Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Colour image coding with wavelets and matching pursuit

This thesis considers sparse approximation of still images as the basis of a lossy compression system. The Matching Pursuit (MP) algorithm is presented as a method particularly suited for application in lossy scalable image coding. Its multichannel extension, capable of exploiting inter-channel correlations, is found to be an efficient way to represent colour data in RGB colour space. Known problems with MP, high computational complexity of encoding and dictionary design, are tackled by finding an appropriate partitioning of an image. The idea of performing MP in the spatio-frequency domain after transform such as Discrete Wavelet Transform (DWT) is explored. The main challenge, though, is to encode the image representation obtained after MP into a bit-stream. Novel approaches for encoding the atomic decomposition of a signal and colour amplitudes quantisation are proposed and evaluated. The image codec that has been built is capable of competing with scalable coders such as JPEG 2000 and SPIHT in terms of compression ratio.

A socio-economic approach to online vision graph generation and handover in distributed smart camera networks

In this paper we propose an approach based on self-interested autonomous cameras, which exchange responsibility for tracking objects in a market mechanism, in order to maximise their own utility. A novel ant-colony inspired mechanism is used to grow the vision graph during runtime, which may then be used to optimise communication between cameras. The key benefits of our completely decentralised approach are on the one hand generating the vision graph online which permits the addition and removal cameras to the network during runtime and on the other hand relying only on local information, increasing the robustness of the system. Since our market-based approach does not rely on a priori topology information, the need for any multi-camera calibration can be avoided. © 2011 IEEE.

Simulation in the supply chain context:matching the simulation tool to the problem

The supply chain can be a source of competitive advantage for the firm. Simulation is an effective tool for investigating supply chain problems. The three main simulation approaches in the supply chain context are System Dynamics (SD), Discrete Event Simulation (DES) and Agent Based Modelling (ABM). A sample from the literature suggests that whilst SD and ABM have been used to address strategic and planning problems, DES has mainly been used on planning and operational problems., A review of received wisdom suggests that historically, driven by custom and practice, certain simulation techniques have been focused on certain problem types. A theoretical review of the techniques, however, suggests that the scope of their application should be much wider and that supply chain practitioners could benefit from applying them in this broader way.

Oblique matching pursuit

A method for selecting a suitable subspace for discriminating signal components through an oblique projection is proposed. The selection criterion is based on the consistency principle introduced by Unser and Aldroubi and extended by Elder. An effective implementation of this principle for the purpose of subspace selection is achieved by updating of the dual vectors yielding the corresponding oblique projector. © 2007 IEEE.

Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core

We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides. © 2013 Optical Society of America.

The multiple pheromone Ant clustering algorithm

Ant Colony Optimisation algorithms mimic the way ants use pheromones for marking paths to important locations. Pheromone traces are followed and reinforced by other ants, but also evaporate over time. As a consequence, optimal paths attract more pheromone, whilst the less useful paths fade away. In the Multiple Pheromone Ant Clustering Algorithm (MPACA), ants detect features of objects represented as nodes within graph space. Each node has one or more ants assigned to each feature. Ants attempt to locate nodes with matching feature values, depositing pheromone traces on the way. This use of multiple pheromone values is a key innovation. Ants record other ant encounters, keeping a record of the features and colony membership of ants. The recorded values determine when ants should combine their features to look for conjunctions and whether they should merge into colonies. This ability to detect and deposit pheromone representative of feature combinations, and the resulting colony formation, renders the algorithm a powerful clustering tool. The MPACA operates as follows: (i) initially each node has ants assigned to each feature; (ii) ants roam the graph space searching for nodes with matching features; (iii) when departing matching nodes, ants deposit pheromones to inform other ants that the path goes to a node with the associated feature values; (iv) ant feature encounters are counted each time an ant arrives at a node; (v) if the feature encounters exceed a threshold value, feature combination occurs; (vi) a similar mechanism is used for colony merging. The model varies from traditional ACO in that: (i) a modified pheromone-driven movement mechanism is used; (ii) ants learn feature combinations and deposit multiple pheromone scents accordingly; (iii) ants merge into colonies, the basis of cluster formation. The MPACA is evaluated over synthetic and real-world datasets and its performance compares favourably with alternative approaches.

Socio-economic vision graph generation and handover in distributed smart camera networks

In this article we present an approach to object tracking handover in a network of smart cameras, based on self-interested autonomous agents, which exchange responsibility for tracking objects in a market mechanism, in order to maximise their own utility. A novel ant-colony inspired mechanism is used to learn the vision graph, that is, the camera neighbourhood relations, during runtime, which may then be used to optimise communication between cameras. The key benefits of our completely decentralised approach are on the one hand generating the vision graph online, enabling efficient deployment in unknown scenarios and camera network topologies, and on the other hand relying only on local information, increasing the robustness of the system. Since our market-based approach does not rely on a priori topology information, the need for any multicamera calibration can be avoided. We have evaluated our approach both in a simulation study and in network of real distributed smart cameras.

Outlier-resisting graph embedding

Graph embedding is a general framework for subspace learning. However, because of the well-known outlier-sensitiveness disadvantage of the L2-norm, conventional graph embedding is not robust to outliers which occur in many practical applications. In this paper, an improved graph embedding algorithm (termed LPP-L1) is proposed by replacing L2-norm with L1-norm. In addition to its robustness property, LPP-L1 avoids small sample size problem. Experimental results on both synthetic and real-world data demonstrate these advantages. © 2009 Elsevier B.V. All rights reserved.

On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.

An improved memory management scheme for large scale graph computing engine GraphChi

GraphChi is the first reported disk-based graph engine that can handle billion-scale graphs on a single PC efficiently. GraphChi is able to execute several advanced data mining, graph mining and machine learning algorithms on very large graphs. With the novel technique of parallel sliding windows (PSW) to load subgraph from disk to memory for vertices and edges updating, it can achieve data processing performance close to and even better than those of mainstream distributed graph engines. GraphChi mentioned that its memory is not effectively utilized with large dataset, which leads to suboptimal computation performances. In this paper we are motivated by the concepts of 'pin ' from TurboGraph and 'ghost' from GraphLab to propose a new memory utilization mode for GraphChi, which is called Part-in-memory mode, to improve the GraphChi algorithm performance. The main idea is to pin a fixed part of data inside the memory during the whole computing process. Part-in-memory mode is successfully implemented with only about 40 additional lines of code to the original GraphChi engine. Extensive experiments are performed with large real datasets (including Twitter graph with 1.4 billion edges). The preliminary results show that Part-in-memory mode memory management approach effectively reduces the GraphChi running time by up to 60% in PageRank algorithm. Interestingly it is found that a larger portion of data pinned in memory does not always lead to better performance in the case that the whole dataset cannot be fitted in memory. There exists an optimal portion of data which should be kept in the memory to achieve the best computational performance.

The Application of Graph Model for Automation of the User Interface Construction

The ability of automatic graphic user interface construction is described. It is based on the building of user interface as reflection of the data domain logical definition. The submitted approach to development of the information system user interface enables dynamic adaptation of the system during their operation. This approach is used for creation of information systems based on CASE-system METAS.

The Development of Parallel Resolution Algorithms Using the Graph Representation

The parallel resolution procedures based on graph structures method are presented. OR-, AND- and DCDP- parallel inference on connection graph representation is explored and modifications to these algorithms using heuristic estimation are proposed. The principles for designing these heuristic functions are thoroughly discussed. The colored clause graphs resolution principle is presented. The comparison of efficiency (on the Steamroller problem) is carried out and the results are presented. The parallel unification algorithm used in the parallel inference procedure is briefly outlined in the final part of the paper.

Normal ECG Recognition for Express-Diagnostics Based on Scale-Space Representation and Dynamic Matching

A novel approach of normal ECG recognition based on scale-space signal representation is proposed. The approach utilizes curvature scale-space signal representation used to match visual objects shapes previously and dynamic programming algorithm for matching CSS representations of ECG signals. Extraction and matching processes are fast and experimental results show that the approach is quite robust for preliminary normal ECG recognition.