A computational procedure to generate difference equations from differential equations

In this paper we have developed methods to compute maps from differential equations. We take two examples. First is the case of the harmonic oscillator and the second is the case of Duffing's equation. First we convert these equations to a canonical form. This is slightly nontrivial for the Duffing's equation. Then we show a method to extend these differential equations. In the second case, symbolic algebra needs to be used. Once the extensions are accomplished, various maps are generated. The Poincare sections are seen as a special case of such generated maps. Other applications are also discussed.

DMT of Multihop Networks: End Points and Computational Tools

In this paper, the diversity-multiplexing gain tradeoff (DMT) of single-source, single-sink (ss-ss), multihop relay networks having slow-fading links is studied. In particular, the two end-points of the DMT of ss-ss full-duplex networks are determined, by showing that the maximum achievable diversity gain is equal to the min-cut and that the maximum multiplexing gain is equal to the min-cut rank, the latter by using an operational connection to a deterministic network. Also included in the paper, are several results that aid in the computation of the DMT of networks operating under amplify-and-forward (AF) protocols. In particular, it is shown that the colored noise encountered in amplify-and-forward protocols can be treated as white for the purpose of DMT computation, lower bounds on the DMT of lower-triangular channel matrices are derived and the DMT of parallel MIMO channels is computed. All protocols appearing in the paper are explicit and rely only upon AF relaying. Half-duplex networks and explicit coding schemes are studied in a companion paper.

Computational investigations on covalent dimerization/oligomerization of polyacenes: Is it relevant to soot formation?

We have postulated a novel pathway that could assist in the nucleation of soot particles through covalent dimerization and oligomerizations of a variety of PAHs. DFT calculations were performed with the objective of obtaining the relative thermal stabilities and formation probabilities of oligomeric species that exploit the facile dimerization that is known to occur in linear oligoacenes. We propose that the presence of small stretches of linear oligoacence (tetracene or longer) in extended PAH, either embedded or tethered, would be adequate for enabling the formation of such dimeric and oligomeric adducts; these could then serve as nuclei for the growth of soot particles. Our studies also reveal the importance of p-stacking interactions between extended aromatic frameworks in governing the relative stabilities of the oligomeric species that are formed. (c) 2012 Wiley Periodicals, Inc.

Mesh Simplification Based on Edge Collapsing Could Improve Computational Efficiency in Near Infrared Optical Tomographic Imaging

The diffusion equation-based modeling of near infrared light propagation in tissue is achieved by using finite-element mesh for imaging real-tissue types, such as breast and brain. The finite-element mesh size (number of nodes) dictates the parameter space in the optical tomographic imaging. Most commonly used finite-element meshing algorithms do not provide the flexibility of distinct nodal spacing in different regions of imaging domain to take the sensitivity of the problem into consideration. This study aims to present a computationally efficient mesh simplification method that can be used as a preprocessing step to iterative image reconstruction, where the finite-element mesh is simplified by using an edge collapsing algorithm to reduce the parameter space at regions where the sensitivity of the problem is relatively low. It is shown, using simulations and experimental phantom data for simple meshes/domains, that a significant reduction in parameter space could be achieved without compromising on the reconstructed image quality. The maximum errors observed by using the simplified meshes were less than 0.27% in the forward problem and 5% for inverse problem.

Computational algorithms inspired by biological processes and evolution

In recent times computational algorithms inspired by biological processes and evolution are gaining much popularity for solving science and engineering problems. These algorithms are broadly classified into evolutionary computation and swarm intelligence algorithms, which are derived based on the analogy of natural evolution and biological activities. These include genetic algorithms, genetic programming, differential evolution, particle swarm optimization, ant colony optimization, artificial neural networks, etc. The algorithms being random-search techniques, use some heuristics to guide the search towards optimal solution and speed-up the convergence to obtain the global optimal solutions. The bio-inspired methods have several attractive features and advantages compared to conventional optimization solvers. They also facilitate the advantage of simulation and optimization environment simultaneously to solve hard-to-define (in simple expressions), real-world problems. These biologically inspired methods have provided novel ways of problem-solving for practical problems in traffic routing, networking, games, industry, robotics, economics, mechanical, chemical, electrical, civil, water resources and others fields. This article discusses the key features and development of bio-inspired computational algorithms, and their scope for application in science and engineering fields.

Bromenium-Catalysed Tandem Ring Opening/Cyclisation of Vinylcyclopropanes and Vinylcyclobutanes: A Metal-Free 3+2+1]/4+2+1] Cascade for the Synthesis of Chiral Amidines and Computational Investigation

We present a detailed study of a 3+2+1] cascade cyclisation of vinylcyclopropanes (VCP) catalysed by a bromenium species (Brd+?Xd-) generated in situ, which results in the synthesis of chiral bicyclic amidines in a tandem one-pot operation. The formation of amidines involves the ring-opening of VCPs with Br?X, followed by a Ritter-type reaction with chloramine-T and a tandem cyclisation. The reaction has been further extended to vinylcyclobutane systems and involves a 4+2+1] cascade cyclisation with the same reagents. The versatility of the methodology has been demonstrated by careful choice of VCPs and VCBs to yield bicyclo4.3.0]-, -4.3.1]- and -4.4.0]amidines in enantiomerically pure form. On the basis of the experimental observations and DFT calculations, a reasonable mechanism has been put forth to account for the formation of the products and the observed stereoselectivity. We propose the existence of a p-stabilised homoallylic carbocation at the cyclopropane carbon as the reason for high stereoselectivity. DFT studies at B3LYP/6-311+G** and M06-2X/6-31+G* levels of theory in gas-phase calculations suggest the ring-opening of VCP is initiated at the p-complex stage (between the double bond and Br?X). This can be clearly perceived from the solution-phase (acetonitrile) calculations using the polarisable continuum model (PCM) solvation model, from which the extent of the ring opening of VCP was found to be noticeably high. Studies also show that the formation of zero-bridge bicyclic amidines is favoured over other bridged bicyclic amidines. The energetics of competing reaction pathways is compared to explain the product selectivity.

Single nucleotide polymorphisms in genes that are common targets of luteotropin and luteolysin in primate corpus luteum: Computational exploration

Luteal insufficiency affects fertility and hence study of mechanisms that regulate corpus luteum (CL) function is of prime importance to overcome infertility problems. Exploration of human genome sequence has helped to study the frequency of single nucleotide polymorphisms (SNPs). Clinical benefits of screening SNPs in infertility are being recognized well in recent times. Examining SNPs in genes associated with maintenance and regression of CL may help to understand unexplained luteal insufficiency and related infertility. Publicly available microarray gene expression databases reveal the global gene expression patterns in primate CL during the different functional state. We intend to explore computationally the deleterious SNPs of human genes reported to be common targets of luteolysin and luteotropin in primate CL Different computational algorithms were used to dissect out the functional significance of SNPs in the luteinizing hormone sensitive genes. The results raise the possibility that screening for SNPs might be integrated to evaluate luteal insufficiency associated with human female infertility for future studies. (C) 2012 Elsevier B.V. All rights reserved,

Computational tools for mechanistic discrimination in the reductive and metathesis coupling reactions mediated by titanium(IV) isopropoxide

A theoretical study has been carried out at the B3LYP/LANL2DZ level to compare the reactivity of phenyl isocyanate and phenyl isothiocyanate towards titanium(IV) alkoxides. Isocyanates are shown to favour both mono insertion and double insertion reactions. Double insertion in a head-to-tail fashion is shown to be more exothermic than double insertion in a head-to-head fashion. The head-to-head double insertion leads to the metathesis product, a carbodiimide, after the extrusion of carbon dioxide. In the case of phenyl isothiocyanate, calculations favour the formation of only mono insertion products. Formation of a double insertion product is highly unfavourable. Further, these studies indicate that the reverse reaction involving the metathesis of N,N-'-diphenyl carbodiimide with carbon dioxide is likely to proceed more efficiently than the metathesis reaction with carbon disulphide. This is in excellent agreement with experimental results as metathesis with carbon disulphide fails to occur. In a second study, multilayer MM/QM calculations are carried out on intermediates generated from reduction of titanium(IV) alkoxides to investigate the effect of alkoxy bridging on the reactivity of multinuclear Ti species. Bimolecular coupling of imines initiated by Ti(III) species leads to a mixture of diastereomers and not diastereoselective coupling of the imine. However if the reaction is carried out by a trimeric biradical species, diastereoselective coupling of the imine is predicted. The presence of alkoxy bridges greatly favours the formation of the d,l (+/-) isomer, whereas the intermediate without alkoxy bridges favours the more stable meso isomer. As a bridged trimeric species, stabilized by bridging alkoxy groups, correctly explains the diastereoselective reaction, it is the most likely intermediate in the reaction.

Air oxygenation chemistry of 4-TBC catalyzed by chloro bridged dinuclear copper(II) complexes of pyrazole based tridentate ligands: synthesis, structure, magnetic and computational studies

Four dinuclear bis(mu-Cl) bridged copper(II) complexes, Cu-2(mu-Cl)(2)(L-X)(2)](ClO4)(2) (L-X = N,N-bis(3,5-dimethylpyrazole-1-yl)-methyl]benzylamine with X = H(1), OMe(2), Me(3) and Cl(4)), have been synthesized and characterized by the single crystal X-ray diffraction method. In these complexes, each copper(II) center is penta-coordinated with square-pyramidal geometry. In addition to the tridentate L-X ligand, a chloride ion occupies the last position of the square plane. This chloride ion is also bonded to the neighboring Cu(II) site in its axial position forming an SP-I dinuclear Cu(II) unit that exhibits small intramolecular ferromagnetic interactions and supported by DFT calculations. The complexes 1-3 exhibit methylmonooxygenase (pMMO) behaviour and oxidise 4-tert-butylcatechol (4-TBCH2) with molecular oxygen in MeOH or MeCN to 4-tert-butyl-benzoquinone (4-TBQ), 5-methoxy-4-tert-butyl-benzoquinone (5-MeO-4-TBQ) as the major products along with 6,6'-Bu-t-biphenyl-3,4,3',4'-tetraol and others as minor products. These are further confirmed by ESI- and FAB-mass analyses. A tentative catalytic cycle has been framed based on the mass spectral analysis of the products and DFT calculations on individual intermediates that are energetically feasible.

Computational studies on histidine kinase protein BaeS to target multidrug-resistant Salmonella

Multidrug-resistant Salmonella serovars have been a recent concern in curing infectious diseases like typhoid. Salmonella BaeS and BaeR are the two-component system (TCS) that signal transduction proteins found to play an important role in its multidrug resistance. A canonical TCS comprises a histidine kinase (HK) and its cognate partner response regulator (RR). The general approaches for therapeutic targeting are either the catalytic ATP-binding domain or the dimerization domain HisKA (DHp) of the HK, and in some cases, the receiver or the regulatory domain of the RR proteins. Earlier efforts of identifying novel drugs targeting the signal transduction protein have not been quite successful, as it shares similar ATP-binding domain with the key house keeping gene products of the mammalian GHL family. However, targeting the dimerization domain of HisKA through which the signals are received from the RR can be a better approach. In this article, we show stepwise procedure to specifically identify the key interacting residues involved in the dimerization with the RR along with effective targeting by ligands screened from the public database. We have found a few inhibitors which target effectively the important residues for the dimerization activity. Our results suggest a plausible de novo design of better DHp domain inhibitors.

Computational interrogation of cis-regulatory elements of genes that are common targets of luteotropin and luteolysin in the primate corpus luteum

The rapid recent increase in microarray-based gene expression studies in the corpus luteum (CL) utilizing macaque models gathered increasing volume of data in publically accessible microarray expression databases. Examining gene pathways in different functional states of CL may help to understand the factors that control luteal function and hence human fertility. Co-regulation of genes in microarray experiments may imply common transcriptional regulation by sequence-specific DNA-binding transcriptional factors. We have computationally analyzed the transcription factor binding sites (TFBS) in a previously reported macaque luteal microarray gene set (n = 15) that are common targets of luteotropin (luteinizing hormone (LH) and human chorionic gonadotropin (hCG)) and luteolysin (prostaglandin (PG) F-2 alpha). This in silico approach can reveal transcriptional networks that control these important genes which are representative of the interplay between luteotropic and luteolytic factors in the control of luteal function. Our computational analyses revealed 6 matrix families whose binding sites are significantly over-represented in promoters of these genes. The roles of these factors are discussed, which might help to understand the transcriptional regulatory network in the control of luteal function. These factors might be promising experimental targets for investigation of human luteal insufficiency. (C) 2012 Elsevier B.V. All rights reserved.

A computational study of heat transfer, soot production and transport in an acetylene-air laminar diffusion flame in the field of a line vortex

The present work involves a computational study of soot formation and transport in case of a laminar acetylene diffusion flame perturbed by a co nvecting line vortex. The topology of the soot contours (as in an earlier experimental work [4]) have been investigated. More soot was produced when vortex was introduced from the air si de in comparison to a fuel side vortex. Also the soot topography was more diffused in case of the air side vortex. The computational model was found to be in good agreement with the ex perimental work [4]. The computational simulation enabled a study of the various parameters affecting soot transport. Temperatures were found to be higher in case of air side vortex as compared to a fuel side vortex. In case of the fuel side vortex, abundance of fuel in the vort ex core resulted in stoichiometrically rich combustion in the vortex core, and more discrete so ot topography. Overall soot production too was low. In case of the air side vortex abundan ce of air in the core resulted in higher temperatures and more soot yield. Statistical techniques like probability density fun ction, correlation coefficient and conditional probability function were introduced to explain the transient dependence of soot yield and transport on various parameters like temperature, a cetylene concentration.

A computational study of flame dynamics on soot production and transport for an acetylene-air laminar diffusion flame in the field of a convecting line vortex

The present work involves a computational study of soot formation and transport in case of a laminar acetylene diffusion flame perturbed by a convecting line vortex. The topology of the soot contours (as in an earlier experimental work [4]) have been investigated. More soot was produced when vortex was introduced from the air side in comparison to a fuel side vortex. Also the soot topography was more diffused in case of the air side vortex. The computational model was found to be in good agreement with the experimental work [4]. The computational simulation enabled a study of the various parameters affecting soot transport. Temperatures were found to be higher in case of air side vortex as compared to a fuel side vortex. In case of the fuel side vortex, abundance of fuel in the vort ex core resulted in stoichiometrically rich combustion in the vortex core, and more discrete soot topography. Overall soot production too was low. In case of the air side vortex abundance of air in the core resulted in higher temperatures and more soot yield. Statistical techniques like probability density function, correlation coefficient and conditional probability function were introduced to explain the transient dependence of soot yield and transport on various parameters like temperature, a cetylene concentration.

Computational representations for multi state design tasks and enumeration of mechanical device behaviour

The role of a computer emerged from modeling and analyzing concepts (ideas) to generate concepts. Research into methods for supporting conceptual design using automated synthesis had attracted much attention in the past decades. To find out how designers synthesize solution concepts for multi-state mechanical devices, ten experimental studies were conducted. Observations from these empirical studies would be used as the basis to develop knowledge involved in the multi-state design synthesis process. In this paper, we propose a computational representation for expressing the multi-state design task and for enumerating multi-state behaviors of kinematic pairs and mechanisms. This computational representation would be used to formulate computational methods for the synthesis process to develop a system for supporting design synthesis of multiple state mechanical devices by generating a comprehensive variety of solution alternatives.