Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

Modified Adomian Decomposition Method for Van der Pol equations

In the paper, the well known Adomian Decomposition Method (ADM) is modified to solve the parabolic equations. The present method is quite different than the numerical method. The results are compared with the existing exact or analytical method. The already known existing Adomian Decomposition Method is modified to improve the accuracy and convergence. Thus, the modified method is named as Modified Adomian Decomposition Method (MADM). The Modified Adomian Decomposition Method results are found to converge very quickly and are more accurate compared to ADM and numerical methods. MADM is quite efficient and is practically well suited for use in these problems. Several examples are given to check the reliability of the present method. Modified Adomian Decomposition Method is a non-numerical method which can be adapted for solving parabolic equations. In the current paper, the principle of the decomposition method is described, and its advantages are shown in the form of parabolic equations. (C) 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations

The periodic 3D Navier-Stokes equations are analyzed in terms of dimensionless, scaled, L-2m-norms of vorticity D-m (1 <= m <= infinity). The first in this hierarchy, D-1, is the global enstrophy. Three regimes naturally occur in the D-1-D-m plane. Solutions in the first regime, which lie between two concave curves, are shown to be regular, owing to strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics lie in this heavily depleted regime 1]; new numerical evidence for this is presented. Estimates for the dimension of a global attractor and a corresponding inertial range are given for this regime. However, two more regimes can theoretically exist. In the second, which lies between the upper concave curve and a line, the depletion is insufficient to regularize solutions, so no more than Leray's weak solutions exist. In the third, which lies above this line, solutions are regular, but correspond to extreme initial conditions. The paper ends with a discussion on the possibility of transition between these regimes.

Transition from dissipative to conservative dynamics in equations of hydrodynamics

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity (alpha) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case alpha -> infinity U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008)], is now shown to be true for any large, but finite, value of alpha greater than a crossover value alpha(crossover). We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows.

Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar, Dukkipati, & Bhatnagar, 2014), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on SF algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms. (C) 2014 Elsevier Ltd. All rights reserved.

Effect of functional groups on separating carbon dioxide from CO2/N-2 gas mixtures using edge functionalized graphene nanoribbons

Development of microporous adsorbents for separation and sequestration of carbon dioxide from flue gas streams is an area of active research. In this study, we assess the influence of specific functional groups on the adsorption selectivity of CO2/N-2 mixtures through Grand Canonical Monte Carlo (GCMC) simulations. Our model system consists of a bilayer graphene nanoribbon that has been edge functionalized with OH, NH2, NO2, CH3 and COOH. Ab initio Moller-Plesset (MP2) calculations with functionalized benzenes are used to obtain binding energies and optimized geometries for CO2 and N-2. This information is used to validate the choice classical forcefields in GCMC simulations. In addition to simulations of adsorption from binary mixtures of CO2 and N-2, the ideal adsorbed solution theory (IAST) is used to predict mixture isotherms. Our study reveals that functionalization always leads to an increase in the adsorption of both CO2 and N-2 with the highest for COOH. However, significant enhancement in the selectivity for CO2 is only seen with COOH functionalized nanoribbons. The COOH functionalization gives a 28% increase in selectivity compared to H terminated nanoribbons, whereas the improvement in the selectivity for other functional groups are much Enure modest. Our study suggests that specific functionalization with COOH groups can provide a material's design strategy to improve CO2 selectivity in microporous adsorbents. Synthesis of graphene nanoplatelets with edge functionalized COOH, which has the potential for large scale production, has recently been reported (Jeon el, al., 2012). (C) 2014 Elsevier Ltd. All rights reserved,

Paralogous cAMP Receptor Proteins in Mycobacterium smegmatis Show Biochemical and Functional Divergence

The cyclic AMP receptor protein (CRP) family of transcription factors consists of global regulators of bacterial gene expression. Here, we identify two paralogous CRPs in the genome of Mycobacterium smegmatis that have 78% identical sequences and characterize them biochemically and functionally. The two proteins (MSMEG_0539 and MSMEG_6189) show differences in cAMP binding affinity, trypsin sensitivity, and binding to a CRP site that we have identified upstream of the msmeg_3781 gene. MSMEG_6189 binds to the CRP site readily in the absence of cAMP, while MSMEG_0539 binds in the presence of cAMP, albeit weakly. msmeg_6189 appears to be an essential gene, while the ?msmeg_0539 strain was readily obtained. Using promoter-reporter constructs, we show that msmeg_3781 is regulated by CRP binding, and its transcription is repressed by MSMEG_6189. Our results are the first to characterize two paralogous and functional CRPs in a single bacterial genome. This gene duplication event has subsequently led to the evolution of two proteins whose biochemical differences translate to differential gene regulation, thus catering to the specific needs of the organism.

Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

In this paper, we consider a singularly perturbed boundary-value problem for fourth-order ordinary differential equation (ODE) whose highest-order derivative is multiplied by a small perturbation parameter. To solve this ODE, we transform the differential equation into a coupled system of two singularly perturbed ODEs. The classical central difference scheme is used to discretize the system of ODEs on a nonuniform mesh which is generated by equidistribution of a positive monitor function. We have shown that the proposed technique provides first-order accuracy independent of the perturbation parameter. Numerical experiments are provided to validate the theoretical results.

Simple three parameter equations for correlating liquid phase compositions in subcritical and supercritical systems

Two Chrastil type expressions have been developed to model the solubility of supercritical fluids/gases in liquids. The three parameter expressions proposed correlates the solubility as a function of temperature, pressure and density. The equation can also be used to check the self-consistency of the experimental data of liquid phase compositions for supercritical fluid-liquid equilibria. Fifty three different binary systems (carbon-dioxide + liquid) with around 2700 data points encompassing a wide range of compounds like esters, alcohols, carboxylic acids and ionic liquids were successfully modeled for a wide range of temperatures and pressures. Besides the test for self-consistency, based on the data at one temperature, the model can be used to predict the solubility of supercritical fluids in liquids at different temperatures. (C) 2014 Elsevier B.V. All rights reserved.

Dendritic atrophy constricts functional maps in resonance and impedance properties of hippocampal model neurons

A gradient in the density of hyperpolarization-activated cyclic-nucleotide gated (HCN) channels is necessary for the emergence of several functional maps within hippocampal pyramidal neurons. Here, we systematically analyzed the impact of dendritic atrophy on nine such functional maps, related to input resistance and local/transfer impedance properties, using conductance-based models of hippocampal pyramidal neurons. We introduced progressive dendritic atrophy in a CA1 pyramidal neuron reconstruction through a pruning algorithm, measured all functional maps in each pruned reconstruction, and arrived at functional forms for the dependence of underlying measurements on dendritic length. We found that, across frequencies, atrophied neurons responded with higher efficiency to incoming inputs, and the transfer of signals across the dendritic tree was more effective in an atrophied reconstruction. Importantly, despite the presence of identical HCN-channel density gradients, spatial gradients in input resistance, local/transfer resonance frequencies and impedance profiles were significantly constricted in reconstructions with dendrite atrophy, where these physiological measurements across dendritic locations converged to similar values. These results revealed that, in atrophied dendritic structures, the presence of an ion channel density gradient alone was insufficient to sustain homologous functional maps along the same neuronal topograph. We assessed the biophysical basis for these conclusions and found that this atrophy-induced constriction of functional maps was mediated by an enhanced spatial spread of the influence of an HCN-channel cluster in atrophied trees. These results demonstrated that the influence fields of ion channel conductances need to be localized for channel gradients to express themselves as homologous functional maps, suggesting that ion channel gradients are necessary but not sufficient for the emergence of functional maps within single neurons.

Study of structures, energies and vibrational frequencies of (O-2)(n)(+) (n=2-5) clusters by GGA and meta-GGA density functional methods

Using Generalized Gradient Approximation (GGA) and meta-GGA density functional methods, structures, binding energies and harmonic vibrational frequencies for the clusters O-4(+), O-6(+), O-8(+) and O-10(+) have been calculated. The stable structures of O-4(+), O-6(+), O-8(+) and O-10(+) have point groups D-2h, D-3h, D-4h, and D-5h optimized on the quartet, sextet, octet and dectet potential energy surfaces, respectively. Rectangular (D-2h) O-4(+) has been found to be more stable compared to trans-planar (C-2h) on the quartet potential energy surface. Cyclic structure (D-3h) of CA cluster ion has been calculated to be more stable than other structures. Binding energy (B.E.) of the cyclic O-6(+) is in good agreement with experimental measurement. The zero-point corrected B.E. of O-8(+) with D4h symmetry on the octet potential energy surface and zero-point corrected B.E. of O-10(+) with D-5h symmetry on the dectet potential energy surface are also in good agreement with experimental values. The B.E. value for O-4(+) is close to the experimental value when single point energy is calculated by Brueckner coupled-cluster method, BD(T). (C) 2014 Elsevier B.V. All rights reserved.

Structural and functional analysis of two universal stress proteins YdaA and YnaF from Salmonella typhimurium: possible roles in microbial stress tolerance

In many organisms ``Universal Stress Proteins'' CUSPS) are induced in response to a variety of environmental stresses. Here we report the structures of two USPs, YnaF and YdaA from Salmonella typhimurium determined at 1.8 angstrom and 2.4 angstrom resolutions, respectively. YnaF consists of a single USP domain and forms a tetrameric organization stabilized by interactions mediated through chloride ions. YdaA is a larger protein consisting of two tandem USP domains. Two protomers of YdaA associate to form a structure similar to the YnaF tetramer. YdaA showed ATPase activity and an ATP binding motif G-2X-G-9X-G(S/T/N) was found in its C-terminal domain. The residues corresponding to this motif were not conserved in YnaF although YnaF could bind ATP. However, unlike YdaA, YnaF did not hydrolyse ATP in vitro. Disruption of interactions mediated through chloride ions by selected mutations converted YnaF into an ATPase. Residues that might be important for ATP hydrolysis could be identified by comparing the active sites of native and mutant structures. Only the C-terminal domain of YdaA appears to be involved in ATP hydrolysis. The structurally similar N-terminal domain was found to bind a zinc ion near the segment equivalent to the phosphate binding loop of the C-terminal domain. Mass spectrometric analysis showed that YdaA might bind a ligand of approximate molecular weight 800 daltons. Structural comparisons suggest that the ligand, probably related to an intermediate in lipid A biosynthesis, might bind at a site close to the zinc ion. Therefore, the N-terminal domain of YdaA binds zinc and might play a role in lipid metabolism. Thus, USPs appear to perform several distinct functions such as ATP hydrolysis, altering membrane properties and chloride sensing. (C) 2015 Elsevier Inc. All rights reserved.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

Metallophosphoesterases: structural fidelity with functional promiscuity

Calcineurin-like metallophosphoesterases (MPEs) form a large superfamily of binuclear metal-ion-centre-containing enzymes that hydrolyse phosphomono-, phosphodi-or phosphotri-esters in a metal-dependent manner. The MPE domain is found in Mre11/SbcD DNA-repair enzymes, mammalian phosphoprotein phosphatases, acid sphingomyelinases, purple acid phosphatases, nucleotidases and bacterial cyclic nucleotide phosphodiesterases. Despite this functional diversity, MPEs show a remarkably similar structural fold and active-site architecture. In the present review, we summarize the available structural, biochemical and functional information on these proteins. We also describe how diversification and specialization of the core MPE fold in various MPEs is achieved by amino acid substitution in their active sites, metal ions and regulatory effects of accessory domains. Finally, we discuss emerging roles of these proteins as non-catalytic protein-interaction scaffolds. Thus we view the MPE superfamily as a set of proteins with a highly conserved structural core that allows embellishment to result in dramatic and niche-specific diversification of function.

Molecular and Functional Characterization of RecD, a Novel Member of the SF1 Family of Helicases, from Mycobacterium tuberculosis

Background: The heterotrimeric M. tuberculosis RecBCD complex, or each of its individual subunits, remains uncharacterized. Results: MtRecD exists as a homodimer in solution, catalyzes ssDNA-dependent ATP hydrolysis, unwinding of DNA replication/recombination intermediates, and interacts with RecA. Conclusion: MtRecD possesses strong 5 3- and weak 3 5-helicase activities. Significance: These findings provide insights into the mechanism underlying DSB repair and homologous recombination in mycobacteria. The annotated whole-genome sequence of Mycobacterium tuberculosis revealed the presence of a putative recD gene; however, the biochemical characteristics of its encoded protein product (MtRecD) remain largely unknown. Here, we show that MtRecD exists in solution as a stable homodimer. Protein-DNA binding assays revealed that MtRecD binds efficiently to single-stranded DNA and linear duplexes containing 5 overhangs relative to the 3 overhangs but not to blunt-ended duplex. Furthermore, MtRecD bound more robustly to a variety of Y-shaped DNA structures having 18-nucleotide overhangs but not to a similar substrate containing 5-nucleotide overhangs. MtRecD formed more salt-tolerant complexes with Y-shaped structures compared with linear duplex having 3 overhangs. The intrinsic ATPase activity of MtRecD was stimulated by single-stranded DNA. Site-specific mutagenesis of Lys-179 in motif I abolished the ATPase activity of MtRecD. Interestingly, although MtRecD-catalyzed unwinding showed a markedly higher preference for duplex substrates with 5 overhangs, it could also catalyze significant unwinding of substrates containing 3 overhangs. These results support the notion that MtRecD is a bipolar helicase with strong 5 3 and weak 3 5 unwinding activities. The extent of unwinding of Y-shaped DNA structures was approximate to 3-fold lower compared with duplexes with 5 overhangs. Notably, direct interaction between MtRecD and its cognate RecA led to inhibition of DNA strand exchange promoted by RecA. Altogether, these studies provide the first detailed characterization of MtRecD and present important insights into the type of DNA structure the enzyme is likely to act upon during the processes of DNA repair or homologous recombination.