Abstract Characteristic Function

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S)(z, w) = ( 1 - z(w)over bar)- 1 for |z|, |w| < 1, by means of (1/k(S))( T, T *) = 0, we consider an arbitrary open connected domain Omega in C(n), a kernel k on Omega so that 1/k is a polynomial and a tuple T = (T(1), T(2), ... , T(n)) of commuting bounded operators on a complex separable Hilbert spaceHsuch that (1/k)( T, T *) >= 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Structure-function relationship in serine hydroxymethyltransferase

Serine hydroxymethyltransferase (SHMT), a pyridoxal-5V-phosphate (PLP)-dependent enzyme catalyzes thetetrahydrofolate (H4-folate)- dependent retro-aldol cleavage of serine to form 5,10-methylene H4-folate and glycine. The structure–function relationship of SHMT wasstudied in our laboratory initially by mutation of residues that are conserved in all SHMTs and later by structure-based mutagenesis of residues located in the active site. The analysis of mutants showed that K71, Y72, R80, D89, W110, S202, C203, H304, H306 and H356 residues are involved in maintenance of the oligomeric structure. The mutation of D227, a residue involved in charge relay system, led to the formation of inactive dimers, indicating that this residue has a role in maintaining the tetrameric structure and catalysis. E74, a residue appropriately positioned in the structure of the enzyme to carry out proton abstraction, was shown by characterization of E74Q and E74K mutants to be involved in conversion of the enzyme from an ‘open’ to ‘closed’ conformation rather than proton abstraction from the hydroxylgroup of serine. K256, the residue involved in the formation of Schiffs base with PLP, also plays a crucial role in the maintenance of the tetrameric structure. Mutation of R262 residue established the importance of distal interactions in facilitating catalysis and Y82 is not involved in the formaldehyde transfer via the postulated hemiacetal intermediate but plays a role in stabilizing the quinonoid intermediate.The mutational analysis of scSHMT along with the structure of recombinant Bacillus stearothermophilus SHMT and its substrate(s)complexes was used to provide evidence for a direct transfer mechanism rather than retro-aldol cleavage for the reaction catalyzed by SHMT.

From anomalies in neat liquid to structure, dynamics and function in the biological world

Water brings its remarkable thermodynamic and dynamic anomalies in the pure liquid state to biological world where water molecules face a multitude of additional interactions that frustrate its hydrogen bond network. Yet the water molecules participate and control enormous number of biological processes in manners which are yet to be understood at a molecular level. We discuss thermodynamics, structure, dynamics and properties of water around proteins and DNA, along with those in reverse micelles. We discuss the roles of water in enzyme kinetics, in drug-DNA intercalation and in kinetic-proof reading ( the theory of lack of errors in biosynthesis). We also discuss how water may play an important role in the natural selection of biomolecules. (C) 2011 Elsevier B. V. All rights reserved.

Learning polyhedral classifiers using logistic function

In this paper we propose a new algorithm for learning polyhedral classifiers. In contrast to existing methods for learning polyhedral classifier which solve a constrained optimization problem, our method solves an unconstrained optimization problem. Our method is based on a logistic function based model for the posterior probability function. We propose an alternating optimization algorithm, namely, SPLA1 (Single Polyhedral Learning Algorithm1) which maximizes the loglikelihood of the training data to learn the parameters. We also extend our method to make it independent of any user specified parameter (e.g., number of hyperplanes required to form a polyhedral set) in SPLA2. We show the effectiveness of our approach with experiments on various synthetic and real world datasets and compare our approach with a standard decision tree method (OC1) and a constrained optimization based method for learning polyhedral sets.

Construction of equivalent circuit of a transformer winding from driving-point impedance function - analytical approach

Analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically realisable ladder network with inductive coupling between any two sections and losses considered. The number of sections in the ladder network can vary, but its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalised expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple and guarantees a unique network. Presently, the formulation can synthesise a unique ladder network up to six sections.

Insights into differential modulation of receptor function by hinge region using novel agonistic lutropin receptor and inverse agonistic thyrotropin receptor antibodies

We report two antibodies, scFv 13B1 and MAb PD1.37, against the hinge regions of LHR and TSHR, respectively, which have similar epitopes but different effects on receptor function. While neither of them affected hormone binding, with marginal effects on hormone response, scFv 13B1 stimulated LHR in a dose-dependent manner, whereas MAb PD1.37 acted as an inverse agonist of TSHR. Moreover, PD1.37 could decrease the basal activity of hinge region CAMs, but had varied effects on those present in ECLs, whereas 13B1 was refractory to any CAMs in LHR. Using truncation mutants and peptide phage display, we compared the differential roles of the hinge region cysteine box-2/3 as well as the exoloops in the activation of these two homologus receptors. (C) 2012 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Partition function for hindered, one-and multi-dimensional rotors

Writing the hindered rotor (hr) partition function as the trace of (rho) over cap = e(-beta(H) over cap hr), we approximate it by the sum of contributions from a set of points in position space. The contribution of the density matrix from each point is approximated by performing a local harmonic expansion around it. The highlight of this method is that it can be easily extended to multidimensional systems. Local harmonic expansion leads to a breakdown of the method a low temperatures. In order to calculate the partition function at low temperatures, we suggest a matrix multiplication procedure. The results obtained using these methods closely agree with the exact partition function at all temperature ranges. Our method bypasses the evaluation of eigenvalues and eigenfunctions and evaluates the density matrix for internal rotation directly. We also suggest a procedure to account for the antisymmetry of the total wavefunction in the same. (C) 2012 Elsevier B.V. All rights reserved.

An Online Actor-Critic Algorithm with Function Approximation for Constrained Markov Decision Processes

We develop an online actor-critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process (MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multi-stage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.

Emitter near an arbitrary body: Purcell effect, optical theorem and the Wheeler-Feynman absorber

The altered spontaneous emission of an emitter near an arbitrary body can be elucidated using an energy balance of the electromagnetic field. From a classical point of view it is trivial to show that the field scattered back from any body should alter the emission of the source. But it is not at all apparent that the total radiative and non-radiative decay in an arbitrary body can add to the vacuum decay rate of the emitter (i.e.) an increase of emission that is just as much as the body absorbs and radiates in all directions. This gives us an opportunity to revisit two other elegant classical ideas of the past, the optical theorem and the Wheeler-Feynman absorber theory of radiation. It also provides us alternative perspectives of Purcell effect and generalizes many of its manifestations, both enhancement and inhibition of emission. When the optical density of states of a body or a material is difficult to resolve (in a complex geometry or a highly inhomogeneous volume) such a generalization offers new directions to solutions. (c) 2012 Elsevier Ltd. All rights reserved.

MS_RHII-RSD, a Dual-Function RNase HII-(p)ppGpp Synthetase from Mycobacterium smegmatis

In the noninfectious soil saprophyte Mycobacterium smegmatis, intracellular levels of the stress alarmones guanosine tetraphosphate and guanosine pentaphosphate, together termed (p)ppGpp, are regulated by the enzyme Rel(Msm). This enzyme consists of a single, bifunctional polypeptide chain that is capable of both synthesizing and hydrolyzing (p)ppGpp. The rel(Msm), knockout strain of M. smegmatis (Delta rel(Msm)) is expected to show a (p)ppGpp null (p)ppGpp(0)] phenotype. Contrary to this expectation, the strain is capable of synthesizing (p)ppGpp in vivo. In this study, we identify and functionally characterize the open reading frame (ORF), MSMEG_5849, that encodes a second functional (p)ppGpp synthetase in M. smegmatis. In addition to (p)ppGpp synthesis, the 567-amino-acid-long protein encoded by this gene is capable of hydrolyzing RNA(.)DNA hybrids and bears similarity to the conventional RNase HII enzymes. We have classified this protein as actRel(Msm) in accordance with the recent nomenclature proposed and have named it MS_RHII-RSD, indicating the two enzymatic activities present RHII, RNase HII domain, originally identified as (d) under bar omain of (u) under bar nknown (f) under bar unction 429 (DUF429), and RSD, RelA_SpoT nucleotidyl transferase domain, the SYNTH domain responsible for (p)ppGpp synthesis activity]. MS_RHII-RSD is expressed and is constitutively active in vivo and behaves like a monofunctional (p)ppGpp synthetase in vitro. The occurrence of the RNase HII and (p)ppGpp synthetase domains together on the same polypeptide chain is suggestive of an in vivo role for this novel protein as a link connecting the essential life processes of DNA replication, repair, and transcription to the highly conserved stress survival pathway, the stringent response.

PocketAnnotate: towards site-based function annotation

A computational pipeline PocketAnnotate for functional annotation of proteins at the level of binding sites has been proposed in this study. The pipeline integrates three in-house algorithms for site-based function annotation: PocketDepth, for prediction of binding sites in protein structures; PocketMatch, for rapid comparison of binding sites and PocketAlign, to obtain detailed alignment between pair of binding sites. A novel scheme has been developed to rapidly generate a database of non-redundant binding sites. For a given input protein structure, putative ligand-binding sites are identified, matched in real time against the database and the query substructure aligned with the promising hits, to obtain a set of possible ligands that the given protein could bind to. The input can be either whole protein structures or merely the substructures corresponding to possible binding sites. Structure-based function annotation at the level of binding sites thus achieved could prove very useful for cases where no obvious functional inference can be obtained based purely on sequence or fold-level analyses. An attempt has also been made to analyse proteins of no known function from Protein Data Bank. PocketAnnotate would be a valuable tool for the scientific community and contribute towards structure-based functional inference. The web server can be freely accessed at http://proline.biochem.iisc.ernet.in/pocketannotate/.

Relation between the work function and Young's modulus of RhSi and estimate of Schottky-barrier height at RhSi/Si interface: An ab-initio study

Density-functional calculations are performed to explore the relationship between the work function and Young's modulus of RhSi, and to estimate the p-Schottky-barrier height (SBH) at the Si/RhSi(010) interface. It is shown that the Young's modulus and the workfunction of RhSi satisfy the generic sextic relation, proposed recently for elemental metals. The calculated p-SBH at the Si/RhSi interface is found to differ only by 0.04 eV in opposite limits, viz., no-pinning and strong pinning. We find that the p-SBH is reduced as much as by 0.28 eV due to vacancies at the interface. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4761994]

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Spectral analysis on SL(2, R)

Let G be the group . For this group we prove a version of Schwartz's theorem on spectral analysis for the group G. We find the sharp range of Lebesgue spaces L (p) (G) for which a smooth function is not mean periodic unless it is a cusp form. Failure of the Schwartz-like theorem is also proved when C (a)(G) is replaced by L (p) (G) with suitable p. We show that the last result is linked with the failure of the Wiener-tauberian theorem for G.

A UNIFIED APPROACH FOR OPTIMIZATION OF SNAKUSCULES AND OVUSCULES

Automated image segmentation techniques are useful tools in biological image analysis and are an essential step in tracking applications. Typically, snakes or active contours are used for segmentation and they evolve under the influence of certain internal and external forces. Recently, a new class of shape-specific active contours have been introduced, which are known as Snakuscules and Ovuscules. These contours are based on a pair of concentric circles and ellipses as the shape templates, and the optimization is carried out by maximizing a contrast function between the outer and inner templates. In this paper, we present a unified approach to the formulation and optimization of Snakuscules and Ovuscules by considering a specific form of affine transformations acting on a pair of concentric circles. We show how the parameters of the affine transformation may be optimized for, to generate either Snakuscules or Ovuscules. Our approach allows for a unified formulation and relies only on generic regularization terms and not shape-specific regularization functions. We show how the calculations of the partial derivatives may be made efficient thanks to the Green's theorem. Results on synthesized as well as real data are presented.