Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

Abdominal tuberculosis: Diagnosis and demographics, a 10-year retrospective review from a single centre.

AIM: To review all cases of abdominal tuberculosis (ATB) for demographic details, diagnostic work up and evidence of vitamin D deficiency. METHODS: This was a retrospective analysis of all patients diagnosed with ATB from June 2003 to August 2013 at St George's Hospital, London. Demographic data was available from the local tuberculosis database. Further clinical information was collected from electronic patient records, including radiology, endoscopy, microbiology, histology, biochemistry and serology. Patients were classified as either confirmed ATB [if mycobacteria tuberculosis (MTB) was cultured from abdominal site] or presumed ATB (if suggestive findings or high clinical suspicion). Subtypes of ATB were classified as tuberculosis (TB) peritonitis, luminal TB, solid organ TB or from a combination of sites. RESULTS: There were a total of 65 cases identified in this time period, with a mean of 6.5 cases per year (range 4-9). Mean age 42 years, 49.2% females. Fifty-two point three percent were South Asian, 38.5% African. Forty-nine point two percent had gastrointestinal endoscopy, 30.8% paracentesis and 24.6% surgery in order to obtain samples. Forty-seven point seven percent were defined as confirmed ATB with positive culture of MTB from abdominal sites, the rest were treated as presumed ATB. Twenty-four point six percent had co-existing sputum culture positive for MTB, and 30.8% had an abnormal chest X-ray. Subtypes of ATB: 35.4% had TB peritonitis; 27.7% luminal TB; 3.1% solid organ TB; and 33.8% TB at a combination of abdominal sites. Thirteen point nine percent were human immunodeficiency virus positive, all with CD4 count less than 300 cells/μL. Seventy point five percent had severe vitamin D deficiency, and 25% were vitamin D deficient. CONCLUSION: ATB mainly affects young South Asian and African patients, with difficulties in confirming diagnosis despite a range of non-invasive and invasive diagnostic tests

Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $N \times N$ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection symmetry exists and the probability factors into two other related probabilities, defined on single intervals. Our investigation uses the system of partial differential equations arising from the Fredholm determinant expression for the gap probability and the differential-recurrence equations satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find second and third order nonlinear ordinary differential equations defining the probabilities in the general $N$ case. For N=1 and N=2 the probabilities and thus the solution of the equations are given explicitly. An asymptotic expansion for large gap size is obtained from the equation in the Hermite case, and also studied is the scaling at the edge of the Hermite spectrum as $N \to \infty$, and the Jacobi to Hermite limit; these last two studies make correspondence to other cases reported here or known previously. Moreover, the differential equation arising in the Hermite ensemble is solved in terms of an explicit rational function of a {Painlev\'e-V} transcendent and its derivative, and an analogous solution is provided in the two Jacobi cases but this time involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2

Accelerated return to sport after osteochondral autograft plug transfer

Background:Previous studies have reported varying return-to-sport protocols after knee cartilage restoration procedures.Purpose:To (1) evaluate the time for return to sport in athletes with an isolated chondral injury who underwent an accelerated return-to-sport protocol after osteochondral autograft plug transfer (OAT) and (2) evaluate clinical outcomes to assess for any consequences from the accelerated return to sport.Study Design:Case series; Level of evidence, 4.Methods:An institutional cohort of 152 OAT procedures was reviewed, of which 20 competitive athletes met inclusion and exclusion criteria. All patients underwent a physician-directed accelerated rehabilitation program after their procedure. Return to sport was determined for all athletes. Clinical outcomes were assessed using International Knee Documentation Committee (IKDC) and Tegner scores as well as assessment of level of participation on return to sport.Results:Return-to-sport data were available for all 20 athletes; 13 of 20 athletes (65%) were available for clinical evaluation at a mean 4.4-year follow-up. The mean time for return to sport for all 20 athletes was 82.9 ± 25 days (range, 38-134 days). All athletes were able to return to sport at their previous level and reported that they were satisfied or very satisfied with their surgical outcome and ability to return to sport. The mean postoperative IKDC score was 84.5 ± 9.5. The mean Tegner score prior to injury was 8.9 ± 1.7; it was 7.7 ± 1.9 at final follow-up.Conclusion:Competitive athletes with traumatic chondral defects treated with OAT managed using this protocol had reduced time to preinjury activity levels compared with what is currently reported, with excellent clinical outcomes and no serious long-term sequelae.</jats:sec

A Technical Focus on Antegrade Dissection and Re-entry for Coronary Chronic Total Occlusions: a Practice Update for 2019.

Coronary chronic total occlusions (CTOs) are a commonly encountered lesion. These present in a diverse patient population with variable anatomy. Technical success rates of ~90% are achievable for CTO lesions in centers with appropriate expertise. Many lesions can be crossed with wire-based techniques. However, the most anatomically complex and technically challenging lesions will often require more advanced approaches such as retrograde access and/or the application of blunt dissection techniques in the vessel to safely navigate long and/or ambiguous CTO segments. Retrograde dissection and re-entry (RDR) and antegrade dissection and re-entry (ADR) strategies are often needed to treat such lesions. In many circumstances, ADR offers a safe and efficient means to successfully cross a CTO lesion. Therefore, operators must remain cognizant of the risks and benefits of differing technical approaches during CTO percutaneous coronary intervention, particularly when both ADR and RDR are feasible. This article provides an overview of the ADR technique in addition to updated approaches in contemporary clinical practice

Stage-specific action of matrix metalloproteinases influences progressive hereditary kidney disease.

BackgroundGlomerular basement membrane (GBM), a key component of the blood-filtration apparatus in the in the kidney, is formed through assembly of type IV collagen with laminins, nidogen, and sulfated proteoglycans. Mutations or deletions involving alpha3(IV), alpha4(IV), or alpha5(IV) chains of type IV collagen in the GBM have been identified as the cause for Alport syndrome in humans, a progressive hereditary kidney disease associated with deafness. The pathological mechanisms by which such mutations lead to eventual kidney failure are not completely understood.Methods and findingsWe showed that increased susceptibility of defective human Alport GBM to proteolytic degradation is mediated by three different matrix metalloproteinases (MMPs)--MMP-2, MMP-3, and MMP-9--which influence the progression of renal dysfunction in alpha3(IV)-/- mice, a model for human Alport syndrome. Genetic ablation of either MMP-2 or MMP-9, or both MMP-2 and MMP-9, led to compensatory up-regulation of other MMPs in the kidney glomerulus. Pharmacological ablation of enzymatic activity associated with multiple GBM-degrading MMPs, before the onset of proteinuria or GBM structural defects in the alpha3(IV)-/- mice, led to significant attenuation in disease progression associated with delayed proteinuria and marked extension in survival. In contrast, inhibition of MMPs after induction of proteinuria led to acceleration of disease associated with extensive interstitial fibrosis and early death of alpha3(IV)-/- mice.ConclusionsThese results suggest that preserving GBM/extracellular matrix integrity before the onset of proteinuria leads to significant disease protection, but if this window of opportunity is lost, MMP-inhibition at the later stages of Alport disease leads to accelerated glomerular and interstitial fibrosis. Our findings identify a crucial dual role for MMPs in the progression of Alport disease in alpha3(IV)-/- mice, with an early pathogenic function and a later protective action. Hence, we propose possible use of MMP-inhibitors as disease-preventive drugs for patients with Alport syndrome with identified genetic defects, before the onset of proteinuria

Constructing Integrable Third Order Systems:The Gambier Approach

We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that bears his name. Our study is carried through for both continuous and discrete systems. In both cases the investigation is based on the study of the singularities of the system (the Painlev\'e method for ODE's and the singularity confinement method for mappings).Comment: 14 pages, TEX FIL

Watersheds dynamics following wildfires: Nonlinear feedbacks and implications on hydrologic responses

In recent years, wildfires in the western United States have occurred with increasing frequency and scale. Climate change scenarios in California predict prolonged periods of droughts with even greater potential for conditions amenable to wildfires. The Sierra Nevada Mountains provide 70% of water resources in California, yet how wildfires will impact watershed-scale hydrology is highly uncertain. In this work, we assess the impacts of wildfires perturbations on watershed hydrodynamics using a physically based integrated hydrologic model in a high-performance-computing framework. A representative Californian watershed, the Cosumnes River, is used to demonstrate how postwildfire conditions impact the water and energy balance. Results from the high-resolution model show counterintuitive feedbacks that occur following a wildfire and allow us to identify the regions most sensitive to wildfires conditions, as well as the hydrologic processes that are most affected. For example, whereas evapotranspiration generally decreases in the postfire simulations, some regions experience an increase due to changes in surface water run-off patterns in and near burn scars. Postfire conditions also yield greater winter snowpack and subsequently greater summer run-off as well as groundwater storage in the postfire simulations. Comparisons between dry and wet water years show that climate is the main factor controlling the timing at which some hydrologic processes occur (such as snow accumulation) whereas postwildfire changes to other metrics (such as streamflow) show seasonally dependent impacts primarily due to the timing of snowmelt, illustrative of the integrative nature of hydrologic processes across the Sierra Nevada-Central Valley interface

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.Comment: To be published in Classical and Quantum Gravit