Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page

Recursive least squares background prediction of univariate syndromic surveillance data

<p>Abstract</p> <p>Background</p> <p>Surveillance of univariate syndromic data as a means of potential indicator of developing public health conditions has been used extensively. This paper aims to improve the performance of detecting outbreaks by using a background forecasting algorithm based on the adaptive recursive least squares method combined with a novel treatment of the Day of the Week effect.</p> <p>Methods</p> <p>Previous work by the first author has suggested that univariate recursive least squares analysis of syndromic data can be used to characterize the background upon which a prediction and detection component of a biosurvellance system may be built. An adaptive implementation is used to deal with data non-stationarity. In this paper we develop and implement the RLS method for background estimation of univariate data. The distinctly dissimilar distribution of data for different days of the week, however, can affect filter implementations adversely, and so a novel procedure based on linear transformations of the sorted values of the daily counts is introduced. Seven-days ahead daily predicted counts are used as background estimates. A signal injection procedure is used to examine the integrated algorithm's ability to detect synthetic anomalies in real syndromic time series. We compare the method to a baseline CDC forecasting algorithm known as the W2 method.</p> <p>Results</p> <p>We present detection results in the form of Receiver Operating Characteristic curve values for four different injected signal to noise ratios using 16 sets of syndromic data. We find improvements in the false alarm probabilities when compared to the baseline W2 background forecasts.</p> <p>Conclusion</p> <p>The current paper introduces a prediction approach for city-level biosurveillance data streams such as time series of outpatient clinic visits and sales of over-the-counter remedies. This approach uses RLS filters modified by a correction for the weekly patterns often seen in these data series, and a threshold detection algorithm from the residuals of the RLS forecasts. We compare the detection performance of this algorithm to the W2 method recently implemented at CDC. The modified RLS method gives consistently better sensitivity at multiple background alert rates, and we recommend that it should be considered for routine application in bio-surveillance systems.</p

Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Crohn's Disease and Early Exposure to Domestic Refrigeration

Environmental risk factors playing a causative role in Crohn's Disease (CD) remain largely unknown. Recently, it has been suggested that refrigerated food could be involved in disease development. We thus conducted a pilot case control study to explore the association of CD with the exposure to domestic refrigeration in childhood.Using a standard questionnaire we interviewed 199 CD cases and 207 age-matched patients with irritable bowel syndrome (IBS) as controls. Cases and controls were followed by the same gastroenterologists of tertiary referral clinics in Tehran, Iran. The questionnaire focused on the date of the first acquisition of home refrigerator and freezer. Data were analysed by a multivariate logistic model. The current age was in average 34 years in CD cases and the percentage of females in the case and control groups were respectively 48.3% and 63.7%. Patients were exposed earlier than controls to the refrigerator (X2 = 9.9, df = 3, P = 0.04) and refrigerator exposure at birth was found to be a risk factor for CD (OR = 2.08 (95% CI: 1.01-4.29), P = 0.05). Comparable results were obtained looking for the exposure to freezer at home. Finally, among the other recorded items reflecting the hygiene and comfort at home, we also found personal television, car and washing machine associated with CD.This study supports the opinion that CD is associated with exposure to domestic refrigeration, among other household factors, during childhood

The Study to Explore Early Development (SEED): A Multisite Epidemiologic Study of Autism by the Centers for Autism and Developmental Disabilities Research and Epidemiology (CADDRE) Network

The Study to Explore Early Development (SEED), a multisite investigation addressing knowledge gaps in autism phenotype and etiology, aims to: (1) characterize the autism behavioral phenotype and associated developmental, medical, and behavioral conditions and (2) investigate genetic and environmental risks with emphasis on immunologic, hormonal, gastrointestinal, and sociodemographic characteristics. SEED uses a case–control design with population-based ascertainment of children aged 2–5 years with an autism spectrum disorder (ASD) and children in two control groups—one from the general population and one with non-ASD developmental problems. Data from parent-completed questionnaires, interviews, clinical evaluations, biospecimen sampling, and medical record abstraction focus on the prenatal and early postnatal periods. SEED is a valuable resource for testing hypotheses regarding ASD characteristics and causes

Unimolecular dissociation of peptides: statistical vs. non-statistical fragmentation mechanisms and time scales

International audienceIn the present work we have investigated mechanisms of gas phase unimolecular dissociation of a relatively simple dipeptide, the di-proline anion, by means of chemical dynamics simulations, using the PM3 semi-empirical Hamiltonian. In particular, we have considered two activation processes that are representative limits of what occurs in collision induced dissociation experiments: (i) thermal activation, corresponding to several low energy collisions, in which the system is prepared with a microcanonical distribution of energy; (ii) collisional activation where a single shock of hundreds of kcal mol−1 (300 kcal mol−1 in the present case) can transfer sufficient energy to allow dissociation. From these two activation processes we obtained different product abundances, and for one particular fragmentation pathway a clear mechanistic difference for the two activation processes. This mechanism corresponds to the leaving of an OH− group and subsequent formation of water by taking a proton from the remaining molecule. This last reaction is always observed in thermal activation while in collisional activation it is less favoured and the formation of OH− as a final product is observed. More importantly, we show that while in thermal activation unimolecular dissociation follows exponential decay, in collision activation the initial population decays with non-exponential behaviour. Finally, from the thermal activation simulations it was possible to obtain rate constants as a function of temperature that show Arrhenius behaviour. Thus activation energies have also been extracted from these simulations

Model Simulations of the Thermal Dissociation of the TIK(H⁺)₂ Tripeptide: Mechanisms and Kinetic Parameters

International audienceDirect dynamics simulations, utilizing the RM1 semiempirical electronic structure theory, were performed to study the thermal dissociation of the doubly protonated tripeptide threonine–isoleucine–lysine ion, TIK(H+)2, for temperatures of 1250–2500 K, corresponding to classical energies of 1778–3556 kJ/mol. The number of different fragmentation pathways increases with increase in temperature. At 1250 K there are only three fragmentation pathways, with one contributing 85% of the fragmentation. In contrast, at 2500 K, there are 61 pathways, and not one dominates. The same ion is often formed via different pathways, and at 2500 K there are only 14 m/z values for the product ions. The backbone and side-chain fragmentations occur by concerted reactions, with simultaneous proton transfer and bond rupture, and also by homolytic bond ruptures without proton transfer. For each temperature the TIK(H+)2 fragmentation probability versus time is exponential, in accord with the Rice–Ramsperger–Kassel–Marcus and transition state theories. Rate constants versus temperature were determined for two proton transfer and two bond rupture pathways. From Arrhenius plots activation energies Ea and A-factors were determined for these pathways. They are 62–78 kJ/mol and (2–3) × 1012 s–1 for the proton transfer pathways and 153–168 kJ/mol and (2–4) × 1014 s–1 for the bond rupture pathways. For the bond rupture pathways, the product cation radicals undergo significant structural changes during the bond rupture as a result of hydrogen bonding, which lowers their entropies and also their Ea and A parameters relative to those for C–C bond rupture pathways in hydrocarbon molecules. The Ea values determined from the simulation Arrhenius plots are in very good agreement with the reaction barriers for the RM1 method used in the simulations. A preliminary simulation of TIK(H+)2 collision-induced dissociation (CID), at a collision energy of 13 eV (1255 kJ/mol), was also performed to compare with the thermal dissociation simulations. Though the energy transferred to TIK(H+)2 in the collisions is substantially less than the energy for the thermal excitations, there is substantial fragmentation as a result of the localized, nonrandom excitation by the collisions. CID results in different fragmentation pathways with a significant amount of short time nonstatistical fragmentation. Backbone fragmentation is less important, and side-chain fragmentation is more important for the CID simulations as compared to the thermal simulations. The thermal simulations provide information regarding the long-time statistical fragmentation