Belief revision and small loops in Gallager-type error-correcting codes

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Belief propagation vs. TAP for decoding corrupted messages

We employ two different methods, based on belief propagation and TAP,for decoding corrupted messages encoded by employing Sourlas's method, where the code word comprises products of K bits selected randomly from the original message. We show that the equations obtained by the two approaches are similar and provide the same solution as the one obtained by the replica approach in some cases K=2. However, we also show that for K>=3 and unbiased messages the iterative solution is sensitive to the initial conditions and is likely to provide erroneous solutions; and that it is generally beneficial to use Nishimori's temperature, especially in the case of biased messages.

The belief in TAP

We show the similarity between belief propagation and TAP, for decoding corrupted messages encoded by Sourlas's method. The latter is a special case of the Gallager error- correcting code, where the code word comprises products of K bits selected randomly from the original message. We examine the efficacy of solutions obtained by the two methods for various values of K and show that solutions for K>=3 may be sensitive to the choice of initial conditions in the case of unbiased patterns. Good approximations are obtained generally for K=2 and for biased patterns in the case of K>=3, especially when Nishimori's temperature is being used.

Inference by belief propagation in composite systems

We devise a message passing algorithm for probabilistic inference in composite systems, consisting of a large number of variables, that exhibit weak random interactions among all variables and strong interactions with a small subset of randomly chosen variables; the relative strength of the two interactions is controlled by a free parameter. We examine the performance of the algorithm numerically on a number of systems of this type for varying mixing parameter values.

Person-oriented and process-oriented teachers : an investigation of the links between ESOL teachers' personal belief systems and approaches to teaching

This thesis looks to two traditions in research into language teaching, teacher beliefs and classroom interaction, in order to investigate the question: Do teachers of ESOL have an identifiable and coherent system of beliefs about teaching and learning that may account for different approaches to teaching? A qualitative approach to research is taken, following a case study tradition, in order to carry out an in-depth study into the beliefs of six ESOL teachers. Five teachers participated in an initial pilot study and two subsequently became the main case studies for the research. The beliefs of a sixth teacher were then investigated to verify the findings. Semi-structured interviews and classroom observations were carried out with all the teachers. The teachers in the study were found to have personal belief systems that cohere around two orientations to teaching and learning - a person orientation and a process orientation. Moreover, the findings suggest that underlying the orientations is the perception that teachers have of their teacher identity, in terms of whether this is seen as a separate identity or as part of their personality. It is suggested that the two orientations may offer a powerful tool for teacher education as it is increasingly recognised that, in order to be effective, teacher educators must take into account the beliefs that teachers bring with them to training and development programmes. An initial investigations into the teachers’ classroom behaviour suggests that while their methodologies approach may be very similar there are fundamental differences in their interactions patterns and these differences may be a result of their own orientation. However, while teachers’ personal belief systems undoubtedly underlie their approach to teaching, further research is needed to establish the extent and the nature of the relationship between orientation and classroom interaction.

Strategic orientations in practice:Exploring the strategic belief structures of line-managers embedded in practice

Recently researchers have started to investigate the cognitive strategic orientations of individual top managers and have pointed out these may be key in determining the direction and success of their organizations in terms of performance, but they have been unable to effectively operationalize this notion in empirical research and this is holding up knowledge development. To make a contribution that helps overcome this limitation a theoretical framework is developed which specifies the different possible cognitive strategic orientations of top managers as well as those of managers at lower organizational levels involved in the strategy process. This theoretical framework is investigated in the empirical phase of the study into strategic orientations in practice. Additional contributions to knowledge of strategic orientation are made in three main domains. Firstly, current knowledge of strategic orientation is largely limited to analysis at the level of the firm whereas there is a lack of understanding of any relationships with practice at lower organizational levels. The exploratory research undertaken for this thesis contributes to new knowledge of different rational, developmental and interactive strategic orientations of front-line managers and this contributes to a cognitive explanation for emergent strategy linked to strategy processes embedded in practice. In theorising the presence of different strategic orientations in practice the discussion highlights the importance of network and spatial embeddedness within enacted environments. Secondly, a contribution to further knowledge of the links between strategy processes and the content of strategies within a retail context is made. The research highlights different strategy processes used in practice by retail front-line managers in a branch network of stores and these are linked to consequences such as different objectives, performance expectations and the fulfilment of personal goals. Thirdly, a contribution to research methodology is made by addressing problems associated with the comparison of cognitive maps.

Predicting and diagnosing faults in wastewater treatment process by Bayesian Belief Networks

Diagnosing faults in wastewater treatment, like diagnosis of most problems, requires bi-directional plausible reasoning. This means that both predictive (from causes to symptoms) and diagnostic (from symptoms to causes) inferences have to be made, depending on the evidence available, in reasoning for the final diagnosis. The use of computer technology for the purpose of diagnosing faults in the wastewater process has been explored, and a rule-based expert system was initiated. It was found that such an approach has serious limitations in its ability to reason bi-directionally, which makes it unsuitable for diagnosing tasks under the conditions of uncertainty. The probabilistic approach known as Bayesian Belief Networks (BBNS) was then critically reviewed, and was found to be well-suited for diagnosis under uncertainty. The theory and application of BBNs are outlined. A full-scale BBN for the diagnosis of faults in a wastewater treatment plant based on the activated sludge system has been developed in this research. Results from the BBN show good agreement with the predictions of wastewater experts. It can be concluded that the BBNs are far superior to rule-based systems based on certainty factors in their ability to diagnose faults and predict systems in complex operating systems having inherently uncertain behaviour.

Wittgenstein and the justification of religious belief

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Palette-colouring: a belief propagation approach

We consider a variation of the prototype combinatorial optimization problem known as graph colouring. Our optimization goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximize the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call palette-colouring, has been recently addressed as a basic example of a problem arising in the context of distributed data storage. Even though it has not been proved to be NP-complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach at the cost of increased computational effort. We also investigate the emergence of a satisfiable-to-unsatisfiable 'phase transition' as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ('thermodynamic') limit.

Using min-sum loopy belief propagation for decentralised supply chain formation

Modern business trends such as agile manufacturing and virtual corporations require high levels of flexibility and responsiveness to consumer demand, and require the ability to quickly and efficiently select trading partners. Automated computational techniques for supply chain formation have the potential to provide significant advantages in terms of speed and efficiency over the traditional manual approach to partner selection. Automated supply chain formation is the process of determining the participants within a supply chain and the terms of the exchanges made between these participants. In this thesis we present an automated technique for supply chain formation based upon the min-sum loopy belief propagation algorithm (LBP). LBP is a decentralised and distributed message-passing algorithm which allows participants to share their beliefs about the optimal structure of the supply chain based upon their costs, capabilities and requirements. We propose a novel framework for the application of LBP to the existing state-of-the-art case of the decentralised supply chain formation problem, and extend this framework to allow for application to further novel and established problem cases. Specifically, the contributions made by this thesis are: • A novel framework to allow for the application of LBP to the decentralised supply chain formation scenario investigated using the current state-of-the-art approach. Our experimental analysis indicates that LBP is able to match or outperform this approach for the vast majority of problem instances tested. • A new solution goal for supply chain formation in which economically motivated producers aim to maximise their profits by intelligently altering their profit margins. We propose a rational pricing strategy that allows producers to earn significantly greater profits than a comparable LBP-based profitmaking approach. • An LBP-based framework which allows the algorithm to be used to solve supply chain formation problems in which goods are exchanged in multiple units, a first for a fully decentralised technique. As well as multiple-unit exchanges, we also model in this scenario realistic constraints such as factory capacities and input-to-output ratios. LBP continues to be able to match or outperform an extended version of the existing state-of-the-art approach in this scenario. • Introduction of a dynamic supply chain formation scenario in which participants are able to alter their properties or to enter or leave the process at any time. Our results suggest that LBP is able to deal easily with individual occurences of these alterations and that performance degrades gracefully when they occur in larger numbers.

Decentralised supply chain formation:a belief propagation-based approach

Decentralised supply chain formation involves determining the set of producers within a network able to supply goods to one or more consumers at the lowest cost. This problem is frequently tackled using auctions and negotiations. In this paper we show how it can be cast as an optimisation of a pairwise cost function. Optimising this class of functions is NP-hard but good approximations to the global minimum can be obtained using Loopy Belief Propagation (LBP). Here we detail a LBP-based approach to the supply chain formation problem, involving decentralised message-passing between potential participants. Our approach is evaluated against a well-known double-auction method and an optimal centralised technique, showing several improvements: it obtains better solutions for most networks that admit a competitive equilibrium Competitive equilibrium as defined in [3] is used as a means of classifying results on certain networks to allow for minor inefficiencies in their auction protocol and agent bidding strategies. while also solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions.

Seminars and examinations:students' perceptions of the seminar in their examination revision strategy

Students’ performance in examinations is often weaker than in other forms of assessment. Yet it should not be assumed that examination technique is innate or skill based. Successful examination performance calls on students to synthesize information and to demonstrate academic competence. Successful academic performance is primarily concerned with articulatory principles of subject formation and appropriation. However, research into seminars, lectures and examination performances mostly seek to establish a relationship between ‘performance’ and ‘potential’, with much attention focused discretely upon either organizational considerations or the reluctant learner. By emphasizing the social construction of learning situations, this project locates the learning process within a notion of collective social experiences and mutual cooperation. In the broader sense it is interested in questions of meaning and understanding and the process by which concepts are constructed and understood. This process depends on ‘ritualization’, ‘participation frameworks’ and ‘embedding’ (Goffman, 1981). Some students experience difficulties in participating in the ritualized behaviour, which may affect their academic development. By seeking to investigate students’ perception of how they use seminars to develop their academic expertise, this project seeks to contribute to our understanding of the learning process, in particular, the relationship between students’ participation in the examination process and assessment strategies.

Building belief in organizational learning: the role of organizational learning efficacy

There appears to be a missing dimension in OL literature to embrace the collective experience of emotion, both within groups and communities and also across the organization as a whole. The concept of OL efficacy- as a stimulus offering energy and direction for learning - remains unexplored. This research involved engaging with a company we have called ‘Electroco’ in depth to create a rich and nuanced representation of OL and members’ perceptions of OL over an extended time-frame (five years). We drew upon grounded theory research methodology (Locke, 2001), to elicit feedback from the organization, which was then used to inform future research plans and/ or refine emerging ideas. The concept of OL efficacy gradually emerged as a factor to be considered when exploring the relationship between individual learning and OL. . Bearing in mind Bandura’s (1982) conceptualization of self-efficacy (linked with mastery, modelling, verbal persuasion and emotional arousal), we developed a coding strategy encompassing these four factors as conceptualized at the organizational level. We added a fifth factor: ‘control of OL.’ We focused on feelings across the organization and the extent of consensus or otherwise around these five attributes. The construct has potential significance for how people are managed in many ways. Not only is OL efficacy is difficult for competitors to copy (arising as it does from the collective experience of working within a specific context); the self-efficacy concept suggests that success can be engineered with ‘small wins’ to reinforce mastery perceptions. Leaders can signal the importance of interaction with the external context, and encourage reflection on the strategies adopted by competitors or benchmark organizations (modelling). The theory also underlines the key role managers may play in persuading others about their organization’s propensity to learn (by focusing on success stories, for example). Research is set to continue within other sectors, including the high-performance financial service sector as well as the health-care technology sector.

Decentralized supply chain formation using max-sum loopy belief propagation

Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation-based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP-hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max-sum LBP-based approach to the supply chain formation problem, involving decentralized message-passing between supply chain participants. Our approach is evaluated against a well-known decentralized double-auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non-negative surplus and agents not in the allocation would acquire non-positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions. © 2012 Wiley Periodicals, Inc.