SPSA algorithms with measurement reuse

Four algorithms, all variants of Simultaneous Perturbation Stochastic Approximation (SPSA), are proposed. The original one-measurement SPSA uses an estimate of the gradient of objective function L containing an additional bias term not seen in two-measurement SPSA. As a result, the asymptotic covariance matrix of the iterate convergence process has a bias term. We propose a one-measurement algorithm that eliminates this bias, and has asymptotic convergence properties making for easier comparison with the two-measurement SPSA. The algorithm, under certain conditions, outperforms both forms of SPSA with the only overhead being the storage of a single measurement. We also propose a similar algorithm that uses perturbations obtained from normalized Hadamard matrices. The convergence w.p. 1 of both algorithms is established. We extend measurement reuse to design two second-order SPSA algorithms and sketch the convergence analysis. Finally, we present simulation results on an illustrative minimization problem.

Elimination of cross-talk in diffuse optical tomographic reconstructions through a weighted update procedure: results of simulation study - art. no. 61640S

Reconstructions in optical tomography involve obtaining the images of absorption and reduced scattering coefficients. The integrated intensity data has greater sensitivity to absorption coefficient variations than scattering coefficient. However, the sensitivity of intensity data to scattering coefficient is not zero. We considered an object with two inhomogeneities (one in absorption and the other in scattering coefficient). The standard iterative reconstruction techniques produced results, which were plagued by cross talk, i.e., the absorption coefficient reconstruction has a false positive corresponding to the location of scattering inhomogeneity, and vice-versa. We present a method to remove cross talk in the reconstruction, by generating a weight matrix and weighting the update vector during the iteration. The weight matrix is created by the following method: we first perform a simple backprojection of the difference between the experimental and corresponding homogeneous intensity data. The built up image has greater weightage towards absorption inhomogeneity than the scattering inhomogeneity and its appropriate inverse is weighted towards the scattering inhomogeneity. These two weight matrices are used as multiplication factors in the update vectors, normalized backprojected image of difference intensity for absorption inhomogeneity and the inverse of the above for the scattering inhomogeneity, during the image reconstruction procedure. We demonstrate through numerical simulations, that cross-talk is fully eliminated through this modified reconstruction procedure.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Studies on optical absorption and photoluminescenceproperties of Pr3+ and Nd3+ doped mixed alkali chloroborate glasses

This article presents the optical absorption and emission properties of Pr3+ and Nd3+ doped two different mixed alkali chloroborate glass matrices of the type 70B(2)O(3)center dot xLiCl center dot(30 - x)NaCl and 70B(2)O(3)center dot xLiCl center dot(30 - x)KCl (x = 5, 10, 15.20 and 25). The variation of Judd-Ofelt parameters (Omega(2), Omega(4) and Omega(6)), total radiative transition probabilities (A(T)), radiative lifetimes (tau(R)) and emission cross-sections (sigma(p)) with the variation of alkali contents in the glass matrix have been discussed in detail. The changes in the peak wavelengths of the hypersensitive transition and intensity parameters with x are correlated to the structural changes in the host matrix. The estimated radiative lifetimes of certain excited states of Pr3+ and Nd3+ in these two glass matrices are reported. Peak stimulated emission cross-sections (sigma(p)) are reported for the observed emission transitions of Pr3+ and Nd3+ ions. Branching ratios (beta) of the observed emission transitions obtained from the Judd-Ofelt theory are compared with the values obtained from the emission spectra. (C) 2010 Elsevier B.V. All rights reserved.

Asynchronous behaviour in some three-atom linear concerted radical-exchange reactions

A few simple three-atom thermoneutral radical exchange reactions (i.e. A + BC --> AB + C) are examined by ab initio SCF methods. Emphasis is laid on the detailed analysis of density matrices rather than on energetics. Results reveal that the sum of the bond orders of the breaking and forming bonds is not conserved to unity, due to development of free valence on the migrating atom 'B' in the transition state. Bond orders, free valence and spin densities on the atoms are calculated. The present analysis shows that the bond-cleavage process is always more advanced than the bond-formation process in the transition state. Further analysis shows a development of the negative spin density on the migrating atom 'B' in the transition state. The depletion of the alpha-spin density on the radical site "A" in the reactant during the reaction lags behind the growth of the alpha-spin density on the terminal atom "C" of the reactant bond, 'B-C' in the transition state. But all these processes are completed simultaneously at the end of the reaction. Hence, the reactions are asynchronous but kinetically concerted in most cases.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

sRNAscanner: A Computational Tool for Intergenic Small RNA Detection in Bacterial Genomes

Background:Bacterial non-coding small RNAs (sRNAs) have attracted considerable attention due to their ubiquitous nature and contribution to numerous cellular processes including survival, adaptation and pathogenesis. Existing computational approaches for identifying bacterial sRNAs demonstrate varying levels of success and there remains considerable room for improvement. Methodology/Principal Findings: Here we have proposed a transcriptional signal-based computational method to identify intergenic sRNA transcriptional units (TUs) in completely sequenced bacterial genomes. Our sRNAscanner tool uses position weight matrices derived from experimentally defined E. coli K-12 MG1655 sRNA promoter and rho-independent terminator signals to identify intergenic sRNA TUs through sliding window based genome scans. Analysis of genomes representative of twelve species suggested that sRNAscanner demonstrated equivalent sensitivity to sRNAPredict2, the best performing bioinformatics tool available presently. However, each algorithm yielded substantial numbers of known and uncharacterized hits that were unique to one or the other tool only. sRNAscanner identified 118 novel putative intergenic sRNA genes in Salmonella enterica Typhimurium LT2, none of which were flagged by sRNAPredict2. Candidate sRNA locations were compared with available deep sequencing libraries derived from Hfq-co-immunoprecipitated RNA purified from a second Typhimurium strain (Sittka et al. (2008) PLoS Genetics 4: e1000163). Sixteen potential novel sRNAs computationally predicted and detected in deep sequencing libraries were selected for experimental validation by Northern analysis using total RNA isolated from bacteria grown under eleven different growth conditions. RNA bands of expected sizes were detected in Northern blots for six of the examined candidates. Furthermore, the 5'-ends of these six Northern-supported sRNA candidates were successfully mapped using 5'-RACE analysis. Conclusions/Significance: We have developed, computationally examined and experimentally validated the sRNAscanner algorithm. Data derived from this study has successfully identified six novel S. Typhimurium sRNA genes. In addition, the computational specificity analysis we have undertaken suggests that similar to 40% of sRNAscanner hits with high cumulative sum of scores represent genuine, undiscovered sRNA genes. Collectively, these data strongly support the utility of sRNAscanner and offer a glimpse of its potential to reveal large numbers of sRNA genes that have to date defied identification. sRNAscanner is available from: http://bicmku.in:8081/sRNAscanner or http://cluster.physics.iisc.ernet.in/sRNAscanner/.

A simple classical approach for the melting temperature of inert-gas nanoparticles

Like the metal and semiconductor nanoparticles, the melting temperature of free inert-gas nanoparticles decreases with decreasing size. The variation is linear with the inverse of the particle size for large nanoparticles and deviates from the linearity for small nanoparticles. The decrease in the melting temperature is slower for free nanoparticles with non-wetting surfaces, while the decrease is faster for nanoparticles with wetting surfaces. Though the depression of the melting temperature has been reported for inert-gas nanoparticles in porous glasses, superheating has also been observed when the nanoparticles are embedded in some matrices. By using a simple classical approach, the influence of size, geometry and the matrix on the melting temperature of nanoparticles is understood quantitatively and shown to be applicable for other materials. It is also shown that the classical approach can be applied to understand the size-dependent freezing temperature of nanoparticles.

A Training-Based Iterative Detection/Channel Estimation Scheme for Large Non-Orthogonal STBC MIMO Systems

In this paper, we propose a training-based channel estimation scheme for large non-orthogonal space-time block coded (STBC) MIMO systems.The proposed scheme employs a block transmission strategy where an N-t x N-t pilot matrix is sent (for training purposes) followed by several N-t x N-t square data STBC matrices, where Nt is the number of transmit antennas. At the receiver, we iterate between channel estimation (using an MMSE estimator) and detection (using a low-complexity likelihood ascent search (LAS) detector) till convergence or for a fixed number of iterations. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed scheme at low complexities. The fact that we could show such good results for large STBCs (e.g., 16 x 16 STBC from cyclic division algebras) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot-based channel estimation and turbo coding) establishes the effectiveness of the proposed scheme.

On computing an equivalent symmetric matrix for a nonsymmetric matrix

A real or a complex symmetric matrix is defined here as an equivalent symmetric matrix for a real nonsymmetric matrix if both have the same eigenvalues. An equivalent symmetric matrix is useful in computing the eigenvalues of a real nonsymmetric matrix. A procedure to compute equivalent symmetric matrices and its mathematical foundation are presented.

Synthesis, structure and DNA cleavage studies of coumarin analogues of tetrahydroisoquinoline and protoberberine alkaloids

Novel molecular matrices have been derived from coumarin-4-acetic acids and beta-phenylethylamines using the Bischler-Napieralski protocol which has led to the synthesis of analogues of tetrahydropapaverine in which the dimethoxybenzene moiety has been replaced by substituted coumarins. One carbon homologation has led to cyclization at the C3 position of coumarin generating the protoberberine skeleton. Structures have been confirmed by diffraction studies. The results showed that compounds 6e, 6f, 7e and 7f were found to be very effective against DNA samples of Gram positive bacterium Staphylococcus aureus and fungus Aspergillus niger. (C) 2010 Elsevier Masson SAS. All rights reserved.

Reactive hot pressing of ZrB2-ZrCx ultra-high temperature ceramic composites with the addition of SiC particulate

Starting with non-stoichiometric Zr-B4C powder mixture ZrB2-ZrC matrix composites with SiC particulate addition have been made. It was found that variable amounts (5-25 vol%) of SiC could be incorporated and reactively hot pressed (RHPed) to relative densities of 97-99% at 1400-1500 degrees C. This technique has the potential to fabricate ZrB2-based matrices at low temperatures with a variety of reinforcements whose composition and volume fraction are not limited by stoichiometric considerations. The hardness of the composites is in the range of 17-22 GPa. (C) 2010 Elsevier Ltd. All rights reserved.

An algorithm to find distant repeats in a pair of protein sequences

Distant repeats between a pair of protein sequences can be exploited to study the various aspects of proteins such as structure-function relationship, disorders due to protein malfunction, evolutionary analysis, etc. An in-depth analysis of the distant repeats would facilitate to establish a stable evolutionary relation of the repeats with respect to their three-dimensional structure. To this effect, an algorithm has been devised to identify the distant repeats in a pair of protein sequences by essentially using the scores of PAM (Percent Accepted Mutation) matrices. The proposed algorithm will be of much use to researchers involved in the comparative study of various organisms based on the amino-acid repeats in protein sequences. (C) 2010 Elsevier B.V. All rights reserved.

Leachability of trace elements from two stabilized low lime Indian fly ashes

Fly ash is a waste by-product obtained from the burning of coal by thermal power plants for generating electricity. When bulk quantities are involved, in order to arrest the fugitive dust, it is stored wet rather than dry. Fly ash contains trace concentrations of heavy metals and other substances in sufficient quantities to be able to leach out over a period of time. In this study an attempt was made to study the leachabilities of a few selected trace metals: Cd, Cu, Cr, Mn, Pb and Zn from two different types of class F fly ashes. Emphasis is also laid on developing an alternative in order to arrest the relative leachabilities of heavy metals after amending them with suitable additives. A standard laboratory leaching test for combustion residues has been employed to study the leachabilities of these trace elements as a function of liquid to solid ratio and pH. The leachability tests were conducted on powdered fly ash samples before and after amending them suitably with the matrices lime and gypsum; they were compacted to their respective proctor densities and cured for periods of 28 and 180 days. A marked reduction in the relative leachabilities of the trace elements was observed to be present at the end of 28 days. These relative leachability values further reduced marginally when tests were performed at the end of 180 days.

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.