Solitons and Vertex Operators in Twisted Affine Toda Field Theories

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields display interesting patterns in their masses and coupling and which have recently been shown to extend to the classical soliton solutions arising when the couplings are imaginary. Here these results are extended from the untwisted to the twisted algebras. The new soliton solutions and their masses are found by a folding procedure which can be applied to the affine Kac-Moody algebras themselves to provide new insights into their structures. The relevant foldings are related to inner automorphisms of the associated finite dimensional Lie group which are calculated explicitly and related to what is known as the twisted Coxeter element. The fact that the twisted affine Kac-Moody algebras possess vertex operator constructions emerges naturally and is relevant to the soliton solutions.Comment: 27 pages (harvmac) + 3 figures (LaTex) at the end of the file, Swansea SWAT/93-94/1

Data Assimilation using a GPU Accelerated Path Integral Monte Carlo Approach

The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a Graphics Processing Unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 300, compared to an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.Comment: 5 figures, submitted to Journal of Computational Physic

Yangians, Integrable Quantum Systems and Dorey's rule

We study tensor products of fundamental representations of Yangians and show that the fundamental quotients of such tensor products are given by Dorey's rule.Comment: We have made corrections to the results for the Yangians associated to the non--simply laced algebra

Rho GTPase function in flies: insights from a developmental and organismal perspective.

Morphogenesis is a key event in the development of a multicellular organism and is reliant on coordinated transcriptional and signal transduction events. To establish the segmented body plan that underlies much of metazoan development, individual cells and groups of cells must respond to exogenous signals with complex movements and shape changes. One class of proteins that plays a pivotal role in the interpretation of extracellular cues into cellular behavior is the Rho family of small GTPases. These molecular switches are essential components of a growing number of signaling pathways, many of which regulate actin cytoskeletal remodeling. Much of our understanding of Rho biology has come from work done in cell culture. More recently, the fruit fly Drosophila melanogaster has emerged as an excellent genetic system for the study of these proteins in a developmental and organismal context. Studies in flies have greatly enhanced our understanding of pathways involving Rho GTPases and their roles in development

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease