Nonlinear Modulation of Multi-Dimensional Lattice Waves

The equations governing weakly nonlinear modulations of $N$-dimensional lattices are considered using a quasi-discrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations describing the evolution of long wavelength acoustic modes in two and three dimensional lattices are also presented. Then the modulational instability of a $N$-dimensional Stokes lattice wave is discussed based on the $N$-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.Comment: Submitted to PR

Towards a global partnership model in interprofessional education for cross-sector problem-solving

Objectives A partnership model in interprofessional education (IPE) is important in promoting a sense of global citizenship while preparing students for cross-sector problem-solving. However, the literature remains scant in providing useful guidance for the development of an IPE programme co-implemented by external partners. In this pioneering study, we describe the processes of forging global partnerships in co-implementing IPE and evaluate the programme in light of the preliminary data available. Methods This study is generally quantitative. We collected data from a total of 747 health and social care students from four higher education institutions. We utilized a descriptive narrative format and a quantitative design to present our experiences of running IPE with external partners and performed independent t-tests and analysis of variance to examine pretest and posttest mean differences in students’ data. Results We identified factors in establishing a cross-institutional IPE programme. These factors include complementarity of expertise, mutual benefits, internet connectivity, interactivity of design, and time difference. We found significant pretest–posttest differences in students’ readiness for interprofessional learning (teamwork and collaboration, positive professional identity, roles, and responsibilities). We also found a significant decrease in students’ social interaction anxiety after the IPE simulation. Conclusions The narrative of our experiences described in this manuscript could be considered by higher education institutions seeking to forge meaningful external partnerships in their effort to establish interprofessional global health education

Meta-analysis Followed by Replication Identifies Loci in or near CDKN1B, TET3, CD80, DRAM1, and ARID5B as Associated with Systemic Lupus Erythematosus in Asians

Systemic lupus erythematosus (SLE) is a prototype autoimmune disease with a strong genetic involvement and ethnic differences. Susceptibility genes identified so far only explain a small portion of the genetic heritability of SLE, suggesting that many more loci are yet to be uncovered for this disease. In this study, we performed a meta-analysis of genome-wide association studies on SLE in Chinese Han populations and followed up the findings by replication in four additional Asian cohorts with a total of 5,365 cases and 10,054 corresponding controls. We identified genetic variants in or near CDKN1B, TET3, CD80, DRAM1, and ARID5B as associated with the disease. These findings point to potential roles of cell-cycle regulation, autophagy, and DNA demethylation in SLE pathogenesis. For the region involving TET3 and that involving CDKN1B, multiple independent SNPs were identified, highlighting a phenomenon that might partially explain the missing heritability of complex diseases

Human germline heterozygous gain-of-function STAT6 variants cause severe allergic disease

STAT6 (signal transducer and activator of transcription 6) is a transcription factor that plays a central role in the pathophysiology of allergic inflammation. We have identified 16 patients from 10 families spanning three continents with a profound phenotype of early-life onset allergic immune dysregulation, widespread treatment-resistant atopic dermatitis, hypereosinophilia with esosinophilic gastrointestinal disease, asthma, elevated serum IgE, IgE-mediated food allergies, and anaphylaxis. The cases were either sporadic (seven kindreds) or followed an autosomal dominant inheritance pattern (three kindreds). All patients carried monoallelic rare variants in STAT6 and functional studies established their gain-of-function (GOF) phenotype with sustained STAT6 phosphorylation, increased STAT6 target gene expression, and TH2 skewing. Precision treatment with the anti-IL-4Rα antibody, dupilumab, was highly effective improving both clinical manifestations and immunological biomarkers. This study identifies heterozygous GOF variants in STAT6 as a novel autosomal dominant allergic disorder. We anticipate that our discovery of multiple kindreds with germline STAT6 GOF variants will facilitate the recognition of more affected individuals and the full definition of this new primary atopic disorder

Parallel methods for the numerical solution of ordinary differential equations

We study time parallelism for the numerical solution of nonstiff ordinary differential equations. Stability and accuracy are the two main considerations in deriving good numerical o.d.e. methods. However, existing parallel methods have poor stability properties in that their stability regions are smaller than those of good sequential methods of the same order. In this thesis we present a precise understanding of how stability limits the potential of parallelism in o.d.e.'s. We propose a fairly specific approach to construct good parallel methods--we consider zero-stable parallel methods whose stability polynomials are perfect powers of those of simple methods with good stability regions. Based on this approach we derive new efficient parallel methods. The proposed families of block methods have stability regions which do not change as the order increases. These new methods have much better stability properties than the Adams PECE methods of the same order. The above perfect power stability polynomial approach can also be extended to multi-block methods.U of I OnlyETDs are only available to UIUC Users without author permissio

Some Recent Results on Integrable Bilinear Equations

This paper shows that several integrable lattices can be transformed into coupled bilinear di#erential-di#erence equations by introducing auxiliary variables. By testing the Backlund transformations for this type of coupled bilinear equations, a new integrable lattice is found. By using the Backlund transformation, soliton solutions are obtained. By the dependent variable transformation, this new coupled bilinear equations can be reduced to a coupled extended Lotka--Voltera equation and another equation

Journal of Nonlinear Mathematical Physics 2001, V.8, Supplement, 149–155 Proceedings: NEEDS’99 Some Recent Results on Integrable Bilinear Equations

This paper shows that several integrable lattices can be transformed into coupled bilinear differential-difference equations by introducing auxiliary variables. By testing the Bäcklund transformations for this type of coupled bilinear equations, a new integrable lattice is found. By using the Bäcklund transformation, soliton solutions are obtained. By the dependent variable transformation, this new coupled bilinear equations can be reduced to a coupled extended Lotka–Voltera equation and another equation. The purpose of this short paper is to search for new integrable systems in bilinear form. The methods used here are Hirota’s method and Bäcklund transformations [1–7]. As we know, the use of the Hirota bilinear transformation in the search of exact solutions of continuous and discrete systems is now well established [1–5]. More recently, Hirota’s method has been systematically used in the search for new integrable equations in both (1 + 1) and (2+1) dimensions by testing multi-soliton solutions or Bäcklund transformations (see, e.g. [8, 9]). The key points behind these ideas to obtain new integrable systems are to first generalize bilinear forms of known integrable systems and then to test the generalized bilinear forms for multi-soliton solutions or Bäcklund transformations. In this paper, we will focus on the differential-difference case and find some new integrable systems by testing their bilinear Bäcklund transformations. In order to do so, let us first recall the bilinear forms for some known integrable differential-difference equations. Example 1. The so-called Belov–Chaltikian lattice is given by [10] bt(n) =b(n)(b(n+1)−b(n−1))−c(n)+c(n−1), (1) ct(n) =c(n)(b(n+2)−b(n−1)). (2) By the dependent variable transformation b(n) = ln f � n +