13 resultados para foundations of mathematics

em Aston University Research Archive


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Neural networks have often been motivated by superficial analogy with biological nervous systems. Recently, however, it has become widely recognised that the effective application of neural networks requires instead a deeper understanding of the theoretical foundations of these models. Insight into neural networks comes from a number of fields including statistical pattern recognition, computational learning theory, statistics, information geometry and statistical mechanics. As an illustration of the importance of understanding the theoretical basis for neural network models, we consider their application to the solution of multi-valued inverse problems. We show how a naive application of the standard least-squares approach can lead to very poor results, and how an appreciation of the underlying statistical goals of the modelling process allows the development of a more general and more powerful formalism which can tackle the problem of multi-modality.

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This paper examines the role of creative resources in the emergence of the Japanese video game industry. We argue that creative resources nurtured by popular cartoons and animation sector, combined with technological knowledge accumulated in the consumer electronics industry, facilitated the emergence of successful video game industry in Japan. First we trace the development of the industry from its origin to the rise of platform developers and software publishers. Then, knowledge and creative foundations that influenced the developmental trajectory of this industry are analyzed, with links to consumer electronics and in regards to cartoons and animation industry.

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Knowledge is of crucial, and growing importance in social, political and economic relations in modern society. The range and variety of available knowledge dramatically enlarges the available options of social action. This five volume collection brings together a broad array of contributions from a variety of disciplines. Featuring essays from philosophers who have investigated the foundations of knowledge, and addressing different forms of knowledge in society such as common sense and practical knowledge, this collection also discusses the role of knowledge in economic process and gives attention to the role of expert knowledge in political decision making. Including a collection of articles from the sociology of knowledge and science, the set also provides a new introduction by the editors, making it a unique and invaluable research resource for both student and scholar.

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DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

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Background: The prevalence of hearing loss is considerably higher in individuals in residential care than in people within the community-dwelling population, and yet hearing aids and hearing services are relatively underused. Care staff have a key role in supporting access to services. Objectives: This study identifies staff perspectives on hearing loss and their views about potential hearing service improvements. Study design: A four-stage mixed methods study was used, made up of qualitative interviews, observation, a survey and a stakeholder involvement meeting. Results: The qualitative stages indicated that staff were concerned about their levels of interaction with residents. Staff considered maximizing communication as part of their professional role. The quantitative survey indicated that these views were widely held by staff, and the stakeholder stage identified the need for social support and dedicated staff training opportunities. Conclusion: Care home staff regard communication as a shared issue. Future interventions could enhance access to hearing services and provide care home staff with training in hearing loss and hearing aid management. © 2013 Informa Healthcare.

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The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.

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Neural networks are statistical models and learning rules are estimators. In this paper a theory for measuring generalisation is developed by combining Bayesian decision theory with information geometry. The performance of an estimator is measured by the information divergence between the true distribution and the estimate, averaged over the Bayesian posterior. This unifies the majority of error measures currently in use. The optimal estimators also reveal some intricate interrelationships among information geometry, Banach spaces and sufficient statistics.

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A theoretical model is presented which describes selection in a genetic algorithm (GA) under a stochastic fitness measure and correctly accounts for finite population effects. Although this model describes a number of selection schemes, we only consider Boltzmann selection in detail here as results for this form of selection are particularly transparent when fitness is corrupted by additive Gaussian noise. Finite population effects are shown to be of fundamental importance in this case, as the noise has no effect in the infinite population limit. In the limit of weak selection we show how the effects of any Gaussian noise can be removed by increasing the population size appropriately. The theory is tested on two closely related problems: the one-max problem corrupted by Gaussian noise and generalization in a perceptron with binary weights. The averaged dynamics can be accurately modelled for both problems using a formalism which describes the dynamics of the GA using methods from statistical mechanics. The second problem is a simple example of a learning problem and by considering this problem we show how the accurate characterization of noise in the fitness evaluation may be relevant in machine learning. The training error (negative fitness) is the number of misclassified training examples in a batch and can be considered as a noisy version of the generalization error if an independent batch is used for each evaluation. The noise is due to the finite batch size and in the limit of large problem size and weak selection we show how the effect of this noise can be removed by increasing the population size. This allows the optimal batch size to be determined, which minimizes computation time as well as the total number of training examples required.

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Developmental learning disabilities such as dyslexia and dyscalculia have a high rate of co-occurrence in pediatric populations, suggesting that they share underlying cognitive and neurophysiological mechanisms. Dyslexia and other developmental disorders with a strong heritable component have been associated with reduced sensitivity to coherent motion stimuli, an index of visual temporal processing on a millisecond time-scale. Here we examined whether deficits in sensitivity to visual motion are evident in children who have poor mathematics skills relative to other children of the same age. We obtained psychophysical thresholds for visual coherent motion and a control task from two groups of children who differed in their performance on a test of mathematics achievement. Children with math skills in the lowest 10% in their cohort were less sensitive than age-matched controls to coherent motion, but they had statistically equivalent thresholds to controls on a coherent form control measure. Children with mathematics difficulties therefore tend to present a similar pattern of visual processing deficit to those that have been reported previously in other developmental disorders. We speculate that reduced sensitivity to temporally defined stimuli such as coherent motion represents a common processing deficit apparent across a range of commonly co-occurring developmental disorders.

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The revolution in the foundations of physics at the beginning of the twentieth century suggested to several of its most prominent workers that biology was ripe for something similar. In consequence, a number of physicists moved into biology. They were highly influential in initiating a molecular biology in the 1950s. Two decades later it seemed to several of these migrants, and those they had influenced, that the major problems in molecular biology had been solved, and that it was time to move on to what seemed to them the final problem: the nervous system, consciousness, and the age-old mind-body problem. This paper reviews this "double migration" and shows how the hopes of the first generation of physicist-biologists were both realized and dashed. No new physical principles were discovered at work in the foundations of biology or neuroscience. On the other hand, the mind-set of those trained in physics proved immensely valuable in analyzing fundamental issues in both biology and neuroscience. It has been argued that the outcome of the molecular biology of the 1950s was a change in the concept of the gene from that of "a mysterious entity into that of a real molecular object" (Watson, 1965, p.6); the gates and channels which play such crucial roles in the functioning of nervous systems have been transformed in a similar way. Studies on highly simplified systems have also opened the prospect of finding the neural correlatives of numerous behaviors and neuropathologies. This increasing understanding at the molecular level is invaluable not only in devising rational therapies but also, by defining the material substrate of consciousness, in bringing the mind-body problem into sharper focus. Copyright © Taylor & Francis Inc.

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This paper investigates how existing software engineering techniques can be employed, adapted and integrated for the development of systems of systems. Starting from existing system-of-systems (SoS) studies, we identify computing paradigms and techniques that have the potential to help address the challenges associated with SoS development, and propose an SoS development framework that combines these techniques in a novel way. This framework addresses the development of a class of IT systems of systems characterised by high variability in the types of interactions between their component systems, and by relatively small numbers of such interactions. We describe how the framework supports the dynamic, automated generation of the system interfaces required to achieve these interactions, and present a case study illustrating the development of a data-centre SoS using the new framework.

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Our understanding of creativity is limited, yet there is substantial research trying to mimic human creativity in artificial systems and in particular to produce systems that automatically evolve art appreciated by humans. We propose here to study human visual preference through observation of nearly 500 user sessions with a simple evolutionary art system. The progress of a set of aesthetic measures throughout each interactive user session is monitored and subsequently mimicked by automatic evolution in an attempt to produce an image to the liking of the human user.