Brown University Center for Statistical Sciences Seminar
Dave Gordon, Head of the Centre for the Study of Social Exclusion and Social Justice, School for Policy Studies, University of Bristol | |
4th Floor Conference Room |
Abstract: Poverty and health: there is now widespread agreement in the academic community in the UK that poverty is a major cause of ill health. The British government has accepted this link and is now committed to ending child poverty `forever' within a generation (e.g. by 2020). It is hoped that this will first halt and then reverse the widening health gap between the `rich' and the `poor' that has grown over the past twenty years. The major public health and broad social policy implications of these developments will be the subject of this talk.
*Reception following seminar at 167 Angell Street,
2nd floor confrerence room.
Stochastic Systems Seminar
**NEW ANNOUNCEMENT
Special Brown Applied Mathematics Pattern Theory and Vision Seminar
The Phase-Space Dynamics of Systems of Spiking Neurons | |
Note: Arunava Banerjee is a Burroughs Wellcome/Brain Science Program Postdoctoral Candidate |
Brown Analysis Seminar
Scientific Computing Seminar
Abstract: The performance of a system can be meaningfully defined as a measure of the closeness between the observed and the predicted state of the system. Understanding the uncertainty underlying this difference, identifying its controlling factors, and quantifying the propagation of these factors through the mathematical model adopted for the system can lead to the design of systems with improved performance.
With recent advances in sensing and computational technologies, the possibility arises for probing nature at a previously unimagined scale, as well as for predicting its evolution with increasingly complex mathematical models. The significant recent increase in both quality and quantity of experimental observations provides a very fertile ground for the development of various models of data that can be integrated into mechanistic-based models. In particular, probabilistic-based models of data are very appealing in view of the rich mathematical toolbox available for their manipulation.
This talk will present a framework for the propagation of probabilistically-modeled data through mechanistic models of natural and engineered systems. The framework is based on identifying random variables and processes with their projections on the Polynomial Chaos, a basis in a suitable Hilbert space of second order random variables. The problem is thus restated in the context of deterministic approximation theory. A Galerkin projection procedure is utilized to compute an optimal representation of the response of the system as a function of the uncertainties in its data. The format of the solution is particularly well-suited to the analysis of complex systems with interacting subsystems. Post-processing procedures suitable for resource allocation, performance-based design and reliability analysis will also be presented. The framework will be demonstrated by its application to problems in structural and soil dynamics and flow in porous media.
PDE Seminar
Abstract: If it takes N samples to represent a function on an interval, then it will take N^2 samples to represent an analogous function on a square, and N^3 samples for one on a cube. Multiplying matrices in 1D takes N^3 operations, in 2D it takes N^6, and in 3D it takes N^9. In general, a computation that requires E effort in 1D will require E^d effort in dimension d. This effect is known as the Curse of Dimensionality and is the single greatest impediment to performing realistic computations when d>2.
We are developing a technique to bypass the curse. Although at root it is a simple generalization of separation of variables, it provides an important conceptual framework for computing in higher dimensions. This framework is like the idea "banded matrix", which in itself solves nothing, and "most" of the time is not applicable, but is still extremely useful for many problems.
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