Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

LMS tables for waist circumference and waist-to-height ratio among Colombian children and adolescents: The FUPRECOL study

Background: Indices predictive of central obesity include waist circumference (WC) and waist-to-height ratio (WHtR). The aims of this study were 1) to establish a Colombian youth smoothed centile charts and LMS tables for WC and WHtR and 2) to evaluate the utility of these parameters as predictors of overweight and obesity. Method: A cross-sectional study whose sample population comprised 7954 healthy Colombian schoolchildren [boys n=3460 and girls n=4494, mean (standard deviation) age 12.8 (2.3) years old]. Weight, height, body mass index (BMI), WC and WHtR and its percentiles were calculated. Appropriate cut-offs point of WC and WHtR for overweight and obesity, as defined by the International Obesity Task Force (IOTF) definitions, were selected using receiver operating characteristic (ROC) analysis. The discriminating power of WC and WHtR was expressed as area under the curve (AUC). Results: Reference values for WC and WHtR are presented. Mean WC increased and WHtR decreased with age for both genders. We found a moderate positive correlation between WC and BMI (r= 0.756, P < 0.01) and WHtR and BMI (r= 0.604, P < 0.01). The ROC analysis showed a high discrimination power in the identification of overweight and obesity for both measures in our sample population. Overall, WHtR was slightly a better predictor for overweight/obesity (AUC 95% CI 0.868-0.916) than the WC (AUC 95% CI 0.862-0.904). Conclusion: This paper presents the first sex- and age-specific WC and WHtR percentiles for both measures among Colombian children and adolescents aged 9–17.9 years. By providing LMS tables for Latin-American people based on Colombian reference data, we hope to provide quantitative tools for the study of obesity and its comorbidities.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena`s correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low- frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

Genetic heterogeneity in familial acute myelogenous leukemia: Evidence for a second locus at chromosome 16q21-23.2

The identification of genes responsible for the rare cases of familial leukemia may afford insight into the mechanism underlying the more common sporadic occurrences. Here we test a single family with 11 relevant meioses transmitting autosomal dominant acute myelogenous leukemia (AML) and myelodysplasia for linkage to three potential candidate loci. In a different family with inherited AML, linkage to chromosome 21q22.1-22.2 was recently reported; we exclude linkage to 21q22.1-22.2, demonstrating that familial AML is a heterogeneous disease. After reviewing familial leukemia and observing anticipation in the form of a declining age of onset with each generation, we had proposed 9p21-22 and 16q22 as additional candidate loci. Whereas linkage to 9p21-22 can be excluded, the finding of a maximum two-point LOD score of 2.82 with the microsatellite marker D16S522 at a recombination fraction theta = 0 provides evidence supporting linkage to 16q22. Haplotype analysis reveals a 23.5-cM (17.9-Mb) commonly inherited region among all affected family members extending from D16S451 to D1GS289, In order to extract maximum linkage information with missing individuals, incomplete informativeness with individual markers in this interval, and possible deviance from strict autosomal dominant inheritance, we performed nonparametric linkage analysis (NPL) and found a maximum NPL statistic corresponding to a P-value of .00098, close to the maximum conditional probability of linkage expected for a pedigree with this structure. Mutational analysis in this region specifically excludes expansion of the AT-rich minisatellite repeat FRA16B fragile site and the CAG trinucleotide repeat in the E2F-4 transcription factor. The ''repeat expansion detection'' method, capable of detecting dynamic mutation associated with anticipation, more generally excludes large CAG repeat expansion as a cause of leukemia in this family.

Validation of the Edinburgh Postnatal Depression Scale for men, and comparison of item endorsement with their partners

Background: The Edinburgh Postnatal Depression Scale (EPDS) has been validated and used extensively in screening for depression in new mothers, both in English speaking and non-English speaking communities. While some studies have reported the use of the EPDS with Fathers, none have validated it for this group, and thus the appropriate cut-off score for screening for depression or anxiety caseness for this population is not known. Method: Couples were recruited antenatally and interviewed at six weeks postpartum. EPDS scores and distress caseness (depression or anxiety disorders) for 208 fathers and 230 mothers were determined using the Diagnostic Interview Schedule. Results: Analyses of the EPDS for fathers using distress caseness (depression or anxiety disorders) as the criterion shows that a cut-off of 5/6 has optimum receiver operating characteristics. Furthermore acceptable reliability (split-half and internal consistency) and validity (concurrent) coefficients were obtained. For mothers the optimum cut-off screening value to detect distress caseness was 7/8. Item analysis revealed that fathers endorsed seven of the ten items at lower rates to mothers, with the most significant being that referring to crying. Conclusions: The EPDS is a reliable and valid measure of mood in fathers. Screening for depression or anxiety disorders in fathers requires a two point lower cut-off than screening for depression or anxiety in mothers, and we recommend this cut-off to he 5/6. (C) 2001 Elsevier Science B.V. All rights reserved.

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

Virtual simulation of the postsurgical cosmetic outcome in patientswith pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior chest wall, in which several ribs and the sternum grow abnormally. Nowadays, the surgical correction is carried out in children and adults through Nuss technic. This technic has been shown to be safe with major drivers as cosmesis and the prevention of psychological problems and social stress. Nowadays, no application is known to predict the cosmetic outcome of the pectus excavatum surgical correction. Such tool could be used to help the surgeon and the patient in the moment of deciding the need for surgery correction. This work is a first step to predict postsurgical outcome in pectus excavatum surgery correction. Facing this goal, it was firstly determined a point cloud of the skin surface along the thoracic wall using Computed Tomography (before surgical correction) and the Polhemus FastSCAN (after the surgical correction). Then, a surface mesh was reconstructed from the two point clouds using a Radial Basis Function algorithm for further affine registration between the meshes. After registration, one studied the surgical correction influence area (SCIA) of the thoracic wall. This SCIA was used to train, test and validate artificial neural networks in order to predict the surgical outcome of pectus excavatum correction and to determine the degree of convergence of SCIA in different patients. Often, ANN did not converge to a satisfactory solution (each patient had its own deformity characteristics), thus invalidating the creation of a mathematical model capable of estimating, with satisfactory results, the postsurgical outcome

A filter algorithm: comparison with NLP solvers

The purpose of this work is to present an algorithm to solve nonlinear constrained optimization problems, using the filter method with the inexact restoration (IR) approach. In the IR approach two independent phases are performed in each iteration—the feasibility and the optimality phases. The first one directs the iterative process into the feasible region, i.e. finds one point with less constraints violation. The optimality phase starts from this point and its goal is to optimize the objective function into the satisfied constraints space. To evaluate the solution approximations in each iteration a scheme based on the filter method is used in both phases of the algorithm. This method replaces the merit functions that are based on penalty schemes, avoiding the related difficulties such as the penalty parameter estimation and the non-differentiability of some of them. The filter method is implemented in the context of the line search globalization technique. A set of more than two hundred AMPL test problems is solved. The algorithm developed is compared with LOQO and NPSOL software packages.

Conformal symmetry of the critical 3D Ising model inside a sphere

We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a non-perturbative behavior in some characteristic correlation lengths.

Induced quantum metric fluctuations and the validity of semiclassical gravity

We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

P value and the theory of hypothesis testing: an explanation for new researchers.

In the 1920s, Ronald Fisher developed the theory behind the p value and Jerzy Neyman and Egon Pearson developed the theory of hypothesis testing. These distinct theories have provided researchers important quantitative tools to confirm or refute their hypotheses. The p value is the probability to obtain an effect equal to or more extreme than the one observed presuming the null hypothesis of no effect is true; it gives researchers a measure of the strength of evidence against the null hypothesis. As commonly used, investigators will select a threshold p value below which they will reject the null hypothesis. The theory of hypothesis testing allows researchers to reject a null hypothesis in favor of an alternative hypothesis of some effect. As commonly used, investigators choose Type I error (rejecting the null hypothesis when it is true) and Type II error (accepting the null hypothesis when it is false) levels and determine some critical region. If the test statistic falls into that critical region, the null hypothesis is rejected in favor of the alternative hypothesis. Despite similarities between the two, the p value and the theory of hypothesis testing are different theories that often are misunderstood and confused, leading researchers to improper conclusions. Perhaps the most common misconception is to consider the p value as the probability that the null hypothesis is true rather than the probability of obtaining the difference observed, or one that is more extreme, considering the null is true. Another concern is the risk that an important proportion of statistically significant results are falsely significant. Researchers should have a minimum understanding of these two theories so that they are better able to plan, conduct, interpret, and report scientific experiments.

A genomewide scan for early-onset coronary artery disease in 438 families: the GENECARD Study.

A family history of coronary artery disease (CAD), especially when the disease occurs at a young age, is a potent risk factor for CAD. DNA collection in families in which two or more siblings are affected at an early age allows identification of genetic factors for CAD by linkage analysis. We performed a genomewide scan in 1,168 individuals from 438 families, including 493 affected sibling pairs with documented onset of CAD before 51 years of age in men and before 56 years of age in women. We prospectively defined three phenotypic subsets of families: (1) acute coronary syndrome in two or more siblings; (2) absence of type 2 diabetes in all affected siblings; and (3) atherogenic dyslipidemia in any one sibling. Genotypes were analyzed for 395 microsatellite markers. Regions were defined as providing evidence for linkage if they provided parametric two-point LOD scores >1.5, together with nonparametric multipoint LOD scores >1.0. Regions on chromosomes 3q13 (multipoint LOD = 3.3; empirical P value <.001) and 5q31 (multipoint LOD = 1.4; empirical P value <.081) met these criteria in the entire data set, and regions on chromosomes 1q25, 3q13, 7p14, and 19p13 met these criteria in one or more of the subsets. Two regions, 3q13 and 1q25, met the criteria for genomewide significance. We have identified a region on chromosome 3q13 that is linked to early-onset CAD, as well as additional regions of interest that will require further analysis. These data provide initial areas of the human genome where further investigation may reveal susceptibility genes for early-onset CAD.