In this paper, we propose mathematical models for the spread of HIV in a network of prisons. We study the effect of both screening prisoners and quarantining infectives. Efficient algorithms based on Newton’s method are then developed for computing the equilibrium values of the infectives in each prison. We also give an optimization formulation for obtaining the optimal screening and quarantine policy. The models and algorithms developed can be extended to model the spread of a disease in a general network of connected zones.

The goal of unsupervised learning, i.e., clustering, is to determine the intrinsic structure of unlabeled data. Feature selection for clustering improves the performance of grouping by removing irrelevant features. Typical feature selection algorithms select a common feature subset for all the clusters. Consequently, clusters embedded in different feature subspaces are not able to be identified. In this paper, we introduce a probabilistic model based on Gaussian mixture to solve this problem. Particularly, the feature relevance for an individual cluster is treated as a probability, which is represented by localized feature saliency and estimated through Expectation Maximization (EM) algorithm during the clustering process. In addition, the number of clusters is determined simultaneously by integrating a Minimum Message Length (MML) criterion. Experiments carried on both synthetic and real-world datasets illustrate the performance of the proposed approach in finding clusters embedded in feature subspace.

In this paper, we study the application of random network coding in peer-to-peer (P2P) networks. The system we analyze is based on a prototype called Avalanche proposed in Network Coding for Large Scale Content Distribution (C. Gkantsidis and P. Rodriguez) for large scale content distribution on such networks. We present the necessary techniques for analyzing the system and show that random network coding provides the system with both maximum bandwidth efficiency and robustness. We also point out that the model for random network coding in P2P networks is very different from the one that has been studied extensively in the literature.

We present a General Linear Camera (GLC) model that unifies many previous camera models into a single representation. The GLC model is capable of describing all perspective (pinhole), orthographic, and many multiperspective (including pushbroom and two-slit) cameras, as well as epipolar plane images. It also includes three new and previously unexplored multiperspective linear cameras. The GLC model is both general and linear in the sense that, given any vector space where rays are represented as points, it describes all 2D affine subspaces (planes) that can be formed by affine combinations of 3 rays. The incident radiance seen along the rays found on subregions of these 2D linear subspaces are a precise definition of a projected image of a 3D scene. We model the GLC imaging process in terms of two separate stages: the mapping of 3D geometry to rays and the sampling of these rays over an image plane. We derive a closed-form solution to projecting 3D points in a scene to rays in a GLC and a notion of GLC collineation analogous to pinhole cameras. Finally, we develop a GLC ray-tracer for the direct rendering of GLC images. The GLC ray-tracer is able to create a broad class of multiperspective effects and it provides flexible collineation controls to reduce multiperspective distortions.