Quantitative stability analysis of stochastic generalized equations

We consider the solution of a system of stochastic generalized equations (SGE) where the underlying functions are mathematical expectation of random set-valued mappings. SGE has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem or equilibrium conditions of a stochastic equilibrium problem. We derive quantitative continuity of expected value of the set-valued mapping with respect to the variation of the underlying probability measure in a metric space. This leads to the subsequent qualitative and quantitative stability analysis of solution set mappings of the SGE. Under some metric regularity conditions, we derive Aubin's property of the solution set mapping with respect to the change of probability measure. The established results are applied to stability analysis of stochastic variational inequality, stationary points of classical one stage and two stage stochastic minimization problems, two stage stochastic mathematical programs with equilibrium constraints and stochastic programs with second order dominance constraints

Human autoantibodies against the 54 kDa protein of the signal recognition particle block function at multiple stages.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.The 54 kDa subunit of the signal recognition particle (SRP54) binds to the signal sequences of nascent secretory and membrane proteins and it contributes to the targeting of these precursors to the membrane of the endoplasmic reticulum (ER). At the ER membrane, the binding of the signal recognition particle (SRP) to its receptor triggers the release of SRP54 from its bound signal sequence and the nascent polypeptide is transferred to the Sec61 translocon for insertion into, or translocation across, the ER membrane. In the current article, we have characterized the specificity of anti-SRP54 autoantibodies, which are highly characteristic of polymyositis patients, and investigated the effect of these autoantibodies on the SRP function in vitro. We found that the anti-SRP54 autoantibodies had a pronounced and specific inhibitory effect upon the translocation of the secretory protein preprolactin when analysed using a cell-free system. Our mapping studies showed that the anti-SRP54 autoantibodies bind to the amino-terminal SRP54 N-domain and to the central SRP54 G-domain, but do not bind to the carboxy-terminal M-domain that is known to bind ER signal sequences. Nevertheless, anti-SRP54 autoantibodies interfere with signal-sequence binding to SRP54, most probably by steric hindrance. When the effect of anti-SRP autoantibodies on protein targeting the ER membrane was further investigated, we found that the autoantibodies prevent the SRP receptor-mediated release of ER signal sequences from the SRP54 subunit. This observation supports a model where the binding of the homologous GTPase domains of SRP54 and the alpha-subunit of the SRP receptor to each other regulates the release of ER signal sequences from the SRP54 M-domain

Author's personal copy Discrete Optimization A model for dynamic chance constraints in hydro power reservoir management

a b s t r a c t In this paper, a model for (joint) dynamic chance constraints is proposed and applied to an optimization problem in water reservoir management. The model relies on discretization of the decision variables but keeps the probability distribution continuous. Our approach relies on calculating probabilities of rectangles which is particularly useful in the presence of independent random variables but works equally well in the case of correlated variables. Numerical results are provided for two and three stages

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

Increased amino acids levels and the risk of developing of hypertriglyceridemia in a 7-year follow-up

BACKGROUND: Recently, five branched-chain and aromatic amino acids were shown to be associated with the risk of developing type 2 diabetes (T2D). AIM: We set out to examine whether amino acids are also associated with the development of hypertriglyceridemia. MATERIALS AND METHODS: We determined the serum amino acids concentrations of 1,125 individuals of the KORA S4 baseline study, for which follow-up data were available also at the KORA F4 7 years later. After exclusion for hypertriglyceridemia (defined as having a fasting triglyceride level above 1.70 mmol/L) and diabetes at baseline, 755 subjects remained for analyses. RESULTS: Increased levels of leucine, arginine, valine, proline, phenylalanine, isoleucine and lysine were significantly associated with an increased risk of hypertriglyceridemia. These associations remained significant when restricting to those individuals who did not develop T2D in the 7-year follow-up. The increase per standard deviation of amino acid level was between 26 and 40 %. CONCLUSIONS: Seven amino acids were associated with an increased risk of developing hypertriglyceridemia after 7 years. Further studies are necessary to elucidate the complex role of these amino acids in the pathogenesis of metabolic disorders

Genome-Wide Association Study with Targeted and Non-targeted NMR Metabolomics Identifies 15 Novel Loci of Urinary Human Metabolic Individuality

Genome-wide association studies with metabolic traits (mGWAS) uncovered many genetic variants that influence human metabolism. These genetically influenced metabotypes (GIMs) contribute to our metabolic individuality, our capacity to respond to environmental challenges, and our susceptibility to specific diseases. While metabolic homeostasis in blood is a well investigated topic in large mGWAS with over 150 known loci, metabolic detoxification through urinary excretion has only been addressed by few small mGWAS with only 11 associated loci so far. Here we report the largest mGWAS to date, combining targeted and non-targeted 1H NMR analysis of urine samples from 3,861 participants of the SHIP-0 cohort and 1,691 subjects of the KORA F4 cohort. We identified and replicated 22 loci with significant associations with urinary traits, 15 of which are new (HIBCH, CPS1, AGXT, XYLB, TKT, ETNPPL, SLC6A19, DMGDH, SLC36A2, GLDC, SLC6A13, ACSM3, SLC5A11, PNMT, SLC13A3). Two-thirds of the urinary loci also have a metabolite association in blood. For all but one of the 6 loci where significant associations target the same metabolite in blood and urine, the genetic effects have the same direction in both fluids. In contrast, for the SLC5A11 locus, we found increased levels of myo-inositol in urine whereas mGWAS in blood reported decreased levels for the same genetic variant. This might indicate less effective re-absorption of myo-inositol in the kidneys of carriers. In summary, our study more than doubles the number of known loci that influence urinary phenotypes. It thus allows novel insights into the relationship between blood homeostasis and its regulation through excretion. The newly discovered loci also include variants previously linked to chronic kidney disease (CPS1, SLC6A13), pulmonary hypertension (CPS1), and ischemic stroke (XYLB). By establishing connections from gene to disease via metabolic traits our results provide novel hypotheses about molecular mechanisms involved in the etiology of diseases

Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations

In this paper, the Euler–Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method

Body Fat Free Mass Is Associated with the Serum Metabolite Profile in a Population-Based Study

To characterise the influence of the fat free mass on the metabolite profile in serum samples from participants of the population-based KORA (Cooperative Health Research in the Region of Augsburg) S4 study. Analyses were based on metabolite profile from 965 participants of the S4 and 890 weight-stable subjects of its seven-year follow-up study (KORA F4). 190 different serum metabolites were quantified in a targeted approach including amino acids, acylcarnitines, phosphatidylcholines (PCs), sphingomyelins and hexose. Associations between metabolite concentrations and the fat free mass index (FFMI) were analysed using adjusted linear regression models. To draw conclusions on enzymatic reactions, intra-metabolite class ratios were explored. Pairwise relationships among metabolites were investigated and illustrated by means of Gaussian graphical models (GGMs). We found 339 significant associations between FFMI and various metabolites in KORA S4. Among the most prominent associations (p-values 4.75 × 10(-16)-8.95 × 10(-06)) with higher FFMI were increasing concentrations of the branched chained amino acids (BCAAs), ratios of BCAAs to glucogenic amino acids, and carnitine concentrations. For various PCs, a decrease in chain length or in saturation of the fatty acid moieties could be observed with increasing FFMI, as well as an overall shift from acyl-alkyl PCs to diacyl PCs. These findings were reproduced in KORA F4. The established GGMs supported the regression results and provided a comprehensive picture of the relationships between metabolites. In a sub-analysis, most of the discovered associations did not exist in obese subjects in contrast to non-obese subjects, possibly indicating derangements in skeletal muscle metabolism. A set of serum metabolites strongly associated with FFMI was identified and a network explaining the relationships among metabolites was established. These results offer a novel and more complete picture of the FFMI effects on serum metabolites in a data-driven network