Incremental Stochastic Subgradient Algorithms for Convex Optimization

In this paper we study the effect of stochastic errors on two constrained incremental sub-gradient algorithms. We view the incremental sub-gradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. We first study the standard cyclic incremental sub-gradient algorithm in which the agents form a ring structure and pass the iterate in a cycle. We consider the method with stochastic errors in the sub-gradient evaluations and provide sufficient conditions on the moments of the stochastic errors that guarantee almost sure convergence when a diminishing step-size is used. We also obtain almost sure bounds on the algorithm's performance when a constant step-size is used. We then consider \ram{the} Markov randomized incremental subgradient method, which is a non-cyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time non-homogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. We establish the convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant step-sizes, respectively

A Random Search Framework for Convergence Analysis of Distributed Beamforming with Feedback

The focus of this work is on the analysis of transmit beamforming schemes with a low-rate feedback link in wireless sensor/relay networks, where nodes in the network need to implement beamforming in a distributed manner. Specifically, the problem of distributed phase alignment is considered, where neither the transmitters nor the receiver has perfect channel state information, but there is a low-rate feedback link from the receiver to the transmitters. In this setting, a framework is proposed for systematically analyzing the performance of distributed beamforming schemes. To illustrate the advantage of this framework, a simple adaptive distributed beamforming scheme that was recently proposed by Mudambai et al. is studied. Two important properties for the received signal magnitude function are derived. Using these properties and the systematic framework, it is shown that the adaptive distributed beamforming scheme converges both in probability and in mean. Furthermore, it is established that the time required for the adaptive scheme to converge in mean scales linearly with respect to the number of sensor/relay nodes.Comment: 8 pages, 3 figures, presented partially at ITA '08 and PSU School of Info. Theory '0

A highly sensitive liquid chromatography electrospray ionization mass spectrometry method for quantification of TMA, TMAO and creatinine in mouse urine

Our method describes the quantification in mouse urine of trimethylamine (TMA), trimethylamine N-oxide (TMAO) and creatinine. The method combines derivatization of TMA, with ethyl bromoacetate, and LC chromatographic separation on an ACE C18 column. The effluent was continuously electrosprayed into the linear ion trap mass spectrometer (LTQ), which operated in selective ion monitoring (SIM) modes set for targeted analytes and their internal standards (IS). All validation parameters were within acceptable ranges of analytical method validation guidelines. Intra- and inter-day assay precision and accuracy coefficients of variation were <3.1%, and recoveries for TMA and TMAO were 97–104%. The method developed uses a two-step procedure. Firstly, TMA and TMAO are analyzed without a purification step using a 5-min gradient cap-LC- SIMs analysis, then creatinine is analyzed using the same experimental conditions. The method is robust, highly sensitive, reproducible and has the high-throughput capability of detecting TMA, TMAO and creatinine at on-column concentrations as low as 28 pg/mL, 115 pg/mL and 1 ng/mL, respectively. The method is suitable for analysis of TMA, TMAO and creatinine in both male and female mouse urine. / The key benefits of the method are: The small sample volume of urine required, which overcomes the difficulties of collecting sufficient volumes of urine at defined times. / No sample pre-treatment is necessary. / The quantification of TMA, TMAO and creatinine using the same cap-LC-MS method

Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization

We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the iterates to its neighbors. Then, each agent combines weighted averages of the received iterates with its own iterate, and adjusts the iterate by using subgradient information (known with stochastic errors) of its own function and by projecting onto the constraint set. The goal of this paper is to explore the effects of stochastic subgradient errors on the convergence of the algorithm. We first consider the behavior of the algorithm in mean, and then the convergence with probability 1 and in mean square. We consider general stochastic errors that have uniformly bounded second moments and obtain bounds on the limiting performance of the algorithm in mean for diminishing and non-diminishing stepsizes. When the means of the errors diminish, we prove that there is mean consensus between the agents and mean convergence to the optimum function value for diminishing stepsizes. When the mean errors diminish sufficiently fast, we strengthen the results to consensus and convergence of the iterates to an optimal solution with probability 1 and in mean square

Flavin-Containing Monooxygenase 1 Catalyzes the Production of Taurine from Hypotaurine

Taurine is one of the most abundant amino acids in mammalian tissues. It is obtained from the diet and by de novo synthesis, from cysteic acid or hypotaurine. Despite the discovery in 1954 that the oxygenation of hypotaurine produces taurine, the identification of an enzyme catalyzing this reaction has remained elusive. In large part this is due to the incorrect assignment, in 1962, of the enzyme as an NAD-dependent hypotaurine dehydrogenase. For more than 55 years the literature has continued to refer to this enzyme as such. Here we show, both in vivo and in vitro, that the enzyme that oxygenates hypotaurine to produce taurine is flavin-containing monooxygenase 1 (FMO1). Metabolite analysis of the urine of Fmo1-null mice by 1H NMR spectroscopy revealed a build-up of hypotaurine and a deficit of taurine in comparison with the concentrations of these compounds in the urine of wild-type mice. In vitro assays confirmed that human FMO1 catalyzes the conversion of hypotaurine to taurine utilizing either NADPH or NADH as co-factor. FMO1 has a wide substrate range and is best known as a xenobiotic- or drug-metabolizing enzyme. The identification that the endogenous molecule hypotaurine is a substrate for the FMO1-catalyzed production of taurine resolves a long-standing mystery. This finding should help establish the role FMO1 plays in a range of biological processes in which taurine or its deficiency is implicated, including conjugation of bile acids, neurotransmitter, anti-oxidant and anti-inflammatory functions, and the pathogenesis of obesity and skeletal muscle disorders

Dynamical spin-flip susceptibility for a strongly interacting ultracold Fermi gas

The Stoner model predicts that a two-component Fermi gas at increasing repulsive interactions undergoes a ferromagnetic transition. Using the random-phase approximation we study the dynamical properties of the interacting Fermi gas. For an atomic Fermi gas under harmonic confinement we show that the transverse (spin-flip) dynamical susceptibility displays a clear signature of the ferromagnetic phase in a magnon peak emerging from the Stoner particle-hole continuum. The dynamical spin susceptibilities could be experimentally explored via spin-dependent Bragg spectroscopy.Comment: 4 pages, 3 figure

Identification of flavin-containing monooxygenase 5 (FMO5) as a regulator of glucose homeostasis and a potential sensor of gut bacteria

We have previously identified flavin-containing monooxygenase 5 (FMO5) as a regulator of metabolic aging. The aim of the present study was to investigate the role of FMO5 in glucose homeostasis and the impact of diet and gut flora on the phenotype of mice in which the Fmo5 gene has been disrupted (Fmo5−/− mice). In comparison with wild-type (WT) counterparts, Fmo5−/− mice are resistant to age-related changes in glucose homeostasis and maintain the higher glucose tolerance and insulin sensitivity characteristic of young animals. When fed a high-fat diet, they are protected against weight gain and reduction of insulin sensitivity. The phenotype of Fmo5−/− mice is independent of diet and the gut microbiome and is determined solely by the host genotype. Fmo5−/− mice have metabolic characteristics similar to those of germ-free mice, indicating that FMO5 plays a role in sensing or responding to gut bacteria. In WT mice, FMO5 is present in the mucosal epithelium of the gastrointestinal tract where it is induced in response to a high-fat diet. In comparison with WT mice, Fmo5−/− mice have fewer colonic goblet cells, and they differ in the production of the colonic hormone resistin-like molecule β. Fmo5−/− mice have lower concentrations of tumor necrosis factor α in plasma and of complement component 3 in epididymal white adipose tissue, indicative of improved inflammatory tone. Our results implicate FMO5 as a regulator of body weight and of glucose disposal and insulin sensitivity and, thus, identify FMO5 as a potential novel therapeutic target for obesity and insulin resistance