Dynamics of learning with restricted training sets

The dynamics of supervised learning in layered neural networks were studied in the regime where the size of the training set is proportional to the number of inputs. The evolution of macroscopic observables, including the two relevant performance measures can be predicted by using the dynamical replica theory. Three approximation schemes aimed at eliminating the need to solve a functional saddle-point equation at each time step have been derived.

Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases. © 2007 IOP Publishing Ltd.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

Nonlinear σ model for disordered superconductors

We suggest a variant of the nonlinear σ model for the description of disordered superconductors. The main distinction from existing models lies in the fact that the saddle point equation is solved nonperturbatively in the superconducting pairing field. It allows one to use the model both in the vicinity of the metal-superconductor transition and well below its critical temperature with full account for the self-consistency conditions. We show that the model reproduces a set of known results in different limiting cases, and apply it for a self-consistent description of the proximity effect at the superconductor-metal interface.

Verification of floating point programs

In this thesis we present an approach to automated verification of floating point programs. Existing techniques for automated generation of correctness theorems are extended to produce proof obligations for accuracy guarantees and absence of floating point exceptions. A prototype automated real number theorem prover is presented, demonstrating a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The prototype is tested on correctness theorems for two simple yet nontrivial programs, proving exception freedom and tight accuracy guarantees automatically. The prover demonstrates a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The experiments show how function intervals can be used to combat the information loss problems that limit the applicability of traditional interval arithmetic in the context of hard real number theorem proving.

Odour pollution problems within the district of the Wrekin council

This thesis is concerned with various aspects of Air Pollution due to smell, the impact it has on communities exposed to it, the means by which it may be controlled and the manner in which a local authority may investigate the problems it causes. The approach is a practical one drawing on examples occurring within a Local Authority's experience and for that reason the research is anecdotal and is not a comprehensive treatise on the full range of options available. Odour Pollution is not yet a well organised discipline and might be considered esoteric as it is necessary to incorporate elements of science and the humanities. It has been necessary to range widely across a number of aspects of the subject so that discussion is often restricted but many references have been included to enable a reader to pursue a particular point in greater depth. In a `fuzzy' subject there is often a yawning gap separating theory and practice, thus case studies have been used to illustrate the interplay of various disciplines in resolution of a problem. The essence of any science is observation and measurement. Observation has been made of the spread of odour pollution through a community and also of relevant meterological data so that a mathematical model could be constructed and its predictions checked. It has been used to explore the results of some options for odour control. Measurements of odour perception and human behaviour seldom have the precision and accuracy of the physical sciences. However methods of social research enabled individual perception of odour pollution to be quantified and an insight gained into reaction of a community exposed to it. Odours have four attributes that can be measured and together provide a complete description of its perception. No objective techniques of measurement have yet been developed but in this thesis simple, structured procedures of subjective assessment have been improvised and their use enabled the functioning of the components of an odour control system to be assessed. Such data enabled the action of the system to be communicated using terms that are understood by a non specialist audience.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

Clinical decision support system for point of care use: ontology driven design and software implementation

OBJECTIVES: The objective of this research was to design a clinical decision support system (CDSS) that supports heterogeneous clinical decision problems and runs on multiple computing platforms. Meeting this objective required a novel design to create an extendable and easy to maintain clinical CDSS for point of care support. The proposed solution was evaluated in a proof of concept implementation. METHODS: Based on our earlier research with the design of a mobile CDSS for emergency triage we used ontology-driven design to represent essential components of a CDSS. Models of clinical decision problems were derived from the ontology and they were processed into executable applications during runtime. This allowed scaling applications' functionality to the capabilities of computing platforms. A prototype of the system was implemented using the extended client-server architecture and Web services to distribute the functions of the system and to make it operational in limited connectivity conditions. RESULTS: The proposed design provided a common framework that facilitated development of diversified clinical applications running seamlessly on a variety of computing platforms. It was prototyped for two clinical decision problems and settings (triage of acute pain in the emergency department and postoperative management of radical prostatectomy on the hospital ward) and implemented on two computing platforms-desktop and handheld computers. CONCLUSIONS: The requirement of the CDSS heterogeneity was satisfied with ontology-driven design. Processing of application models described with the help of ontological models allowed having a complex system running on multiple computing platforms with different capabilities. Finally, separation of models and runtime components contributed to improved extensibility and maintainability of the system.

What are dynamic optimization problems?

Dynamic Optimization Problems (DOPs) have been widely studied using Evolutionary Algorithms (EAs). Yet, a clear and rigorous definition of DOPs is lacking in the Evolutionary Dynamic Optimization (EDO) community. In this paper, we propose a unified definition of DOPs based on the idea of multiple-decision-making discussed in the Reinforcement Learning (RL) community. We draw a connection between EDO and RL by arguing that both of them are studying DOPs according to our definition of DOPs. We point out that existing EDO or RL research has been mainly focused on some types of DOPs. A conceptualized benchmark problem, which is aimed at the systematic study of various DOPs, is then developed. Some interesting experimental studies on the benchmark reveal that EDO and RL methods are specialized in certain types of DOPs and more importantly new algorithms for DOPs can be developed by combining the strength of both EDO and RL methods.