On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio

In this paper, the distribution of the ratio of extreme eigenvalues of a complex Wishart matrix is studied in order to calculate the exact decision threshold as a function of the desired probability of false alarm for the maximum-minimum eigenvalue (MME) detector. In contrast to the asymptotic analysis reported in the literature, we consider a finite number of cooperative receivers and a finite number of samples and derive the exact decision threshold for the probability of false alarm. The proposed exact formulation is further reduced to the case of two receiver-based cooperative spectrum sensing. In addition, an approximate closed-form formula of the exact threshold is derived in terms of a desired probability of false alarm for a special case having equal number of receive antennas and signal samples. Finally, the derived analytical exact decision thresholds are verified with Monte-Carlo simulations. We show that the probability of detection performance using the proposed exact decision thresholds achieves significant performance gains compared to the performance of the asymptotic decision threshold.

Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Goal Recognition through Goal Graph Analysis

We present a novel approach to goal recognition based on a two-stage paradigm of graph construction and analysis. First, a graph structure called a Goal Graph is constructed to represent the observed actions, the state of the world, and the achieved goals as well as various connections between these nodes at consecutive time steps. Then, the Goal Graph is analysed at each time step to recognise those partially or fully achieved goals that are consistent with the actions observed so far. The Goal Graph analysis also reveals valid plans for the recognised goals or part of these goals. Our approach to goal recognition does not need a plan library. It does not suffer from the problems in the acquisition and hand-coding of large plan libraries, neither does it have the problems in searching the plan space of exponential size. We describe two algorithms for Goal Graph construction and analysis in this paradigm. These algorithms are both provably sound, polynomial-time, and polynomial-space. The number of goals recognised by our algorithms is usually very small after a sequence of observed actions has been processed. Thus the sequence of observed actions is well explained by the recognised goals with little ambiguity. We have evaluated these algorithms in the UNIX domain, in which excellent performance has been achieved in terms of accuracy, efficiency, and scalability.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

Computerised Diagnostic Decision Support System for the Classification of Pre-Invasive Cervical Squamous Lesions.

Previous studies have revealed considerable interobserver and intraobserver variation in the histological classification of preinvasive cervical squamous lesions. The aim of the present study was to develop a decision support system (DSS) for the histological interpretation of these lesions. Knowledge and uncertainty were represented in the form of a Bayesian belief network that permitted the storage of diagnostic knowledge and, for a given case, the collection of evidence in a cumulative manner that provided a final probability for the possible diagnostic outcomes. The network comprised 8 diagnostic histological features (evidence nodes) that were each independently linked to the diagnosis (decision node) by a conditional probability matrix. Diagnostic outcomes comprised normal; koilocytosis; and cervical intraepithelial neoplasia (CIN) 1, CIN II, and CIN M. For each evidence feature, a set of images was recorded that represented the full spectrum of change for that feature. The system was designed to be interactive in that the histopathologist was prompted to enter evidence into the network via a specifically designed graphical user interface (i-Path Diagnostics, Belfast, Northern Ireland). Membership functions were used to derive the relative likelihoods for the alternative feature outcomes, the likelihood vector was entered into the network, and the updated diagnostic belief was computed for the diagnostic outcomes and displayed. A cumulative probability graph was generated throughout the diagnostic process and presented on screen. The network was tested on 50 cervical colposcopic biopsy specimens, comprising 10 cases each of normal, koilocytosis, CIN 1, CIN H, and CIN III. These had been preselected by a consultant gynecological pathologist. Using conventional morphological assessment, the cases were classified on 2 separate occasions by 2 consultant and 2 junior pathologists. The cases were also then classified using the DSS on 2 occasions by the 4 pathologists and by 2 medical students with no experience in cervical histology. Interobserver and intraobserver agreement using morphology and using the DSS was calculated with K statistics. Intraobserver reproducibility using conventional unaided diagnosis was reasonably good (kappa range, 0.688 to 0.861), but interobserver agreement was poor (kappa range, 0.347 to 0.747). Using the DSS improved overall reproducibility between individuals. Using the DSS, however, did not enhance the diagnostic performance of junior pathologists when comparing their DSS-based diagnosis against an experienced consultant. However, the generation of a cumulative probability graph also allowed a comparison of individual performance, how individual features were assessed in the same case, and how this contributed to diagnostic disagreement between individuals. Diagnostic features such as nuclear pleomorphism were shown to be particularly problematic and poorly reproducible. DSSs such as this therefore not only have a role to play in enhancing decision making but also in the study of diagnostic protocol, education, self-assessment, and quality control. (C) 2003 Elsevier Inc. All rights reserved.

Feasibility of online collaborative voltage stability control of power systems

This paper presents the results of feasibility study of a novel concept of power system on-line collaborative voltage stability control. The proposal of the on-line collaboration between power system controllers is to enhance their overall performance and efficiency to cope with the increasing operational uncertainty of modern power systems. In the paper, the framework of proposed on-line collaborative voltage stability control is firstly presented, which is based on the deployment of multi-agent systems and real-time communication for on-line collaborative control. Then two of the most important issues in implementing the proposed on-line collaborative voltage stability control are addressed: (1) Error-tolerant communication protocol for fast information exchange among multiple intelligent agents; (2) Deployment of multi-agent systems by using graph theory to implement power system post-emergency control. In the paper, the proposed on-line collaborative voltage stability control is tested in the example 10-machine 39-node New England power system. Results of feasibility study from simulation are given considering the low-probability power system cascading faults.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

A Survey of Search Methodologies and Automated System Development for Examination Timetabling

Exam timetabling is one of the most important administrative activities that takes place in academic institutions. In this paper we present a critical discussion of the research on exam timetabling in the last decade or so. This last ten years has seen an increased level of attention on this important topic. There has been a range of significant contributions to the scientific literature both in terms of theoretical andpractical aspects. The main aim of this survey is to highlight the new trends and key research achievements that have been carried out in the last decade.We also aim to outline a range of relevant important research issues and challenges that have been generated by this body of work.

We first define the problem and review previous survey papers. Algorithmic approaches are then classified and discussed. These include early techniques (e.g. graph heuristics) and state-of-the-art approaches including meta-heuristics, constraint based methods, multi-criteria techniques, hybridisations, and recent new trends concerning neighbourhood structures, which are motivated by raising the generality of the approaches. Summarising tables are presented to provide an overall view of these techniques. We discuss some issues on decomposition techniques, system tools and languages, models and complexity. We also present and discuss some important issues which have come to light concerning the public benchmark exam timetabling data. Different versions of problem datasetswith the same name have been circulating in the scientific community in the last ten years which has generated a significant amount of confusion. We clarify the situation and present a re-naming of the widely studied datasets to avoid future confusion. We also highlight which research papershave dealt with which dataset. Finally, we draw upon our discussion of the literature to present a (non-exhaustive) range of potential future research directions and open issues in exam timetabling research.

Compact Toffoli gate using weighted graph states

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven, or eight qubits, we show that success probabilities of 1/4, 1/2, and 1, respectively, can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup independent, they could be realized in a variety of systems, including linear optics and ion traps.