Linear Index Coding and Representable Discrete Polymatroids

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections between linear index coding and representable discrete polymatroids. The index coding problem involves a sender which generates a set of messages X = {x(1), x(2), ... x(k)} and a set of receivers R which demand messages. A receiver R is an element of R is specified by the tuple (x, H) where x. X is the message demanded by R and H subset of X \textbackslash {x} is the side information possessed by R. It is first shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

The phenanthroimidazole-based dizinc(II) complex as a fluorescent probe for the pyrophosphate ion as generated in polymerase chain reactions and pyrosequencing

A highly selective and sensitive phenanthroimidazole tagged Mannich base type dizinc(II) fluorescent probe (R-Zn2+) has been developed for the pyrophosphate ion (PPi) with a very low limit of detection (LOD) of 0.25 ppm; this also assesses PPi from DNA polymerization chain reaction (PCR).

Effect of lateral substituent and chain length on mesomorphic properties of novel alkoxy benzyloxy benzoates of cyanophenyl rod-shaped compounds

Three novel homologous series of rod-shaped cyanophenyl alkoxy benzoate liquid crystalline compounds with lateral polar fluorine and chlorine substituent were prepared, and chemical structures of novel materials have been characterized by standard spectral technique and elemental analysis. The mesophase characterization was carried out using the combination of polarized optical microscopy and differential scanning calorimetry. All the compounds exhibit wide thermal range of enantiotropic SmA phase.

On linear series and a conjecture of D. C. Butler

Let C be a smooth irreducible projective curve of genus g and L a line bundle of degree d generated by a linear subspace V of H-0 (L) of dimension n+1. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map V circle times O-C -> L and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.

Poly(alkylene itaconate)s - an interesting class of polyesters with periodically located exo-chain double bonds susceptible to Michael addition

Itaconic acid is a bio-sourced dicarboxylic acid that carries a double bond; although several reports have dealt with the radical-initiated chain polymerization of dialkyl itaconates, only a few studies have utilized it as a di-acid monomer to prepare polyesters. In this study, we demonstrate that dibutyl itaconate can be melt-condensed with aliphatic diols to generate unsaturated polyesters; importantly, we show that the double bonds remain unaffected during the melt polymerization. A particularly useful attribute of these polyesters is that the exo-chain double bonds are conjugated to the ester carbonyl and, therefore, can serve as excellent Michael acceptors. A variety of organic thiols, such as alkane thiols, MPEG thiol, thioglycerol, derivatized cysteine etc., were shown to quantitatively Michael-add to the exo-chain double bonds and generate interesting functionalized polyesters. Similarly, organic amines, such as N-methyl-benzylamine, diallyl amine and proline, also add across the double bond; thus, these poly(alkylene itaconate)s could serve as potentially bio-benign polyesters that could be quantitatively transformed into a variety of interesting and potentially useful functionalized polymers.

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ``energy-like measure'' in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate ``high-frequency'' dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

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.

A micropolar peridynamic theory in linear elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. (C) 2015 Elsevier Ltd. All rights reserved.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Markov chain splitting methods in structural reliability integral estimation

Monte Carlo simulation methods involving splitting of Markov chains have been used in evaluation of multi-fold integrals in different application areas. We examine in this paper the performance of these methods in the context of evaluation of reliability integrals from the point of view of characterizing the sampling fluctuations. The methods discussed include the Au-Beck subset simulation, Holmes-Diaconis-Ross method, and generalized splitting algorithm. A few improvisations based on first order reliability method are suggested to select algorithmic parameters of the latter two methods. The bias and sampling variance of the alternative estimators are discussed. Also, an approximation to the sampling distribution of some of these estimators is obtained. Illustrative examples involving component and series system reliability analyses are presented with a view to bring out the relative merits of alternative methods. (C) 2015 Elsevier Ltd. All rights reserved.

Novel anti IGFBP2 single chain variable fragment inhibits glioma cell migration and invasion

Insulin like growth factor binding protein 2 (IGFBP2) is highly up regulated in glioblastoma (GBM) tissues and has been one of the prognostic indicators. There are compelling evidences suggesting important roles for IGFBP2 in glioma cell proliferation, migration and invasion. Extracellular IGFBP2 through its carboxy terminal arginine glycine aspartate (RGD) motif can bind to cell surface alpha 5 beta 1 integrins and activate pathways downstream to integrin signaling. This IGFBP2 activated integrin signaling is known to play a crucial role in IGFBP2 mediated invasion of glioma cells. Hence a molecular inhibitor of carboxy terminal domain of IGFBP2 which can inhibit IGFBP2-cell surface interaction is of great therapeutic importance. In an attempt to develop molecular inhibitors of IGFBP2, we screened single chain variable fragment (scFv) phage display libraries, Tomlinson I (Library size 1.47 x 10(8)) and Tomlinson J (Library size 1.37 x 10(8)) using human recombinant IGFBP2. After screening we obtained three IGFBP2 specific binders out of which one scFv B7J showed better binding to IGFBP2 at its carboxy terminal domain, blocked IGFBP2-cell surface association, reduced activity of matrix metalloprotease 2 in the conditioned medium of glioma cells and inhibited IGFBP2 induced migration and invasion of glioma cells. We demonstrate for the first time that in vitro inhibition of extracellular IGFBP2 activity by using human scFv results in significant reduction of glioma cell migration and invasion. Therefore, the inhibition of IGFBP2 can serve as a potential therapeutic strategy in the management of GBM.

A Polymatroid Approach to Separable Convex Optimization with Linear Ascending Constraints

We revisit a problem studied by Padakandla and Sundaresan SIAM J. Optim., August 2009] on the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation problems in wireless communication settings. It is also a special case of an optimization of a separable convex function over the bases of a specially structured polymatroid. We give an alternative proof of the correctness of the algorithm of Padakandla and Sundaresan. In the process we relax some of their restrictions placed on the objective function.

Efficient Site-Specific Incorporation of Thioamides into Peptides on a Solid Support

Designing bioactive peptides containing thioamide functionality to modulate their pharmacological properties has been thwarted so far because of various synthetic challenges. The fast, efficient, and inexpensive synthesis and incorporation of a wide range of thionated amino acids into a growing peptide chain on a solid support is reported using standard Fmoc-based chemistry. The commonly employed methodology is comprehensively investigated and optimized with significant improvements regarding the quantity of reagents and reaction conditions. The utility of the protocol is further demonstrated in the synthesis of dithionated linear and monothionated cyclic peptides, which has been a daunting task.

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.