The learning dynamics of a universal approximator

The learning properties of a universal approximator, a normalized committee machine with adjustable biases, are studied for on-line back-propagation learning. Within a statistical mechanics framework, numerical studies show that this model has features which do not exist in previously studied two-layer network models without adjustable biases, e.g., attractive suboptimal symmetric phases even for realizable cases and noiseless data.

The role of biases in on-line learning of two-layer networks

The influence of biases on the learning dynamics of a two-layer neural network, a normalized soft-committee machine, is studied for on-line gradient descent learning. Within a statistical mechanics framework, numerical studies show that the inclusion of adjustable biases dramatically alters the learning dynamics found previously. The symmetric phase which has often been predominant in the original model all but disappears for a non-degenerate bias task. The extended model furthermore exhibits a much richer dynamical behavior, e.g. attractive suboptimal symmetric phases even for realizable cases and noiseless data.

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

Random graph coloring:Statistical physics approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. ©2002 The American Physical Society.

Coloring random graphs and maximizing local diversity

We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.

Magnetization enumerator for real-valued symmetric channels in Gallager error-correcting codes

Using the magnetization enumerator method, we evaluate the practical and theoretical limitations of symmetric channels with real outputs. Results are presented for several regular Gallager code constructions.

Resource allocation in sparse graphs

Resource allocation in sparsely connected networks, a representative problem of systems with real variables, is studied using the replica and Bethe approximation methods. An efficient distributed algorithm is devised on the basis of insights gained from the analysis and is examined using numerical simulations,showing excellent performance and full agreement with the theoretical results. The physical properties of the resource allocation model are discussed.

Message passing for task redistribution on sparse graphs

The problem of resource allocation in sparse graphs with real variables is studied using methods of statistical physics. An efficient distributed algorithm is devised on the basis of insight gained from the analysis and is examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

Symmetric and asymmetric evaluation of the Tokamap in comparison with direct symplectic integration

Comparing the Poincaré plots of the Tokamap and the underlying Hamiltonian system reveals large differences. This stems from the particular choice of evaluation of the singular perturbations present in the system (a series of δ functions). A symmetric evaluation approach is proposed and shown to yield results that almost perfectly match the Hamiltonian system. © 2005 The American Physical Society.

Solvable model for distribution networks on random graphs

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

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.

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

The Internet's unexploited path diversity

The connectivity of the Internet at the Autonomous System level is influenced by the network operator policies implemented. These in turn impose a direction to the announcement of address advertisements and, consequently, to the paths that can be used to reach back such destinations. We propose to use directed graphs to properly represent how destinations propagate through the Internet and the number of arc-disjoint paths to quantify this network's path diversity. Moreover, in order to understand the effects that policies have on the connectivity of the Internet, numerical analyses of the resulting directed graphs were conducted. Results demonstrate that, even after policies have been applied, there is still path diversity which the Border Gateway Protocol cannot currently exploit.

The evolving role of information specialists:change agents in process redesign

The research investigates the past, present and potential future role of Information Specialists (ISps) in process oriented companies. It tests the proposition that ISps in companies that have undertaken formal process reengineering exercises are likely to become more proactive and more business oriented (as opposed to technically oriented) than they had previously been when their organisations were organised along traditional, functional lines. A review of existing literature in the area of Business Process Reengineering and Information Management reveals a lack of consensus amongst researchers concerning the appropriate role for ISps during and after BPR. Opinion is divided as to whether IS professionals should reactively support BPR or whether IT/IS developments should be driving these initiatives. A questionnaire based ‘Descriptive Survey’ with 60 respondents is used as a first stage of primary data gathering. This is followed by follow-up interviews with 20 of the participating organisations to gather further information on their experiences. The final stage of data collection consists of further in-depth interview with four case study companies to provide an even richer picture of their experiences. The results of the questionnaire are analysed and displayed in the form of simple means, frequencies and bar graphs. The ‘NU-DIST’ computer based discourse analysis package was tried in relation to summarising the interview findings, but this proved cumbersome and a visual collation method is preferred. Overall, the researcher contends that the supposition outlined above is proven, and she concludes the research by suggesting the implications of these findings. In particular she offers a ‘Framework for Understanding and Action’ which is deemed to be relevant to both practitioners and future researchers.

The dynamics and control of a remotely piloted plan-symmetric helicopter

Prior to the development of a production standard control system for ML Aviation's plan-symmetric remotely piloted helicopter system, SPRITE, optimum solutions to technical requirements had yet to be found for some aspects of the work. This thesis describes an industrial project where solutions to real problems have been provided within strict timescale constraints. Use has been made of published material wherever appropriate, new solutions have been contributed where none existed previously. A lack of clearly defined user requirements from potential Remotely Piloted Air Vehicle (RPAV) system users is identified, A simulation package is defined to enable the RPAV designer to progress with air vehicle and control system design, development and evaluation studies and to assist the user to investigate his applications. The theoretical basis of this simulation package is developed including Co-axial Contra-rotating Twin Rotor (CCTR), six degrees of freedom motion, fuselage aerodynamics and sensor and control system models. A compatible system of equations is derived for modelling a miniature plan-symmetric helicopter. Rigorous searches revealed a lack of CCTR models, based on closed form expressions to obviate integration along the rotor blade, for stabilisation and navigation studies through simulation. An economic CCTR simulation model is developed and validated by comparison with published work and practical tests. Confusion in published work between attitude and Euler angles is clarified. The implementation of package is discussed. dynamic adjustment of assessment. the theory into a high integrity software Use is made of a novel technique basing the integration time step size on error Simulation output for control system stability verification, cross coupling of motion between control channels and air vehicle response to demands and horizontal wind gusts studies are presented. Contra-Rotating Twin Rotor Flight Control System Remotely Piloted Plan-Symmetric Helicopter Simulation Six Degrees of Freedom Motion ( i i)