On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua

Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density of the sum of two gamma random variables is derived. Then a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed. An explicit expression for the error bound is obtained. The proposed technique is shown to be computationally efficient, i.e. only polynomial in growth in the number of terms compared to the exponential growth of most other methods. It provides a vast improvement in accuracy and shows only logarithmic growth in the required precision. In addition, it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms. As an application, the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with N scalar fields is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio

The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients.

We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions, and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are either fit directly to experimental observables-e.g., the finite ion size-or optimized for agreement with experimental results. Experimental data for this optimization are available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part, we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route toward a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods

Automatic Segmentation of Dermoscopic Images by Iterative Classification

Accurate detection of the borders of skin lesions is a vital first step for computer aided diagnostic systems. This paper presents a novel automatic approach to segmentation of skin lesions that is particularly suitable for analysis of dermoscopic images. Assumptions about the image acquisition, in particular, the approximate location and color, are used to derive an automatic rule to select small seed regions, likely to correspond to samples of skin and the lesion of interest. The seed regions are used as initial training samples, and the lesion segmentation problem is treated as binary classification problem. An iterative hybrid classification strategy, based on a weighted combination of estimated posteriors of a linear and quadratic classifier, is used to update both the automatically selected training samples and the segmentation, increasing reliability and final accuracy, especially for those challenging images, where the contrast between the background skin and lesion is low

Increased markers of cardiac vagal activity in leucine-rich repeat kinase 2-associated Parkinson's disease.

PurposeCardiac autonomic dysfunction manifests as reduced heart rate variability (HRV) in idiopathic Parkinson's disease (PD), but no significant reduction has been found in PD patients who carry the LRRK2 mutation. Novel HRV features have not been investigated in these individuals. We aimed to assess cardiac autonomic modulation through standard and novel approaches to HRV analysis in individuals who carry the LRRK2 G2019S mutation.MethodsShort-term electrocardiograms were recorded in 14 LRRK2-associated PD patients, 25 LRRK2-non-manifesting carriers, 32 related non-carriers, 20 idiopathic PD patients, and 27 healthy controls. HRV measures were compared using regression modeling, controlling for age, sex, mean heart rate, and disease duration. Discriminant analysis highlighted the feature combination that best distinguished LRRK2-associated PD from controls.ResultsBeat-to-beat and global HRV measures were significantly increased in LRRK2-associated PD patients compared with controls (e.g., deceleration capacity of heart rate: p = 0.006) and idiopathic PD patients (e.g., 8th standardized moment of the interbeat interval distribution: p = 0.0003), respectively. LRRK2-associated PD patients also showed significantly increased irregularity of heart rate dynamics, as quantified by Rényi entropy, when compared with controls (p = 0.002) and idiopathic PD patients (p = 0.0004). Ordinal pattern statistics permitted the identification of LRRK2-associated PD individuals with 93% sensitivity and 93% specificity. Consistent results were found in a subgroup of LRRK2-non-manifesting carriers when compared with controls.ConclusionsIncreased beat-to-beat HRV in LRRK2 G2019S mutation carriers compared with controls and idiopathic PD patients may indicate augmented cardiac autonomic cholinergic activity, suggesting early impairment of central vagal feedback loops in LRRK2-associated PD

TOUCAN 2: the all-inclusive open source workbench for regulatory sequence analysis

We present the second and improved release of the TOUCAN workbench for cis-regulatory sequence analysis. TOUCAN implements and integrates fast state-of-the-art methods and strategies in gene regulation bioinformatics, including algorithms for comparative genomics and for the detection of cis-regulatory modules. This second release of TOUCAN has become open source and thereby carries the potential to evolve rapidly. The main goal of TOUCAN is to allow a user to come to testable hypotheses regarding the regulation of a gene or of a set of co-regulated genes. TOUCAN can be launched from this location: