Exact Classification with Two-Layer Neural Nets

AbstractThis paper considers the classification properties of two-layer networks of McCulloch–Pitts units from a theoretical point of view. In particular we consider their ability to realise exactly, as opposed to approximate, bounded decision regions in R2. The main result shows that a two-layer network can realise exactly any finite union of bounded polyhedra in R2whose bounding lines lie in general position, except for some well-characterised exceptions. The exceptions are those unions whose boundaries contain a line which is “inconsistent,” as described in the text. Some of the results are valid for Rn,n⩾2, and the problem of generalising the main result to higher-dimensional situations is discussed

Applications of percolation theory to fungal spread with synergy

There is increasing interest in the use of the percolation paradigm to analyze and predict the progress of disease spreading in spatially-structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is in uenced only by that of its neighbours. In a recent paper the percolation paradigm has been generalised to incorporate synergistic interactions in host infectivity and susceptibility and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by rst formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently tting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model tting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease control strategies that de ect epidemics from invasive to non-invasive regimes are discussed

Model diagnostics and refinement for phylodynamic models

<div><p>Phylodynamic modelling, which studies the joint dynamics of epidemiological and evolutionary processes, has made significant progress in recent years due to increasingly available genomic data and advances in statistical modelling. These advances have greatly improved our understanding of transmission dynamics of many important pathogens. Nevertheless, there remains a lack of effective, targetted diagnostic tools for systematically detecting model mis-specification. Development of such tools is essential for model criticism, refinement, and calibration. The idea of utilising <i>latent residuals</i> for model assessment has already been exploited in general spatio-temporal epidemiological settings. Specifically, by proposing appropriately designed non-centered, re-parameterizations of a given epidemiological process, one can construct latent residuals with known sampling distributions which can be used to quantify evidence of model mis-specification. In this paper, we extend this idea to formulate a novel model-diagnostic framework for phylodynamic models. Using simulated examples, we show that our framework may effectively detect a particular form of mis-specification in a phylodynamic model, particularly in the event of superspreading. We also exemplify our approach by applying the framework to a dataset describing a local foot-and-mouth (FMD) outbreak in the UK, eliciting strong evidence against the assumption of no within-host-diversity in the outbreak. We further demonstrate that our framework can facilitate model calibration in real-life scenarios, by proposing a within-host-diversity model which appears to offer a better fit to data than one that assumes no within-host-diversity of FMD virus.</p></div

Exploring the therapeutic affordances of self-harm online support communities: an online survey of members

Background: A growing number of online communities have been established to support those who self-harm. However, little is known about the therapeutic affordances arising from engagement with these communities and resulting outcomes. Objective: The aim of this study was to explore the presence of therapeutic affordances as reported by members of self-harm online support communities. Methods: In total, 94 respondents (aged 13-63 years, mean=23.5 years; 94% female) completed an online survey exploring their experiences of engaging with a self-harm online support community. Respondents varied in terms of how long they had been accessing an online community, with 22% (21/94) accessing less than 1 year, 39% (37/94) 1 to 2 years, 14% (13/94) 2 to 3 years, and 24.5% (23/94) more than 3 years. Responses were analyzed using deductive thematic analysis. Results: The results of our analysis describe each of the five therapeutic affordances that were present in the data, namely (1) connection, the ability to make contact with others who self-harm for the purposes of mutual support and in so doing reduce feelings of loneliness and isolation; (2) adaptation, that is, how use of online support varies in relation to the personal circumstances of the individual user; (3) exploration, that is, the ability to learn about self-harm and learn about strategies to reduce or stop self-harming behavior; (4) narration, that is, the ability to share experiences, as well as read about the experiences of others; and (5) self-presentation, that is, how and what users present about themselves to others in the online community. Conclusions: Our findings suggest that engagement with self-harm online support communities may confer a range of therapeutic benefits for some users, which may serve to minimize the psychosocial burden of self-harm and promote positive coping strategies. In addition, the online nature of the support available may be helpful to those who are unable to access face-to-face support

Nanometric depth resolution from multi-focal images in microscopy

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels

Evidence-based controls for epidemics using spatio-temporal stochastic models in a Bayesian framework.

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models considered here, are playing an increasing role in the design of control as agencies seek to strengthen the evidence on which selected strategies are based. Here, we investigate a general approach to informing the choice of control strategies using spatio-temporal models within the Bayesian framework. We illustrate the approach for the case of strategies based on pre-emptive removal of individual hosts. For an exemplar model, using simulated data and historic data on an epidemic of Asiatic citrus canker in Florida, we assess a range of measures for prioritizing individuals for removal that take account of observations of an emerging epidemic. These measures are based on the potential infection hazard a host poses to susceptible individuals (hazard), the likelihood of infection of a host (risk) and a measure that combines both the hazard and risk (threat). We find that the threat measure typically leads to the most effective control strategies particularly for clustered epidemics when resources are scarce. The extension of the methods to a range of other settings is discussed. A key feature of the approach is the use of functional-model representations of the epidemic model to couple epidemic trajectories under different control strategies. This induces strong positive correlations between the epidemic outcomes under the respective controls, serving to reduce both the variance of the difference in outcomes and, consequently, the need for extensive simulation.Hola Adrakey was supported during the course of this research by a James Watt Postgraduate Research Scholarship from Heriot–Watt University