qualitatively, or under limited conditions due to restrictions by existing technology or theoretical simplifications. One such important topic is the coupling mechanism that is responsible for the suspension and sedimentation of relatively large, heavy particulates within horizontal, wall-bounded shear flow. Since the development of the contemporary understanding of turbulent burst and sweep structures within boundary layers, it has been speculated that this mechanism is primarily responsible for the suspension and interaction of the particles within the flow. While this work has revolutionized our phenomenological understanding of the flow, continued model development has not matched this progress in multiphase systems due to a lack of quantitative measures of these processes. In light of the above discussion, the current work has focused on trying to resolve some to these issues by utilizing a unique image separation technique to make simultaneous PIV measurements of both the particulate and carrier phase. These measurements allow for the quantification of the important particle/fluid interaction statistics, as well as providing representative instantaneous vector fields of the carrier fluid structure responsible for the interaction. This talk will present an overview of the PIV method and its validation, along with a presentation and interpretation of our current results concerning the particle interaction within the flow.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Computational Annealing, a class of optimization heuristics that are inspired by statistical physics of phase transitions has been demonstrated to be highly effective for large, non--linear combinatorial optimization problems. In many applications in computer vision and pattern recognition one encounters non--linear objective functions with a huge number of discrete and possibly additional continuous variables. Typical cases of such problems are clustering, grouping and image segmentation or assignment problems in motion or stereo analysis or object recognition. For this type of problem, standard integer programming techniques are no longer applicable and one has to resort to optimization heuristics that are fast, yet avoid possibly an exponential number of unfavorable local minima. A particularly powerful, generic class of algorithms is provided by simulated or deterministic annealing techniques. While standard simulated annealing resorts to slow Monte Carlo type sampling of the solution space, deterministic annealing provides an attractive, fast alternative by analytic approximation of the system while cooling down.
This talk provides an elementary introduction to annealing optimization techniques. Simulated annealing and the Gibbs sampler are discussed first to present the basic concepts; then, the theory of deterministic annealing is presented in great detail. An acceleration heuristic, called Multiscale Annealing is introduced to link the approximation quality of the algorithms to their effective spatial resolution. Robustness issues are discussed in a second talk which concentrates on disturbed combinatorial optimization problems.
(This talk summarizes joint work with Jan Puzicha and Thomas Hofmann.)
Brown Analysis Seminar
Scientific Computing Seminar
University at Buffalo, Buffalo, NY 14260 e-mail: abani@eng.buffalo.edu | |
Strategies for 3D Parallel Adaptive hp FEM | |
Abstract: The greatest difficulty in using adaptive hp FEM in high performance computing environments is the design of efficient schemes for data storage, access and distribution, balancing of the load as the computation evolves and efficient solution strategies. An additional complication is provided by the hierarchical memory structures used in most current computer architectures. In this talk we will discuss the development of a suite of integrated data structures, load balancing strategies and domain decomposition based solvers that address these concerns. This infrastructure substantially simplifies the implementation of parallel hp-FEM schemes for a range of applications.
Our approach provides:
a) support for constrained node based
approximations;
b) simple and highly efficient dynamic
data management schemes based on locality preserving
ordering schemes;
c) embedded robust and high quality dynamic load balancer;
d) close integration with equation solvers designed for such
grids;
e) a simple user-friendly application interface for further
development.
We will also discuss the application of this suite of tools to sample applications.
Special Stochastic Systems Seminar
The Brain Science Program and
The Division of Applied Mathematics
(Pattern Theory & Vision Seminar)
Center for the Neural Basis of Cognition, Carnegie Mellon University, Pittsburgh | |
Abstract: David Marr's theory of vision has dominated biological and computer vision research for over twenty years. However, it has become increasingly evident that in many scenarios, early visual processing, such as segmentation and grouping, cannot be completed without the cooperation of high-level perceptual computation, such as shape and object recognition. The pattern theory of vision, developed originally by Ulf Grenander, emphasizes that visual inference is an interactive process of analysis and synthesis. In this talk, I will present some neurophysiological evidence showing how early visual processing in macaque V1 can be modulated by higher level processes such as contour completion and shape from shading as well as by the behavioral experience of the animals. These findings are consistent with the pattern theoretic approach to vision.
Department of Mathematics Colloquium
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