On the solvability of degenerate stochastic partial differential equations in Sobolev spaces

Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric hyperbolic systems.Comment: 26 page

A novel locus for Meckel-Gruber syndrome, MKS3, maps to chromosome 8q24

Meckel-Gruber syndrome (MKS), the most common monogenic cause of neural tube defects, is an autosomal recessive disorder characterised by a combination of renal cysts and variably associated features, including developmental anomalies of the central nervous system (typically encephalcoele), hepatic ductal dysplasia and cysts, and polydactyly. Locus heterogeneity has been demonstrated by the mapping of the MKS1 locus to 17q21-24 in Finnish kindreds, and of MKS2 to 11q13 in North African-Middle Eastern cohorts. In the present study, we have investigated the genetic basis of MKS in eight consanguineous kindreds, originating from the Indian sub-continent, that do not show linkage to either MKS1 or MKS2. We report the localisation of a third MKS locus (MKS3) to chromosome 8q24 in this cohort by a genome-wide linkage search using autozygosity mapping. We identified a 26-cM region of autozygosity between D8S586 and D8S1108 with a maximum cumulative two-point LOD score at D8S1179 (Z(max)=3.04 at theta=0.06). A heterogeneity test provided evidence of one unlinked family. Exclusion of this family from multipoint analysis maximised the cumulative multipoint LOD score at locus D8S1128 (Z(max)=5.65). Furthermore, a heterozygous SNP in DDEF1, a putative candidate gene, suggested that MKS3 mapped within a 15-cM interval. Comparison of the clinical features of MKS3-linked cases with reports of MKS1- and MKS2-linked kindreds suggests that polydactyly (and possibly encephalocele) appear less common in MKS3-linked families

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

An Exact Fluctuating 1/2-BPS Configuration

This work explores the role of thermodynamic fluctuations in the two parameter giant and superstar configurations characterized by an ensemble of arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis illustrates that the chemical and state-space geometric descriptions exhibit an intriguing set of exact pair correction functions and the global correlation lengths. The first principle of statistical mechanics shows that the possible canonical fluctuations may precisely be ascertained without any approximation. Interestingly, our intrinsic geometric study exemplifies that there exist exact fluctuating 1/2-BPS statistical configurations which involve an ensemble of microstates describing the liquid droplets or fuzzballs. The Gaussian fluctuations over an equilibrium chemical and state-space configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds for all physically admissible domains of black hole parameters. An explicit computation demonstrates that the underlying chemical correlations involve ordinary summations, whilst the state-space correlations may simply be depicted by standard polygamma functions. Our construction ascribes definite stability character to the canonical energy fluctuations and to the counting entropy associated with an arbitrary choice of excited boxes from an ensemble of ample boxes constituting a variety of Young tableaux.Comment: Minor changes, added references, 30 pages, 4 figures, PACS numbers: 04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.50.Gh Higher-dimensional black holes, black strings, and related objects; 04.60.Cf Gravitational aspects of string theory, accepted for publication in JHE

Improved measurement of the K+->pi+nu(nu)over-bar branching ratio

An additional event near the upper kinematic limit for K+-->pi(+)nu(nu) over bar has been observed by experiment E949 at Brookhaven National Laboratory. Combining previously reported and new data, the branching ratio is B(K+-->pi(+)nu(nu) over bar)=(1.47(-0.89)(+1.30))x10(-10) based on three events observed in the pion momentum region 211<P<229 MeV/c. At the measured central value of the branching ratio, the additional event had a signal-to-background ratio of 0.9

Maternal fecal microbiome predicts gestational age, birth weight and neonatal growth in rural Zimbabwe.

BACKGROUND: Preterm birth and low birth weight (LBW) affect one in ten and one in seven livebirths, respectively, primarily in low-income and middle-income countries (LMIC) and are major predictors of poor child health outcomes. However, both have been recalcitrant to public health intervention. The maternal intestinal microbiome may undergo substantial changes during pregnancy and may influence fetal and neonatal health in LMIC populations. METHODS: Within a subgroup of 207 mothers and infants enrolled in the SHINE trial in rural Zimbabwe, we performed shotgun metagenomics on 351 fecal specimens provided during pregnancy and at 1-month post-partum to investigate the relationship between the pregnancy gut microbiome and infant gestational age, birth weight, 1-month length-, and weight-for-age z-scores using extreme gradient boosting machines. FINDINGS: Pregnancy gut microbiome taxa and metabolic functions predicted birth weight and WAZ at 1 month more accurately than gestational age and LAZ. Blastoscystis sp, Brachyspira sp and Treponeme carriage were high compared to Western populations. Resistant starch-degraders were important predictors of birth outcomes. Microbiome capacity for environmental sensing, vitamin B metabolism, and signalling predicted increased infant birth weight and neonatal growth; while functions involved in biofilm formation in response to nutrient starvation predicted reduced birth weight and growth. INTERPRETATION: The pregnancy gut microbiome in rural Zimbabwe is characterized by resistant starch-degraders and may be an important metabolic target to improve birth weight. FUNDING: Bill and Melinda Gates Foundation, UK Department for International Development, Wellcome Trust, Swiss Agency for Development and Cooperation, US National Institutes of Health, and UNICEF

Relationship Between Obesity and Diabetes in a US Adult Population: Findings from the National Health and Nutrition Examination Survey, 1999–2006

# The Author(s) 2010. This article is published with open access at Springerlink.com Background Obesity is one of the most important modifiable risk factors for the prevention of type 2 diabetes. The aim of this study was to examine the prevalence of diabetes with increasing severity of obesity and the distribution of HbA1c levels in diabetics participating in the latest National Health and Nutrition Examination Survey (NHANES). Methods Data from a representative sample of adults with diabetes participating in the NHANES between 1999 and 2006 were reviewed. The prevalence of diabetes and levels of fasting glucose, insulin, c-peptide, and HbA1c were examined across different weight classes with normal weight, overweight, and obesity classes 1, 2, and 3 were defined as body mass index (BMI) of &lt;25.0, 25.0–29.9, 30.0–34.9, 35.0–39.9, and equal to 40.0, respectively. The distribution of HbA1c levels among adults with diabetes was also examined. Results There were 2,894 adults with diabetes (13.6%) among the 21,205 surveyed participants. Among the adults with diabetes, the mean age was 59 years, the mean fasting glucose was 155±2 mg/dl, and the mean HbA1c was 7.2%; 80.3 % of diabetics were considered overweight (BMI≥25) and 49.1 % of diabetics were considered obese (BMI≥30). Presented as a poster presentation at the American Society fo