On the numerical evaluation of algebro-geometric solutions to integrable equations

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey-Stewartson and the multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure

Prevalence and effect of parasitic infections on cycling in traditionally managed cattle herds in Bauchi, Nigeria

The incidence of infection and infestation by parasites (i.e. helminth, ectoparasites and haemoparasites) and the relationship between them and cycling in cattle was investigated in 16 traditionally managed herds in Bauchi, Nigeria. Parasitic infection and infestation show seasonality with most infections and infestations occurring in the rainy season. This study also shows some relationship between parasitic infection and infestation with cycling in some poorly managed herds. Good management practices were also shown to be important in disease control and prevention

Certain Expansion Formulae Involving a Basic Analogue of Fox’s H-Function

Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results

Impaired fixation suppression of horizontal vestibular nystagmus during smooth pursuit: pathophysiology and clinical implications.

BACKGROUND AND PURPOSE A peripheral spontaneous nystagmus (SN) is typically enhanced or revealed by removing fixation. Conversely, failure of fixation suppression of SN is usually a sign of a central disorder. Based on Luebke and Robinson (Vision Res 1988, vol. 28 (8), pp. 941-946), who suggested that the normal fixation mechanism is disengaged during pursuit, it is hypothesized that vertical tracking in the light would bring out or enhance a horizontal SN. METHODS Eighteen patients with acute vestibular neuritis were studied. Eye movements were recorded using video-oculography at straight-ahead gaze with and without visual fixation, and during smooth pursuit. The slow-phase velocity and the fixation suppression indices of nystagmus (relative to SN in darkness) were compared in each condition. RESULTS During vertical tracking, the slow-phase velocity of horizontal SN with eyes near straight-ahead gaze was significantly higher (median 2.7°/s) than under static visual fixation (median 1.2°/s). Likewise, the fixation index was significantly higher (worse suppression) during pursuit (median 48%) than during fixation (median 26%). A release of SN was also suggested during horizontal pursuit, if one assumes superposition of SN on a normal and symmetrical pursuit capability

Marichev-Saigo-Maeda fractional integration operators of the Bassel functions

In this paper, we apply generalized operators of fractional integration involving Appell’s function F_3 (.) due to Marichev-Saigo-Maeda, to the Bessel function of first kind. The results are expressed in terms of generalized Wright function and hypergeometric functions _pF_q . Special cases involving this function are mentioned. Results given recently by Kilbas and Sebastian follow as special cases of the theorems establish here

On the exponential transform of lemniscates

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.Comment: 19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Birkhauser Verla

Less in-toeing after femoral derotation osteotomy in adult patients with increased femoral version and posterior hip impingement compared to patients with femoral retroversion

In-toeing of the foot was associated with high femoral version (FV), while Out-toeing was associated with femoral-retroversion. Therefore, we report on (i) foot-progression-angle (FPA), (ii) prevalence of In-toeing and Out-toeing, and (iii) clinical outcome of patients treated with femoral-derotation-osteotomy (FDO). We performed a retrospective analysis involving 20 patients (20 hips) treated with unilateral FDO (2017-18). Of them, 14 patients had increased FV, 6 patients had femoral-retroversion. Follow-up time was mean 1 ± 1 years. All patients had minimal 1-year follow-up and the mean age was 29 ± 8 years. Patients with increased FV (FV > 35°) presented with positive posterior-impingement-test and mean FV was 49 ± 11° (Murphy method). Six patients with femoral-retroversion (FV < 10°) had positive anterior impingement test and mean FV of 5 ± 4°. Instrumented gait analysis was performed preoperatively and at follow-up using the Gaitrite system to measure FPA and was compared to a control group of 18 healthy asymptomatic volunteers (36 feet, mean age 29 ± 6 years). (i) Mean FPA increased significantly (P = 0.006) from preoperative 1.3 ± 7° to 4.5 ± 6° at follow-up for patients with increased FV and was not significantly different compared to the control group (4.0 ± 4.5°). (ii) In-toeing decreased from preoperatively (five patients) to follow-up (two patients) for patients with increased FV. Out-toeing decreased from preoperatively (two patients) to follow-up (no patient) for patients with femoral-retroversion. (iii) Subjective-hip-value of all patients increased significantly (P < 0.001) from preoperative 21 to 78 points at follow-up. WOMAC was 12 ± 8 points at follow-up. Patients with increased FV that underwent FDO walked with less In-toeing. FDO has the potential to reduce In-toeing and Out-toeing and to improve subjective satisfaction at follow-up

Minimal Out-Toeing and Good Hip Scores of Severe SCFE Patients Treated With Modified Dunn Procedure and Contralateral Prophylactic Pinning at Minimal 5-year Follow up

Background: Slipped capital femoral epiphyses (SCFE) is associated with out-toeing of the foot and external rotation gait. But it is unknown if SCFE patients treated with the modified Dunn procedure have out-toeing at follow up.Therefore, we used instrumented gait analysis and questioned (1) do severe SCFE patients treated with a modified Dunn procedure have symmetrical foot progression angle (FPA) compared with contralateral side and compared with asymptomatic volunteers (2) what is the prevalence of out-toeing gait and what are the outcome socres at follow up. Methods: Gait analysis of 22 patients (22 hips) treated with an unilateral modified Dunn procedure for severe SCFE (slip angle >60 degrees, 2002 to 2011) was retrospectively evaluated. Of 38 patients with minimal 5-year follow up, 2 hips (4%) had avascular necrosis of the femoral head and were excluded for gait analysis. Twenty-two patients were available for gait analysis at follow up (mean follow up of 9±2 y). Mean age at follow up was 22±3 years. Mean preoperative slip angle was 64±8 degrees (33% unstable slips) and decreased postoperatively (slip angle of 8±4 degrees). Gait analysis was performed with computer-based instrumented walkway system (GAITRite) to measure FPA with embedded pressure sensors. Patients were compared with control group of 18 healthy asymptomatic volunteers (36 feet, mean age 29±6 y). Results: (1) Mean FPA of SCFE patients (3.6±6.4 degrees) at follow up was not significantly different compared with their contralateral side (5.6±5.5 degrees) and compared with FPA of controls (4.0±4.5 degrees). (2) Of the 22 SCFE patients, most of them (19 hips, 86%) had normal FPA (-5 to 15 degrees), 2 patients had in-toeing (FPA15 degrees) and was not significantly different compared with control group. (3) Mean modified Harris hip score (mHHS) was 93±11 points, mean Hip Disability and Osteoarthritis Outcome Score (HOOS) score was 91±10 points. Three patients (14%) had mHHS 95 points. Conclusions: Patients with severe SCFE treated with modified Dunn procedure had mostly symmetrical FPA and good hip scores at long term follow up. This is in contrast to previous studies. Although 1 patient had out-toeing and 2 patients had in-toeing at follow up, they had good hip scores. Level of evidence: Level III-retrospective comparative study

Whole Blood Profiling of T-cell-Derived microRNA Allows the Development of Prognostic models in Inflammatory Bowel Disease

Background: MicroRNAs [miRNAs] are cell-specific small non-coding RNAs that can regulate gene expression and have been implicated in inflammatory bowel disease [IBD] pathogenesis. Here we define the cell-specific miRNA profiles and investigate its biomarker potential in IBD. Methods: In a two-stage prospective multi-centre case control study, next generation sequencing was performed on a discovery cohort of immunomagnetically separated leukocytes from 32 patients (nine Crohn''s disease [CD], 14 ulcerative colitis [UC], eight healthy controls) and differentially expressed signals were validated in whole blood in 294 patients [97 UC, 98 CD, 98 non-IBD, 1 IBDU] using quantitative PCR. Correlations were analysed with phenotype, including need for early treatment escalation as a marker of progressive disease using Cox proportional hazards. Results: In stage 1, each leukocyte subset [CD4+ and CD8+ T-cells and CD14+ monocytes] was analysed in IBD and controls. Three specific miRNAs differentiated IBD from controls in CD4+ T-cells, including miR-1307-3p [p = 0.01], miR-3615 [p = 0.02] and miR-4792 [p = 0.01]. In the extension cohort, in stage 2, miR-1307-3p was able to predict disease progression in IBD (hazard ratio [HR] 1.98, interquartile range [IQR]: 1.20-3.27; logrank p = 1.80 × 10-3), in particular CD [HR 2.81; IQR: 1.11-3.53, p = 6.50 × 10-4]. Using blood-based multimarker miRNA models, the estimated chance of escalation in CD was 83% if two or more criteria were met and 90% for UC if three or more criteria are met. Interpretation: We have identified and validated unique CD4+ T-cell miRNAs that are differentially regulated in IBD. These miRNAs may be able to predict treatment escalation and have the potential for clinical translation; further prospective evaluation is now indicated