Recursive Methods in Discounted Stochastic Games: An Algorithm for delta Approaching 1 and a Folk Theorem

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period’s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.Stochastic games

The Smoluchowski equation in population dynamics and the spread of infection

This dissertation is a report on an interdisciplinary investigation consisting of an application of random walk techniques to problems in ecology, particularly to the spread of Hantavirus epidemic among rodents that live on an open terrain. The population of mice that we consider is made up of infectious disease-carrying mice and susceptible mice that are disease-free, and each mouse has its own home range around which it executes a random walk. We describe an event of infection transmission in such a population via reaction-diffusion theory. Our simple model consists of two mice, one infected and the other susceptible, the disease being passed upon encounter as the two mice move on the terrain. The existence of home ranges of the mice is included in the model by representing each mouse to be a Smoluchowski random walker. Such a simple model is appropriate for a dilute population where only one infected-susceptible mice pair is considered to meet at a time. However the calculation helps the understanding of underlying microscopic processes of an epidemic outbreak in an arbitrary population density. The two-mice model is formulated in an arbitrary number of dimensions and explicit calculation in 1-dimension is performed first. We uncover an interesting effect of the home ranges on the characteristics of infection-transmission event. We find that there is an optimal configuration of the home ranges for which infection-transmission occurs most efficiently. Furthermore, the practical application of our model to higher dimensions requires an extension of the theory to circumvent a seemingly well-known problem in reaction-diffusion theory that the `reaction\u27 site cannot be a 0-dimensional object for problems considered in higher dimension than 1. We develop a detailed resolution and present a practical extension with an explicit calculation demonstrated in 2-dimensions. Our work is, thus, useful in two ways. One is the further development of reaction-diffusion theory to tethered random walkers and dimensions higher than 1. The other is to gain insights into the practical problem of the spread of the Hantavirus epidemic

User accessible tissue sample image database system and method

The invention is a medical application of content based image retreival system which is capable of searching through a large image database to find images relevant to user queries based upon visual features such as color texture and shape. these feature values are generally descirbed indirectly through the use of example images since it is inconvenient and inherently difficult for humans to express queries in terms of low level visual characteristics. In other wors, the user describes the desired cocept for retrieval by providing relevant image examples. for instance, a user wishing to find images of various flowers can convey the desired feature values by choosing an image of a flower as a query image. Can be used for matching gene expressions, cat MRI and PET scans, and identifying and diagnosing various diseases

Systems and methods of camera-based fingertip tracking

The invention consists of the use of an ordinary computer camera to track fingertip movements. The movie captured from an ordinary computer camera is analyzed frame by frame for our purposes. The current method being used is as follows, which consists of two stages--positioning and tracking. In postioning, each pixel is compared with other neighboring pixels. As the finger tip tends to be brighter than its surroundings, if this pixel is bright than its surroundings, it isconsidered to be a target pixel. This pixel then undergoes the second stage of tracking. In tracking, the background is removed and movement is analyzed by averaging the greyscales of corresponding pixels in the two frames and subtracting the pixel greyscale from the second frame

Fundamental Matrix Computation: Theory and Practice

We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7-parameter Levenberg-Marquardt (LM) search, EFNS, and EFNS-based bundle adjustment. Doing experimental comparison, we show that EFNS and the 7-parameter LM search exhibit the best performance and that additional bundle adjustment does not increase the accuracy to any noticeable degree

Automatic Camera Model Selection for Multibody Motion Segmentation

We study the problem of segmenting independently moving objects in a video sequence. Several algorithms exist for classifying the trajectories of the feature points into independent motions, but the performance depends on the validity of the underlying camera imaging model. In this paper, we present a scheme for automatically selecting the best model using the geometric AIC before the segmentation stage, Using real video sequences, we confirm that the segmentation accuracy indeed improves if the segmentation is based on the selected model. We also show that the trajectory data can be compressed into low-dimensional vectors using the selected model. This is very effective in reducing the computation time for a long video sequence