Rate of convergence of truncated stochastic approximation procedures with moving bounds

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We study convergence and rate of convergence. Main results are supplemented with corollaries to establish various sets of sufficient conditions, with the main emphases on the parametric statistical estimation. The theory is illustrated by examples and special cases.Comment: 30 page

Derivation and external validation of a clinical prognostic model identifying children at risk of death following presentation for diarrheal care

Diarrhea continues to be a leading cause of death for children under-five. Amongst children treated for acute diarrhea, mortality risk remains elevated during and after acute medical management. Identification of those at highest risk would enable better targeting of interventions, but available prognostic tools lack validation. We used clinical and demographic data from the Global Enteric Multicenter Study (GEMS) to build clinical prognostic models (CPMs) to predict death (in-treatment, after discharge, or either) in children aged ≤59 months presenting with moderate-to-severe diarrhea (MSD), in Africa and Asia. We screened variables using random forests, and assessed predictive performance with random forest regression and logistic regression using repeated cross-validation. We used data from the Kilifi Health and Demographic Surveillance System (KHDSS) and Kilifi County Hospital (KCH) in Kenya to externally validate our GEMS-derived CPM. Of 8060 MSD cases, 43 (0.5%) children died in treatment and 122 (1.5% of remaining) died after discharge. MUAC at presentation, respiratory rate, age, temperature, number of days with diarrhea at presentation, number of people living in household, number of children <60 months old living in household, and how much the child had been offered to drink since diarrhea started were predictive of death both in treatment and after discharge. Using a parsimonious 2-variable prediction model, we achieved an area under the ROC curve (AUC) of 0.84 (95% CI: 0.82, 0.86) in the derivation dataset, and an AUC = 0.74 (95% CI 0.71, 0.77) in the external dataset. Our findings suggest it is possible to identify children most likely to die after presenting to care for acute diarrhea. This could represent a novel and cost-effective way to target resources for the prevention of childhood mortality

Initial Steps of Thermal Decomposition of Dihydroxylammonium 5,5′-bistetrazole-1,1′-diolate Crystals from Quantum Mechanics

Dihydroxylammonium 5,5?-bistetrazole-1,1?-diolate (TKX-50) is a recently synthesized energetic material (EM) with most promising performance, including high energy content, high density, low sensitivity, and low toxicity. TKX-50 forms an ionic crystal in which the unit cell contains two bistetrazole dianions {c-((NO)N3C)-[c-(CN3(NO)], formal charge of ?2} and four hydroxylammonium (NH3OH)+ cations (formal charge of +1). We report here quantum mechanics (QM)-based reaction studies to determine the atomistic reaction mechanisms for the initial decompositions of this system. First we carried out molecular dynamics simulations on the periodic TKX-50 crystal using forces from density functional based tight binding calculations (DFTB-MD), which finds that the chemistry is initiated by proton transfer from the cation to the dianion. Continuous heating of this periodic system leads eventually to dissociation of the protonated or diprotonated bistetrazole to release N2 and N2O. To refine the mechanisms observed in the periodic DFTB-MD, we carried out finite cluster quantum mechanics studies (B3LYP) for the unimolecular decomposition of the bistetrazole. We find that for the bistetrazole dianion, the reaction barrier for release of N2 is 45.1 kcal/mol, while release of N2O is 72.2 kcal/mol. However, transferring one proton to the bistetrazole dianion decreases the reaction barriers to 37.2 kcal/mol for N2 release and 59.5 kcal/mol for N2O release. Thus, we predict that the initial decompositions in TKX-50 lead to N2 release, which in turn provides the energy to drive further decompositions. On the basis of this mechanism, we suggest changes to make the system less sensitive while retaining the large energy release. This may help improve the synthesis strategy of developing high nitrogen explosives with further improved performance

Transition state geometry of driven chemical reactions on time-dependent double-well potentials

This paper was accepted for publication in the journal Physical Chemistry Chemical Physics and the definitive published version is available at http://dx.doi.org/10.1039/C6CP02519FReaction rates across time-dependent barriers are difficult to define and difficult to obtain using standard transition state theory approaches because of the complexity of the geometry of the dividing surface separating reactants and products. Using perturbation theory (PT) or Lagrangian descriptors (LDs), we can obtain the transition state trajectory and the associated recrossing-free dividing surface. With the latter, we are able to determine the exact reactant population decay and the corresponding rates to benchmark the PT and LD approaches. Specifically, accurate rates are obtained from a local description regarding only direct barrier crossings and to those obtained from a stability analysis of the transition state trajectory. We find that these benchmarks agree with the PT and LD approaches for obtaining recrossing-free dividing surfaces. This result holds not only for the local dynamics in the vicinity of the barrier top, but also for the global dynamics of particles that are quenched at the reactant or product wells after their sojourn over the barrier region. The double-well structure of the potential allows for long-time dynamics related to collisions with the outside walls that lead to long-time returns in the low-friction regime. This additional global dynamics introduces slow-decay pathways that do not result from the local transition across the recrossing-free dividing surface associated with the transition state trajectory, but can be addressed if that structure is augmented by the population transfer of the long-time returns