Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

Symmetries of Differential Equations via Cartan's Method of Equivalence

We formulate a method of computing invariant 1-forms and structure equations of symmetry pseudo-groups of differential equations based on Cartan's method of equivalence and the moving coframe method introduced by Fels and Olver. Our apparoach does not require a preliminary computation of infinitesimal defining systems, their analysis and integration, and uses differentiation and linear algebra operations only. Examples of its applications are given.Comment: 15 pages, LaTeX 2.0

Nested defects on the boundary of topological superconductors

Helical Majorana edge states at the 2D boundaries of 3D topological superconductors can be gapped by a surface Zeeman field. Here we study the effect nested defects imprinted on the Zeeman field can have on the edge states. We demonstrate that depending on the configuration of the field, we can induce dimensional reduction of gapless Majorana modes from 2D to 1D or quasi-0D at magnetic domain walls. We determine the nature of the Majorana localization on these defects as a function of the magnitude and configuration of the Zeeman field. Finally, we observe a generalization of the index theorem governing the number of gapless modes at the interface between topologically nontrivial systems with partial Chern numbers

Lubiprostone ameliorates the cystic fibrosis mouse intestinal phenotype

<p>Abstract</p> <p>Background</p> <p>Cystic fibrosis (CF) is caused by mutations in the <it>CFTR </it>gene that impair the function of CFTR, a cAMP-regulated anion channel. In the small intestine loss of CFTR function creates a dehydrated, acidic luminal environment which is believed to cause an accumulation of mucus, a phenotype characteristic of CF. CF mice have small intestinal bacterial overgrowth, an altered innate immune response, and impaired intestinal transit. We investigated whether lubiprostone, which can activate the CLC2 Cl^-channel, would improve the intestinal phenotype in CF mice.</p> <p>Methods</p> <p><it>Cftr^tm1UNC</it>(CF) and wildtype (WT) littermate mice on the C57BL/6J background were used. Lubiprostone (10 μg/kg-day) was administered by gavage for two weeks. Mucus accumulation was estimated from crypt lumen widths in periodic acid-Schiff base, Alcian blue stained sections. Luminal bacterial load was measured by qPCR for the bacterial 16<it>S </it>gene. Gastric emptying and small intestinal transit in fasted mice were assessed using gavaged rhodamine dextran. Gene expression was evaluated by Affymetrix Mouse430 2.0 microarray and qRT-PCR.</p> <p>Results</p> <p>Crypt width in control CF mice was 700% that of WT mice (<it>P </it>< 0.001). Lubiprostone did not affect WT crypt width but, unexpectedly, increased CF crypt width 22% (<it>P </it>= 0.001). Lubiprostone increased bacterial load in WT mice to 490% of WT control levels (<it>P </it>= 0.008). Conversely, lubiprostone decreased bacterial overgrowth in CF mice by 60% (<it>P </it>= 0.005). Lubiprostone increased gastric emptying at 20 min postgavage in both WT (<it>P </it>< 0.001) and CF mice (<it>P </it>< 0.001). Lubiprostone enhanced small intestinal transit in WT mice (<it>P </it>= 0.024) but not in CF mice (<it>P </it>= 0.377). Among other innate immune markers, expression of mast cell genes was elevated 4-to 40-fold in the CF intestine as compared to WT, and lubiprostone treatment of CF mice decreased expression to WT control levels.</p> <p>Conclusions</p> <p>These results indicate that lubiprostone has some benefits for the CF intestinal phenotype, especially on bacterial overgrowth and the innate immune response. The unexpected observation of increased mucus accumulation in the crypts of lubiprostone-treated CF mice suggests the possibility that lubiprostone increases mucus secretion.</p

Transport time scales in soil erosion modelling

Unlike sediment transport in rivers, erosion of agricultural soil must overcome its cohesive strength to move soil particles into suspension. Soil particle size variability also leads to fall velocities covering many orders of magnitude, and hence to different suspended travel distances in overland flow. Consequently, there is a large range of inherent time scales involved in transport of eroded soil. For conditions where there is a constant rainfall rate and detachment is the dominant erosion mechanism, we use the Hairsine-Rose (HR) model to analyze these timescales, to determine their magnitude (bounds) and to provide simple approximations for them. We show that each particle size produces both fast and slow timescales. The fast timescale controls the rapid adjustment away from experimental initial conditions – this happens so quickly that it cannot be measured in practice. The slow time scales control the subsequent transition to steady state and are so large that true steady state is rarely achieved in laboratory experiments. Both the fastest and slowest time scales are governed by the largest particle size class. Physically, these correspond to the rate of vertical movement between suspension and the soil bed, and the time to achieve steady state, respectively. For typical distributions of size classes, we also find that there is often a single dominant time scale that governs the growth in the total mass of sediment in the non-cohesive deposited layer. This finding allows a considerable simplification of the HR model leading to analytical expressions for the evolution of suspended and deposited layer concentrations

LIMPRINT in specialist lymphedema services in United Kingdom, France, Italy and Turkey

Background: There is no standardized international model for specialist lymphoedema services, which covers the types of lymphoedema treated and the treatments provided. The aim of this study was to provide a profile of patients attending specialist lymphoedema services in different countries to explore similarities and differences. Methods and Results: The LIMPRINT core tool was used in specialist lymphoedema services in the UK, France, Italy and Turkey. Services in Turkey saw a slightly younger age group with a higher proportion of female patients reflecting a particular focus on breast cancer-related lymphoedema. There were higher levels of obesity and restricted mobility in patients in the UK compared with other countries. Italy and France saw the highest percentage of patients with primary lymphoedema. Diabetes was a common comorbidity in the UK and Turkey. The UK saw the largest number of patients with lower limb lymphoedema. Conclusions: The results show a wide range of complexity of patients treated in specialist lymphoedema services. Some of the differences between countries may reflect different stages in the evolution of specialist lymphoedema services, rather than a true difference in prevalence, with those with 'younger' services treating a high proportion of patients with cancer and those with more established services treating a wider range of different types of lymphoedema including more elderly people with multiple comorbidities

Duloxetine in the treatment of major depressive disorder: an open-label study

<p>Abstract</p> <p>Background</p> <p>Major depressive disorder (MDD) is a chronic and highly disabling condition. Existing pharmacotherapies produce full remission in only 30% to 40% of treated patients. Antidepressants exhibiting dual reuptake inhibition of both serotonin (5-HT) and norepinephrine (NE) may achieve higher rates of remission compared with those acting upon a single neurotransmitter. In this study, the safety and efficacy of duloxetine, a potent dual reuptake inhibitor of 5-HT and NE, were examined.</p> <p>Methods</p> <p>Patients (N = 533) meeting DSM-IV criteria for MDD received open-label duloxetine (60 mg once a day [QD]) for 12 weeks during the initial phase of a relapse prevention trial. Patients were required to have a 17-item Hamilton Rating Scale for Depression (HAMD₁₇) total score ≥18 and a Clinical Global Impression of Severity (CGI-S) score ≥4 at baseline. Efficacy measures included the HAMD₁₇total score, HAMD₁₇subscales, the CGI-S, the Patient Global Impression of Improvement (PGI-I) scale, Visual Analog Scales (VAS) for pain, and the Symptom Questionnaire, Somatic Subscale (SQ-SS). Quality of life was assessed using the Sheehan Disability Scale (SDS) and the Quality of Life in Depression Scale (QLDS). Safety was evaluated by recording spontaneously-reported treatment-emergent adverse events, changes in vital signs and laboratory analytes, and the Patient Global Impression of Sexual Function (PGI-SF) scale.</p> <p>Results</p> <p>The rate of discontinuation due to adverse events was 11.3%. Treatment-emergent adverse events reported by ≥10% duloxetine-treated patients were nausea, headache, dry mouth, somnolence, insomnia, and dizziness. Following 12 weeks of open-label duloxetine therapy, significant improvements were observed in all assessed efficacy and quality of life measures. In assessments of depression severity (HAMD₁₇, CGI-S) the magnitude of symptom improvement continued to increase at each study visit, while for painful physical symptoms the onset of improvement was rapid and reached a maximum after 2 to 3 weeks of treatment.</p> <p>Conclusion</p> <p>In this open-label phase of a relapse prevention study, duloxetine (60 mg QD) was shown to be safe and effective in the treatment of MDD.</p> <p>Trial registration</p> <p>NCT00036309.</p

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts