Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

Adaptive estimation in circular functional linear models

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an orthogonal series estimator of the slope function, by replacing the first m theoretical coefficients of its development in the trigonometric basis by adequate estimators. Wepropose a model selection procedure for m in a set of admissible values, by defining a contrast function minimized by our estimator and a theoretical penalty function; this first step assumes the degree of ill posedness to be known. Then we generalize the procedure to a random set of admissible m's and a random penalty function. The resulting estimator is completely data driven and reaches automatically what is known to be the optimal minimax rate of convergence, in term of a general weighted L2-risk. This means that we provide adaptive estimators of both the slope function and its derivatives

tDCS induced GABA change is associated with the simulated electric field in M1, an effect mediated by grey matter volume in the MRS voxel

Background and objective Transcranial direct current stimulation (tDCS) has wide ranging applications in neuro-behavioural and physiological research, and in neurological rehabilitation. However, it is currently limited by substantial inter-subject variability in responses, which may be explained, at least in part, by anatomical differences that lead to variability in the electric field (E-field) induced in the cortex. Here, we tested whether the variability in the E-field in the stimulated cortex during anodal tDCS, estimated using computational simulations, explains the variability in tDCS induced changes in GABA, a neurophysiological marker of stimulation effect. Methods Data from five previously conducted MRS studies were combined. The anode was placed over the left primary motor cortex (M1, 3 studies, N = 24) or right temporal cortex (2 studies, N = 32), with the cathode over the contralateral supraorbital ridge. Single voxel spectroscopy was performed in a 2x2x2cm voxel under the anode in all cases. MRS data were acquired before and either during or after 1 mA tDCS using either a sLASER sequence (7T) or a MEGA-PRESS sequence (3T). sLASER MRS data were analysed using LCModel, and MEGA-PRESS using FID-A and Gannet. E-fields were simulated in a finite element model of the head, based on individual structural MR images, using SimNIBS. Separate linear mixed effects models were run for each E-field variable (mean and 95th percentile; magnitude, and components normal and tangential to grey matter surface, within the MRS voxel). The model included effects of time (pre or post tDCS), E-field, grey matter volume in the MRS voxel, and a 3-way interaction between time, E-field and grey matter volume. Additionally, we ran a permutation analysis using PALM to determine whether E-field anywhere in the brain, not just in the MRS voxel, correlated with GABA change. Results In M1, higher mean E-field magnitude was associated with greater anodal tDCS-induced decreases in GABA (t(24) = 3.24, p = 0.003). Further, the association between mean E-field magnitude and GABA change was moderated by the grey matter volume in the MRS voxel (t(24) = −3.55, p = 0.002). These relationships were consistent across all E-field variables except the mean of the normal component. No significant relationship was found between tDCS-induced GABA decrease and E-field in the temporal voxel. No significant clusters were found in the whole brain analysis. Conclusions Our data suggest that the electric field induced by tDCS within the brain is variable, and is significantly related to anodal tDCS-induced decrease in GABA, a key neurophysiological marker of stimulation. These findings strongly support individualised dosing of tDCS, at least in M1. Further studies examining E-fields in relation to other outcome measures, including behaviour, will help determine the optimal E-fields required for any desired effects

Absolute polarization angle calibration using polarized diffuse Galactic emission observed by BICEP

We present a method of cross-calibrating the polarization angle of a polarimeter using BICEP Galactic observations. \bicep\ was a ground based experiment using an array of 49 pairs of polarization sensitive bolometers observing from the geographic South Pole at 100 and 150 GHz. The BICEP polarimeter is calibrated to +/-0.01 in cross-polarization and less than +/-0.7 degrees in absolute polarization orientation. BICEP observed the temperature and polarization of the Galactic plane (R.A= 100 degrees ~ 270 degrees and Dec. = -67 degrees ~ -48 degrees). We show that the statistical error in the 100 GHz BICEP Galaxy map can constrain the polarization angle offset of WMAP Wband to 0.6 degrees +\- 1.4 degrees. The expected 1 sigma errors on the polarization angle cross-calibration for Planck or EPIC are 1.3 degrees and 0.3 degrees at 100 and 150 GHz, respectively. We also discuss the expected improvement of the BICEP Galactic field observations with forthcoming BICEP2 and Keck observations.Comment: 13 pages, 10 figures and 2 tables. To appear in Proceedings of SPIE Astronomical Telescopes and Instrumentation 201

Polymorphisms at codons 108 and 189 in murine PrP play distinct roles in the control of scrapie incubation time

Rona Barron - ORCID: 0000-0003-4512-9177 https://orcid.org/0000-0003-4512-9177Item not available from this repository.Susceptibility to transmissible spongiform encephalopathies (TSEs) is associated strongly with PrP polymorphisms in humans, sheep and rodents. In mice, scrapie incubation time is controlled by polymorphisms at PrP codons 108 (leucine or phenylalanine) and 189 (threonine or valine), but the precise role of each polymorphism in the control of disease is unknown. The L108F and T189V polymorphisms are present in distinct structural regions of PrP and thus provide an excellent model with which to investigate the role of PrP structure and gene variation in TSEs. Two unique lines of transgenic mice, in which 108F and 189V have been targeted separately into the endogenous murine Prnp a gene, have been produced. TSE inoculation of inbred lines of mice expressing all allelic combinations at codons 108 and 189 has revealed a complex relationship between PrP allele and incubation time. It has been established that both codons 108 and 189 control TSE incubation time, and that each polymorphism plays a distinct role in the disease process. Comparison of ME7 incubation times in mouse lines that are heterozygous at both codons has also identified a previously unrecognized intramolecular interaction between PrP codons 108 and 189.https://doi.org/10.1099/vir.0.80525-086pubpub

SAEM Response to the National Institutes of Health request for information: Future directions in violence against women research

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An exploration of parents’ preferences for foot care in juvenile idiopathic arthritis: a possible role for the discrete choice experiment

Background: An increased awareness of patients’ and parents’ care preferences regarding foot care is desirable from a clinical perspective as such information may be utilised to optimise care delivery. The aim of this study was to examine parents’ preferences for, and valuations of foot care and foot-related outcomes in juvenile idiopathic arthritis (JIA).<p></p> Methods: A discrete choice experiment (DCE) incorporating willingness-to-pay (WTP) questions was conducted by surveying 42 parents of children with JIA who were enrolled in a randomised-controlled trial of multidisciplinary foot care at a single UK paediatric rheumatology outpatients department. Attributes explored were: levels of pain; mobility; ability to perform activities of daily living (ADL); waiting time; referral route; and footwear. The DCE was administered at trial baseline. DCE data were analysed using a multinomial-logit-regression model to estimate preferences and relative importance of attributes of foot care. A stated-preference WTP question was presented to estimate parents’ monetary valuation of health and service improvements.<p></p> Results: Every attribute in the DCE was statistically significant (p < 0.01) except that of cost (p = 0.118), suggesting that all attributes, except cost, have an impact on parents’ preferences for foot care for their child. The magnitudes of the coefficients indicate that the strength of preference for each attribute was (in descending order): improved ability to perform ADL, reductions in foot pain, improved mobility, improved ability to wear desired footwear, multidisciplinary foot care route, and reduced waiting time. Parents’ estimated mean annual WTP for a multidisciplinary foot care service was £1,119.05.<p></p> Conclusions: In terms of foot care service provision for children with JIA, parents appear to prefer improvements in health outcomes over non-health outcomes and service process attributes. Cost was relatively less important than other attributes suggesting that it does not appear to impact on parents’ preferences.<p></p&gt