Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
*Refreshments Following Seminar at 167 Angell Street, 2nd Floor Conference Room. |
Abstract: Statistical methods aim to answer a variety of questions about observations. A simple example occurs when a fairly reliable test for a condition or substance, C, has given a positive result. Three important types of questions are:
1. Should this observation lead me to believe that C is present?
2. Does this observation justify my acting as if C were present?
3. Is this observation evidence that C is present?
We distinguish between these three questions in terms of the variables and principles that determine their answers. Then we use this framework to understand the scope and limitations of current methods for interpreting statistical data as evidence.
Questions of the third type, concerning the "evidential interpretation" of statistical data, are central to many applications of statistics in science. We see that for answering them current statistical methods are seriously flawed. We find the source of the problems, and propose a solution based on the Law of Likelihood. This law suggests how the dominant statistical paradigm can be altered so as to generate appropriate methods for (i) objective, quantitative representation of the evidence embodied in a specific set of observations, as well as (ii) measurement and control of the probabilities that a study will produce weak or misleading evidence.
Joint Seminar, Division of Engineering and Center for Fluid Mechanics
Abstract: Introducing T-S wave type disturbances into a mixing layer has been proven to be an effective way of controlling the mixing of incompressible mixing layers. However, for compressible mixing layer, this method becomes less and less effective due to the fact that as the compressibility effect increases, the maximum amplification rate of the T-S wave decreases. Motivated by the observations in an experiment done by Wang and Fiedler in TU-Berlin for an incompressible mixing layer confined in a tube, numerical simulations have been done for its 2-D counterpart for compressible mixing layer with a Mach number of 0.6. The results show that the method used by Wang and Fiedler is also much more effective in enhancing the mixing in a compressible mixing layer than the traditional way of introducing T-S waves into the mixing layer.
Brown Analysis Seminar
PDE Seminar
Department of Mathematics Colloquium
1999 Fall Eastern Sectional Meeting of the American Mathematical
Society -- Providence College, Providence, RI
Saturday October 2, 1999 1:30 p.m.-6:00 p.m.
1999 Fall Eastern Sectional Meeting of the American Mathematical
Society
Abstract: The neocortex of the brain is the seat of all our higher intelligence. Neocortex is organized into a characteristic laminar architecture into which columns of cells are embedded within cortical maps. A major unsolved problem concerns how bottom-up, horizontal, and top-down interactions are organized within these cortical layers to generate adaptive behaviors. Otherwise expressed, how does laminar Computing support biological intelligence? This talk will describe a neural model of how these laminar circuits enable the visual cortex to achieve some of its most important properties of seeing. The talk will also show how the cortex can stably self-organize its circuitry to match the statistics of the world, and how the cortex can selectively pay attention to information that it finds interesting. The neural model is defined by a high-dimensional nonlinear dynamical system in which multiple spatial and temporal scales interact. Such a dynamical system represents a new approach to understanding vision and geometry, in which fundamental geometrical notions such as line and surface are recaste. The payoff for applications is that these systems generate high performance in processing complex scenes, whether natural or artificial, and suggest new designs for chips that can self- organize optimal parameters for dealing with different types of environments. Because the laminar architecture of neocortex is found in all sensory and cognitive processing areas, the results for vision promise to generalize to other intelligent behaviors, such as audition, speech, planning, and problem-solving.
1999 Fall Eastern Sectional Meeting of the American Mathematical
Society
Abstract: In his 1812 Essay on Probability, Laplace devotes a small chapter to what we call today the Bayesian decision rule. He remarks that when we see the letters "CONSTANTINOPLE," in that order, we "judge that this arrangement is not the result of chance ... because it is in comparably more probable that some person has thus arranged the aforesaid letters than that this arrangement is due to chance." This argument hinges on the fact that the number of legitimate combinations of letters, in a language, is "incomparably" smaller than the number of possible combinations. The sparseness of allowed combinations is in fact observed at all linguistic articulations (phonetic/syllabic/lexical/syntactic/pragmatic), and such sparseness is also a feature of the rules that govern the hierarchical composition of simple shapes into more complex ones in natural images. Arguably, the sparseness of compositions is what allows us to perform high-level image interpretation in spite of pervasive low-level ambiguities. Compositionality thus appears to be a fundamental aspect of cognition. I shall describe a Bayesian framework, inspired from Rissanen's principle of Minimum Description Length, that Stuart Geman, Dan Potter and I are developing in an attempt to account for compositionality in terms of elementary binding operations. The goal of this research is to make a contribution to machine vision but also to suggest the inestigation of specific mechanisms that the brain may use to implement the necessary binding operations.
1999 Fall Eastern Sectional Meeting of the American Mathematical
Society
Abstract: The classical model of visual processing in cortex is a hierarchy of increasingly sophisticated representations, extending in a natural way the model of simple to complex cells of Hubel and Wiesel. Somewhat surprisingly, very little quantitative modeling has been done in the last 15 years to explore the biological feasibility of this class of models to explain higher level visual processing, such as object recognition. I will review theoretical models and experimental results in viewpoint-invariant object recognition and describe here a new hierarchical model that accounts well for this complex visual task, is consistent with several recent physiological experiments in inferotemporal cortex and makes testable predictions. The model is based on a novel MAX-like operation on the inputs to certain cortical neuron.
The MAX operation was suggested by trying to find the computational equivalent in cortex of a scanning operation which is a key module in a family of successful computer vision algorithms that we have developed during the last few years. In particular, we have implemented a {\em trainable} object detection system that automatically learns to detect objects of a certain class in unconstrained scenes using a Support Vector Machine classifier. We have demonstrated our system in the tasks of finding faces in images and also of detecting pedestrian.
<--- 1999 Index