92 research outputs found

    Some properties of Chebyshev polynomials

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    Preserving Differential Privacy in Convolutional Deep Belief Networks

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    The remarkable development of deep learning in medicine and healthcare domain presents obvious privacy issues, when deep neural networks are built on users' personal and highly sensitive data, e.g., clinical records, user profiles, biomedical images, etc. However, only a few scientific studies on preserving privacy in deep learning have been conducted. In this paper, we focus on developing a private convolutional deep belief network (pCDBN), which essentially is a convolutional deep belief network (CDBN) under differential privacy. Our main idea of enforcing epsilon-differential privacy is to leverage the functional mechanism to perturb the energy-based objective functions of traditional CDBNs, rather than their results. One key contribution of this work is that we propose the use of Chebyshev expansion to derive the approximate polynomial representation of objective functions. Our theoretical analysis shows that we can further derive the sensitivity and error bounds of the approximate polynomial representation. As a result, preserving differential privacy in CDBNs is feasible. We applied our model in a health social network, i.e., YesiWell data, and in a handwriting digit dataset, i.e., MNIST data, for human behavior prediction, human behavior classification, and handwriting digit recognition tasks. Theoretical analysis and rigorous experimental evaluations show that the pCDBN is highly effective. It significantly outperforms existing solutions

    Goal-directed and habitual control in the basal ganglia: implications for Parkinson's disease

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    Progressive loss of the ascending dopaminergic projection in the basal ganglia is a fundamental pathological feature of Parkinson's disease. Studies in animals and humans have identified spatially segregated functional territories in the basal ganglia for the control of goal-directed and habitual actions. In patients with Parkinson's disease the loss of dopamine is predominantly in the posterior putamen, a region of the basal ganglia associated with the control of habitual behaviour. These patients may therefore be forced into a progressive reliance on the goal-directed mode of action control that is mediated by comparatively preserved processing in the rostromedial striatum. Thus, many of their behavioural difficulties may reflect a loss of normal automatic control owing to distorting output signals from habitual control circuits, which impede the expression of goal-directed action. © 2010 Macmillan Publishers Limited. All rights reserved

    Self-reported health experiences of children living with congenital heart defects: Including patient-reported outcomes in a national cohort study

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    Background: Understanding children’s views about living with congenital heart defects (CHDs) is fundamental to supporting their successful participation in daily life, school and peer relationships. As an adjunct to a health and quality of life outcomes questionnaire, we asked school-age children who survived infant heart procedures to describe their experiences of living with CHDs. Methods: In a UK-wide cohort study, children aged 10 to 14 years with CHDs self-completed postal questionnaires that included an open question about having a ‘heart problem’. We compared the characteristics of children with more and less severe cardiac diagnoses and, through collaborative inductive content analysis, investigated the subjective experiences and coping strategies described by children in both clinical severity groups. Results: Text and/or drawings were returned by 436 children (246 boys [56%], mean age 12.1 years [SD 1.0; range 10–14]); 313 had less severe (LS) and 123 more severe (MS) cardiac diagnoses. At the most recent hospital visit, a higher proportion of the MS group were underweight (more than two standard deviations below the mean for age) or cyanosed (underweight: MS 20.0%, LS 9.9%; cyanosed: MS 26.2%, LS 3.5%). Children in the MS group described concerns about social isolation and feeling ‘different’, whereas children with less severe diagnoses often characterised their CHD as ‘not a big thing’. Some coping strategies were common to both severity groups, including managing health information to avoid social exclusion, however only children in the LS group considered their CHD ‘in the past’ or experienced a sense of survivorship. Conclusions: Children’s reported experiences were not dependent on their cardiac diagnosis, although there were clear qualitative differences by clinical severity group. Children’s concerns emphasised social participation and our findings imply a need to shift the clinical focus from monitoring cardiac function to optimising participation. We highlight the potential for informing and evaluating clinical practice and service provision through seeking patient-reported outcomes in paediatric care

    Incomplete Polynomials of Best Approximation

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    Fourier Methods in Practical Approximation

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    A Duality Theorem and Upper Bounds for Approximation

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    Quadrature solution of integral equations: a uniform treatment of Fredholm and Volterra equations

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    On Maximum Modulus of Polynomials with Restricted Zeros

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