Inference and optimization of real edges on sparse graphs:A statistical physics perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory. © 2007 The American Physical Society.

Differences between theoretical predictions and operational performance in a stock control application

Over the past decade, several experienced Operational Researchers have advanced the view that the theoretical aspects of model building have raced ahead of the ability of people to use them. Consequently, the impact of Operational Research on commercial organisations and the public sector is limited, and many systems fail to achieve their anticipated benefits in full. The primary objective of this study is to examine a complex interactive Stock Control system, and identify the reasons for the differences between the theoretical expectations and the operational performance. The methodology used is to hypothesise all the possible factors which could cause a divergence between theory and practice, and to evaluate numerically the effect each of these factors has on two main control indices - Service Level and Average Stock Value. Both analytical and empirical methods are used, and simulation is employed extensively. The factors are divided into two main categories for analysis - theoretical imperfections in the model, and the usage of the system by Buyers. No evidence could be found in the literature of any previous attempts to place the differences between theory and practice in a system in quantitative perspective nor, more specifically, to study the effects of Buyer/computer interaction in a Stock Control system. The study reveals that, in general, the human factors influencing performance are of a much higher order of magnitude than the theoretical factors, thus providing objective evidence to support the original premise. The most important finding is that, by judicious intervention into an automatic stock control algorithm, it is possible for Buyers to produce results which not only attain but surpass the algorithmic predictions. However, the complexity and behavioural recalcitrance of these systems are such that an innately numerate, enquiring type of Buyer needs to be inducted to realise the performance potential of the overall man/computer system.

Competition for shortest paths on sparse graphs

Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of a nonlinear overlap cost that penalizes congestion. Routing becomes more difficult as the number of selected nodes increases and exhibits ergodicity breaking in the case of multiple routers. The ground state of such systems reveals nonmonotonic complex behaviors in average path length and algorithmic convergence, depending on the network topology, and densities of communicating nodes and routers. A distributed linearly scalable routing algorithm is also devised. © 2012 American Physical Society.

Knowledge elicitation and knowledge representation in a large domain with multiple experts

This paper describes the knowledge elicitation and knowledge representation aspects of a system being developed to help with the design and maintenance of relational data bases. The size algorithmic components. In addition, the domain contains multiple experts, but any given expert's knowledge of this large domain is only partial. The paper discusses the methods and techniques used for knowledge elicitation, which was based on a "broad and shallow" approach at first, moving to a "narrow and deep" one later, and describes the models used for knowledge representation, which were based on a layered "generic and variants" approach. © 1995.

Predicting class I major histocompatibility complex (MHC) binders using multivariate statistics:comparison of discriminant analysis and multiple linear regression

The accurate in silico identification of T-cell epitopes is a critical step in the development of peptide-based vaccines, reagents, and diagnostics. It has a direct impact on the success of subsequent experimental work. Epitopes arise as a consequence of complex proteolytic processing within the cell. Prior to being recognized by T cells, an epitope is presented on the cell surface as a complex with a major histocompatibility complex (MHC) protein. A prerequisite therefore for T-cell recognition is that an epitope is also a good MHC binder. Thus, T-cell epitope prediction overlaps strongly with the prediction of MHC binding. In the present study, we compare discriminant analysis and multiple linear regression as algorithmic engines for the definition of quantitative matrices for binding affinity prediction. We apply these methods to peptides which bind the well-studied human MHC allele HLA-A*0201. A matrix which results from combining results of the two methods proved powerfully predictive under cross-validation. The new matrix was also tested on an external set of 160 binders to HLA-A*0201; it was able to recognize 135 (84%) of them.

An adaptive hierarchical approach to the extraction of high resolution medial surfaces

We introduce a novel algorithm for medial surfaces extraction that is based on the density-corrected Hamiltonian analysis. The approach extracts the skeleton directly from a triangulated mesh and adopts an adaptive octree-based approach in which only skeletal voxels are refined to a lower level of the hierarchy, resulting in robust and accurate skeletons at extremely high resolution. The quality of the extracted medial surfaces is confirmed by an extensive set of experiments. © 2012 IEEE.

Efficient algorithm for routing optimization via statistical mechanics

Many practical routing algorithms are heuristic, adhoc and centralized, rendering generic and optimal path configurations difficult to obtain. Here we study a scenario whereby selected nodes in a given network communicate with fixed routers and employ statistical physics methods to obtain optimal routing solutions subject to a generic cost. A distributive message-passing algorithm capable of optimizing the path configuration in real instances is devised, based on the analytical derivation, and is greatly simplified by expanding the cost function around the optimized flow. Good algorithmic convergence is observed in most of the parameter regimes. By applying the algorithm, we study and compare the pros and cons of balanced traffic configurations to that of consolidated traffic, which provides important implications to practical communication and transportation networks. Interesting macroscopic phenomena are observed from the optimized states as an interplay between the communication density and the cost functions used. © 2013 IEEE.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Practical 3D reconstruction based on photometric stereo

Photometric Stereo is a powerful image based 3D reconstruction technique that has recently been used to obtain very high quality reconstructions. However, in its classic form, Photometric Stereo suffers from two main limitations: Firstly, one needs to obtain images of the 3D scene under multiple different illuminations. As a result the 3D scene needs to remain static during illumination changes, which prohibits the reconstruction of deforming objects. Secondly, the images obtained must be from a single viewpoint. This leads to depth-map based 2.5 reconstructions, instead of full 3D surfaces. The aim of this Chapter is to show how these limitations can be alleviated, leading to the derivation of two practical 3D acquisition systems: The first one, based on the powerful Coloured Light Photometric Stereo method can be used to reconstruct moving objects such as cloth or human faces. The second, permits the complete 3D reconstruction of challenging objects such as porcelain vases. In addition to algorithmic details, the Chapter pays attention to practical issues such as setup calibration, detection and correction of self and cast shadows. We provide several evaluation experiments as well as reconstruction results. © 2010 Springer-Verlag Berlin Heidelberg.