Sufficient conditions for convergence of the Sum-Product Algorithm

We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. We compare our bounds with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, we derive sufficient conditions that take into account local evidence (i.e., single variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.Comment: 15 pages, 5 figures. Major changes and new results in this revised version. Submitted to IEEE Transactions on Information Theor

Modeling the structure and evolution of discussion cascades

We analyze the structure and evolution of discussion cascades in four popular websites: Slashdot, Barrapunto, Meneame and Wikipedia. Despite the big heterogeneities between these sites, a preferential attachment (PA) model with bias to the root can capture the temporal evolution of the observed trees and many of their statistical properties, namely, probability distributions of the branching factors (degrees), subtree sizes and certain correlations. The parameters of the model are learned efficiently using a novel maximum likelihood estimation scheme for PA and provide a figurative interpretation about the communication habits and the resulting discussion cascades on the four different websites.Comment: 10 pages, 11 figure

Energy deposition in microscopic volumes by high-energy protons

Microscopic energy deposition from passing protons in tissue spher

Changes in the frequency distribution of energy deposited in short pathlengths as a function of energy degradation of the primary beam

Frequency distributions of event size in deposition of energy over small pathlengths measured after penetration of 44.3 MeV protons through thicknesses of tissue-like materia

Learning Price-Elasticity of Smart Consumers in Power Distribution Systems

Demand Response is an emerging technology which will transform the power grid of tomorrow. It is revolutionary, not only because it will enable peak load shaving and will add resources to manage large distribution systems, but mainly because it will tap into an almost unexplored and extremely powerful pool of resources comprised of many small individual consumers on distribution grids. However, to utilize these resources effectively, the methods used to engage these resources must yield accurate and reliable control. A diversity of methods have been proposed to engage these new resources. As opposed to direct load control, many methods rely on consumers and/or loads responding to exogenous signals, typically in the form of energy pricing, originating from the utility or system operator. Here, we propose an open loop communication-lite method for estimating the price elasticity of many customers comprising a distribution system. We utilize a sparse linear regression method that relies on operator-controlled, inhomogeneous minor price variations, which will be fair to all the consumers. Our numerical experiments show that reliable estimation of individual and thus aggregated instantaneous elasticities is possible. We describe the limits of the reliable reconstruction as functions of the three key parameters of the system: (i) ratio of the number of communication slots (time units) per number of engaged consumers; (ii) level of sparsity (in consumer response); and (iii) signal-to-noise ratio.Comment: 6 pages, 5 figures, IEEE SmartGridComm 201

Linear PDEs and eigenvalue problems corresponding to ergodic stochastic optimization problems on compact manifolds

We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the metric induced by the noise. The long term stochastic dynamics on the manifold will be completely characterized by the long term density $\rho$ and the long term current density $J$. As such, control problems may be reformulated as variational problems over $\rho$ and $J$. We discuss several optimization problems: the problem in which both $\rho$ and $J$ are varied freely, the problem in which $\rho$ is fixed and the one in which $J$ is fixed. These problems lead to different kinds of operator problems: linear PDEs in the first two cases and a nonlinear PDE in the latter case. These results are obtained through through variational principle using infinite dimensional Lagrange multipliers. In the case where the initial dynamics are reversible we obtain the result that the optimally controlled diffusion is also symmetrizable. The particular case of constraining the dynamics to be reversible of the optimally controlled process leads to a linear eigenvalue problem for the square root of the density process

Structure-based Targeting of Transcriptional Regulatory Complexes Implicated in Human Disease: A Dissertation

Transcriptional regulatory complexes control gene expression patterns and permit cellular responses to stimuli. Deregulation of complex components upsets target gene expression and can lead to disease. This dissertation examines proteins involved in two distinct regulatory complexes: C-terminal binding protein (CtBP) 1 and 2, and Interferon Regulatory Factors (IRF) 3 and 5. Although critical in developmental processes and injury response, CtBP transcriptional repression of cell adhesion proteins, pro-apoptotic factors, and tumor suppressors has been linked to the pathogenesis of multiple forms of cancer. IRFs function in the immune system and have been implicated in autoimmune disorders. Understanding IRF activation is critical to treating pathogens that target IRF function or for future autoimmune disease therapies. We attempted to determine crystal structures that would provide the details of IRF activation, allowing insight into mechanisms of pathogen immune evasion and autoimmune disorders. Although no new structures were solved, we have optimized expression of C-terminal IRF-3 / co-activator complexes, as well as full-length IRF3 and IRF5 constructs. Modifying the constructs coupled with new crystal screening will soon result in structures which detail IRF activation, advancing understanding of the roles of IRF family members in disease. Through structural and biochemical characterization we sought to identify and develop inhibitors of CtBP transcriptional regulatory functions. High concentrations of CtBP substrate, 4-Methylthio 2-oxobutyric acid (MTOB), have been shown in different cancer models to interfere with CtBP transcriptional regulation. We began the process of structure based drug design by solving crystal structures of both CtBP family members bound to MTOB. The resulting models identified critical ligand contacts and unique active site features, which were utilized in inhibitor design. Potential CtBP inhibitors were identified and co-crystallized with CtBP1. One such compound binds to CtBP more than 1000 times more tightly than does MTOB, as a result of our structure-based inclusion of a phenyl ring and a novel pattern of hydrogen bonding. This molecule provides a starting point for the development of compounds that will both bind more tightly and interfere with transcriptional signaling as we progress towards pharmacologically targeting CtBP as a therapy for specific cancers