The use of mixture density networks in the emulation of complex epidemiological individual-based models

Complex, highly-computational, individual-based models are abundant in epidemiology. For epidemics such as macro-parasitic diseases, detailed modelling of human behaviour and pathogen life-cycle are required in order to produce accurate results. This can often lead to models that are computationally-expensive to analyse and perform model fitting, and often require many simulation runs in order to build up sufficient statistics. Emulation can provide a more computationally-efficient output of the individual-based model, by approximating it using a statistical model. Previous work has used Gaussian processes (GPs) in order to achieve this, but these can not deal with multi-modal, heavy-tailed, or discrete distributions. Here, we introduce the concept of a mixture density network (MDN) in its application in the emulation of epidemiological models. MDNs incorporate both a mixture model and a neural network to provide a flexible tool for emulating a variety of models and outputs. We develop an MDN emulation methodology and demonstrate its use on a number of simple models incorporating both normal, gamma and beta distribution outputs. We then explore its use on the stochastic SIR model to predict the final size distribution and infection dynamics. MDNs have the potential to faithfully reproduce multiple outputs of an individual-based model and allow for rapid analysis from a range of users. As such, an open-access library of the method has been released alongside this manuscript

AMPA Receptor Phosphorylation and Synaptic Colocalization on Motor Neurons Drive Maladaptive Plasticity below Complete Spinal Cord Injury.

Clinical spinal cord injury (SCI) is accompanied by comorbid peripheral injury in 47% of patients. Human and animal modeling data have shown that painful peripheral injuries undermine long-term recovery of locomotion through unknown mechanisms. Peripheral nociceptive stimuli induce maladaptive synaptic plasticity in dorsal horn sensory systems through AMPA receptor (AMPAR) phosphorylation and trafficking to synapses. Here we test whether ventral horn motor neurons in rats demonstrate similar experience-dependent maladaptive plasticity below a complete SCI in vivo. Quantitative biochemistry demonstrated that intermittent nociceptive stimulation (INS) rapidly and selectively increases AMPAR subunit GluA1 serine 831 phosphorylation and localization to synapses in the injured spinal cord, while reducing synaptic GluA2. These changes predict motor dysfunction in the absence of cell death signaling, suggesting an opportunity for therapeutic reversal. Automated confocal time-course analysis of lumbar ventral horn motor neurons confirmed a time-dependent increase in synaptic GluA1 with concurrent decrease in synaptic GluA2. Optical fractionation of neuronal plasma membranes revealed GluA2 removal from extrasynaptic sites on motor neurons early after INS followed by removal from synapses 2 h later. As GluA2-lacking AMPARs are canonical calcium-permeable AMPARs (CP-AMPARs), their stimulus- and time-dependent insertion provides a therapeutic target for limiting calcium-dependent dynamic maladaptive plasticity after SCI. Confirming this, a selective CP-AMPAR antagonist protected against INS-induced maladaptive spinal plasticity, restoring adaptive motor responses on a sensorimotor spinal training task. These findings highlight the critical involvement of AMPARs in experience-dependent spinal cord plasticity after injury and provide a pharmacologically targetable synaptic mechanism by which early postinjury experience shapes motor plasticity

Aggregation dynamics explain vegetation patch-size distributions

Vegetation patch-size distributions have been an intense area of study for theoreticians and applied ecologists alike in recent years. Of particular interest is the seemingly ubiquitous nature of power-law patch-size distributions emerging in a number of diverse ecosystems. The leading explanation of the emergence of these power-laws is due to local facilitative mechanisms. There is also a common transition from power law to exponential distribution when a system is under global pressure, such as grazing or lack of rainfall. These phenomena require a simple mechanistic explanation. Here, we study vegetation patches from a spatially implicit, patch dynamic viewpoint. We show that under minimal assumptions a power-law patch-size distribution appears as a natural consequence of aggregation. A linear death term also leads to an exponential term in the distribution for any non-zero death rate. This work shows the origin of the breakdown of the power-law under increasing pressure and shows that in general, we expect to observe a power law with an exponential cutoff (rather than pure power laws). The estimated parameters of this distribution also provide insight into the underlying ecological mechanisms of aggregation and death

Structural investigation of graphitic carbon nitride via XRD and neutron diffraction

We thank EPSRC for support through the EPSRC/NSF chemistry programme and the Royal Society for a Wolfson Merit award.Graphitic carbon nitride (g-C3N4) has, since 2009, attracted great attention for its activity as a visible-light-active photocatalyst for hydrogen evolution. Since it was synthesized in 1834, g-C3N4 has been extensively studied both catalytically and structurally. Although its 2D structure seems to have been solved, its 3D crystal structure has not yet been confirmed. This study attempts to solve the 3D structure of graphitic carbon nitride by means of X-ray diffraction and of neutron scattering. Initially, various structural models are considered and their XRD patterns compared to the measured one. After selecting possible candidates as g-C3N4 structure, neutron scattering is employed to identify the best model that describes the 3D structure of graphitic carbon nitride. Parallel chains of tri-s-triazine units organized in layers with an A–B stacking motif are found to describe the structure of the synthesized graphitic carbon nitride well. A misalignment of the layers is favorable because of the decreased π–π repulsive interlayer interactions.PostprintPostprintPeer reviewe

Projected free energies for polydisperse phase equilibria

A `polydisperse' system has an infinite number of conserved densities. We give a rational procedure for projecting its infinite-dimensional free energy surface onto a subspace comprising a finite number of linear combinations of densities (`moments'), in which the phase behavior is then found as usual. If the excess free energy of the system depends only on the moments used, exact cloud, shadow and spinodal curves result; two- and multi-phase regions are approximate, but refinable indefinitely by adding extra moments. The approach is computationally robust and gives new geometrical insights into the thermodynamics of polydispersity.Comment: 4 pages, REVTeX, uses multicol.sty and epsf.sty, 1 postscript figure include

Disease transmission promotes evolution of host spatial patterns

Ecological dynamics can produce a variety of striking patterns. On ecological time scales, pattern formation has been hypothesized to be due to the interaction between a species and its local environment. On longer time scales, evolutionary factors must be taken into account. To examine the evolutionary robustness of spatial pattern formation, we construct a spatially explicit model of vegetation in the presence of a pathogen. Initially, we compare the dynamics for vegetation parameters that lead to competition induced spatial patterns and those that do not. Over ecological time scales, banded spatial patterns dramatically reduced the ability of the pathogen to spread, lowered its endemic density and hence increased the persistence of the vegetation. To gain an evolutionary understanding, each plant was given a heritable trait defining its resilience to competition; greater competition leads to lower vegetation density but stronger spatial patterns. When a disease is introduced, the selective pressure on the plant's resilience to the competition parameter is determined by the transmission of the disease. For high transmission, vegetation that has low resilience to competition and hence strong spatial patterning is an evolutionarily stable strategy. This demonstrates a novel mechanism by which striking spatial patterns can be maintained by disease-driven selection

Reflection impulsivity in binge drinking: behavioural and volumetric correlates.

The degree to which an individual accumulates evidence prior to making a decision, also known as reflection impulsivity, can be affected in psychiatric disorders. Here, we study decisional impulsivity in binge drinkers, a group at elevated risk for developing alcohol use disorders, comparing two tasks assessing reflection impulsivity and a delay discounting task, hypothesizing impairments in both subtypes of impulsivity. We also assess volumetric correlates of reflection impulsivity focusing on regions previously implicated in functional magnetic resonance imaging studies. Sixty binge drinkers and healthy volunteers were tested using two different information-gathering paradigms: the beads task and the Information Sampling Task (IST). The beads task was analysed using a behavioural approach and a Bayesian model of decision making. Delay discounting was assessed using the Monetary Choice Questionnaire. Regression analyses of primary outcomes were conducted with voxel-based morphometry analyses. Binge drinkers sought less evidence prior to decision in the beads task compared with healthy volunteers in both the behavioural and computational modelling analysis. There were no group differences in the IST or delay discounting task. Greater impulsivity as indexed by lower evidence accumulation in the beads task was associated with smaller dorsolateral prefrontal cortex and inferior parietal volumes. In contrast, greater impulsivity as indexed by lower evidence accumulation in the IST was associated with greater dorsal cingulate and precuneus volumes. Binge drinking is characterized by impaired reflection impulsivity suggesting a deficit in deciding on the basis of future outcomes that are more difficult to represent. These findings emphasize the role of possible therapeutic interventions targeting decision-making deficits.The study was supported by theWellcome Trust grant to VV (093705/10/Z) and to NA Harrison. PB is supported by the Portuguese Foundation for Science and Technology (individual fellowship to PB: SFRH/BD/33889/ 2009). YW is supported by the Fyssen Fondation. MM is supported by the Welcome Trust and the Biomedical Research Centre.Wewould also like to thank theWolfson Brain Imaging Center staff for their expertise with collecting the imaging data and all the participants for their involvement in this study. The Behavioural and Clinical Neuroscience Institute is supported by the Wellcome Trust and Medical Research Council.This is the final published version. It first appeared from Wiley via http://dx.doi.org/10.1111/adb.1222

Understanding the relationship between prevalence of microfilariae and antigenaemia using a model of lymphatic filariasis infection.

BACKGROUND: Lymphatic filariasis is a debilitating neglected tropical disease that affects impoverished communities. Rapid diagnostic tests of antigenaemia are a practical alternative to parasitological tests of microfilaraemia for mapping and surveillance. However the relationship between these two methods of measuring burden has previously been difficult to interpret. METHODS: A statistical model of the distribution of worm burden and microfilariae (mf) and resulting antigenaemic and mf prevalence was developed and fitted to surveys of two contrasting sentinel sites undergoing interventions. The fitted model was then used to explore the relationship in various pre- and post-intervention scenarios. RESULTS: The model had good quantitative agreement with the data and provided estimates of the reduction in mf output due to treatment. When extrapolating the results to a range of prevalences there was good qualitative agreement with published data. CONCLUSIONS: The observed relationship between antigenamic and mf prevalence is a natural consequence of the relationship between prevalence and intensity of adult worms and mf production. The method described here allows the estimation of key epidemiological parameters and consequently gives insight into the efficacy of an intervention programme