{\bf τ\tau-Function Evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles}

It has recently been emphasized that all known exact evaluations of gap probabilities for classical unitary matrix ensembles are in fact $\tau$-functions for certain Painlev\'e systems. We show that all exact evaluations of gap probabilities for classical orthogonal matrix ensembles, either known or derivable from the existing literature, are likewise $\tau$-functions for certain Painlev\'e systems. In the case of symplectic matrix ensembles all exact evaluations, either known or derivable from the existing literature, are identified as the mean of two $\tau$-functions, both of which correspond to Hamiltonians satisfying the same differential equation, differing only in the boundary condition. Furthermore the product of these two $\tau$-functions gives the gap probability in the corresponding unitary symmetry case, while one of those $\tau$-functions is the gap probability in the corresponding orthogonal symmetry case.Comment: AMS-Late

Characterization of heat transfer in nutrient materials, part 2

A thermal model is analyzed that takes into account phase changes in the nutrient material. The behavior of fluids in low gravity environments is discussed along with low gravity heat transfer. Thermal contact resistance in the Skylab food heater is analyzed. The original model is modified to include: equivalent conductance due to radiation, radial equivalent conductance, wall equivalent conductance, and equivalent heat capacity. A constant wall-temperature model is presented

TIME-VARIANT SPECTRAL ANALYSIS OF SURFACE EMG SIGNALS – EXEMPLARILY SHOWN FOR ARCHERY

To analyse the spectral density of electromyographic (EMG) signals Fourier transforms are commonly used. The prerequisite of this transform is that the analysed signal is stationary. Generally, this can not be assumed for the electromyograms of muscle contractions of human movement. A new method to analyse non-stationary biological signals is the time-variant spectral analysis. The aim of this paper is to use the timevariant spectral analysis in a realistic sport application to show connections of the athlete’s level and the spectral density of the EMG. Five top-level archers participated in the study. The results suggest, that a higher level of performance generally corresponds to lower median-frequencies and a smaller variability of the median-frequencies of the EMG-signals

Bariatric surgery and brain health: A longitudinal observational study investigating the effect of surgery on cognitive function and gray matter volume

Dietary modifications leading to weight loss have been suggested as a means to improve brain health. In morbid obesity, bariatric surgery (BARS)—including different procedures, such as vertical sleeve gastrectomy (VSG), gastric banding (GB), or Roux-en-Y gastric bypass (RYGB) surgery—is performed to induce rapid weight loss. Combining reduced food intake and malabsorption of nutrients, RYGB might be most effective, but requires life-long follow-up treatment. Here, we tested 40 patients before and six months after surgery (BARS group) using a neuropsychological test battery and compared them with a waiting list control group. Subsamples of both groups underwent structural MRI and were examined for differences between surgical procedures. No substantial differences between BARS and control group emerged with regard to cognition. However, larger gray matter volume in fronto-temporal brain areas accompanied by smaller volume in the ventral striatum was seen in the BARS group compared to controls. RYGB patients compared to patients with restrictive treatment alone (VSG/GB) had higher weight loss, but did not benefit more in cognitive outcomes. In sum, the data of our study suggest that BARS might lead to brain structure reorganization at long-term follow-up, while the type of surgical procedure does not differentially modulate cognitive performance

Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-function of the sixth Painlev\'e system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-classical weights, for which the diagonal Ising correlations arise as the leading coefficient of the polynomials specialised appropriately. Here we demonstrate that the next-to-diagonal correlations of the anisotropic Ising model are evaluated as one of the elements of this isomonodromic system or essentially as the Cauchy-Hilbert transform of one of the bi-orthogonal polynomials.Comment: 11 pages, 1 figur

Random Matrix Theory and the Sixth Painlev\'e Equation

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be $\tau$-functions for Painlev\'e systems, allowing for the former to be characterised as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the $\sigma$ form of \PVI. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at $t=0,1,\infty$ of $\sigma$\PVI displayed by a generalisation of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the $\tau$-function of $\sigma$\PVI in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to \PVI.Comment: Dedicated to the centenary of the publication of the Painlev\'e VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Development of algorithms for determining heart failure with reduced and preserved ejection fraction using nationwide electronic healthcare records in the UK

Background: Determining heart failure (HF) phenotypes in routine electronic health records (EHR) is challenging. We aimed to develop and validate EHR algorithms for identification of specific HF phenotypes, using Read codes in combination with selected patient characteristics. Methods: We used The Healthcare Improvement Network (THIN). The study population included a random sample of individuals with HF diagnostic codes (HF with reduced ejection fraction (HFrEF), HF with preserved ejection fraction (HFpEF) and non-specific HF) selected from all participants registered in the THIN database between 1 January 2015 and 30 September 2017. Confirmed diagnoses were determined in a randomly selected subgroup of 500 patients via GP questionnaires including a review of all available cardiovascular investigations. Confirmed diagnoses of HFrEF and HFpEF were based on four criteria. Based on these data, we calculated a positive predictive value (PPV) of predefined algorithms which consisted of a combination of Read codes and additional information such as echocardiogram results and HF medication records. Results: The final cohort from which we drew the 500 patient random sample consisted of 10 275 patients. Response rate to the questionnaire was 77.2%. A small proportion (18%) of the overall HF patient population were coded with specific HF phenotype Read codes. For HFrEF, algorithms achieving over 80% PPV included definite, possible or non-specific HF HFrEF codes when combined with at least two of the drugs used to treat HFrEF. Only in non-specific HF coding did the use of three drugs (rather than two) contribute to an improvement of the PPV for HFrEF. HFpEF was only accurately defined with specific codes. In the absence of specific coding for HFpEF, the PPV was consistently below 50%. Conclusions: Prescription for HF medication can reliably be used to find HFrEF patients in the UK, even in the absence of a specific Read code for HFrEF. Algorithms using non-specific coding could not reliably find HFpEF patients