Spectra of modular and small-world matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing shortcuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz-type singular behaviour of the spectral density in a localized region of small |?| values. In the case of modular networks, we can identify contributions of local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalization results.

Neural network regression with input uncertainty

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise or corruption. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which allows for input noise given that some model of the noise process exists. In the limit where this noise process is small and symmetric it is shown, using the Laplace approximation, that there is an additional term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable and sampling this jointly with the network's weights, using Markov Chain Monte Carlo methods, it is demonstrated that it is possible to infer the unbiassed regression over the noiseless input.

Neural Network Modelling with Input Uncertainty: Theory and Application

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which accounts for input noise provided that a model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method adds an extra term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable, and sampling this jointly with the network’s weights, using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input. This leads to the possibility of training an accurate model of a system using less accurate, or more uncertain, data. This is demonstrated on both the, synthetic, noisy sine wave problem and a real problem of inferring the forward model for a satellite radar backscatter system used to predict sea surface wind vectors.

Going it alone? North Korea’s adaptability as a small power in a changing world

This article uses small states scholarship to map North Korea’s evolution from a post-colonial small state to a system-influencing state due to its nuclear weapons programme. The framework allows for contributions to: (1) The DPRK literature which in some parts has suggested the future collapse of the state, (2) The small states literature that suggests they can only survive if they integrate larger political and/or economic units, (3) The mainstream IR literature and its dominant realist streak that considers great powers and their will as the main drivers in contemporary world politics.

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

A novel neural network technique for exploratory data analysis

This paper surveys the context of feature extraction by neural network approaches, and compares and contrasts their behaviour as prospective data visualisation tools in a real world problem. We also introduce and discuss a hybrid approach which allows us to control the degree of discriminatory and topographic information in the extracted feature space.

What difference a writing centre makes:a small scale study

Purpose – Academic writing is often considered to be a weakness in contemporary students, while good reporting and writing skills are highly valued by graduate employers. A number of universities have introduced writing centres aimed at addressing this problem; however, the evaluation of such centres is usually qualitative. The paper seeks to consider the efficacy of a writing centre by looking at the impact of attendance on two “real world” quantitative outcomes – achievement and progression. Design/methodology/approach – Data mining was used to obtain records of 806 first-year students, of whom 45 had attended the writing centre and 761 had not. Findings – A highly significant association between writing centre attendance and achievement was found. Progression to year two was also significantly associated with writing centre attendance. Originality/value – Further, quantitative evaluation of writing centres is advocated using random allocation to a comparison condition to control for potential confounds such as motivation.

Robust automatic mapping algorithms in a network monitoring scenario

Automatically generating maps of a measured variable of interest can be problematic. In this work we focus on the monitoring network context where observations are collected and reported by a network of sensors, and are then transformed into interpolated maps for use in decision making. Using traditional geostatistical methods, estimating the covariance structure of data collected in an emergency situation can be difficult. Variogram determination, whether by method-of-moment estimators or by maximum likelihood, is very sensitive to extreme values. Even when a monitoring network is in a routine mode of operation, sensors can sporadically malfunction and report extreme values. If this extreme data destabilises the model, causing the covariance structure of the observed data to be incorrectly estimated, the generated maps will be of little value, and the uncertainty estimates in particular will be misleading. Marchant and Lark [2007] propose a REML estimator for the covariance, which is shown to work on small data sets with a manual selection of the damping parameter in the robust likelihood. We show how this can be extended to allow treatment of large data sets together with an automated approach to all parameter estimation. The projected process kriging framework of Ingram et al. [2007] is extended to allow the use of robust likelihood functions, including the two component Gaussian and the Huber function. We show how our algorithm is further refined to reduce the computational complexity while at the same time minimising any loss of information. To show the benefits of this method, we use data collected from radiation monitoring networks across Europe. We compare our results to those obtained from traditional kriging methodologies and include comparisons with Box-Cox transformations of the data. We discuss the issue of whether to treat or ignore extreme values, making the distinction between the robust methods which ignore outliers and transformation methods which treat them as part of the (transformed) process. Using a case study, based on an extreme radiological events over a large area, we show how radiation data collected from monitoring networks can be analysed automatically and then used to generate reliable maps to inform decision making. We show the limitations of the methods and discuss potential extensions to remedy these.

The n-tuple network: coping with sub-optimality

The subject of this thesis is the n-tuple net.work (RAMnet). The major advantage of RAMnets is their speed and the simplicity with which they can be implemented in parallel hardware. On the other hand, this method is not a universal approximator and the training procedure does not involve the minimisation of a cost function. Hence RAMnets are potentially sub-optimal. It is important to understand the source of this sub-optimality and to develop the analytical tools that allow us to quantify the generalisation cost of using this model for any given data. We view RAMnets as classifiers and function approximators and try to determine how critical their lack of' universality and optimality is. In order to understand better the inherent. restrictions of the model, we review RAMnets showing their relationship to a number of well established general models such as: Associative Memories, Kamerva's Sparse Distributed Memory, Radial Basis Functions, General Regression Networks and Bayesian Classifiers. We then benchmark binary RAMnet. model against 23 other algorithms using real-world data from the StatLog Project. This large scale experimental study indicates that RAMnets are often capable of delivering results which are competitive with those obtained by more sophisticated, computationally expensive rnodels. The Frequency Weighted version is also benchmarked and shown to perform worse than the binary RAMnet for large values of the tuple size n. We demonstrate that the main issues in the Frequency Weighted RAMnets is adequate probability estimation and propose Good-Turing estimates in place of the more commonly used :Maximum Likelihood estimates. Having established the viability of the method numerically, we focus on providillg an analytical framework that allows us to quantify the generalisation cost of RAMnets for a given datasetL. For the classification network we provide a semi-quantitative argument which is based on the notion of Tuple distance. It gives a good indication of whether the network will fail for the given data. A rigorous Bayesian framework with Gaussian process prior assumptions is given for the regression n-tuple net. We show how to calculate the generalisation cost of this net and verify the results numerically for one dimensional noisy interpolation problems. We conclude that the n-tuple method of classification based on memorisation of random features can be a powerful alternative to slower cost driven models. The speed of the method is at the expense of its optimality. RAMnets will fail for certain datasets but the cases when they do so are relatively easy to determine with the analytical tools we provide.

A simulation study of a localised computer network

An investigation is carried out into the design of a small local computer network for eventual implementation on the University of Aston campus. Microprocessors are investigated as a possible choice for use as a node controller for reasons of cost and reliability. Since the network will be local, high speed lines of megabit order are proposed. After an introduction to several well known networks, various aspects of networks are discussed including packet switching, functions of a node and host-node protocol. Chapter three develops the network philosophy with an introduction to microprocessors. Various organisations of microprocessors into multicomputer and multiprocessor systems are discussed, together with methods of achieving reliabls computing. Chapter four presents the simulation model and its implentation as a computer program. The major modelling effort is to study the behaviour of messages queueing for access to the network and the message delay experienced on the network. Use is made of spectral analysis to determine the sampling frequency while Sxponentially Weighted Noving Averages are used for data smoothing.

Temporal correlations of local network losses

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics.

Finding structures in information networks using the affinity network

This thesis proposes a novel graphical model for inference called the Affinity Network,which displays the closeness between pairs of variables and is an alternative to Bayesian Networks and Dependency Networks. The Affinity Network shares some similarities with Bayesian Networks and Dependency Networks but avoids their heuristic and stochastic graph construction algorithms by using a message passing scheme. A comparison with the above two instances of graphical models is given for sparse discrete and continuous medical data and data taken from the UCI machine learning repository. The experimental study reveals that the Affinity Network graphs tend to be more accurate on the basis of an exhaustive search with the small datasets. Moreover, the graph construction algorithm is faster than the other two methods with huge datasets. The Affinity Network is also applied to data produced by a synchronised system. A detailed analysis and numerical investigation into this dynamical system is provided and it is shown that the Affinity Network can be used to characterise its emergent behaviour even in the presence of noise.

Network lifetime maximization with cross-layer design in wireless sensor networks

This paper investigates a cross-layer design approach for minimizing energy consumption and maximizing network lifetime (NL) of a multiple-source and single-sink (MSSS) WSN with energy constraints. The optimization problem for MSSS WSN can be formulated as a mixed integer convex optimization problem with the adoption of time division multiple access (TDMA) in medium access control (MAC) layer, and it becomes a convex problem by relaxing the integer constraint on time slots. Impacts of data rate, link access and routing are jointly taken into account in the optimization problem formulation. Both linear and planar network topologies are considered for NL maximization (NLM). With linear MSSS and planar single-source and single-sink (SSSS) topologies, we successfully use Karush-Kuhn-Tucker (KKT) optimality conditions to derive analytical expressions of the optimal NL when all nodes are exhausted simultaneously. The problem for planar MSSS topology is more complicated, and a decomposition and combination (D&C) approach is proposed to compute suboptimal solutions. An analytical expression of the suboptimal NL is derived for a small scale planar network. To deal with larger scale planar network, an iterative algorithm is proposed for the D&C approach. Numerical results show that the upper-bounds of the network lifetime obtained by our proposed optimization models are tight. Important insights into the NL and benefits of cross-layer design for WSN NLM are obtained.

Energy efficient radio access architectures for green radio:large versus small cell size deployment

In this paper new architectural approaches that improve the energy efficiency of a cellular radio access network (RAN) are investigated. The aim of the paper is to characterize both the energy consumption ratio (ECR) and the energy consumption gain (ECG) of a cellular RAN when the cell size is reduced for a given user density and service area. The paper affirms that reducing the cell size reduces the cell ECR as desired while increasing the capacity density but the overall RAN energy consumption remains unchanged. In order to trade the increase in capacity density with RAN energy consumption, without degrading the cell capacity provision, a sleep mode is introduced. In sleep mode, cells without active users are powered-off, thereby saving energy. By combining a sleep mode with a small-cell deployment architecture, the paper shows that the ECG can be increased by the factor n = (R/R) while the cell ECR continues to decrease with decreasing cell size.

Loss fluctuations and temporal correlations in network queues

We consider data losses in a single node of a packet- switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router. Both models have a built-in critical behavior with a sharp transition from exponentially small to finite losses. It turns out that the finite capacity of a buffer and the packet-dropping procedure give rise to specific boundary conditions which lead to strong loss rate fluctuations at the critical point even in the absence of such fluctuations in the data arrival process.