Identification of local variations within secondary structures of proteins

Secondary-structure elements (SSEs) play an important role in the folding of proteins. Identification of SSEs in proteins is a common problem in structural biology. A new method, ASSP (Assignment of Secondary Structure in Proteins), using only the path traversed by the C atoms has been developed. The algorithm is based on the premise that the protein structure can be divided into continuous or uniform stretches, which can be defined in terms of helical parameters, and depending on their values the stretches can be classified into different SSEs, namely -helices, 3(10)-helices, -helices, extended -strands and polyproline II (PPII) and other left-handed helices. The methodology was validated using an unbiased clustering of these parameters for a protein data set consisting of 1008 protein chains, which suggested that there are seven well defined clusters associated with different SSEs. Apart from -helices and extended -strands, 3(10)-helices and -helices were also found to occur in substantial numbers. ASSP was able to discriminate non--helical segments from flanking -helices, which were often identified as part of -helices by other algorithms. ASSP can also lead to the identification of novel SSEs. It is believed that ASSP could provide a better understanding of the finer nuances of protein secondary structure and could make an important contribution to the better understanding of comparatively less frequently occurring structural motifs. At the same time, it can contribute to the identification of novel SSEs. A standalone version of the program for the Linux as well as the Windows operating systems is freely downloadable and a web-server version is also available at .

A Family of Domains Associated with mu-Synthesis

We introduce a family of domains-which we call the -quotients-associated with an aspect of -synthesis. We show that the natural association that the symmetrized polydisc has with the corresponding spectral unit ball is also exhibited by the -quotient and its associated unit `` -ball''. Here, is the structured singular value for the case Specifically: we show that, for such an E, the Nevanlinna-Pick interpolation problem with matricial data in a unit `` -ball'', and in general position in a precise sense, is equivalent to a Nevanlinna-Pick interpolation problem for the associated -quotient. Along the way, we present some characterizations for the -quotients.

A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

Analysis of OSNR Requirements for Higher Modulation Schemes for Various Local Oscillator Powers

To meet the growing demands of data traffic in long haul communication, it is necessary to efficiently use the low-loss region(C-band) of the optical spectrum, by increasing the no. of optical channels and increasing the bit rate on each channel But narrow pulses occupy higher spectral bandwidth. To circumvent this problem, higher order modulation schemes such as QPSK and QAM can be used to modulate the bits, which increases the spectral efficiency without demanding any extra spectral bandwidth. On the receiver side, to meet a satisfy, a given BER, the received optical signal requires to have minimum OSNR. In our study in this paper, we analyses for different modulation schemes, the OSNR required with and without preamplifier. The theoretical limit of OSNR requirement for a modulation scheme is compared for a given link length by varying the local oscillator (LO) power. Our analysis shows that as we increase the local oscillator (LO) power, the OSNR requirement decreases for a given BER. Also a combination of preamplifier and local oscillator (LO) gives the OSNR closest to theoretical limit.

Two player game variant of the Erdos-Szekeres problem

The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.

A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.

Protein Structure and Function: Looking through the Network of Side-Chain Interactions

Network theory has become an excellent method of choice through which biological data are smoothly integrated to gain insights into complex biological problems. Understanding protein structure, folding, and function has been an important problem, which is being extensively investigated by the network approach. Since the sequence uniquely determines the structure, this review focuses on the networks of non-covalently connected amino acid side chains in proteins. Questions in structural biology are addressed within the framework of such a formalism. While general applications are mentioned in this review, challenging problems which have demanded the attention of scientific community for a long time, such as allostery and protein folding, are considered in greater detail. Our aim has been to explore these important problems through the eyes of networks. Various methods of constructing protein structure networks (PSN) are consolidated. They include the methods based on geometry, edges weighted by different schemes, and also bipartite network of protein-nucleic acid complexes. A number of network metrics that elegantly capture the general features as well as specific features related to phenomena, such as allostery and protein model validation, are described. Additionally, an integration of network theory with ensembles of equilibrium structures of a single protein or that of a large number of structures from the data bank has been presented to perceive complex phenomena from network perspective. Finally, we discuss briefly the capabilities, limitations, and the scope for further explorations of protein structure networks.

Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model

Present paper is the first one in the series devoted to the dynamics of traveling waves emerging in the uncompressed, tri-atomic granular crystals. This work is primarily concerned with the dynamics of one-dimensional periodic granular trimer (tri-atomic) chains in the state of acoustic vacuum. Each unit cell consists of three spherical particles of different masses subject to periodic boundary conditions. Hertzian interaction law governs the mutual interaction of these particles. Under the assumption of zero pre-compression, this interaction is modeled as purely nonlinear, which means the absence of linear force component. The dynamics of such chains is governed by the two system parameters that scale the mass ratios between the particles of the unit cell. Such a system supports two different classes of periodic solutions namely the traveling and standing waves. The primary objective of the present study is the numerical analysis of the bifurcation structure of these solutions with emphasis on the dynamics of traveling waves. In fact, understanding of the bifurcation structure of the traveling wave solutions emerging in the unit-cell granular trimer is rather important and can shed light on the more complex nonlinear wave phenomena emerging in semi-infinite trimer chains. (c) 2016 Elsevier B.V. All rights reserved.

On the issues of resolving a low melting combination as a definite eutectic or an elusive cocrystal: A critical evaluation

Cocrystals and eutectics are different yet related crystalline multi-component adducts with diverse applications in pharmaceutical and materials fields. Recently, they were shown to be alternate products of cocrystallization experiments. Whereas a cocrystal shows distinct diffraction, spectroscopic and thermal signatures as compared to parent components, the hallmark of a eutectic is its low melting nature. However, in certain cases, there can be a problem when one resorts to design a cocrystal and assess its formation vis-A -vis a eutectic. In the absence of a gold standard method to make a cocrystal, it is often difficult to judge how exhaustive should the cocrystallization trials be to ensure the accomplishment of a desired/putative cocrystal. Further, a cocrystal can manifest with intermolecular interactions and/or crystal structure similar to that of its parent compounds such that the conventional diffraction and spectroscopic techniques will be of little help to conclusively infer the formation of cocrystal in the lack of single crystals. Such situations combined with low melting behavior of a combination brings the complication of resolving the combination as a cocrystal or eutectic since now both the adducts share common features. Based on the curious case of Caffeine-Benzoic acid combination, this study aims to unfold the intricate issues related to the design, formation and characterization of cocrystals and eutectics for a way forward. The utility of heteronuclear seeding methodology in establishing a given combination as a cocrystal-forming one or a eutectic-forming one in four known systems is appraised.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Application of enthalpy method for moving boundary problem in laser surface melting

A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization. The enthalpy method was applied to solve this two-phase axisymmetrical melting problem Computational results of temperature fields were obtained, which provide useful information to practical laser treatment processing. The validity of enthalpy method in solving such problems is presented.