BELIEF PROPAGATION FOR OPTIMAL EDGE COVER IN THE RANDOM COMPLETE GRAPH

We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the random assignment problem. A proof via the objective method is useful because it provides us with more information on the nature of the edge's incident on a typical root in the minimum-cost edge cover. We further show that a belief propagation algorithm converges asymptotically to the optimal solution. This can be applied in a computational linguistics problem of semantic projection. The belief propagation algorithm yields a near optimal solution with lesser complexity than the known best algorithms designed for optimality in worst-case settings.

Algorithm for Autonomous Reorganization of Mobile Wireless Camera Sensor Networks to Improve Coverage

In this paper, sensing coverage by wireless camera-embedded sensor networks (WCSNs), a class of directional sensors is studied. The proposed work facilitates the autonomous tuning of orientation parameters and displacement of camera-sensor nodes in the bounded field of interest (FoI), where the network coverage in terms of every point in the FoI is important. The proposed work is first of its kind to study the problem of maximizing coverage of randomly deployed mobile WCSNs which exploits their mobility. We propose an algorithm uncovered region exploration algorithm (UREA-CS) that can be executed in centralized and distributed modes. Further, the work is extended for two special scenarios: 1) to suit autonomous combing operations after initial random WCSN deployments and 2) to improve the network coverage with occlusions in the FoI. The extensive simulation results show that the performance of UREA-CS is consistent, robust, and versatile to achieve maximum coverage, both in centralized and distributed modes. The centralized and distributed modes are further analyzed with respect to the computational and communicational overheads.

A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation: Application to Image Denoising

In big data image/video analytics, we encounter the problem of learning an over-complete dictionary for sparse representation from a large training dataset, which cannot be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm that exploits the inherent clustered structure of the training data and make use of a divide-and-conquer approach. The fundamental idea behind the algorithm is to partition the training dataset into smaller clusters, and learn local dictionaries for each cluster. Subsequently, the local dictionaries are merged to form a global dictionary. Merging is done by solving another dictionary learning problem on the atoms of the locally trained dictionaries. This algorithm is referred to as the split-and-merge algorithm. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy, which operates on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography

This paper deals with a new approach to study the nonlinear inviscid flow over arbitrary bottom topography. The problem is formulated as a nonlinear boundary value problem which is reduced to a Dirichlet problem using certain transformations. The Dirichlet problem is solved by applying Plemelj-Sokhotski formulae and it is noticed that the solution of the Dirichlet problem depends on the solution of a coupled Fredholm integral equation of the second kind. These integral equations are solved numerically by using a modified method. The free-surface profile which is unknown at the outset is determined. Different kinds of bottom topographies are considered here to study the influence of bottom topography on the free-surface profile. The effects of the Froude number and the arbitrary bottom topography on the free-surface profile are demonstrated in graphical forms for the subcritical flow. Further, the nonlinear results are validated with the results available in the literature and compared with the results obtained by using linear theory. (C) 2015 Elsevier Inc. All rights reserved.

SMO: An Integrated Approach to Intra-array and Inter-array Storage Optimization

The polyhedral model provides an expressive intermediate representation that is convenient for the analysis and subsequent transformation of affine loop nests. Several heuristics exist for achieving complex program transformations in this model. However, there is also considerable scope to utilize this model to tackle the problem of automatic memory footprint optimization. In this paper, we present a new automatic storage optimization technique which can be used to achieve both intra-array as well as inter-array storage reuse with a pre-determined schedule for the computation. Our approach works by finding statement-wise storage partitioning hyper planes that partition a unified global array space so that values with overlapping live ranges are not mapped to the same partition. Our heuristic is driven by a fourfold objective function which not only minimizes the dimensionality and storage requirements of arrays required for each high-level statement, but also maximizes inter statement storage reuse. The storage mappings obtained using our heuristic can be asymptotically better than those obtained by any existing technique. We implement our technique and demonstrate its practical impact by evaluating its effectiveness on several benchmarks chosen from the domains of image processing, stencil computations, and high-performance computing.

Singularity characteristics for a lip-shaped crack subjected to remote biaxial loading

In this paper, the conformal mapping method was adopted to solve the problem of an infinite plate containing a central lip-shaped crack subjected to remote biaxial loading. A kind of leaf-shaped configuration was also constructed in order to solve the problem. The analytical result showed that the singularity order of the stress field at the tip of a lip-shaped crack remains -1/2, despite the difference in notch-crack width.

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.

A singularly perturbed linear two-point boundary-value problem

We consider the following singularly perturbed linear two-point boundary-value problem:

Ly(x) ≡ Ω(ε)D_xy(x) - A(x,ε)y(x) = f(x,ε) 0≤x≤1 (1a)

By ≡ L(ε)y(0) + R(ε)y(1) = g(ε) ε → 0^+ (1b)

Here Ω(ε) is a diagonal matrix whose first m diagonal elements are 1 and last m elements are ε. Aside from reasonable continuity conditions placed on A, L, R, f, g, we assume the lower right mxm principle submatrix of A has no eigenvalues whose real part is zero. Under these assumptions a constructive technique is used to derive sufficient conditions for the existence of a unique solution of (1). These sufficient conditions are used to define when (1) is a regular problem. It is then shown that as ε → 0^+ the solution of a regular problem exists and converges on every closed subinterval of (0,1) to a solution of the reduced problem. The reduced problem consists of the differential equation obtained by formally setting ε equal to zero in (1a) and initial conditions obtained from the boundary conditions (1b). Several examples of regular problems are also considered.

A similar technique is used to derive the properties of the solution of a particular difference scheme used to approximate (1). Under restrictions on the boundary conditions (1b) it is shown that for the stepsize much larger than ε the solution of the difference scheme, when applied to a regular problem, accurately represents the solution of the reduced problem.

Furthermore, the existence of a similarity transformation which block diagonalizes a matrix is presented as well as exponential bounds on certain fundamental solution matrices associated with the problem (1).

Edge function method applied to thin plates resting on Winkler foundation

The Edge Function method formerly developed by Quinlan⁽²⁵⁾ is applied to solve the problem of thin elastic plates resting on spring supported foundations subjected to lateral loads the method can be applied to plates of any convex polygonal shapes, however, since most plates are rectangular in shape, this specific class is investigated in this thesis. The method discussed can also be applied easily to other kinds of foundation models (e.g. springs connected to each other by a membrane) as long as the resulting differential equation is linear. In chapter VII, solution of a specific problem is compared with a known solution from literature. In chapter VIII, further comparisons are given. The problems of concentrated load on an edge and later on a corner of a plate as long as they are far away from other boundaries are also given in the chapter and generalized to other loading intensities and/or plates springs constants for Poisson's ratio equal to 0.2

Formal methods for control synthesis in partially observed environments : application to autonomous robotic manipulation

Modern robots are increasingly expected to function in uncertain and dynamically challenging environments, often in proximity with humans. In addition, wide scale adoption of robots requires on-the-fly adaptability of software for diverse application. These requirements strongly suggest the need to adopt formal representations of high level goals and safety specifications, especially as temporal logic formulas. This approach allows for the use of formal verification techniques for controller synthesis that can give guarantees for safety and performance. Robots operating in unstructured environments also face limited sensing capability. Correctly inferring a robot's progress toward high level goal can be challenging.

This thesis develops new algorithms for synthesizing discrete controllers in partially known environments under specifications represented as linear temporal logic (LTL) formulas. It is inspired by recent developments in finite abstraction techniques for hybrid systems and motion planning problems. The robot and its environment is assumed to have a finite abstraction as a Partially Observable Markov Decision Process (POMDP), which is a powerful model class capable of representing a wide variety of problems. However, synthesizing controllers that satisfy LTL goals over POMDPs is a challenging problem which has received only limited attention.

This thesis proposes tractable, approximate algorithms for the control synthesis problem using Finite State Controllers (FSCs). The use of FSCs to control finite POMDPs allows for the closed system to be analyzed as finite global Markov chain. The thesis explicitly shows how transient and steady state behavior of the global Markov chains can be related to two different criteria with respect to satisfaction of LTL formulas. First, the maximization of the probability of LTL satisfaction is related to an optimization problem over a parametrization of the FSC. Analytic computation of gradients are derived which allows the use of first order optimization techniques.

The second criterion encourages rapid and frequent visits to a restricted set of states over infinite executions. It is formulated as a constrained optimization problem with a discounted long term reward objective by the novel utilization of a fundamental equation for Markov chains - the Poisson equation. A new constrained policy iteration technique is proposed to solve the resulting dynamic program, which also provides a way to escape local maxima.

The algorithms proposed in the thesis are applied to the task planning and execution challenges faced during the DARPA Autonomous Robotic Manipulation - Software challenge.

Structure Prediction of G-Protein Coupled Receptors

G-protein coupled receptors (GPCRs) form a large family of proteins and are very important drug targets. They are membrane proteins, which makes computational prediction of their structure challenging. Homology modeling is further complicated by low sequence similarly of the GPCR superfamily.

In this dissertation, we analyze the conserved inter-helical contacts of recently solved crystal structures, and we develop a unified sequence-structural alignment of the GPCR superfamily. We use this method to align 817 human GPCRs, 399 of which are nonolfactory. This alignment can be used to generate high quality homology models for the 817 GPCRs.

To refine the provided GPCR homology models we developed the Trihelix sampling method. We use a multi-scale approach to simplify the problem by treating the transmembrane helices as rigid bodies. In contrast to Monte Carlo structure prediction methods, the Trihelix method does a complete local sampling using discretized coordinates for the transmembrane helices. We validate the method on existing structures and apply it to predict the structure of the lactate receptor, HCAR1. For this receptor, we also build extracellular loops by taking into account constraints from three disulfide bonds. Docking of lactate and 3,5-dihydroxybenzoic acid shows likely involvement of three Arg residues on different transmembrane helices in binding a single ligand molecule.

Protein structure prediction relies on accurate force fields. We next present an effort to improve the quality of charge assignment for large atomic models. In particular, we introduce the formalism of the polarizable charge equilibration scheme (PQEQ) and we describe its implementation in the molecular simulation package Lammps. PQEQ allows fast on the fly charge assignment even for reactive force fields.

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

The River Lune strategic stock assessment survey 1991 with particular reference to salmonids

In the past stock assessment surveys were generally reactive in response to a particular problem e.g. a pollution incident and as such were limited in the information they provided. A programme of strategic stock assessment would be more beneficial, providing up to date information on the status and composition of the stock. On a national level this could reveal trends in population dynamics and enable comparisons to be made between key rivers and between regions. The Stock Assessment Task Group (1991) has recommended annual strategic surveys for juvenile salmonids and triennial strategic surveys for coarse fish and non- migratory salmonids. The aim of this pilot study was to gain information on species distribution and their relative abundance within the River Lune catchment, and to compare the findings with the surveys carried out between 1981-1985. This would provide valuable information on the current status of the stock and provide an indication of the resources required to conduct such strategic surveys on other river catchments in the North West Region of the National Rivers Authority.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Effects of reducing nutrient loads to surface waters within the Mississippi River Basin and the Gulf of Mexico: Topic 4 Report for the Integrated Assessment on Hypoxia in the Gulf of Mexico

The overall goal of this assessment was to evaluate the effects of nutrient-source reductions that may be implemented in the Mississippi River Basin (MRB) to reduce the problem of low oxygen conditions (hypoxia) in the nearshore Gulf of Mexico. Such source reductions would affect the quality of surface waters—streams, rivers, and reservoirs—in the drainage basin itself, as well as nearshore Gulf waters. The task group’s work was divided into addressing the effects of nutrient-source reductions on: (1) surface waters in the MRB and (2) hypoxia in the Gulf of Mexico.