Stability and Convergence analysis of a Crank-Nicolson Galerkin scheme for the fractional Korteweg-de Vries equation

In this paper we study the convergence of a fully discrete Crank-Nicolson Galerkin scheme for the initial value problem associated with the fractional Korteweg-de Vries (KdV) equation, which involves the fractional Laplacian and non-linear convection terms. Our proof relies on the Kato type local smoothing effect to estimate the localized $H^{\alpha/2}$-norm of the approximated solution, where $\alpha \in [1,2)$. We demonstrate that the scheme converges strongly in $L^2(0,T;L^2_{loc}(\mathbb{R}))$ to a weak solution of the fractional KdV equation provided the initial data in $L^2(\mathbb{R})$. Assuming the initial data is sufficiently regular, we obtain the rate of convergence for the numerical scheme. Finally, the theoretical convergence rates are justified numerically through various numerical illustrations

Sliding Window along with EEGNet based Prediction of EEG Motor Imagery

The need for repeated calibration and accounting for inter subject variability is a major challenge for the practical applications of a brain-computer interface. The problem becomes more severe when it is applied for the neurorehabilitation of stroke patients where the brain-activation pattern may differ quite a bit as compared to healthy individuals due to the altered neurodynamics because of a lesion. There were several approaches to handle this problem in the past that depend on creating customized features that can be generalized among the individual subjects. Recently, several deep learning architectures came into the picture although they often failed to produce superior accuracy as compared to the traditional approaches and mostly do not follow an end-to-end architecture as they depend on custom features. However, a few of them have the promising ability to create more generalizable features in an end-to-end fashion such as the popular EEGNet architecture. Although EEGNet was applied for decoding stroke patient’s motor imagery (MI) data with limited success it failed to achieve superior performance over the traditional methods. In this study, we have augmented the EEGNet based decoding by introducing a post-processing step called the longest consecutive repetition (LCR) in a sliding window-based approach and named it EEGNet+LCR. The proposed approach was tested on a dataset of 10 hemiparetic stroke patients’ MI data set yielding superior performance against the only EEGNet and a more traditional approach such as common spatial pattern (CSP)+support vector machine (SVM) for both within- and cross-subject decoding of MI signals. We also observed comparable and satisfactory performance of the EEGNet+LCR in both the within- and cross-subject categories which are rarely found in literature making it a promising candidate to realize practically feasible BCI for stroke rehabilitation

Elimination of visceral leishmaniasis in the Indian subcontinent: a comparison of predictions from three transmission models.

We present three transmission models of visceral leishmaniasis (VL) in the Indian subcontinent (ISC) with structural differences regarding the disease stage that provides the main contribution to transmission, including models with a prominent role of asymptomatic infection, and fit them to recent case data from 8 endemic districts in Bihar, India. Following a geographical cross-validation of the models, we compare their predictions for achieving the WHO VL elimination targets with ongoing treatment and vector control strategies. All the transmission models suggest that the WHO elimination target (<1 new VL case per 10,000 capita per year at sub-district level) is likely to be met in Bihar, India, before or close to 2020 in sub-districts with a pre-control incidence of 10 VL cases per 10,000 people per year or less, when current intervention levels (60% coverage of indoor residual spraying (IRS) of insecticide and a delay of 40days from onset of symptoms to treatment (OT)) are maintained, given the accuracy and generalizability of the existing data regarding incidence and IRS coverage. In settings with a pre-control endemicity level of 5/10,000, increasing the effective IRS coverage from 60 to 80% is predicted to lead to elimination of VL 1-3 years earlier (depending on the particular model), and decreasing OT from 40 to 20days to bring elimination forward by approximately 1year. However, in all instances the models suggest that L. donovani transmission will continue after 2020 and thus that surveillance and control measures need to remain in place until the longer-term aim of breaking transmission is achieved

Development and Evaluation of Active Case Detection Methods to Support Visceral Leishmaniasis Elimination in India.

As India moves toward the elimination of visceral leishmaniasis (VL) as a public health problem, comprehensive timely case detection has become increasingly important, in order to reduce the period of infectivity and control outbreaks. During the 2000s, localized research studies suggested that a large percentage of VL cases were never reported in government data. However, assessments conducted from 2013 to 2015 indicated that 85% or more of confirmed cases were eventually captured and reported in surveillance data, albeit with significant delays before diagnosis. Based on methods developed during these assessments, the CARE India team evolved new strategies for active case detection (ACD), applicable at large scale while being sufficiently effective in reducing time to diagnosis. Active case searches are triggered by the report of a confirmed VL case, and comprise two major search mechanisms: 1) case identification based on the index case's knowledge of other known VL cases and searches in nearby houses (snowballing); and 2) sustained contact over time with a range of private providers, both formal and informal. Simultaneously, house-to-house searches were conducted in 142 villages of 47 blocks during this period. We analyzed data from 5030 VL patients reported in Bihar from January 2018 through July 2019. Of these 3033 were detected passively and 1997 via ACD (15 (0.8%) via house-to-house and 1982 (99.2%) by light touch ACD methods). We constructed multinomial logistic regression models comparing time intervals to diagnosis (30-59, 60-89 and ≥90 days with =90 days compared to the referent of <30 days for ACD vs PCD were 0.88, 0.56 and 0.42 respectively. These ACD strategies not only reduce time to diagnosis, and thus risk of transmission, but also ensure that there is a double check on the proportion of cases actually getting captured. Such a process can supplement passive case detection efforts that must go on, possibly perpetually, even after elimination as a public health problem is achieved

Nitrogen plasma treatment in two-step temperature deposited FePt bilayer media

Tailoring writability and obtaining better signal-to-noise ratio performance by tuning the magnetic and microstructural properties of FePt media is of great interest in the bid to achieve high areal densities for next generation hard disk drives (HDDs). Conventional ways to tune FePt media are primarily by either the insertion of additional layers, or by inclusion of segregants such as B, C, Ni, SiO2 etc. Here we describe an approach that involves modifying growth kinetics by N inclusion, via plasma treatment in FePt bilayers (consisting of a hard and a soft FePt layer). The soft FePt layer aids in obtaining easy writability, while nitrogen plasma treatment of the interface of the two FePt layers facilitates suitable tailoring of the microstructure. This approach contributed to lowering of grain dimension as well as reduction in domain sizes in the FePt bilayers, but with the unwanted side-effects of reduction in squareness and ordering. However, we further propose a method to alleviate these concerns by the deposition of the soft FePt layer in partial nitrogen atmosphere, that restored the squareness and ordering while retaining the smaller domains obtained by nitrogen plasma treatment. Thus, the proposed approach provides a potential direction towards meeting the mutually conflicting requirements of easy writability and better signal-to-noise ratio performance in FePt media.ASTAR (Agency for Sci., Tech. and Research, S’pore)Accepted versio

Epidemiologic Correlates of Mortality among Symptomatic Visceral Leishmaniasis Cases: Findings from Situation Assessment in High Endemic Foci in India - Fig 1

<p>Estimates of the cumulative survival probabilities (Kaplan-Meier estimates) of VL patients, from the time of diagnosis, stratified by the categories of: (A) age of the patient; (B) gender of the patient; (C) caste of the patient; (D) place from which VL treatment was received; (E) facility where VL was diagnosed; (F) interval between symptom onset and diagnosis; (G) type of drug used for VL treatment; and (H) completion of the course of VL treatment. Bihar, 2012–13. (N = 4925).</p

Hazard ratios (and 95% confidence intervals) of death among VL cases, since the time of diagnosis, from crude and adjusted Cox proportional hazards models.

<p>Bihar, 2012–13. (N = 4925).^{<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0005150#t002fn001" target="_blank">*</a>}</p

Comparison of socio-demographic and disease-related characteristics between the dead and surviving (till date of interview) VL cases in 8 districts of Bihar. 2012–13 (N = 4925)

<p>Comparison of socio-demographic and disease-related characteristics between the dead and surviving (till date of interview) VL cases in 8 districts of Bihar. 2012–13 (N = 4925)</p

Elimination of visceral leishmaniasis in the Indian subcontinent: a comparison of predictions from three transmission models

A set of R packages produced to model transmission of visceral leishmaniasis (VL) in the Indian subcontinent (ISC) and fit them to recent case data from 8 endemic districts in Bihar, India

Additional file 2: Table S2. of Variations in visceral leishmaniasis burden, mortality and the pathway to care within Bihar, India

Distribution of continuous variables (age, waiting times and house size) for the eight study districts. (DOCX 15 kb