Determinants of weighted path matrices
Talaska, Kelli
2012-01-01
We find rational expressions for all minors of the weighted path matrix of a directed graph, generalizing the classical Lindstrom/Gessel-Viennot result for acyclic directed graphs. The formulas are given in terms of certain flows in the graph.
Updating weighting matrices by Cross-Entropy
Esteban Fernández Vázquez
2011-01-01
Full Text Available El enfoque clásico para estimar modelos espaciales parte de la elección de una matriz de pesos espaciales que refleje la interacción entre las diferentes zonas. Se asume que la regla para definir esta matriz es que sea lo más parecida a la «verdadera» red de relaciones espaciales, pero para el investigador es difícil dilucidar cuándo la elección de esta matriz es correcta. Este paso clave en el proceso de estimación de modelos espaciales es una elección arbitraria, como Anselin (2002 señaló, y puede ser visto como uno de sus principales problemas metodológicos. En esta nota se propone no imponer los elementos de la matriz, sino su estimación basándose en la técnica de Entropía Cruzada (CE. Como las matrices de pesos espaciales son frecuentemente normalizadas por filas, cada una de ellas se puede entender como una distribución de probabilidad. La econometría basada en medidas de entropía es una herramienta útil para la obtención de distribuciones de probabilidad desconocidas, y su aplicación permite la estimación de los elementos de la matriz de pesos espaciales. Así, la matriz ya no depende de una elección impuesta por el investigador, sino de una estimación empírica. Este artículo compara los estimadores clásicos con los basados en medidas de entropía por medio de simulaciones de Monte Carlo en varios escenarios. Los resultados muestran que estas estimaciones superan a las obtenidas por estimadores tradicionales, especialmente cuando la especificación de la matriz no es similar a la real. Este resultado destaca la utilidad de las técnicas CE a la hora de reducir el grado de arbitrariedad impuesta en la estimación de modelos espaciales.
Laplacian matrices of weighted digraphs represented as quantum states
Adhikari, Bibhas; Banerjee, Subhashish; Adhikari, Satyabrata; Kumar, Atul
2017-03-01
Representing graphs as quantum states is becoming an increasingly important approach to study entanglement of mixed states, alternate to the standard linear algebraic density matrix-based approach of study. In this paper, we propose a general weighted directed graph framework for investigating properties of a large class of quantum states which are defined by three types of Laplacian matrices associated with such graphs. We generalize the standard framework of defining density matrices from simple connected graphs to density matrices using both combinatorial and signless Laplacian matrices associated with weighted directed graphs with complex edge weights and with/without self-loops. We also introduce a new notion of Laplacian matrix, which we call signed Laplacian matrix associated with such graphs. We produce necessary and/or sufficient conditions for such graphs to correspond to pure and mixed quantum states. Using these criteria, we finally determine the graphs whose corresponding density matrices represent entangled pure states which are well known and important for quantum computation applications. We observe that all these entangled pure states share a common combinatorial structure.
On the extraction of weights from pairwise comparison matrices
Dijkstra, Theo K.
2013-01-01
We study properties of weight extraction methods for pairwise comparison matrices that minimize suitable measures of inconsistency, 'average error gravity' measures, including one that leads to the geometric row means. The measures share essential global properties with the AHP inconsistency measure
3D Weight Matrices in Modeling Real Estate Prices
Mimis, A.
2016-10-01
Central role in spatial econometric models of real estate data has the definition of the weight matrix by which we capture the spatial dependence between the observations. The weight matrices presented in literature so far, treats space in a two dimensional manner leaving out the effect of the third dimension or in our case the difference in height where the property resides. To overcome this, we propose a new definition of the weight matrix including the third dimensional effect by using the Hadamard product. The results illustrated that the level effect can be absorbed into the new weight matrix.
A weighting orthogonal method for constant beamwidth beamforming matrices
DU Jinxiang; YAN Shenggang; LI Zhishun
2007-01-01
A weighting orthogonal method for constant beamwidth beamforming matrices is proposed. This method multiplies weighting factors to each orthogonal beamforming matrix corresponding to different frequency bins. The method proposed doesn't cause waveform aberration, and doesn't cause additional loss of array signal-to-noise ratio when the sources have uniform spectrum. The waveform aberration and additional loss of array signal-to-noise ratio can not be avoided simultaneously by ordinary orthogonal method. So we can get good detection and estimation performances at the same time by the weighting method. Simulation results and water tank experiments are presented to confirm the conclusion above.
Weighted automata as coalgebras in categories of matrices
Oliveira, José Nuno Fonseca
2013-01-01
The evolution from non-deterministic to weighted automata represents a shift from qual- itative to quantitative methods in computer science. The trend calls for a language able to reconcile quantitative reasoning with formal logic and set theory, which have for so many years supported qualitative reasoning. Such a lingua franca should be typed, poly- morphic, diagrammatic, calculational and easy to blend with conventional notation. This paper puts forward typed linear algebra as a candidat...
Galeano, Javier; Iriondo, Jose M
2008-01-01
We have developed a graphical user interface (GUI) running in Matlab, called Weighted-Interaction Nestedness Estimator, WINE (Fig. 1). WINE is a Matlab application developed to perform the calculation of the new weighted nestedness estimator. This program allows the user to: open a data file, select the range of data to be analysed, and calculate the results, obtaining two graphics and three indices. The indices shown in the graphical interface are: a) weighted nestedness of the frequency matrix, b) average weighted nestedness of 100 random matrices of similar characteristics, and c) the new weighted- interaction nestedness estimator, which compares the two previous results.
KRIJNEN, WP
1994-01-01
De Vries (1993) discusses Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank-correlation coefficient for assessing the association between the rows of two proximity matrices. For each of these he introduces a weighted average variant and a rowwise variant. In this
KRIJNEN, WP
De Vries (1993) discusses Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank-correlation coefficient for assessing the association between the rows of two proximity matrices. For each of these he introduces a weighted average variant and a rowwise variant. In this
Yu, Yi-Kuo
2007-02-01
We construct a metric measure among weight matrices that are commonly used in non-interacting statistical physics systems, computational biology problems, as well as in general applications such as hidden Markov models. The metric distance between two weight matrices is obtained via aligning the matrices and thus can be evaluated by dynamic programming. Capable of allowing reverse complements in distance evaluation, this metric accommodates both gapless and gapped alignments between two weight matrices. The distance statistics among random motifs is also studied. We find that the average square distance and its standard error grow with different powers of motif length, and the normalized square distance follows a Gaussian distribution for large motif lengths.
Construction of microRNA functional families by a mixture model of position weight matrices
Je-Keun Rhee
2013-10-01
Full Text Available MicroRNAs (miRNAs are small regulatory molecules that repress the translational processes of their target genes by binding to their 3′ untranslated regions (3′ UTRs. Because the target genes are predominantly determined by their sequence complementarity to the miRNA seed regions (nucleotides 2–7 which are evolutionarily conserved, it is inferred that the target relationships and functions of the miRNA family members are conserved across many species. Therefore, detecting the relevant miRNA families with confidence would help to clarify the conserved miRNA functions, and elucidate miRNA-mediated biological processes. We present a mixture model of position weight matrices for constructing miRNA functional families. This model systematically finds not only evolutionarily conserved miRNA family members but also functionally related miRNAs, as it simultaneously generates position weight matrices representing the conserved sequences. Using mammalian miRNA sequences, in our experiments, we identified potential miRNA groups characterized by similar sequence patterns that have common functions. We validated our results using score measures and by the analysis of the conserved targets. Our method would provide a way to comprehensively identify conserved miRNA functions.
Construction of microRNA functional families by a mixture model of position weight matrices.
Rhee, Je-Keun; Shin, Soo-Yong; Zhang, Byoung-Tak
2013-01-01
MicroRNAs (miRNAs) are small regulatory molecules that repress the translational processes of their target genes by binding to their 3' untranslated regions (3' UTRs). Because the target genes are predominantly determined by their sequence complementarity to the miRNA seed regions (nucleotides 2-7) which are evolutionarily conserved, it is inferred that the target relationships and functions of the miRNA family members are conserved across many species. Therefore, detecting the relevant miRNA families with confidence would help to clarify the conserved miRNA functions, and elucidate miRNA-mediated biological processes. We present a mixture model of position weight matrices for constructing miRNA functional families. This model systematically finds not only evolutionarily conserved miRNA family members but also functionally related miRNAs, as it simultaneously generates position weight matrices representing the conserved sequences. Using mammalian miRNA sequences, in our experiments, we identified potential miRNA groups characterized by similar sequence patterns that have common functions. We validated our results using score measures and by the analysis of the conserved targets. Our method would provide a way to comprehensively identify conserved miRNA functions.
Efficient and accurate P-value computation for Position Weight Matrices
Varré Jean-Stéphane
2007-12-01
Full Text Available Abstract Background Position Weight Matrices (PWMs are probabilistic representations of signals in sequences. They are widely used to model approximate patterns in DNA or in protein sequences. The usage of PWMs needs as a prerequisite to knowing the statistical significance of a word according to its score. This is done by defining the P-value of a score, which is the probability that the background model can achieve a score larger than or equal to the observed value. This gives rise to the following problem: Given a P-value, find the corresponding score threshold. Existing methods rely on dynamic programming or probability generating functions. For many examples of PWMs, they fail to give accurate results in a reasonable amount of time. Results The contribution of this paper is two fold. First, we study the theoretical complexity of the problem, and we prove that it is NP-hard. Then, we describe a novel algorithm that solves the P-value problem efficiently. The main idea is to use a series of discretized score distributions that improves the final result step by step until some convergence criterion is met. Moreover, the algorithm is capable of calculating the exact P-value without any error, even for matrices with non-integer coefficient values. The same approach is also used to devise an accurate algorithm for the reverse problem: finding the P-value for a given score. Both methods are implemented in a software called TFM-PVALUE, that is freely available. Conclusion We have tested TFM-PVALUE on a large set of PWMs representing transcription factor binding sites. Experimental results show that it achieves better performance in terms of computational time and precision than existing tools.
Deng, Weibin; Majumdar, Soumyajit; Singh, Abhilasha; Shah, Sejal; Mohammed, Noorullah Naqvi; Jo, Seongbong; Pinto, Elanor; Tewari, Divya; Durig, Thomas; Repka, Michael A
2013-02-01
The objective of this study was to improve the dissolution rate and to enhance the stability of a poorly water-soluble and low glass-trasition temperature (T(g)) model drug, fenofibrate, in low molecular weight grades of hydroxypropylcellulose matrices produced by hot-melt extrusion (HME). Percent drug loading had a significant effect on the extrudability of the formulations. Dissolution rate of fenofibrate from melt extruded pellets was faster than that of the pure drug (p polymers were evaluated as stabilizing agents among which polyvinylpyrrolidone 17PF and amino methacrylate copolymer exhibited a significant inhibitory effect on fenofibrate recrystallization in the hot-melt extrudates. Subsequently immediate-release fenofibrate tablets were successfully developed and complete drug release was achieved within 5 min. The dissolution profile was comparable to that of a currently marketed formulation. The hot-melt extruded fenofibrate tablets were stable, and exhibited an unchanged drug release profile after 3-month storage at 40°C/75% RH.
Elkin, Kyle R; Slingsby, Rosanne; Bryant, Ray B
2016-08-15
A two-dimensional chromatography method for analyzing phytate or other ionic targets in matrices containing high molecular weight, charged organic species is described. Prior to quantification by anion exchange chromatography, the sample matrix was prepared by size exclusion chromatography, which removed the majority of the matrix. Quantification of phytate on the AS11-HC was sensitive (0.25µM, 0.17mg/l) and reproducible (4.6% RSD) allowing this method to provide baseline separation of phytate from a manure extract within 14min. The method is simple, requiring only sample filtering, reproducible (between-run variation 5% RSD) and linear from 0.38 to 76µM (0.25-50mg/l). The method is suitable for routine determination of phytate in high organic matrices such as manure extracts.
P.I. Kogut
2012-08-01
Full Text Available We study the compactness property of the weak convergence in variable Sobolev spaces of the following sequences $\\left\\{ (A_n,u_n \\in L^1(\\Omega; {\\mathbb{R}}^{N\\times N} \\times W_{A_n}(\\Omega; {\\Gamma}_D \\right\\}$, where the squared symmetric matrices $A\\colon \\Omega \\rightarrow {\\mathbb{R}}^{N\\times N}$ belong to the Lebesgue space $L^1(\\Omega; {\\mathbb{R}}^{N\\times N}$ and their eigenvalues may vanish on subdomains of $\\Omega$ with zero Lebesgue measure.
On the weighted enumeration of Alternating Sign Matrices and Descending Plane Partitions
Behrend, R E; Zinn-Justin, P
2011-01-01
We prove a conjecture of Mills, Robbins and Rumsey [J. Combin. Theory Ser. A 34, 340--359 (1983)] that, for any n, k, m and p, the number of nxn alternating sign matrices (ASMs) for which the 1 of the first row is in column k+1 and there are exactly m -1's and m+p inversions is equal to the number of descending plane partitions (DPPs) for which each part is at most n and there are exactly k parts equal to n, m special parts and p nonspecial parts. The proof involves expressing the associated generating functions for ASMs and DPPs with fixed n as determinants of nxn matrices, and using elementary transformations to show that these determinants are equal. The determinants themselves are obtained by standard methods: for ASMs this involves using the Izergin--Korepin formula for the partition function of the six-vertex model with domain-wall boundary conditions, together with a bijection between ASMs and configurations of this model, and for DPPs it involves using the Lindstrom--Gessel--Viennot theorem, together ...
A weighted mixed-sensitivity H-infinity-control design for irrational transfer matrices
Curtain, RF; Zhou, YS
1996-01-01
Approximate solutions to a weighted mixed-sensitivity H-x-control problem for an irrational transfer matrix are obtained by solving the same problem for a reduced-order (rational) transfer matrix. Upper and lower bounds for the sensitivity are obtained in terms of the sensitivity for the reduced-ord
Metamotifs - a generative model for building families of nucleotide position weight matrices
Down Thomas A
2010-06-01
Full Text Available Abstract Background Development of high-throughput methods for measuring DNA interactions of transcription factors together with computational advances in short motif inference algorithms is expanding our understanding of transcription factor binding site motifs. The consequential growth of sequence motif data sets makes it important to systematically group and categorise regulatory motifs. It has been shown that there are familial tendencies in DNA sequence motifs that are predictive of the family of factors that binds them. Further development of methods that detect and describe familial motif trends has the potential to help in measuring the similarity of novel computational motif predictions to previously known data and sensitively detecting regulatory motifs similar to previously known ones from novel sequence. Results We propose a probabilistic model for position weight matrix (PWM sequence motif families. The model, which we call the 'metamotif' describes recurring familial patterns in a set of motifs. The metamotif framework models variation within a family of sequence motifs. It allows for simultaneous estimation of a series of independent metamotifs from input position weight matrix (PWM motif data and does not assume that all input motif columns contribute to a familial pattern. We describe an algorithm for inferring metamotifs from weight matrix data. We then demonstrate the use of the model in two practical tasks: in the Bayesian NestedMICA model inference algorithm as a PWM prior to enhance motif inference sensitivity, and in a motif classification task where motifs are labelled according to their interacting DNA binding domain. Conclusions We show that metamotifs can be used as PWM priors in the NestedMICA motif inference algorithm to dramatically increase the sensitivity to infer motifs. Metamotifs were also successfully applied to a motif classification problem where sequence motif features were used to predict the family of
Pathological rate matrices: from primates to pathogens
Knight Rob
2008-12-01
Full Text Available Abstract Background Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation. Results We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability, both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Pad�� algorithm on trinucleotide matrices that were attributable to machine precision. Although the Pad
Remarkable selective constraints on exonic dinucleotide repeats.
Haasl, Ryan J; Payseur, Bret A
2014-09-01
Long dinucleotide repeats found in exons present a substantial mutational hazard: mutations at these loci occur often and generate frameshifts. Here, we provide clear and compelling evidence that exonic dinucleotides experience strong selective constraint. In humans, only 18 exonic dinucleotides have repeat lengths greater than six, which contrasts sharply with the genome-wide distribution of dinucleotides. We genotyped each of these dinucleotides in 200 humans from eight 1000 Genomes Project populations and found a near-absence of polymorphism. More remarkably, divergence data demonstrate that repeat lengths have been conserved across the primate phylogeny in spite of what is likely considerable mutational pressure. Coalescent simulations show that even a very low mutation rate at these loci fails to explain the anomalous patterns of polymorphism and divergence. Our data support two related selective constraints on the evolution of exonic dinucleotides: a short-term intolerance for any change to repeat length and a long-term prevention of increases to repeat length. In general, our results implicate purifying selection as the force that eliminates new, deleterious mutants at exonic dinucleotides. We briefly discuss the evolution of the longest exonic dinucleotide in the human genome--a 10 x CA repeat in fibroblast growth factor receptor-like 1 (FGFRL1)--that should possess a considerably greater mutation rate than any other exonic dinucleotide and therefore generate a large number of deleterious variants. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.
A two-dimensional chromatography method for analyzing anionic targets (specifically phytate) in complex matrices is described. Prior to quantification by anion exchange chromatography, the sample matrix was prepared by size exclusion chromatography, which removed the majority of matrix complexities....
On weighted group invertibility for rectangular matrices over an arbitrary ring%关于环上长方矩阵的加权群可逆性
章劲鸥
2013-01-01
研究任意环上长方矩阵的加权群逆和加权{1,5}-逆。利用矩阵分解,得到了长方矩阵积的加权群逆存在的一些等价条件和计算方法及任意环上长方矩阵的加权{1,5}-逆的刻画表达式。得到的定理推广了有关方阵群逆和{1,5}-逆的相关结果。结果还可适合应用于加法范畴中的态射。%The weighted group inverses of rectangular matrices and the weighted{1, 5}-inverse of a rectangular matrix over an arbitrary ring are studied. Using Matrix decomposition method,First, the weighted group inverse of a rectangular matrix product P AQ for which there exist P′ and Q′ such that P′P A=A=AQQ′ can be characterized and computed. Moreover, the expressions are given for the weighted{1, 5}-inverse of a rectangular matrix over an arbitrary ring. This generalizes recent results obtained for the group inverse of square matricesand the weighted{1, 5}-inverse of a rectangular matrix over an arbitrary ring . The results also apply to morphisms in (additive) categories.
Curtain, RF; Weiss, M; Zhou, Y
1996-01-01
Approximate solutions to a weighted mixed-sensitivity H-infinity-control problem for an irrational transfer matrix are obtained by solving the same problem for a reduced-order (rational) transfer matrix. Upper and lower bounds are given in terms of the solution to the reduced-order problem and the a
Automated genotyping of dinucleotide repeat markers
Perlin, M.W.; Hoffman, E.P. [Carnegie Mellon Univ., Pittsburgh, PA (United States)]|[Univ. of Pittsburgh, PA (United States)
1994-09-01
The dinucleotide repeats (i.e., microsatellites) such as CA-repeats are a highly polymorphic, highly abundant class of PCR-amplifiable markers that have greatly streamlined genetic mapping experimentation. It is expected that over 30,000 such markers (including tri- and tetranucleotide repeats) will be characterized for routine use in the next few years. Since only size determination, and not sequencing, is required to determine alleles, in principle, dinucleotide repeat genotyping is easily performed on electrophoretic gels, and can be automated using DNA sequencers. Unfortunately, PCR stuttering with these markers generates not one band for each allele, but a pattern of bands. Since closely spaced alleles must be disambiguated by human scoring, this poses a key obstacle to full automation. We have developed methods that overcome this obstacle. Our model is that the observed data is generated by arithmetic superposition (i.e., convolution) of multiple allele patterns. By quantitatively measuring the size of each component band, and exploiting the unique stutter pattern associated with each marker, closely spaced alleles can be deconvolved; this unambiguously reconstructs the {open_quotes}true{close_quotes} allele bands, with stutter artifact removed. We used this approach in a system for automated diagnosis of (X-linked) Duchenne muscular dystrophy; four multiplexed CA-repeats within the dystrophin gene were assayed on a DNA sequencer. Our method accurately detected small variations in gel migration that shifted the allele size estimate. In 167 nonmutated alleles, 89% (149/167) showed no size variation, 9% (15/167) showed 1 bp variation, and 2% (3/167) showed 2 bp variation. We are currently developing a library of dinucleotide repeat patterns; together with our deconvolution methods, this library will enable fully automated genotyping of dinucleotide repeats from sizing data.
Mehta, Madan Lal
1990-01-01
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading
Bin Raies, Arwa
2013-10-16
Background:In a number of diseases, certain genes are reported to be strongly methylated and thus can serve as diagnostic markers in many cases. Scientific literature in digital form is an important source of information about methylated genes implicated in particular diseases. The large volume of the electronic text makes it difficult and impractical to search for this information manually.Methodology:We developed a novel text mining methodology based on a new concept of position weight matrices (PWMs) for text representation and feature generation. We applied PWMs in conjunction with the document-term matrix to extract with high accuracy associations between methylated genes and diseases from free text. The performance results are based on large manually-classified data. Additionally, we developed a web-tool, DEMGD, which automates extraction of these associations from free text. DEMGD presents the extracted associations in summary tables and full reports in addition to evidence tagging of text with respect to genes, diseases and methylation words. The methodology we developed in this study can be applied to similar association extraction problems from free text.Conclusion:The new methodology developed in this study allows for efficient identification of associations between concepts. Our method applied to methylated genes in different diseases is implemented as a Web-tool, DEMGD, which is freely available at http://www.cbrc.kaust.edu.sa/demgd/. The data is available for online browsing and download. © 2013 Bin Raies et al.
Arwa Bin Raies
Full Text Available BACKGROUND: In a number of diseases, certain genes are reported to be strongly methylated and thus can serve as diagnostic markers in many cases. Scientific literature in digital form is an important source of information about methylated genes implicated in particular diseases. The large volume of the electronic text makes it difficult and impractical to search for this information manually. METHODOLOGY: We developed a novel text mining methodology based on a new concept of position weight matrices (PWMs for text representation and feature generation. We applied PWMs in conjunction with the document-term matrix to extract with high accuracy associations between methylated genes and diseases from free text. The performance results are based on large manually-classified data. Additionally, we developed a web-tool, DEMGD, which automates extraction of these associations from free text. DEMGD presents the extracted associations in summary tables and full reports in addition to evidence tagging of text with respect to genes, diseases and methylation words. The methodology we developed in this study can be applied to similar association extraction problems from free text. CONCLUSION: The new methodology developed in this study allows for efficient identification of associations between concepts. Our method applied to methylated genes in different diseases is implemented as a Web-tool, DEMGD, which is freely available at http://www.cbrc.kaust.edu.sa/demgd/. The data is available for online browsing and download.
Angie Hennessy
2009-04-01
Full Text Available
A methodology is proposed to develop a measuring instrument (metric for evaluating subjects from a population that cannot provide data to facilitate the development of such a metric (e.g. pre-term infants in the neonatal intensive care unit. Central to this methodology is the employment of an expert group that decides on the items to be included in the metric, the weights assigned to these items, and an index associated with the Likert scale points for each item. The experts supply pairwise ratios of an importance between items, and the geometric mean method is applied to these to establish the item weights – a well-established procedure in multi-criteria decision analysis. The ratios are found by having a managed discussion before asking the members of the expert panel to mark a visual analogue scale for each item.
Opsomming
‘n Metode word aangebied waarmee ‘n meetinstrument (metriek ontwikkel kan word vir die evaluering van persone uit ‘n populasie wat nie self die data vir die ontwikkeling van die metriek kan voorsien nie (bv. vroeggebore babas in die neonatale intensiewe sorgeenheid. Die kern van hierdie werkswyse is die gebruik van ‘n deskundige groep wat die items vir die meetinstrument kies, gewigte aan die items toeken, en vir elke item ‘n indeks opstel wat met die Likert-skaal punte geassosieer word. Die deskundiges het paarsgewyse verhoudings tussen items verskaf en die meetkundig-gemiddelde metode is hierop toegepas om die itemgewigte te verkry – ‘n goedgevestigde gebruik in meerdoelwitbesluitkunde. Die paarsgewyse verhoudings is gewerf deur die deskundiges, na ‘n bestuurde bespreking, vir elke item ‘n visuele analoogskaal te laat invul.
How to cite this article:
Becker, P.J., Wolvaardt, J.S., Hennessy, A. & Maree, C., 2009, 'A composite score for a measuring instrument utilising re-scaled Likert values and item weights from matrices of pair wise ratios
Stephanov, M A; Wettig, T
2005-01-01
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper originally appeared as an article in the Wiley Encyclopedia of Electrical and Electronics Engineering.
Synthesis and Chiral Separation of Dinucleotide(TpAZT) Phosphoramidates
Chang Xue LIN; Hua FU; Guang Zhong TU; Yu Fen ZHAO
2003-01-01
Dinucleotide (TpAZT) phosphoramidates were synthesized by Todd reaction of dinucleoside H-phosphonates and amino acid methyl esters, and their diastereomers (Rp and Sp) were separated by crystallization, and the results showed that natural and cheap methyl esters of alanine and phenylalanine can be used for large-scale synthesis of dinucleotide analogs.
Krylov, Piotr
2017-01-01
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...
Nicotinamide adenine dinucleotide biosynthesis promotes liver regeneration.
Mukherjee, Sarmistha; Chellappa, Karthikeyani; Moffitt, Andrea; Ndungu, Joan; Dellinger, Ryan W; Davis, James G; Agarwal, Beamon; Baur, Joseph A
2017-02-01
The regenerative capacity of the liver is essential for recovery from surgical resection or injuries induced by trauma or toxins. During liver regeneration, the concentration of nicotinamide adenine dinucleotide (NAD) falls, at least in part due to metabolic competition for precursors. To test whether NAD availability restricts the rate of liver regeneration, we supplied nicotinamide riboside (NR), an NAD precursor, in the drinking water of mice subjected to partial hepatectomy. NR increased DNA synthesis, mitotic index, and mass restoration in the regenerating livers. Intriguingly, NR also ameliorated the steatosis that normally accompanies liver regeneration. To distinguish the role of hepatocyte NAD levels from any systemic effects of NR, we generated mice overexpressing nicotinamide phosphoribosyltransferase, a rate-limiting enzyme for NAD synthesis, specifically in the liver. Nicotinamide phosphoribosyltransferase overexpressing mice were mildly hyperglycemic at baseline and, similar to mice treated with NR, exhibited enhanced liver regeneration and reduced steatosis following partial hepatectomy. Conversely, mice lacking nicotinamide phosphoribosyltransferase in hepatocytes exhibited impaired regenerative capacity that was completely rescued by administering NR.
Analysis of dinucleotide signatures in HIV-1 subtype B genomes
Aridaman Pandit; Jyothirmayi Vadlamudi; Somdatta Sinha
2013-12-01
Dinucleotide usage is known to vary in the genomes of organisms. The dinucleotide usage profiles or genome signatures are similar for sequence samples taken from the same genome, but are different for taxonomically distant species. This concept of genome signatures has been used to study several organisms including viruses, to elucidate the signatures of evolutionary processes at the genome level. Genome signatures assume greater importance in the case of host–pathogen interactions, where molecular interactions between the two species take place continuously, and can influence their genomic composition. In this study, analyses of whole genome sequences of the HIV-1 subtype B, a retrovirus that caused global pandemic of AIDS, have been carried out to analyse the variation in genome signatures of the virus from 1983 to 2007.We show statistically significant temporal variations in some dinucleotide patterns highlighting the selective evolution of the dinucleotide profiles of HIV-1 subtype B, possibly a consequence of host specific selection.
Water-soluble, electroactive, and photoluminescent quaterthiophene-dinucleotide conjugates.
Alesi, Silvia; Brancolini, Giorgia; Melucci, Manuela; Capobianco, Massimo Luigi; Venturini, Alessandro; Camaioni, Nadia; Barbarella, Giovanna
2008-01-01
Quaterthiophene-dinucleotide conjugates 5'TA3'-t4-3'AT5', 5'AA3'-t4-3'AA5', and 5'TT3'-t4-3'TT5' (TA: thymidine-adenosine, AA: adenosine-adenosine, TT: thymidine-thymidine) were synthesized and analyzed by a combination of spectroscopy and microscopy, electrical characterization, and theoretical calculations. Circular dichroism (CD) experiments demonstrated a transfer of chirality from the dinucleotides to quaterthiophene at high ionic strength and in cast films. The films were photoluminescent and electroactive. CD and photoluminescence spectra and current density/voltage plots (measured under dynamic vacuum) displayed significant variation on changing the dinucleotide scaffold. Molecular mechanics and molecular dynamics calculations indicated that the conformation and packing modes of the conjugates are the result of a balance between intra- and intermolecular nucleobase-thiophene stacking interactions and intramolecular hydrogen bonding between the nucleobases.
Inverse m-matrices and ultrametric matrices
Dellacherie, Claude; San Martin, Jaime
2014-01-01
The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warsaw (Poland); Kus, Marek [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warsaw (Poland); Slomczynski, Wojciech [Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Cracow (Poland); Sommers, Hans-Juergen [Fachbereich 7 Physik, Universitaet Essen, 45117 Essen (Germany)
2003-03-28
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N)). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and orthostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.
Zyczkowski, K.; Slomczynski, W.; Kus, M.; Sommers, H. -J.
2001-01-01
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and ortostochastic matrices in the complex p...
Dinucleotide controlled null models for comparative RNA gene prediction
Gesell Tanja
2008-05-01
Full Text Available Abstract Background Comparative prediction of RNA structures can be used to identify functional noncoding RNAs in genomic screens. It was shown recently by Babak et al. [BMC Bioinformatics. 8:33] that RNA gene prediction programs can be biased by the genomic dinucleotide content, in particular those programs using a thermodynamic folding model including stacking energies. As a consequence, there is need for dinucleotide-preserving control strategies to assess the significance of such predictions. While there have been randomization algorithms for single sequences for many years, the problem has remained challenging for multiple alignments and there is currently no algorithm available. Results We present a program called SISSIz that simulates multiple alignments of a given average dinucleotide content. Meeting additional requirements of an accurate null model, the randomized alignments are on average of the same sequence diversity and preserve local conservation and gap patterns. We make use of a phylogenetic substitution model that includes overlapping dependencies and site-specific rates. Using fast heuristics and a distance based approach, a tree is estimated under this model which is used to guide the simulations. The new algorithm is tested on vertebrate genomic alignments and the effect on RNA structure predictions is studied. In addition, we directly combined the new null model with the RNAalifold consensus folding algorithm giving a new variant of a thermodynamic structure based RNA gene finding program that is not biased by the dinucleotide content. Conclusion SISSIz implements an efficient algorithm to randomize multiple alignments preserving dinucleotide content. It can be used to get more accurate estimates of false positive rates of existing programs, to produce negative controls for the training of machine learning based programs, or as standalone RNA gene finding program. Other applications in comparative genomics that require
GENERALIZED NEKRASOV MATRICES AND APPLICATIONS
Mingxian Pang; Zhuxiang Li
2003-01-01
In this paper, the concept of generalized Nekrasov matrices is introduced, some properties of these matrices are discussed, obtained equivalent representation of generalized diagonally dominant matrices.
Introduction into Hierarchical Matrices
Litvinenko, Alexander
2013-12-05
Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.
BLOCK H-MATRICES AND SPECTRUM OF BLOCK MATRICES
黄廷祝; 黎稳
2002-01-01
The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations claracterized by Gfunctions for block matrices are got.
Circulant conference matrices for new complex Hadamard matrices
Dita, Petre
2011-01-01
The circulant real and complex matrices are used to find new real and complex conference matrices. With them we construct Sylvester inverse orthogonal matrices by doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into complex Hadamard matrices. The method is used for $n=6$ conference matrices and in this way we find new parametrisations of Hadamard matrices for dimension $ n=12$.
Conformational control of benzophenone-sensitized charge transfer in dinucleotides
Merz, Thomas; Wenninger, Matthias; Weinberger, Michael; Riedle, Eberhard; Wagenknecht, Hans-Achim; Schuetz, Martin
2013-01-01
Charge transfer in DNA cannot be understood without addressing the complex conformational flexibility, which occurs on a wide range of timescales. In order to reduce this complexity four dinucleotide models 1X consisting of benzophenone linked by a phosphodiester to one of the natural nucleosides X = A, G, T, C were studied in water and methanol. The theoretical work focuses on the dynamics and electronic structure of 1G. Predominant conformations in the two solvents were obtained by molecula...
Cyclic dinucleotide detection with riboswitch-G-quadruplex hybrid.
Tsuji, Genichiro; Sintim, Herman O
2016-03-01
A cyclic dinucleotide riboswitch has been fused with a G-quadruplex motif to produce a conditional riboswitch-peroxidase-mimicking sensor that oxidizes both colorimetric and fluorogenic substrates in the presence of c-di-GMP. We find that signal-to-noise ratio could be improved by using a two-, not three-, floor split G-quadruplex for this conditional peroxidase-mimicking riboswitch.
Evolution of function in the "two dinucleotide binding domains" flavoproteins.
Sunil Ojha
2007-07-01
Full Text Available Structural and biochemical constraints force some segments of proteins to evolve more slowly than others, often allowing identification of conserved structural or sequence motifs that can be associated with substrate binding properties, chemical mechanisms, and molecular functions. We have assessed the functional and structural constraints imposed by cofactors on the evolution of new functions in a superfamily of flavoproteins characterized by two-dinucleotide binding domains, the "two dinucleotide binding domains" flavoproteins (tDBDF superfamily. Although these enzymes catalyze many different types of oxidation/reduction reactions, each is initiated by a stereospecific hydride transfer reaction between two cofactors, a pyridine nucleotide and flavin adenine dinucleotide (FAD. Sequence and structural analysis of more than 1,600 members of the superfamily reveals new members and identifies details of the evolutionary connections among them. Our analysis shows that in all of the highly divergent families within the superfamily, these cofactors adopt a conserved configuration optimal for stereospecific hydride transfer that is stabilized by specific interactions with amino acids from several motifs distributed among both dinucleotide binding domains. The conservation of cofactor configuration in the active site restricts the pyridine nucleotide to interact with FAD from the re-side, limiting the flow of electrons from the re-side to the si-side. This directionality of electron flow constrains interactions with the different partner proteins of different families to occur on the same face of the cofactor binding domains. As a result, superimposing the structures of tDBDFs aligns not only these interacting proteins, but also their constituent electron acceptors, including heme and iron-sulfur clusters. Thus, not only are specific aspects of the cofactor-directed chemical mechanism conserved across the superfamily, the constraints they impose are
Creation of bioorthogonal redox systems depending on nicotinamide flucytosine dinucleotide.
Ji, Debin; Wang, Lei; Hou, Shuhua; Liu, Wujun; Wang, Jinxia; Wang, Qian; Zhao, Zongbao K
2011-12-28
Many enzymes catalyzing biological redox chemistry depend on the omnipresent cofactor, nicotinamide adenine dinucleotide (NAD). NAD is also involved in various nonredox processes. It remains challenging to disconnect one particular NAD-dependent reaction from all others. Here we present a bioorthogonal system that catalyzes the oxidative decarboxylation of l-malate with a dedicated abiotic cofactor, nicotinamide flucytosine dinucleotide (NFCD). By screening the multisite saturated mutagenesis libraries of the NAD-dependent malic enzyme (ME), we identified the mutant ME-L310R/Q401C, which showed excellent activity with NFCD, yet marginal activity with NAD. We found that another synthetic cofactor, nicotinamide cytosine dinucleotide (NCD), also displayed similar activity with the ME mutants. Inspired by these observations, we mutated d-lactate dehydrogenase (DLDH) and malate dehydrogenase (MDH) to DLDH-V152R and MDH-L6R, respectively, and both mutants showed fully active with NFCD. When coupled with DLDH-V152R, ME-L310R/Q401C required only a catalytic amount of NFCD to convert l-malate. Our results opened the window to engineer bioorthogonal redox systems for a wide variety of applications in systems biology and synthetic biology.
Cappellini, Valerio [' Mark Kac' Complex Systems Research Centre, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Krakow (Poland); Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Duisburg, 47048 Duisburg (Germany); Bruzda, Wojciech; Zyczkowski, Karol [Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Krakow (Poland)], E-mail: valerio@ictp.it, E-mail: h.j.sommers@uni-due.de, E-mail: w.bruzda@uj.edu.pl, E-mail: karol@cft.edu.pl
2009-09-11
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N = 2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary N we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
Cappellini, V; Bruzda, W; Zyczkowski, K
2009-01-01
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
Electrospun human keratin matrices as templates for tissue regeneration.
Sow, Wan Ting; Lui, Yuan Siang; Ng, Kee Woei
2013-04-01
The aim of this work was to study the feasibility of fabricating human hair keratin matrices through electrospinning and to evaluate the potential of these matrices for tissue regeneration. Keratin was extracted from human hair using Na2S and blended with poly(ethylene oxide) in the weight ratio of 60:1 for electrospinning. Physical morphology and chemical properties of the matrices were characterized using scanning electron microscopy and Fourier transform infrared spectroscopy, respectively. Cell viability and morphology of murine and human fibroblasts cultured on the matrices were evaluated through the Live/Dead(®) assay and scanning electron microscopy. Electrospun keratin matrices were successfully produced without affecting the chemical conformation of keratin. Fibroblasts cultured on keratin matrices showed healthy morphology and penetration into matrices at day 7. Electrospun human hair keratin matrices provide a bioinductive and structural environment for cell growth and are thus attractive as alternative templates for tissue regeneration.
Complex Hadamard matrices from Sylvester inverse orthogonal matrices
Dita, Petre
2009-01-01
A novel method to obtain parametrizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into complex Hadamard matrices, and in this way we find new parametrizations of Hadamard matrices for dim...
Matrices and linear transformations
Cullen, Charles G
1990-01-01
""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first
Methods for detection of methyl-CpG dinucleotides
Dunn, John J
2013-11-26
The invention provides methods for enriching methyl-CpG sequences from a DNA sample. The method makes use of conversion of cytosine residues to uracil under conditions in which methyl-cytosine residues are preserved. Additional methods of the invention enable to preservation of the context of me-CpG dinucleotides. The invention also provides a recombinant, full length and substantially pure McrA protein (rMcrA) for binding and isolation of DNA fragments containing the sequence 5'-C.sup.MeCpGG-3'. Methods for making and using the rMcrA protein, and derivatives thereof are provided.
A Simple Cocyclic Jacket Matrices
Moon Ho Lee
2008-01-01
Full Text Available We present a new class of cocyclic Jacket matrices over complex number field with any size. We also construct cocyclic Jacket matrices over the finite field. Such kind of matrices has close relation with unitary matrices which are a first hand tool in solving many problems in mathematical and theoretical physics. Based on the analysis of the relation between cocyclic Jacket matrices and unitary matrices, the common method for factorizing these two kinds of matrices is presented.
邓自立; 李春波
2007-01-01
For the multisensor systems with unknown noise statistics, using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation models, and based on the solution of the matrix equations for correlation function, estimators of the noise variances are obtained, and under the linear minimum variance optimal information fusion criterion weighted by diagonal matrices, a self-tuning information fusion Kalman predictor is presented, which realizes the self-tuning decoupled fusion Kalman predictors for the state components. Based on the dynamic error system, a new convergence analysis method is presented for self-tuning fuser. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. It is strictly proved that if the parameter estimation of the MA innovation models is consistent, then the self-tuning fusion Kalman predictor will converge to the optimal fusion Kalman predictor in a realization, or with probability one, so that it has asymptotic optimality. It can reduce the computational burden, and is suitable for real time applications. A simulation example for a target tracking system shows its effectiveness.
Codon Pair Bias Is a Direct Consequence of Dinucleotide Bias
Dusan Kunec
2016-01-01
Full Text Available Codon pair bias is a remarkably stable characteristic of a species. Although functionally uncharacterized, robust virus attenuation was achieved by recoding of viral proteins using underrepresented codon pairs. Because viruses replicate exclusively inside living cells, we posited that their codon pair preferences reflect those of their host(s. Analysis of many human viruses showed, however, that the encoding of viruses is influenced only marginally by host codon pair preferences. Furthermore, examination of codon pair preferences of vertebrate, insect, and arthropod-borne viruses revealed that the latter do not utilize codon pairs overrepresented in arthropods more frequently than other viruses. We found, however, that codon pair bias is a direct consequence of dinucleotide bias. We conclude that codon pair bias does not play a major role in the encoding of viral proteins and that virus attenuation by codon pair deoptimization has the same molecular underpinnings as attenuation based on an increase in CpG/TpA dinucleotides.
The overlapping host responses to bacterial cyclic dinucleotides.
Abdul-Sater, Ali A; Grajkowski, Andrzej; Erdjument-Bromage, Hediye; Plumlee, Courtney; Levi, Assaf; Schreiber, Michael T; Lee, Carolyn; Shuman, Howard; Beaucage, Serge L; Schindler, Christian
2012-02-01
Macrophages respond to infection with Legionella pneumophila by the induction of inflammatory mediators, including type I Interferons (IFN-Is). To explore whether the bacterial second messenger cyclic 3'-5' diguanylate (c-diGMP) activates some of these mediators, macrophages were infected with L. pneumophila strains in which the levels of bacterial c-diGMP had been altered. Intriguingly, there was a positive correlation between c-diGMP levels and IFN-I expression. Subsequent studies with synthetic derivatives of c-diGMP, and newly described cyclic 3'-5' diadenylate (c-diAMP), determined that these molecules activate overlapping inflammatory responses in human and murine macrophages. Moreover, UV crosslinking studies determined that both dinucleotides physically associate with a shared set of host proteins. Fractionation of macrophage extracts on a biotin-c-diGMP affinity matrix led to the identification of a set of candidate host binding proteins. These studies suggest that mammalian macrophages can sense and mount a specific inflammatory response to bacterial dinucleotides.
On greedy and submodular matrices
Faigle, U.; Kern, Walter; Peis, Britta; Marchetti-Spaccamela, Alberto; Segal, Michael
2011-01-01
We characterize non-negative greedy matrices, i.e., 0-1 matrices $A$ such that max $\\{c^Tx|Ax \\le b,\\,x \\ge 0\\}$ can be solved greedily. We identify submodular matrices as a special subclass of greedy matrices. Finally, we extend the notion of greediness to $\\{-1,0,+1\\}$-matrices. We present
Gaussian Fibonacci Circulant Type Matrices
Zhaolin Jiang
2014-01-01
Full Text Available Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices for n>2 and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively.
Justino, Júlia
2017-06-01
Matrices with coefficients having uncertainties of type o (.) or O (.), called flexible matrices, are studied from the point of view of nonstandard analysis. The uncertainties of the afore-mentioned kind will be given in the form of the so-called neutrices, for instance the set of all infinitesimals. Since flexible matrices have uncertainties in their coefficients, it is not possible to define the identity matrix in an unique way and so the notion of spectral identity matrix arises. Not all nonsingular flexible matrices can be turned into a spectral identity matrix using Gauss-Jordan elimination method, implying that that not all nonsingular flexible matrices have the inverse matrix. Under certain conditions upon the size of the uncertainties appearing in a nonsingular flexible matrix, a general theorem concerning the boundaries of its minors is presented which guarantees the existence of the inverse matrix of a nonsingular flexible matrix.
Upadhyay, Mohita; Samal, Jasmine; Kandpal, Manish; Vasaikar, Suhas; Biswas, Banhi; Gomes, James; Vivekanandan, Perumal
2013-12-01
Parvoviruses are rapidly evolving viruses that infect a wide range of hosts, including vertebrates and invertebrates. Extensive methylation of the parvovirus genome has been recently demonstrated. A global pattern of methylation of CpG dinucleotides is seen in vertebrate genomes, compared to "fractional" methylation patterns in invertebrate genomes. It remains unknown if the loss of CpG dinucleotides occurs in all viruses of a given DNA virus family that infect host species spanning across vertebrates and invertebrates. We investigated the link between the extent of CpG dinucleotide depletion among autonomous parvoviruses and the evolutionary lineage of the infected host. We demonstrate major differences in the relative abundance of CpG dinucleotides among autonomous parvoviruses which share similar genome organization and common ancestry, depending on the infected host species. Parvoviruses infecting vertebrate hosts had significantly lower relative abundance of CpG dinucleotides than parvoviruses infecting invertebrate hosts. The strong correlation of CpG dinucleotide depletion with the gain in TpG/CpA dinucleotides and the loss of TpA dinucleotides among parvoviruses suggests a major role for CpG methylation in the evolution of parvoviruses. Our data present evidence that links the relative abundance of CpG dinucleotides in parvoviruses to the methylation capabilities of the infected host. In sum, our findings support a novel perspective of host-driven evolution among autonomous parvoviruses.
Modeling regulatory networks with weight matrices
Weaver, D.C.; Workman, Christopher; Stormo, Gary D.
1999-01-01
Systematic gene expression analyses provide comprehensive information about the transcriptional responseto different environmental and developmental conditions. With enough gene expression data points,computational biologists may eventually generate predictive computer models of transcription reg...
On the tensor Permutation Matrices
Rakotonirina, Christian
2011-01-01
A property that tensor permutation matrices permutate tensor product of rectangle matrices is shown. Some examples, in the particular case of tensor commutation matrices, for studying some linear matricial equations are given.
Britz, Thomas
Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessa...... and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices....
Britz, Thomas
Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessa...... and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices....
Topological algebras of rapidly decreasing matrices and generalizations
Glockner, Helge
2010-01-01
It is a folklore fact that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion map is continuous. We provide a direct proof, which applies more generally to a large class of algebras of weighted matrices with entries in a Banach algebra.
Narendra Singh
2003-01-01
Assuming a relation between the quark mass matrices of the two sectors a unique solution can be obtained for the CKM ﬂavor mixing matrix. A numerical example is worked out which is in excellent agreement with experimental data.
Dinucleotide composition in animal RNA viruses is shaped more by virus family than host species.
Di Giallonardo, Francesca; Schlub, Timothy E; Shi, Mang; Holmes, Edward C
2017-02-01
Viruses use the cellular machinery of their hosts for replication. It has therefore been proposed that the nucleotide and dinucleotide composition of viruses should match that of their host species. If upheld, it may then be possible to use dinucleotide composition to predict the true host species of viruses sampled in metagenomic surveys. However, it is also clear that different taxonomic groups of viruses tend to have distinctive patterns of dinucleotide composition that may be independent of host species. To determine the relative strength of the effect of host versus virus family in shaping dinucleotide composition we performed a comparative analysis of 20 RNA virus families from 15 host groupings, spanning two animal phyla and more than 900 virus species. In particular, we determined the odds ratios for the 16 possible dinucleotides and performed a discriminant analysis to evaluate the capability of virus dinucleotide composition to predict the correct virus family or host taxon from which it was isolated. Notably, while 81% of the data analyzed here were predicted to the correct virus family, only 62% of these data were predicted to their correct subphylum/class host, and a mere 32% to their correct mammalian order. Similarly, dinucleotide composition has a weak predictive power for different hosts within individual virus families. We therefore conclude that dinucleotide composition is generally uniform within a virus family but less well reflects that of its host species. This has obvious implications for attempts to accurately predict host species from virus genome sequences alone.
Discrepancy variation of dinucleotide microsatellite repeats in eukaryotic genomes.
Gao, Huan; Cai, Shengli; Yan, Binlun; Chen, Baiyao; Yu, Fei
2009-01-01
To address whether there are differences of variation among repeat motif types and among taxonomic groups, we present here an analysis of variation and correlation of dinucleotide microsatellite repeats in eukaryotic genomes. Ten taxonomic groups were compared, those being primates, mammalia (excluding primates and rodentia), rodentia, birds, fish, amphibians and reptiles, insects, molluscs, plants and fungi, respectively. The data used in the analysis is from the literature published in the Journal of Molecular Ecology Notes. Analysis of variation reveals that there are no significant differences between AC and AG repeat motif types. Moreover, the number of alleles correlates positively with the copy number in both AG and AC repeats. Similar conclusions can be obtained from each taxonomic group. These results strongly suggest that the increase of SSR variation is almost linear with the increase of the copy number of each repeat motif. As well, the results suggest that the variability of SSR in the genomes of low-ranking species seem to be more than that of high-ranking species, excluding primates and fungi.
Mohita Upadhyay
Full Text Available Papillomaviruses and polyomaviruses are small ds-DNA viruses infecting a wide-range of vertebrate hosts. Evidence supporting co-evolution of the virus with the host does not fully explain the evolutionary path of papillomaviruses and polyomaviruses. Studies analyzing CpG dinucleotide frequencies in virus genomes have provided interesting insights on virus evolution. CpG dinucleotide depletion has not been extensively studied among papillomaviruses and polyomaviruses. We sought to analyze the relative abundance of dinucleotides and the relative roles of evolutionary pressures in papillomaviruses and polyomaviruses.We studied 127 full-length sequences from papillomaviruses and 56 full-length sequences from polyomaviruses. We analyzed the relative abundance of dinucleotides, effective codon number (ENC, differences in synonymous codon usage. We examined the association, if any, between the extent of CpG dinucleotide depletion and the evolutionary lineage of the infected host. We also investigated the contribution of mutational pressure and translational selection to the evolution of papillomaviruses and polyomaviruses.All papillomaviruses and polyomaviruses are CpG depleted. Interestingly, the evolutionary lineage of the infected host determines the extent of CpG depletion among papillomaviruses and polyomaviruses. CpG dinucleotide depletion was more pronounced among papillomaviruses and polyomaviruses infecting human and other mammals as compared to those infecting birds. Our findings demonstrate that CpG depletion among papillomaviruses is linked to mutational pressure; while CpG depletion among polyomaviruses is linked to translational selection. We also present evidence that suggests methylation of CpG dinucleotides may explain, at least in part, the depletion of CpG dinucleotides among papillomaviruses but not polyomaviruses.The extent of CpG depletion among papillomaviruses and polyomaviruses is linked to the evolutionary lineage of the
Matrices in Engineering Problems
Tobias, Marvin
2011-01-01
This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo
Infinite matrices and sequence spaces
Cooke, Richard G
2014-01-01
This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi
Conformational control of benzophenone-sensitized charge transfer in dinucleotides.
Merz, Thomas; Wenninger, Matthias; Weinberger, Michael; Riedle, Eberhard; Wagenknecht, Hans-Achim; Schütz, Martin
2013-11-14
Charge transfer in DNA cannot be understood without addressing the complex conformational flexibility, which occurs on a wide range of timescales. In order to reduce this complexity four dinucleotide models 1X consisting of benzophenone linked by a phosphodiester to one of the natural nucleosides X = A, G, T, C were studied in water and methanol. The theoretical work focuses on the dynamics and electronic structure of 1G. Predominant conformations in the two solvents were obtained by molecular dynamics simulations. 1G in MeOH adopts mainly an open geometry with a distance of 12–16 Å between the two aromatic parts. In H2O the two parts of 1G form primarily a stacked conformation yielding a distance of 5–6 Å. The low-lying excited states were investigated by electronic structure theory in a QM/MM environment for representative snapshots of the trajectories. Photo-induced intramolecular charge transfer in the S1 state occurs exclusively in the stacked conformation. Ultrafast transient absorption spectroscopy with 1X reveals fast charge transfer from S1 in both solvents with varying yields. Significant charge transfer from the T1 state is only found for the nucleobases with the lowest oxidation potential: in H2O, charge transfer occurs with 3.2 × 10(9) s(-1) for 1A and 6.0 × 10(9) s(-1) for 1G. The reorganization energy remains nearly unchanged going from MeOH to the more polar H2O. The electronic coupling is rather low even for the stacked conformation with H(AB) = 3 meV and explains the moderate charge transfer rates. The solvent controls the conformational distribution and therefore gates the charge transfer due to differences in distance and stacking.
OTOTOXIC MODEL OF OXALIPLATIN AND PROTECTION FROM NICOTINAMIDE ADENINE DINUCLEOTIDE
DING Dalian; JIANG Haiyan; FU Yong; LI Yongqi; Richard Salvi; Shinichi Someya; Masaru Tanokura
2013-01-01
Oxaliplatin, an anticancer drug commonly used to treat colorectal cancer and other tumors, has a number of serious side effects, most notably neuropathy and ototoxicity. To gain insights into its ototoxic profile, oxaliplatin was applied to rat cochlear organ cultures. Consistent with it neurotoxic propensity, oxaliplatin selectively damaged nerve fibers at a very low dose 1 µM. In contrast, the dose required to damage hair cells and spiral ganglion neurons was 50 fold higher (50 µM). Oxailiplatin-induced cochlear lesions initial-ly increased with dose, but unexpectedly decreased at very high doses. This non-linear dose response could be related to depressed oxaliplatin uptake via active transport mechanisms. Previous studies have demon-strated that axonal degeneration involves biologically active processes which can be greatly attenuated by nicotinamide adenine dinucleotide (NAD+). To determine if NAD+would protect spiral ganglion axons and the hair cells from oxaliplatin damage, cochlear cultures were treated with oxaliplatin alone at doses of 10 µM or 50 µM respectively as controls or combined with 20 mM NAD+. Treatment with 10 µM oxaliplatin for 48 hours resulted in minor damage to auditory nerve fibers, but spared cochlear hair cells. However, when cochlear cultures were treated with 10 µM oxaliplatin plus 20 mM NAD+, most auditory nerve fibers were intact. 50 µM oxaliplatin destroyed most of spiral ganglion neurons and cochlear hair cells with apop-totic characteristics of cell fragmentations. However, 50 µM oxaliplatin plus 20 mM NAD+treatment great-ly reduced neuronal degenerations and hair cell missing. The results suggested that NAD+provides signifi-cant protection against oxaliplatin-induced neurotoxicity and ototoxicity, which may be due to its actions of antioxidant, antiapoptosis, and energy supply.
Korn, Joseph A; Urban, Jan; Dang, Andy; Nguyen, Huong T H; Tureček, František
2017-09-07
We report the generation of deoxyriboadenosine dinucleotide cation radicals by gas-phase electron transfer to dinucleotide dications and their noncovalent complexes with crown ether ligands. Stable dinucleotide cation radicals of a novel hydrogen-rich type were generated and characterized by tandem mass spectrometry and UV-vis photodissociation (UVPD) action spectroscopy. Electron structure theory analysis indicated that upon electron attachment the dinucleotide dications underwent a conformational collapse followed by intramolecular proton migrations between the nucleobases to give species whose calculated UV-vis absorption spectra matched the UVPD action spectra. Hydrogen-rich cation radicals generated from chimeric riboadenosine 5'-diesters gave UVPD action spectra that pointed to novel zwitterionic structures consisting of aromatic π-electron anion radicals intercalated between stacked positively charged adenine rings. Analogies with DNA ionization are discussed.
Presynaptic signalling mediated by mono- and dinucleotides in the central nervous system.
Miras-Portugal, M T; Díaz-Hernández, M; Gomez-Villafuerte, R; Gualix, J; Castro, E; Pintor, J
2000-07-01
Synaptosomal preparations from rat midbrain exhibit specific responses to both ATP and Ap(5)A, which elicit a Ca(2+) entrance to the presynaptic terminals. Studies of isolated single terminals showed that not all the terminals contain ionotropic receptors for nucleotides, in fact only 46% of them do. Of these, 12% responded only to the dinucleotide Ap(5)A, and 20% to the mononucleotide ATP. At the presynaptic level, diinosine pentaphosphate, Ip(5)I, is a good tool to specifically block dinucleotide responses, which are inhibited at low nM concentration, versus the high microM concentrations required to block ATP responses. There is evidence for a presynaptic control of mononucleotide and dinucleotide responses, mediated by metabotropic and ionotropic receptors. Stimulation of adenosine A1 receptors increases the affinity of dinucleotide receptors by five orders of magnitude, from 30 microM to 680 pM for control and in the presence of A1 agonist, respectively.
Introduction to matrices and vectors
Schwartz, Jacob T
2001-01-01
In this concise undergraduate text, the first three chapters present the basics of matrices - in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.
Paraunitary matrices and group rings
Barry Hurley
2014-03-01
Full Text Available Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structuresare presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Paraunitary matrices play a central role in signal processing, inparticular in the areas of filterbanks and wavelets.
Ferrers Matrices Characterized by the Rook Polynomials
MAHai-cheng; HUSheng-biao
2003-01-01
In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m+1} is a repeated set,W(A) is weight of A.
Domcke, Valerie
2016-01-01
We study natural lepton mass matrices, obtained assuming the stability of physical flavour observables with respect to the variations of individual matrix elements. We identify all four possible stable neutrino textures from algebraic conditions on their entries. Two of them turn out to be uniquely associated to specific neutrino mass patterns. We then concentrate on the semi-degenerate pattern, corresponding to an overall neutrino mass scale within the reach of future experiments. In this context we show that i) the neutrino and charged lepton mixings and mass matrices are largely constrained by the requirement of stability, ii) naturalness considerations give a mild preference for the Majorana phase most relevant for neutrinoless double-beta decay, $\\alpha \\sim \\pi/2$, and iii) SU(5) unification allows to extend the implications of stability to the down quark sector. The above considerations would benefit from an experimental determination of the PMNS ratio $|U_{32}/U_{31}|$, i.e. of the Dirac phase $\\delta...
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Gil, José J; José, Ignacio San
2015-01-01
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical depolarizer has the property of fully randomizing, the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, of potential usefulness to experimentalists dealing with such media.
Nanoceramic Matrices: Biomedical Applications
Willi Paul
2006-01-01
Full Text Available Natural bone consisted of calcium phosphate with nanometer-sized needle-like crystals of approximately 5-20 nm width by 60 nm length. Synthetic calcium phosphates and Bioglass are biocompatible and bioactive as they bond to bone and enhance bone tissue formation. This property is attributed to their similarity with the mineral phase of natural bone except its constituent particle size. Calcium phosphate ceramics have been used in dentistry and orthopedics for over 30 years because of these properties. Several studies indicated that incorporation of growth hormones into these ceramic matrices facilitated increased tissue regeneration. Nanophase calcium phosphates can mimic the dimensions of constituent components of natural tissues; can modulate enhanced osteoblast adhesion and resorption with long-term functionality of tissue engineered implants. This mini review discusses some of the recent developments in nanophase ceramic matrices utilized for bone tissue engineering.
On Random Correlation Matrices
1988-10-28
the spectral features of the resulting matrices are unknown. Method 2: Perturbation about a Mean This method is discussed by Marsaglia and Okin,10...complete regressor set. Finally, Marsaglia and Olkin (1984, Reference 10) give a rigorous mathematical description of Methods 2 through 4 described in the...short paper by Marsaglia 46 has a review of these early contributions, along with an improved method. More recent references are the pragmatic paper
Concentration for noncommutative polynomials in random matrices
2011-01-01
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries and unitary or orthogonal matrices.
Human nucleosomes: special role of CG dinucleotides and Alu-nucleosomes
Trifonov Edward N
2011-05-01
Full Text Available Abstract Background The periodical occurrence of dinucleotides with a period of 10.4 bases now is undeniably a hallmark of nucleosome positioning. Whereas many eukaryotic genomes contain visible and even strong signals for periodic distribution of dinucleotides, the human genome is rather featureless in this respect. The exact sequence features in the human genome that govern the nucleosome positioning remain largely unknown. Results When analyzing the human genome sequence with the positional autocorrelation method, we found that only the dinucleotide CG shows the 10.4 base periodicity, which is indicative of the presence of nucleosomes. There is a high occurrence of CG dinucleotides that are either 31 (10.4 × 3 or 62 (10.4 × 6 base pairs apart from one another - a sequence bias known to be characteristic of Alu-sequences. In a similar analysis with repetitive sequences removed, peaks of repeating CG motifs can be seen at positions 10, 21 and 31, the nearest integers of multiples of 10.4. Conclusions Although the CG dinucleotides are dominant, other elements of the standard nucleosome positioning pattern are present in the human genome as well. The positional autocorrelation analysis of the human genome demonstrates that the CG dinucleotide is, indeed, one visible element of the human nucleosome positioning pattern, which appears both in Alu sequences and in sequences without repeats. The dominant role that CG dinucleotides play in organizing human chromatin is to indicate the involvement of human nucleosomes in tuning the regulation of gene expression and chromatin structure, which is very likely due to cytosine-methylation/-demethylation in CG dinucleotides contained in the human nucleosomes. This is further confirmed by the positions of CG-periodical nucleosomes on Alu sequences. Alu repeats appear as monomers, dimers and trimers, harboring two to six nucleosomes in a run. Considering the exceptional role CG dinucleotides play in the
Pankiewicz, Krzysztof W; Watanabe, Kyoichi A; Lesiak-Watanabe, Krystyna; Goldstein, Barry M; Jayaram, Hiremagalur N
2002-04-01
Oncolytic C-nucleosides, tiazofurin (2-beta-D-ribofuranosylthiazole-4-carboxamide) and benzamide riboside (3-beta-D-ribofuranosylbenzamide) are converted in cell into active metabolites thiazole-4-carboxamide- and benzamide adenine dinucleotide, TAD and BAD, respectively. TAD and BAD as NAD analogues were found to bind at the nicotinamide adenine dinucleotide (cofactor NAD) site of inosine monophosphate dehydrogenase (IMPDH), an important target in cancer treatment. The synthesis and evaluation of anticancer activity of a number of C-nucleosides related to tiazofurin and nicotinamide riboside then followed and are reviewed herein. Interestingly, pyridine C-nucleosides (such as C-nicotinamide riboside) are not metabolized into the corresponding NAD analogues in cell. Their conversion by chemical methods is described. As dinucleotides these compounds show inhibition of IMPDH in low micromolar level. Also, the synthesis of BAD in metabolically stable bis(phosphonate) form is discussed indicating the usefulness of such preformed inhibitors in drug development. Among tiazofurin analogues, Franchetti and Grifantini found, that the replacement of the sulfur by oxygen (as in oxazafurin) but not the removal of nitrogen (tiophenfurin) of the thiazole ring resulted in inactive compounds. The anti cancer activity of their synthetic dinucleotide analogues indicate that inactive compounds are not only poorly metabolized in cell but also are weak inhibitors of IMPDH as dinucleotides.
Hiroshi NAKASHIMA; Yuka KURODA
2011-01-01
The occurrence frequencies of the dinucleotides of genes of three thermophilic and three mesophilic species from both archaea and eubacteria were investigated in this study. The genes encoding water soluble proteins were rich in the dinucleotides of purine dimers, whereas the genes encoding membrane proteins were rich in pyrimidine dimers. The dinucleotides of purine dimers are the counterparts of pyrimidine dimers in a double-stranded DNA. The purine/pyrimidine dimers were favored in the thermophiles but not in the mesophiles, based on comparisons of observed and expected frequencies. This finding is in agreement with our previous study which showed that purine/pyrimidine dimers are positive factors that increase the thermal stability of DNA. The dinucleotides AA, AG, and GA are components of the codons of charged residues of Glu, Asp, Lys, and Arg, and the dinucleotides TT, CT, and TC are components of the codons of hydrophobic residues of Leu, He, and Phe. This is consistent with the suitabilities of the different amino acid residues for water soluble and membrane proteins. Our analysis provides a picture of how thermophilic species produce water soluble and membrane proteins with distinctive characters: the genes encoding water soluble proteins use DNA sequences rich in purine dimers, and the genes encoding membrane proteins use DNA sequences rich in pyrimidine dimers on the opposite strand.
Schneider, Hans
1989-01-01
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t
Universality of Covariance Matrices
Pillai, Natesh S
2011-01-01
We prove the universality of covariance matrices of the form $H_{N \\times N} = {1 \\over N} \\tp{X}X$ where $[X]_{M \\times N}$ is a rectangular matrix with independent real valued entries $[x_{ij}]$ satisfying $\\E \\,x_{ij} = 0$ and $\\E \\,x^2_{ij} = {1 \\over M}$, $N, M\\to \\infty$. Furthermore it is assumed that these entries have sub-exponential tails. We will study the asymptotics in the regime $N/M = d_N \\in (0,\\infty), \\lim_{N\\to \\infty}d_N \
M Wedderburn, J H
1934-01-01
It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results-the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. -Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. -Jahrbuch über die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from sp
Zhao, Yan; Guan, Yun-Feng; Zhou, Xiao-Ming; Li, Guo-Qiang; Li, Zhi-Yong; Zhou, Can-Can; Wang, Pei; Miao, Chao-Yu
2015-07-01
Nicotinamide adenine dinucleotide (NAD) is a ubiquitous fundamental metabolite. Nicotinamide phosphoribosyltransferase (Nampt) is the rate-limiting enzyme for mammalian NAD salvage synthesis and has been shown to protect against acute ischemic stroke. In this study, we investigated the role of Nampt-NAD cascade in brain regeneration after ischemic stroke. Nampt transgenic (Nampt-Tg) mice and H247A mutant enzymatic-dead Nampt transgenic (ΔNampt-Tg) mice were subjected with experimental cerebral ischemia by middle cerebral artery occlusion. Activation of neural stem cells, neurogenesis, and neurological function recovery were measured. Besides, nicotinamide mononucleotide and NAD, two chemical enzymatic product of Nampt, were administrated in vivo and in vitro. Compared with wild-type mice, Nampt-Tg mice showed enhanced number of neural stem cells, improved neural functional recovery, increased survival rate, and accelerated body weight gain after middle cerebral artery occlusion, which were not observed in ΔNampt-Tg mice. A delayed nicotinamide mononucleotide administration for 7 days with the first dose at 12 hours post middle cerebral artery occlusion did not protect acute brain infarction and neuronal deficit; however, it still improved postischemic regenerative neurogenesis. Nicotinamide mononucleotide and NAD(+) promoted proliferation and differentiation of neural stem cells in vitro. Knockdown of NAD-dependent deacetylase sirtuin 1 (SIRT1) and SIRT2 inhibited the progrowth action of Nampt-NAD axis, whereas knockdown of SIRT1, SIRT2, and SIRT6 compromised the prodifferentiation effect of Nampt-NAD axis. Our data demonstrate that the Nampt-NAD cascade may act as a centralizing switch in postischemic regeneration through controlling different sirtuins and therefore represent a promising therapeutic target for long-term recovery of ischemic stroke. © 2015 American Heart Association, Inc.
Rodríguez, Santiago; Chen, Xiao-He; Day, Ian N M
2004-04-01
Polymorphic dinucleotide repeat loci ('microsatellite markers') are found in varying abundance throughout the genomes of most organisms. They have been extensively used for genetic studies, but conventional techniques used for their genotyping require sophisticated equipment. Microplate array diagonal gel electrophoresis (MADGE) has previously been extended to economical high-throughput genotyping of trinucleotide and tetranucleotide microsatellite amplicons. However, the capability of this technique to resolve the alleles of dinucleotide repeat loci has not been explored previously. Here we show that a modified microsatellite-MADGE approach can provide sufficient resolution for dinucleotide repeat typing. This enables economical and convenient set up for analysis of single markers in many samples in parallel, suitable, for example, for population association studies.
Truncations of random unitary matrices
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
1999-01-01
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M/N. For the truncated CUE we derive analytically the joint density of eigenvalues from which easily all correlation functions are obtained. For N-M fixed and N--> infinity the universal resonance-width distribution with N-M open channels is recovered.
Criteria of the Nonsingular H-Matrices
GAO jian; LIU Futi; HUANG Tingzhu
2004-01-01
The nonsingular H-matrices play an important role in the study of the matrix theory and the iterative method of systems of linear equations,etc.It has always been searched how to verify nonsingular H-matrices.In this paper,nonsingular H-matrices is studies by applying diagonally dominant matrices,irreducible diagonally dominant matrices and comparison matrices and several practical criteria for identifying nonsingular H-matrices are obtained.
Generalisations of Fisher Matrices
Alan Heavens
2016-06-01
Full Text Available Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a situations where the data (in the form of ( x , y pairs have errors in both x and y; (b modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c Derivative Approximation for LIkelihoods (DALI - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence.
Generalisations of Fisher Matrices
Heavens, Alan
2016-01-01
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a) situations where the data (in the form of (x,y) pairs) have errors in both x and y; (b) modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c) Derivative Approximation for LIkelihoods (DALI) - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d) extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence.
VanderLaan Circulant Type Matrices
Hongyan Pan
2015-01-01
Full Text Available Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g-circulant matrix.
Polynomial Fibonacci-Hessenberg matrices
Esmaeili, Morteza [Dept. of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan (Iran, Islamic Republic of)], E-mail: emorteza@cc.iut.ac.ir; Esmaeili, Mostafa [Dept. of Electrical and Computer Engineering, Isfahan University of Technology, 84156-83111 Isfahan (Iran, Islamic Republic of)
2009-09-15
A Fibonacci-Hessenberg matrix with Fibonacci polynomial determinant is referred to as a polynomial Fibonacci-Hessenberg matrix. Several classes of polynomial Fibonacci-Hessenberg matrices are introduced. The notion of two-dimensional Fibonacci polynomial array is introduced and three classes of polynomial Fibonacci-Hessenberg matrices satisfying this property are given.
Enhancing Understanding of Transformation Matrices
Dick, Jonathan; Childrey, Maria
2012-01-01
With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…
Enhancing Understanding of Transformation Matrices
Dick, Jonathan; Childrey, Maria
2012-01-01
With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…
Hierarchical matrices algorithms and analysis
Hackbusch, Wolfgang
2015-01-01
This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists ...
Kellogg, Richard M.; Kruizinga, Wim; Bystrykh, Leonid V.; Dijkhuizen, Lubbert; Harder, Wim
1992-01-01
Alcohol oxidase (MOX), a major peroxisomal protein of methanol-utilizing yeasts, contains two different forms of flavin adenine dinucleotide, one of which is identical with natural FAD whereas the other (mFAD) is a stereochemical modification of the natural coenzyme. This modification occurs spontan
Modification of flavin adenine dinucleotide in alcohol oxidase of the yeast Hansenula polymorpha
Bystrykh, Leonid V.; Dijkhuizen, Lubbert; Harder, Willem
1991-01-01
Alcohol oxidase, a major peroxisomal protein of methanol-utilizing yeasts, may possess two different forms of flavin adenine dinucleotide, classical FAD and so-called modified FAD (mFAD). Conversion of FAD into mFAD was observed both in purified preparations of the enzyme and in cells grown in batch
Dinucleotide microsatellite DNA loci from the ant Myrmica scabrinodis
Zeisset, Inga; Ebsen, Jon R.; Boomsma, Jacobus Jan
2005-01-01
We describe the isolation and characterization of five dinucleotide microsatellite loci in the ant Myrmica scabrinodis, which were obtained using a magnetic bead hybridization selection protocol. The PCR primers were tested on nine to 11 individuals. The number of alleles ranged from two to 13, a...
Kellogg, Richard M.; Kruizinga, Wim; Bystrykh, Leonid V.; Dijkhuizen, Lubbert; Harder, Wim
1992-01-01
Alcohol oxidase (MOX), a major peroxisomal protein of methanol-utilizing yeasts, contains two different forms of flavin adenine dinucleotide, one of which is identical with natural FAD whereas the other (mFAD) is a stereochemical modification of the natural coenzyme. This modification occurs spontan
Tulloch, Fiona; Atkinson, Nicky J; Evans, David J; Ryan, Martin D; Simmonds, Peter
2014-12-09
Mutating RNA virus genomes to alter codon pair (CP) frequencies and reduce translation efficiency has been advocated as a method to generate safe, attenuated virus vaccines. However, selection for disfavoured CPs leads to unintended increases in CpG and UpA dinucleotide frequencies that also attenuate replication. We designed and phenotypically characterised mutants of the picornavirus, echovirus 7, in which these parameters were independently varied to determine which most influenced virus replication. CpG and UpA dinucleotide frequencies primarily influenced virus replication ability while no fitness differences were observed between mutants with different CP usage where dinucleotide frequencies were kept constant. Contrastingly, translation efficiency was unaffected by either CP usage or dinucleotide frequencies. This mechanistic insight is critical for future rational design of live virus vaccines and their safety evaluation; attenuation is mediated through enhanced innate immune responses to viruses with elevated CpG/UpA dinucleotide frequencies rather the viruses themselves being intrinsically defective.
Estimating sparse precision matrices
Padmanabhan, Nikhil; White, Martin; Zhou, Harrison H.; O'Connell, Ross
2016-08-01
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological precision matrices are often approximately sparse, the method allows one to exploit this sparsity of the precision matrix to more quickly converge to an asymptotic 1/sqrt{N_sim} rate while simultaneously providing an error model for all of the terms. Such an estimate can be used as the starting point for further regularization efforts which can improve upon the 1/sqrt{N_sim} limit above, and incorporating such additional steps is straightforward within this framework. We demonstrate the technique with toy models and with an example motivated by large-scale structure two-point analysis, showing significant improvements in the rate of convergence. For the large-scale structure example, we find errors on the precision matrix which are factors of 5 smaller than for the sample precision matrix for thousands of simulations or, alternatively, convergence to the same error level with more than an order of magnitude fewer simulations.
Generating random density matrices
Zyczkowski, Karol; Nechita, Ion; Collins, Benoit
2010-01-01
We study various methods to generate ensembles of quantum density matrices of a fixed size N and analyze the corresponding probability distributions P(x), where x denotes the rescaled eigenvalue, x=N\\lambda. Taking a random pure state of a two-partite system and performing the partial trace over one subsystem one obtains a mixed state represented by a Wishart--like matrix W=GG^{\\dagger}, distributed according to the induced measure and characterized asymptotically, as N -> \\infty, by the Marchenko-Pastur distribution. Superposition of k random maximally entangled states leads to another family of explicitly derived distributions, describing singular values of the sum of k independent random unitaries. Taking a larger system composed of 2s particles, constructing $s$ random bi-partite states, performing the measurement into a product of s-1 maximally entangled states and performing the partial trace over the remaining subsystem we arrive at a random state characterized by the Fuss-Catalan distribution of order...
Graph-theoretical matrices in chemistry
Janezic, Dusanka; Nikolic, Sonja; Trinajstic, Nenad
2015-01-01
Graph-Theoretical Matrices in Chemistry presents a systematic survey of graph-theoretical matrices and highlights their potential uses. This comprehensive volume is an updated, extended version of a former bestseller featuring a series of mathematical chemistry monographs. In this edition, nearly 200 graph-theoretical matrices are included.This second edition is organized like the previous one-after an introduction, graph-theoretical matrices are presented in five chapters: The Adjacency Matrix and Related Matrices, Incidence Matrices, The Distance Matrix and Related Matrices, Special Matrices
Hadamard Matrices and Their Applications
Horadam, K J
2011-01-01
In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book expl
Alesi, Silvia; Brancolini, Giorgia; Viola, Ilenia; Capobianco, Massimo Luigi; Venturini, Alessandro; Camaioni, Nadia; Gigli, Giuseppe; Melucci, Manuela; Barbarella, Giovanna
2009-01-01
The synthesis and properties of (5')TA(3')-t5 (8a) and (5')CG(3')-t5 (8b) conjugates, in which the self-complementary dinucleotides TA and CG are covalently bound to the central ring of alpha-quinquethiophene (t5), are described. According to molecular mechanics calculations, the preferred conformation of both 8a and 8b is that with the dinucleotide folded over the planar t5 backbone, with the nucleobases facing t5 at stacking distance. The calculations show that the aggregation process of 8a and 8b is driven by a mix of nucleobase-thiophene interactions, hydrogen bonding between nucleobases (non Watson-Crick (W&C) in TA, and W&C in CG), van der Waals, and electrostatic interactions. While 8b is scarcely soluble in any solvents, 8a is soluble in water, indicating that the aggregates of the former are more stable than those of the latter. Microfluidic-induced self-assembly studies of 8a showed the formation of lamellar, spherulitic, and dendritic supramolecular structures, depending on the concentration and solvent evaporation time. The self-assembled structures displayed micrometer dimensions in the xy plane of the substrate and nanometer dimensions in the z direction. Spatially resolved confocal microscopy and spectroscopy showed that the aggregates were characterized by intense fluorescence emission. Cast films of 8a from water solutions showed chirality transfer from the dinucleotide to t5. The hole mobility of the cast films of 8a was estimated using a two-electrode device under high vacuum and found to be up to two orders of magnitude greater than those previously measured for dinucleotide-quarterthiophene conjugates under the same experimental conditions.
Identification of prophages in bacterial genomes by dinucleotide relative abundance difference.
K V Srividhya
Full Text Available BACKGROUND: Prophages are integrated viral forms in bacterial genomes that have been found to contribute to interstrain genetic variability. Many virulence-associated genes are reported to be prophage encoded. Present computational methods to detect prophages are either by identifying possible essential proteins such as integrases or by an extension of this technique, which involves identifying a region containing proteins similar to those occurring in prophages. These methods suffer due to the problem of low sequence similarity at the protein level, which suggests that a nucleotide based approach could be useful. METHODOLOGY: Earlier dinucleotide relative abundance (DRA have been used to identify regions, which deviate from the neighborhood areas, in genomes. We have used the difference in the dinucleotide relative abundance (DRAD between the bacterial and prophage DNA to aid location of DNA stretches that could be of prophage origin in bacterial genomes. Prophage sequences which deviate from bacterial regions in their dinucleotide frequencies are detected by scanning bacterial genome sequences. The method was validated using a subset of genomes with prophage data from literature reports. A web interface for prophage scan based on this method is available at http://bicmku.in:8082/prophagedb/dra.html. Two hundred bacterial genomes which do not have annotated prophages have been scanned for prophage regions using this method. CONCLUSIONS: The relative dinucleotide distribution difference helps detect prophage regions in genome sequences. The usefulness of this method is seen in the identification of 461 highly probable loci pertaining to prophages which have not been annotated so earlier. This work emphasizes the need to extend the efforts to detect and annotate prophage elements in genome sequences.
ON STABLE PERTURBATIONS OF THE STIFFLY WEIGHTED PSEUDOINVERSE AND WEIGHTED LEAST SQUARES PROBLEM
Mu-sheng Wei
2005-01-01
In this paper we study perturbations of the stiffly weighted pseudoinverse (W1/2 A)+W1/2 and the related stiffly weighted least squares problem, where both the matrices A and W are given with W positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices (^)A = A+δA satisfy several row rank preserving conditions.
Bayes linear adjustment for variance matrices
Wilkinson, Darren J
2008-01-01
We examine the problem of covariance belief revision using a geometric approach. We exhibit an inner-product space where covariance matrices live naturally --- a space of random real symmetric matrices. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability specifications.
Multiplicative equations over commuting matrices
Babai, L. [Univ. of Chicago, IL (United States)]|[Eotvos Univ., Budapest (Hungary); Beals, R. [Rutgers Univ., Piscataway, NJ (United States); Cai, Jin-Yi [SUNY, Buffalo, NY (United States)] [and others
1996-12-31
We consider the solvability of the equation and generalizations, where the A{sub i} and B are given commuting matrices over an algebraic number field F. In the semigroup membership problem, the variables x{sub i} are constrained to be nonnegative integers. While this problem is NP-complete for variable k, we give a polynomial time algorithm if k is fixed. In the group membership problem, the matrices are assumed to be invertible, and the variables x{sub i} may take on negative values. In this case we give a polynomial time algorithm for variable k and give an explicit description of the set of all solutions (as an affine lattice). The special case of 1 x 1 matrices was recently solved by Guoqiang Ge; we heavily rely on his results.
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Immanant Conversion on Symmetric Matrices
Purificação Coelho M.
2014-01-01
Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.
Iterative methods for Toeplitz-like matrices
Huckle, T. [Universitaet Wurzburg (Germany)
1994-12-31
In this paper the author will give a survey on iterative methods for solving linear equations with Toeplitz matrices, Block Toeplitz matrices, Toeplitz plus Hankel matrices, and matrices with low displacement rank. He will treat the following subjects: (1) optimal (w)-circulant preconditioners is a generalization of circulant preconditioners; (2) Optimal implementation of circulant-like preconditioners in the complex and real case; (3) preconditioning of near-singular matrices; what kind of preconditioners can be used in this case; (4) circulant preconditioning for more general classes of Toeplitz matrices; what can be said about matrices with coefficients that are not l{sub 1}-sequences; (5) preconditioners for Toeplitz least squares problems, for block Toeplitz matrices, and for Toeplitz plus Hankel matrices.
Sign pattern matrices that admit M-, N-, P- or inverse M-matrices
Araújo, C. Mendes; Torregrosa, Juan R.
2009-01-01
In this paper we identify the sign pattern matrices that occur among the N–matrices, the P–matrices and the M–matrices. We also address to the class of inverse M–matrices and the related admissibility of sign pattern matrices problem. Fundação para a Ciência e a Tecnologia (FCT) Spanish DGI grant number MTM2007-64477
Hamiltonian formalism and symplectic matrices; Formalisme Hamiltonien et Matrices symplectiques
Bertrand, P. [Project SPIRAL, Grand Accelerateur National d`Ions Lourds, BP 5027, Bd. H. Becquerel, 14076 Caen cedex 5 (France)
1997-12-31
This work consists of five sections. The first one introduces the Lagrangian formalism starting from the fundamental equation of the dynamics. The sections 2 to 4 are devoted to the Hamiltonian formalism and to symplectic matrices. Lie algebra and groups were avoided, although these notions are very useful if higher order effects have to be investigated. The paper is dealing with the properties of the transfer matrices describing different electromagnetic objects like, for instance: dipoles, quadrupoles, cyclotrons, electrostatic deflectors, spiral inflectors, etc. A remarkable property of the first order exact transfer matrices, is the symplecticity which in case of a 3-D object, described in 6-D phase space, provides 15 non-linear equations relating the matrix coefficients. The symplectic matrix ensemble forms an multiplication non-commuting group, consequently the product of n symplectic matrices is still a symplectic matrix. This permits the global description of a system of n objects. Thus, the notion symplecticity is fundamental for the selection of a given electromagnetic object, for its optimization and insertion in a line of beam transfer. The symplectic relations indicate actually that if a given beam characteristic is modified, then another characteristic will be affected and as a result the spurious effects can be limited when a line is to be adjusted. The last section is devoted to the application of the elaborated procedure to describe the drift of non-relativistic and relativistic particles, the dipole and the Muller inflector. Hopefully, this elementary Hamiltonian formalism will help in the familiarization with the symplectic matrices extensively utilized at GANIL 10 refs.
Fractal Structure of Random Matrices
Hussein, M S
2000-01-01
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the transition between the universality ensembles of random matrix theory and Poisson .
Open string fields as matrices
Kishimoto, Isao; Masuda, Toru; Takahashi, Tomohiko; Takemoto, Shoko
2015-03-01
We show that the action expanded around Erler-Maccaferri's N D-brane solution describes the N+1 D-brane system where one D-brane disappears due to tachyon condensation. String fields on multi-branes can be regarded as block matrices of a string field on a single D-brane in the same way as matrix theories.
Open String Fields as Matrices
Kishimoto, Isao; Takahashi, Tomohiko; Takemoto, Shoko
2014-01-01
We show that the action expanded around Erler-Maccaferri's N D-branes solution describes the N+1 D-branes system where one D-brane disappears due to tachyon condensation. String fields on the multi-branes can be regarded as block matrices of a string field on a single D-brane in the same way as matrix theories.
Arnold's Projective Plane and -Matrices
K. Uchino
2010-01-01
Full Text Available We will explain Arnold's 2-dimensional (shortly, 2D projective geometry (Arnold, 2005 by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular -matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.
Fibonacci Identities, Matrices, and Graphs
Huang, Danrun
2005-01-01
General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…
Scattering matrices with block symmetries
Życzkowski, Karol
1997-01-01
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a system with or without the time reversal invariance. An interpolating formula for the case of gradual time reversal symmetry breaking is proposed.
Making almost commuting matrices commute
Hastings, Matthew B [Los Alamos National Laboratory
2008-01-01
Suppose two Hermitian matrices A, B almost commute ({parallel}[A,B]{parallel} {<=} {delta}). Are they close to a commuting pair of Hermitian matrices, A', B', with {parallel}A-A'{parallel},{parallel}B-B'{parallel} {<=} {epsilon}? A theorem of H. Lin shows that this is uniformly true, in that for every {epsilon} > 0 there exists a {delta} > 0, independent of the size N of the matrices, for which almost commuting implies being close to a commuting pair. However, this theorem does not specifiy how {delta} depends on {epsilon}. We give uniform bounds relating {delta} and {epsilon}. The proof is constructive, giving an explicit algorithm to construct A' and B'. We provide tighter bounds in the case of block tridiagonal and tridiagnonal matrices. Within the context of quantum measurement, this implies an algorithm to construct a basis in which we can make a projective measurement that approximately measures two approximately commuting operators simultaneously. Finally, we comment briefly on the case of approximately measuring three or more approximately commuting operators using POVMs (positive operator-valued measures) instead of projective measurements.
Skills Underlying Coloured Progressive Matrices
Kirby, J. R.; Das, J. P.
1978-01-01
Raven's Coloured Progressive Matrices and a battery of ability tests were administered to a sample of 104 male fourth graders for purposes of investigating the relationships between 2 previously identified subscales of the Raven and the ability tests. Results indicated use of a spatial strategy and to a lesser extent, use of reasoning, indicating…
The diagonalization of cubic matrices
Cocolicchio, D.; Viggiano, M.
2000-08-01
This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.
Spectral problems for operator matrices
Bátkai, A.; Binding, P.; Dijksma, A.; Hryniv, R.; Langer, H.
2005-01-01
We study spectral properties of 2 × 2 block operator matrices whose entries are unbounded operators between Banach spaces and with domains consisting of vectors satisfying certain relations between their components. We investigate closability in the product space, essential spectra and generation of
Shanmugasundaram, Muthian; Charles, Irudaya; Kore, Anilkumar R
2016-03-15
The first example of the synthesis of new dinucleotide cap analog containing propargyl group such as m(7,3'-O-propargyl)G[5']ppp[5']G is reported. The effect of propargyl cap analog with standard cap was evaluated with respect to their capping efficiency, in vitro T7 RNA polymerase transcription efficiency, and translation activity using cultured HeLa cells. It is noteworthy that propargyl cap analog outperforms standard cap by 3.1 fold in terms of translational properties. The propargyl cap analog forms a more stable complex with translation initiation factor eIF4E based on the molecular modeling studies.
Association of flavin adenine dinucleotide with the Arabidopsis blue light receptor CRY1
Lin, C.; Robertson, D.E.; Ahmad, M. [Univ. of Pennsylvania, Philadelphia, PA (United States)] [and others
1995-08-18
The Arabidopsis thaliana HY4 gene encodes CRY1, a 75-kilodalton flavoprotein mediating blue light-dependent regulation of seedling development. CRY1 is demonstrated here to noncovalently bind stoichiometric amounts of flavin adenine dinucleotide (FAD). The redox properties of FAD bound by CRY1 include an unexpected stability of the neutral radical flavosemiquinone (FADH{center_dot}). The absorption properties of this flavosemiquinone provide a likely explanation for the additional sensitivity exhibited by CRY1-mediated responses in the green region of the visible spectrum. Despite the sequence homology to microbial DNA photolyases, CRY1 was found to have no detectable photolyase activity. 27 refs., 4 figs.
张晓东; 杨尚骏
2001-01-01
本文探讨矩阵的一个重要子类（F-矩阵）的性质.F-矩阵包含以下在理论及应用中都很重要的三个矩阵类：对称正半定矩阵，M-矩阵和完全非负矩阵.我们首先证明F-矩阵的一些有趣性，特别是给出n-阶F-矩阵A满足detA=an…ann的充分必要条件.接着研究逆F-矩阵的性质，特别是证明逆M-矩阵和逆完全非负矩阵都是F-矩阵，从而满足Fischer不等式.最后我们引入F-矩阵一个子类:W-矩阵并证明逆W-矩阵也是F-矩阵.%We investigate a class of P0-matrices, called F-matrices, whichcontains well known three important classes of matrices satisfying Hadamard's inequality and Fischer's inequality-positive semidefinite symmetric matrices, M-matrices and totally nonnegative matrices. Firstly we prove some interesting properties of F-matrices and give the necessary and sufficient condition for an n×n F-matrix to satisfy det A=a11…ann. Then we investigate inverse F-matrices and prove both inverse M-matrices and inverse totally nonnegative matrices are F-matrices. Finally we introduce a new class of F-matrices, i.e. W-matrices and prove both W-matrices and inverse W-matrices are also F-matrices.
STABILITY FOR SEVERAL TYPES OF INTERVAL MATRICES
NianXiaohong; GaoJintai
1999-01-01
The robust stability for some types of tlme-varying interval raatrices and nonlineartime-varying interval matrices is considered and some sufficient conditions for robust stability of such interval matrices are given, The main results of this paper are only related to the verticesset of a interval matrices, and therefore, can be easily applied to test robust stability of interval matrices. Finally, some examples are given to illustrate the results.
Eigenvalue variance bounds for covariance matrices
Dallaporta, Sandrine
2013-01-01
This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for Wigner matrices and stated the results for covariance matrices. They are proved in the present paper. Relying on the LUE example, which needs to be investigated first, the main bounds are extended to complex covariance matrices by means of the Tao, Vu and Wan...
The Bessel Numbers and Bessel Matrices
Sheng Liang YANG; Zhan Ke QIAO
2011-01-01
In this paper,using exponential Riordan arrays,we investigate the Bessel numbers and Bessel matrices.By exploring links between the Bessel matrices,the Stirling matrices and the degenerate Stirling matrices,we show that the Bessel numbers are special case of the degenerate Stirling numbers,and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.
Quantum Hilbert matrices and orthogonal polynomials
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|matrices...... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....
Simultaneous diagonalization of two quaternion matrices
ZhouJianhua
2003-01-01
The simultaneous diagonalization by congruence of pairs of Hermitian quatemion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quatemion matrix. It is proved that any two semi-positive definite Hermitian quatemion matrices can be simultaneously diagonalized by congruence.
Structural Flexibility and Conformation Features of Cyclic Dinucleotides in Aqueous Solutions.
Che, Xing; Zhang, Jun; Zhu, Yanyu; Yang, Lijiang; Quan, Hui; Gao, Yi Qin
2016-03-17
Cyclic dinucleotides are able to trigger the innate immune system by activating STING. It was found that the binding affinity of asymmetric 2'3'-cGAMP to symmetric dimer of STING is 3 orders of magnitude higher than that of the symmetric 3'3'-cyclic dinucleotides. Such a phenomenon has not been understood yet. Here we show that the subtle changes in phosphodiester linkage of CDNs lead to their distinct structural properties which correspond to the varied binding affinities. 2'-5' and/or 3'-5' linked CDNs adopt specific while different types of ribose puckers and backbone conformations. That ribose conformations and base types have different propensities for anti or syn glycosidic conformations further affects the overall flexibility of CDNs. The counterbalance between backbone ring tension and electrostatic repulsion, both affected by the ring size, also contributes to the different flexibility of CDNs. Our calculations reveal that the free energy cost for 2'3'-cGAMP to adopt the STING-bound structure is smaller than that for 3'3'-cGAMP and cyclic-di-GMP. These findings may serve as a reference for design of CDN-analogues as vaccine adjuvants. Moreover, the cyclization pattern of CDNs closely related to their physiological roles suggests the importance of understanding structural properties in the study of protein-ligand interactions.
Bombardelli, Diego
2016-08-01
In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU(2), SU(3) chiral Gross-Neveu models. In loving memory of Lilia Grandi.
Rotationally invariant ensembles of integrable matrices.
Yuzbashyan, Emil A; Shastry, B Sriram; Scaramazza, Jasen A
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)-a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
Rotationally invariant ensembles of integrable matrices
Yuzbashyan, Emil A.; Shastry, B. Sriram; Scaramazza, Jasen A.
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)—a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N -M independent commuting N ×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
Workman, Christopher; Krogh, Anders Stærmose
1999-01-01
This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly...... different from random sequences with the same dinucleotide distribution. For random sequences with the same mononucleotide distribution it has previously been shown that the native mRNA sequences have a lower predicted free energy, which indicates a more stable structure than random sequences. However......, dinucleotide content is important when assessing the significance of predicted free energy as the physical stability of RNA secondary structure is known to depend on dinucleotide base stacking energies. Even known RNA secondary structures, like tRNAs, can be shown to have predicted free energies...
Weak commutation relations and eigenvalue statistics for products of rectangular random matrices.
Ipsen, Jesper R; Kieburg, Mario
2014-03-01
We study the joint probability density of the eigenvalues of a product of rectangular real, complex, or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only restriction is the invariance under left and right multiplication by orthogonal, unitary, or unitary symplectic matrices, respectively. We show that a product of rectangular matrices is statistically equivalent to a product of square matrices. Hereby we prove a weak commutation relation of the random matrices at finite matrix sizes, which previously has been discussed for infinite matrix size. Moreover, we derive the joint probability densities of the eigenvalues. To illustrate our results, we apply them to a product of random matrices drawn from Ginibre ensembles and Jacobi ensembles as well as a mixed version thereof. For these weights, we show that the product of complex random matrices yields a determinantal point process, while the real and quaternion matrix ensembles correspond to Pfaffian point processes. Our results are visualized by numerical simulations. Furthermore, we present an application to a transport on a closed, disordered chain coupled to a particle bath.
Chitanda, Jackson M; Zhang, Haixia; Pahl, Erica; Purves, Randy W; El-Aneed, Anas
2016-10-01
The utility of novel functionalized nanodiamonds (NDs) as matrices for matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS) is described herein. MALDI-MS analysis of small organic compounds (matrices. To expand the use of MALDI for the analysis of small molecules, novel matrices were designed by covalently linking conventional matrices (or a lysine moiety) to detonated NDs. Four new functionalized NDs were evaluated for their ionization capabilities using five pharmaceuticals with varying molecular structures. Two ND matrices were able to ionize all tested pharmaceuticals in the negative ion mode, producing the deprotonated ions [M - H](-). Ion intensity for target analytes was generally strong with enhanced signal-to-noise ratios compared with conventional matrices. The negative ion mode is of great importance for biological samples as interference from endogenous compounds is inherently minimized in the negative ion mode. Since the molecular structures of the tested pharmaceuticals did not suggest that negative ion mode would be preferable, this result magnifies the importance of these findings. On the other hand, conventional matrices primarily facilitated the ionization as expected in the positive ion mode, producing either the protonated molecules [M + H](+) or cationic adducts (typically producing complex spectra with numerous adduct peaks). The data presented in this study suggests that these matrices may offer advantages for the analysis of low molecular weight pharmaceuticals/metabolites. Graphical Abstract ᅟ.
Structured LDPC Codes from Permutation Matrices Free of Small Trapping Sets
Nguyen, Dung Viet; Marcellin, Michael; Chilappagari, Shashi Kiran
2010-01-01
This paper introduces a class of structured lowdensity parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some matrix operations. They are chosen so that the Tanner graphs do not contain subgraphs harmful to iterative decoding algorithms. The construction of column-weight-three codes is presented. Although the codes are optimized for the Gallager A/B algorithm over the binary symmetric channel (BSC), their error performance is very good on the additive white Gaussian noise channel (AWGNC) as well.
Mikulski, Damian; Szeląg, Małgorzata; Molski, Marcin
2011-12-01
Trans-resveratrol, a natural phytoalexin present in red wine and grapes, has gained considerable attention because of its antiproliferative, chemopreventive and proapoptotic activity against human cancer cells. The accurate quantum-chemical computations based on the density functional theory (DFT) and ab initio second-order Møller-Plesset perturbation method (MP2) have been performed for the first time to study interactions of trans-resveratrol with guanine-thymine dinucleotide and DNA-derived nitrogenous bases: adenine, guanine, cytosine and thymine in vacuum and water medium. This compound is found to show high affinity to nitrogenous bases and guanine-thymine dinucleotide. The electrostatic interactions from intermolecular hydrogen bonding increase the stability of complexes studied. In particular, significantly strong hydrogen bonds between 4'-H atom of trans-resveratrol and imidazole nitrogen as well as carbonyl oxygen atoms of nucleobases studied stabilize these systems. The stabilization energies computed reveal that the negatively charged trans-resveratrol-dinucleotide complex is more energetically stable in water medium than in vacuum. MP2 method gives more reliable and significantly high values of stabilization energy of trans-resveratrol-dinucleotide, trans-resveratrol-guanine and trans-resveratrol-thymine complexes than B3LYP exchange-correlation functional because it takes into account London dispersion energy. According to the results, in the presence of trans-resveratrol the 3'-5' phosphodiester bond in dinucleotide can be cleaved and the proton from 4'-OH group of trans-resveratrol migrates to the 3'-O atom of dinucleotide. It is concluded that trans-resveratrol is able to break the DNA strand. Hence, the findings obtained help understand antiproliferative and anticancer properties of this polyphenol.
Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
Yanai, Haruo; Takane, Yoshio
2011-01-01
Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because
Cordiglieri, Chiara; Odoardi, Francesca; Zhang, Bo; Nebel, Merle; Kawakami, Naoto; Klinkert, Wolfgang E. F.; Lodygin, Dimtri; Lühder, Fred; Breunig, Esther; Schild, Detlev; Ulaganathan, Vijay Kumar; Dornmair, Klaus; Dammermann, Werner; Potter, Barry V. L.; Guse, Andreas H.
2010-01-01
Nicotinic acid adenine dinucleotide phosphate represents a newly identified second messenger in T cells involved in antigen receptor-mediated calcium signalling. Its function in vivo is, however, unknown due to the lack of biocompatible inhibitors. Using a recently developed inhibitor, we explored the role of nicotinic acid adenine dinucleotide phosphate in autoreactive effector T cells during experimental autoimmune encephalomyelitis, the animal model for multiple sclerosis. We provide in vitro and in vivo evidence that calcium signalling controlled by nicotinic acid adenine dinucleotide phosphate is relevant for the pathogenic potential of autoimmune effector T cells. Live two photon imaging and molecular analyses revealed that nicotinic acid adenine dinucleotide phosphate signalling regulates T cell motility and re-activation upon arrival in the nervous tissues. Treatment with the nicotinic acid adenine dinucleotide phosphate inhibitor significantly reduced both the number of stable arrests of effector T cells and their invasive capacity. The levels of pro-inflammatory cytokines interferon-gamma and interleukin-17 were strongly diminished. Consecutively, the clinical symptoms of experimental autoimmune encephalomyelitis were ameliorated. In vitro, antigen-triggered T cell proliferation and cytokine production were evenly suppressed. These inhibitory effects were reversible: after wash-out of the nicotinic acid adenine dinucleotide phosphate antagonist, the effector T cells fully regained their functions. The nicotinic acid derivative BZ194 induced this transient state of non-responsiveness specifically in post-activated effector T cells. Naïve and long-lived memory T cells, which express lower levels of the putative nicotinic acid adenine dinucleotide phosphate receptor, type 1 ryanodine receptor, were not targeted. T cell priming and recall responses in vivo were not reduced. These data indicate that the nicotinic acid adenine dinucleotide phosphate
Musiał-Kulik, Monika; Kasperczyk, Janusz; Jelonek, Katarzyna; Dobrzyński, Piotr; Gebarowska, Katarzyna; Janeczek, Henryk; Libera, Marcin
2010-01-01
Biodegradable polymers have become common materials used in pharmacy and medicine due to their properties such as mechanical strength, biocompatibility and non-toxic degradation products. Different compositions of copolymers and also their chain microstructure may have an effect on matrices degradation and thus on the drug release profile. In our study, we aimed at the influence of paclitaxel content on hydrolytic degradation process of terpolymeric matrices. Hydrolytic degradation of three kinds of matrices (with 5 or 10% of paclitaxel and drug free matrices) prepared from three types of terpolymers was performed in vitro at 37 degrees C in phosphate buffer solution (PBS, pH 7,4). The 1H and 13C NMR spectra of terpolymers were recorded. Thermal properties were monitored by differential scanning calorimetry (DSC). Molecular weight dispersity (D) and molecular weight were determined using gel permeation chromatography (GPC). The surface morphology was studied by means of the scanning electron microscopy (SEM). The most significant degradation was observed in case of poly(L-lactide-co-glycolide-co-epsilon-caprolactone) 44:32:24. Weight loss and water uptake were similar in the event of the same type of matrices obtained from the two poly(L-lactide-co-glycolide-co-TMC). Decelerated paclitaxel release in case of matrices with 51:26:23 molar ratio was noticed and it can be connected with higher content of carbonate units. Knowledge of paclitaxel influence on hydrolytic degradation process may contribute to receive valuable information about its release mechanisms from biodegradable terpolymers.
Tozaki Teruaki
2000-11-01
Full Text Available Abstract Background The autoimmune thyroid diseases (AITDs, comprising Graves' disease (GD and Hashimoto's thyroiditis (HT, appear to develop as a result of complex interactions between predisposing genes and environmental triggers. Susceptibility to AITDs is conferred by genes in the human leukocyte antigen (HLA and genes unlinked to HLA, including the CTLA-4 gene. Recently, an association to some estrogen receptor (ERα genotypes with breast cancer, hypertension, osteoporosis, generalized osteoarthritis, and some autoimmune diseases such as rheumatoid arthritis has been reported. We have analyzed a dinucleotide (TAn repeat polymorphism lying upstream of the human ERα gene in patients with AITDs and in normal subjects. Results Seventeen different alleles were found in 130 patients with GD, 93 patients with HT, and 190 control subjects. There was no significant difference in the distributions of ERα alleles between patients and controls. Conclusions The present results do not support an association between the ERα gene and AITD in the Japanese population.
Moye, W S; Amuro, N; Rao, J K; Zalkin, H
1985-07-15
The yeast GDH1 gene encodes NADP-dependent glutamate dehydrogenase. This gene was isolated by complementation of an Escherichia coli glutamate auxotroph. NADP-dependent glutamate dehydrogenase was overproduced 6-10-fold in Saccharomyces cerevisiae bearing GDH1 on a multicopy plasmid. The nucleotide sequence of the 1362-base pair coding region and 5' and 3' flanking sequences were determined. Transcription start sites were located by S1 nuclease mapping. Regulation of GDH1 was not maintained when the gene was present on a multicopy plasmid. Protein secondary structure predictions identified a region with potential to form the dinucleotide-binding domain. The amino acid sequences of the yeast and Neurospora crassa enzymes are 63% conserved. Unlike the N. crassa gene, yeast GDH1 has no introns.
Autosomal recessive chronic granulomatous disease caused by deletion at a dinucleotide repeat
Casimir, C.M.; Bu-Ghanim, H.N.; Rowe, P.; Segal, A.W. (University College London (England)); Rodaway, A.R.F.; Bentley, D.L. (Imperial Cancer Research Fund Lab., London (England))
1991-04-01
Chronic granulomatous disease (CGD) is a rare inherited condition rendering neutrophils incapable of killing invading pathogens. This condition is due to the failure of a multicomponent microbicidal oxidase that normally yields a low-midpoint-potential b cytochrome (cytochrome b{sub 245}). Although defects in the X chromosome-linked cytochrome account for the majority of CGD patients, as many as 30% of CGD cases are due to an autosomal recessive disease. Of these, {gt}90% have been shown to be defective in the synthesis of a 47-kDa cytosolic component of the oxidase. The authors demonstrate here in three unrelated cases of autosomal recessive CGD that the identical underlying molecular lesion is a dinucleotide deletion at a GTGT tandem repeat, corresponding to the acceptor site of the first intron - exon junction. Slippage of the DNA duplex at this site may contribute to the high frequency of defects in this gene.
Detecting horizontally transferred and essential genes based on dinucleotide relative abundance.
Baran, Robert H; Ko, Hanseok
2008-10-01
Various methods have been developed to detect horizontal gene transfer in bacteria, based on anomalous nucleotide composition, assuming that compositional features undergo amelioration in the host genome. Evolutionary theory predicts the inevitability of false positives when essential sequences are strongly conserved. Foreign genes could become more detectable on the basis of their higher order compositions if such features ameliorate more rapidly and uniformly than lower order features. This possibility is tested by comparing the heterogeneities of bacterial genomes with respect to strand-independent first- and second-order features, (i) G + C content and (ii) dinucleotide relative abundance, in 1 kb segments. Although statistical analysis confirms that (ii) is less inhomogeneous than (i) in all 12 species examined, extreme anomalies with respect to (ii) in the Escherichia coli K12 genome are typically co-located with essential genes.
Affinity of dinucleotide cap analogues for human decapping scavenger (hDcpS).
Darzynkiewicz, Zbigniew M; Bojarska, Elzbieta; Stepinski, Janusz; Jemielity, Jacek; Jankowska-Anyszka, Marzena; Davis, Richard E; Darzynkiewicz, Edward
2007-01-01
Eukaryotic cells utilize scavenger decapping enzymes to degrade cap structure following 3'-5' mRNA decay. Human DcpS recently has been described as a highly specific hydrolase (a member of the HIT family) that catalyses the cleavage of m(7)GpppG and short capped oligoribonucleotides. We have demonstrated here that cap-1 (m(7)GpppGm) is a preferred substrate among several investigated dinucleotide cap analogues m(7)Gp(n)N (n = 3-5, N is a purine or pyrimidine base) and m(7)GMP is always one of the reaction product. Cap analogues containing pyrimidine base instead of guanine or diphosphate chain are resistant to hydrolysis catalyzed by human scavenger. Contrary to the other enzymes of HIT family, hDcpS activity is not stimulated by Mg(2+).
Random matrices and Riemann hypothesis
Pierre, Christian
2011-01-01
The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of Langlands whose fundamental structures are shifted quantized conjugacy class representatives of bilinear algebraic semigroups.The considered symmetry behind this phenomenology is the differential bilinear Galois semigroup shifting the product,right by left,of automorphism semigroups of cofunctions and functions on compact transcendental quanta.
Sparse Matrices in Frame Theory
Lemvig, Jakob; Krahmer, Felix; Kutyniok, Gitta
2014-01-01
Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames...... yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices...
Cosmetic crossings and Seifert matrices
Balm, Cheryl; Kalfagianni, Efstratia; Powell, Mark
2011-01-01
We study cosmetic crossings in knots of genus one and obtain obstructions to such crossings in terms of knot invariants determined by Seifert matrices. In particular, we prove that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for twisted Whitehead doubles of non-cable knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 12 crossings.
Superalgebraic representation of Dirac matrices
Monakhov, V. V.
2016-01-01
We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Chakrabarti G
2015-03-01
Full Text Available Gaurab Chakrabarti,1,2,4 David E Gerber,3,4 David A Boothman1,2,4 1Department of Pharmacology, 2Department of Radiation Oncology, 3Division of Hematology and Oncology, 4Harold C Simmons Comprehensive Cancer Center, UT Southwestern Medical Center, Dallas, TX, USA Abstract: Nicotinamide adenine dinucleotide phosphate (NADPH biogenesis is an essential mechanism by which both normal and cancer cells maintain redox balance. While antitumor approaches to treat cancers through elevated reactive oxygen species (ROS are not new ideas, depleting specific NADPH-biogenesis pathways that control recovery and repair pathways are novel, viable approaches to enhance cancer therapy. However, to elicit efficacious therapies exploiting NADPH-biogenic pathways, it is crucial to understand and specifically define the roles of NADPH-biogenesis pathways used by cancer cells for survival or recovery from cell stress. It is equally important to select NADPH-biogenic pathways that are expendable or not utilized in normal tissue to avoid unwanted toxicity. Here, we address recent literature that demonstrates specific tumor-selective NADPH-biogenesis pathways that can be exploited using agents that target specific cancer cell pathways normally not utilized in normal cells. Defining NADPH-biogenesis profiles of specific cancer-types should enable novel strategies to exploit these therapeutic windows for increased efficacy against recalcitrant neoplastic disease, such as pancreatic cancers. Accomplishing the goal of using ROS as a weapon against cancer cells will also require agents, such as NQO1 bioactivatable drugs, that selectively induce elevated ROS levels in cancer cells, while normal cells are protected. Keywords: reactive oxygen species (ROS, NQO1-bioactivatable drugs, nicotinamide adenine dinucleotide phosphate (NADPH, glutathione (GSH, biogenic pathways, antioxidant
Searching for partial Hadamard matrices
Álvarez, Víctor; Frau, María-Dolores; Gudiel, Félix; Güemes, María-Belén; Martín, Elena; Osuna, Amparo
2012-01-01
Three algorithms looking for pretty large partial Hadamard matrices are described. Here "large" means that hopefully about a third of a Hadamard matrix (which is the best asymptotic result known so far, [dLa00]) is achieved. The first one performs some kind of local exhaustive search, and consequently is expensive from the time consuming point of view. The second one comes from the adaptation of the best genetic algorithm known so far searching for cliques in a graph, due to Singh and Gupta [SG06]. The last one consists in another heuristic search, which prioritizes the required processing time better than the final size of the partial Hadamard matrix to be obtained. In all cases, the key idea is characterizing the adjacency properties of vertices in a particular subgraph G_t of Ito's Hadamard Graph Delta (4t) [Ito85], since cliques of order m in G_t can be seen as (m+3)*4t partial Hadamard matrices.
A concise guide to complex Hadamard matrices
Tadej, W; Tadej, Wojciech; Zyczkowski, Karol
2005-01-01
Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for dimension N=2,...,16. In particular, we explicitly write down some families of complex Hadamard matrices for N=12,14 and 16, which we could not find in the existing literature.
Hou, C T; Patel, R; Laskin, A I; Barnabe, N; Marczak, I
1981-01-01
Nicotine adenine dinucleotide-linked primary alcohol dehydrogenase and a newly discovered secondary alcohol dehydrogenase coexist in most strains of methanol-grown yeasts. Alcohol dehydrogenases from methanol-grown yeasts oxidize (--)-2-butanol preferentially over its (+) enantiomorph. This is substantially different from alcohol dehydrogenases from bakers' yeast and horse liver.
Evers, Melchior E.; Titorenko, Vladimir; Harder, Wim; Klei, Ida van der; Veenhuis, Marten
1996-01-01
We have studied the role of flavin adenine dinucleotide (FAD) in the in vivo assembly of peroxisomal alcohol oxidase (AO) in the yeast Hansenula polymorpha. In previous studies, using a riboflavin (Rf) autotrophic mutant, an unequivocal judgement could not be made, since Rf-limitation led to a parti
Lambda-matrices and vibrating systems
Lancaster, Peter; Stark, M; Kahane, J P
1966-01-01
Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with late
Matrices with totally positive powers and their generalizations
Kushel, Olga Y.
2013-01-01
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of eventually positive matrices. We mainly focus on the spectral properties of such matrices. We also study eventually J-sign-symmetric matrices and matrices, whose powers are P-matrices.
A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES
Qi-Ming HE; Eldon GUNN
2003-01-01
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices.
YANG Lizhen; CHEN Kefei
2004-01-01
In this paper, we analyze the structure of the orders of matrices (mod n), and present the relation between the orders of matrices over finite fields and their Jordan normal forms. Then we generalize 2-dimensional Arnold transformation matrix to two types of n-dimensional Arnold transformation matrices: A-type Arnold transformation matrix and B-type transformation matrix, and analyze their orders and other properties based on our earlier results about the orders of matrices.
The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices.
Wang, Dafei; Zhang, Xumei
2017-01-01
The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced. Furthermore, based on the estimation for the rank, some sufficient conditions for nonsingular matrices are obtained.
Chitanda, Jackson M.; Zhang, Haixia; Pahl, Erica; Purves, Randy W.; El-Aneed, Anas
2016-10-01
The utility of novel functionalized nanodiamonds (NDs) as matrices for matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS) is described herein. MALDI-MS analysis of small organic compounds (MALDI for the analysis of small molecules, novel matrices were designed by covalently linking conventional matrices (or a lysine moiety) to detonated NDs. Four new functionalized NDs were evaluated for their ionization capabilities using five pharmaceuticals with varying molecular structures. Two ND matrices were able to ionize all tested pharmaceuticals in the negative ion mode, producing the deprotonated ions [M - H]-. Ion intensity for target analytes was generally strong with enhanced signal-to-noise ratios compared with conventional matrices. The negative ion mode is of great importance for biological samples as interference from endogenous compounds is inherently minimized in the negative ion mode. Since the molecular structures of the tested pharmaceuticals did not suggest that negative ion mode would be preferable, this result magnifies the importance of these findings. On the other hand, conventional matrices primarily facilitated the ionization as expected in the positive ion mode, producing either the protonated molecules [M + H]+ or cationic adducts (typically producing complex spectra with numerous adduct peaks). The data presented in this study suggests that these matrices may offer advantages for the analysis of low molecular weight pharmaceuticals/metabolites.
A note on "Block H-matrices and spectrum of block matrices"
LIU Jian-zhou; HUANG Ze-jun
2008-01-01
In this paper, we make further discussions and improvements on the results presented in the previously published work "Block H-matrices and spectrum of block matrices". Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.
A partial classification of primes in the positive matrices and in the doubly stochastic matrices
G. Picci; J.M. van den Hof; J.H. van Schuppen (Jan)
1995-01-01
textabstractThe algebraic structure of the set of square positive matrices is that of a semi-ring. The concept of a prime in the positive matrices has been introduced. A few examples of primes in the positive matrices are known but there is no general classification. In this paper a partial
Dynamical invariance for random matrices
Unterberger, Jeremie
2016-01-01
We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\\beta$. These dynamics describe for $\\beta=2$ the time evolution of the eigenvalues of $N\\times N$ random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\\"odinger-Virasoro algebra.
Quantum Racah matrices and 3-strand braids in irreps R with |R|=4
Mironov, A; Morozov, An; Sleptsov, A
2016-01-01
We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation R=[2,2] for quantum groups U_q(sl_N). Most of them have sizes 2, 3, and 4 and are fully described by the eigenvalue hypothesis. Of two 6x6 matrices, one is also described in this way, but the other one corresponds to the case of degenerate eigenvalues and is evaluated by the highest weight method. Together with the much harder calculation for R=[3,1] in arXiv:1605.02313 and with the new method to extract exclusive matrices S and \\bar S from the inclusive ones, this completes the story of Racah matrices for |R|\\leq 4 and allows one to calculate and investigate the corresponding colored HOMFLY polynomials for arbitrary 3-strand and arborescent knots.
Tensor Products of Random Unitary Matrices
Tkocz, Tomasz; Kus, Marek; Zeitouni, Ofer; Zyczkowski, Karol
2012-01-01
Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M=2, N become large or M become large and N=2.
Products of Generalized Stochastic Sarymsakov Matrices
Xia, Weiguo; Liu, Ji; Cao, Ming; Johansson, Karl; Basar, Tamer
2015-01-01
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the inﬁnitely long left-product of the elements from a compact subset converges to a rank-one matrix. In
Abel-Grassmann's Groupoids of Modulo Matrices
Muhammad Rashad
2016-01-01
Full Text Available The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z n of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n > 3. Various properties of these structures are explored like: (i Every AG-groupoid of matrices over Z n is transitively commutative AG-groupoid and is a cancellative AG-groupoid ifn is prime. (ii Every AG-groupoid of matrices over Z n of Type-II is a T3-AG-groupoid. (iii An AG-groupoid of matrices over Z n ; G nAG(t,u, is an AG-band, ift+ u=1(mod n.
Bounds of Spectral Radii of Weighted Trees
杨华中; 胡冠章; 洪渊
2003-01-01
Graphs for the design of networks or electronic circuits are usually weighted and the spectrum of weighted graphs are often analyzed to solve problems. This paper discusses the spectrum and the spectral radii of trees with edge weights. We derive expressions for the spectrum and the spectral radius of a weighted star, together with the boundary limits of the spectral radii for weighted paths and weighted trees. The analysis uses the theory of nonnegative matrices and applies the "moving edge" technique. Some simple examples of weighted paths and trees are presented to explain the results. Then, we propose some open problems in this area.
iSS-PseDNC: identifying splicing sites using pseudo dinucleotide composition.
Chen, Wei; Feng, Peng-Mian; Lin, Hao; Chou, Kuo-Chen
2014-01-01
In eukaryotic genes, exons are generally interrupted by introns. Accurately removing introns and joining exons together are essential processes in eukaryotic gene expression. With the avalanche of genome sequences generated in the postgenomic age, it is highly desired to develop automated methods for rapid and effective detection of splice sites that play important roles in gene structure annotation and even in RNA splicing. Although a series of computational methods were proposed for splice site identification, most of them neglected the intrinsic local structural properties. In the present study, a predictor called "iSS-PseDNC" was developed for identifying splice sites. In the new predictor, the sequences were formulated by a novel feature-vector called "pseudo dinucleotide composition" (PseDNC) into which six DNA local structural properties were incorporated. It was observed by the rigorous cross-validation tests on two benchmark datasets that the overall success rates achieved by iSS-PseDNC in identifying splice donor site and splice acceptor site were 85.45% and 87.73%, respectively. It is anticipated that iSS-PseDNC may become a useful tool for identifying splice sites and that the six DNA local structural properties described in this paper may provide novel insights for in-depth investigations into the mechanism of RNA splicing.
Decrease in nicotinamide adenine dinucleotide dehydrogenase is related to skin pigmentation.
Nakama, Mitsuo; Murakami, Yuhko; Tanaka, Hiroshi; Nakata, Satoru
2012-03-01
Skin pigmentation is caused by various physical and chemical factors. It might also be influenced by changes in the physiological function of skin with aging. Nicotinamide adenine dinucleotide (NADH) dehydrogenase is an enzyme related to the mitochondrial electron transport system and plays a key role in cellular energy production. It has been reported that the functional decrease in this system causes Parkinson's disease. Another study reports that the amount of NADH dehydrogenase in heart and skeletal muscle decreases with aging. A similar decrease in the skin would probably affect its physiological function. However, no reports have examined the age-related change in levels of NADH dehydrogenase in human skin. In this study, we investigated this change and its effect on skin pigmentation using cultured human epidermal keratinocytes. The mRNA expression of NDUFA1, NDUFB7, and NDUFS2, subunits of NADH dehydrogenase, and its activity were significantly decreased in late passage keratinocytes compared to early passage cells. Conversely, the mRNA expression of melanocyte-stimulating cytokines, interleukin-1 alpha and endothelin 1, was increased in late passage cells. On the other hand, the inhibition of NADH dehydrogenase upregulated the mRNA expression of melanocyte-stimulating cytokines. Moreover, the level of NDUFB7 mRNA was lower in pigmented than in nonpigmented regions of skin in vivo. These results suggest the decrease in NADH dehydrogenase with aging to be involved in skin pigmentation.
Leung, Kevin Ka Ki; Litchfield, David W; Shilton, Brian H
2012-01-01
Quinone reductase 2 (NQO2) is a broadly expressed enzyme implicated in responses to a number of compounds, including protein kinase inhibitors, resveratrol, and antimalarial drugs. NQO2 includes a flavin adenine dinucleotide (FAD) cofactor, but X-ray crystallographic analysis of human NQO2 expressed in Escherichia coli showed that electron density for the isoalloxazine ring of FAD was weak and there was no electron density for the adenine mononucleotide moiety. Reversed-phase high-performance liquid chromatography (HPLC) of the NQO2 preparation indicated that FAD was not present and only 38% of the protomers contained flavin mononucleotide (FMN), explaining the weak electron density for FAD in the crystallographic analysis. A method for purifying NQO2 and reconstituting with FAD such that the final content approaches 100% occupancy with FAD is presented here. The enzyme prepared in this manner has a high specific activity, and there is strong electron density for the FAD cofactor in the crystal structure. Analysis of NQO2 crystal structures present in the Protein Data Bank indicates that many may have sub-stoichiometric cofactor content and/or contain FMN rather than FAD. This method of purification and reconstitution will help to optimize structural and functional studies of NQO2 and possibly other flavoproteins.
Kim, Hyung-Jin; Oh, Gi-Su; Shen, AiHua; Lee, Su-Bin; Khadka, Dipendra; Pandit, Arpana; Shim, Hyeok; Yang, Sei-Hoon; Cho, Eun-Young; Song, Jeho; Kwak, Tae Hwan; Choe, Seong-Kyu; Park, Raekil; So, Hong-Seob
2015-08-01
Ototoxicity is an important issue in patients receiving cisplatin chemotherapy. Numerous studies have demonstrated that several mechanisms, including oxidative stress, DNA damage, and inflammatory responses, are closely associated with cisplatin-induced ototoxicity. Although much attention has been directed at identifying ways to protect the inner ear from cisplatin-induced damage, the precise underlying mechanisms have not yet been elucidated. The cofactor nicotinamide adenine dinucleotide (NAD(+)) has emerged as an important regulator of cellular energy metabolism and homeostasis. NAD(+) acts as a cofactor for various enzymes including sirtuins (SIRTs) and poly(ADP-ribose) polymerases (PARPs), and therefore, maintaining adequate NAD(+) levels has therapeutic benefits because of its effect on NAD(+)-dependent enzymes. Recent studies demonstrated that disturbance in intracellular NAD(+) levels is critically involved in cisplatin-induced cochlear damage associated with oxidative stress, DNA damage, and inflammatory responses. In this review, we describe the importance of NAD(+) in cisplatin-induced ototoxicity and discuss potential strategies for the prevention or treatment of cisplatin-induced ototoxicity with a particular focus on NAD(+)-dependent cellular pathways. Copyright © 2015 Elsevier B.V. All rights reserved.
Pan, Fu-shih; Chen, Stephen; Mintzer, Robert A.; Chen, Chin-Tu; Schumacker, Paul
1991-03-01
It is of fundamental importance for biological scientists to assess cellular energetics. Under aerobic conditions, the tricarboxylic acid cycle (TCA cycle) is coupled with the mitochondrial electron cascade pathway to provide the cell with energy. The nicotinamide adenine dinucleotide-conjugated pair (NAD and NADH) is the coenzyme in numerous important biomedical reactions which include several important dehydrogenase reactions in the TCA cycle. Based on Le Chatelier's principle, NADH will accumulate when this energy production mechanism is impaired. The relative amounts of NAD and NADH in a cell are defined as the redox state of the cell (Williamson et.al. 1967) which provides a valuable index of cellular energetics. The sum of the amounts of NAD and NADH in a cell may be assumed to be constant during a finite time; therefore, a reliable means of measuring the NADH concentration would provide us with a useful indicator of tissue viability. Traditionally, the quantities of NADH and NAD may be measured by chemical assay methods. We can avoid these tediois analyses by exploiting the significant difference between the ultraviolet absorption spectra of this redox pair. However, because of the opacity of biological samples and the interference of other biochemicals that also absorb ultraviolet radiation, measurement of NADH and NAD+ concentrations in vivo by absorption spectroscopy is not feasible.
Greenhouse, W V; Lehninger, A L
1977-11-01
Measurements of respiration, CO2 and lactate production, and changes in the levels of various key metabolites of the glycolytic sequence and tricarboxylic acid cycle were made on five lines of rodent ascites tumor cells (two strains of Ehrlich ascites tumor cells, Krebs II carcinoma, AS-30D carcinoma, and L1210 cells) incubated aerobically in the presence of uniformly labeled D-[14C]glucose. From these data, as well as earlier evidence demonstrating that the reduced nicotinamide adenine dinucleotide (NADH) shuttle in these cells requires a transaminase step and is thus identified as the malate-aspartate shuttle (W.V.V. Greenhouse and A.L. Lehninger, Cancer Res., 36: 1392-1396, 1976), metabolic flux diagrams were constructed for the five cell lines. These diagrams show the relative rates of glycolysis, the tricarboxylic acid cycle, electron transport, and the malate-aspartate shuttle in these tumors. Large amounts of cytosolic NADH were oxidized by the mitochondrial respiratory chain via the NADH shuttle, comprising anywhere from about 20 to 80% of the total flow of reducing equivalents to oxygen in these tumors. Calculations of the sources of energy for adenosine triphosphate synthesis indicated that on the average about one-third of the respiratory adenosine triphosphate is generated by electron flow originating from cytosolic NADH via the malate-aspartate shuttle.
Sasaki, Yo; Araki, Toshiyuki; Milbrandt, Jeffrey
2006-08-16
Axonal degeneration occurs in many neurodegenerative diseases and after traumatic injury and is a self-destructive program independent from programmed cell death. Previous studies demonstrated that overexpression of nicotinamide mononucleotide adenylyltransferase 1 (Nmnat1) or exogenous application of nicotinamide adenine dinucleotide (NAD) can protect axons of cultured dorsal root ganglion (DRG) neurons from degeneration caused by mechanical or neurotoxic injury. In mammalian cells, NAD can be synthesized from multiple precursors, including tryptophan, nicotinic acid, nicotinamide, and nicotinamide riboside (NmR), via multiple enzymatic steps. To determine whether other components of these NAD biosynthetic pathways are capable of delaying axonal degeneration, we overexpressed each of the enzymes involved in each pathway and/or exogenously administered their respective substrates in DRG cultures and assessed their capacity to protect axons after axotomy. Among the enzymes tested, Nmnat1 had the strongest protective effects, whereas nicotinamide phosphoribosyl transferase and nicotinic acid phosphoribosyl transferase showed moderate protective activity in the presence of their substrates. Strong axonal protection was also provided by Nmnat3, which is predominantly located in mitochondria, and an Nmnat1 mutant localized to the cytoplasm, indicating that the subcellular location of NAD production is not crucial for protective activity. In addition, we showed that exogenous application of the NAD precursors that are the substrates of these enzymes, including nicotinic acid mononucleotide, nicotinamide mononucleotide, and NmR, can also delay axonal degeneration. These results indicate that stimulation of NAD biosynthetic pathways via a variety of interventions may be useful in preventing or delaying axonal degeneration.
Eco-synthesis of graphene and its use in dihydronicotinamide adenine dinucleotide sensing.
Amouzadeh Tabrizi, Mahmoud; Jalilzadeh Azar, Somayeh; Nadali Varkani, Javad
2014-09-01
In this paper, we report a green and eco-friendly approach to synthesize reduced graphene oxide (rGO) via a mild hydrothermal process using malt as a reduced agent. The proposed method is based on the reduction of graphene oxide (GO) in malt solution by making use of the reducing capability of phenolic compounds contained in malt solution. The obtained rGO was characterized by atomic force microscopy (AFM), ultraviolet-visible (UV-vis) absorption spectroscopy, X-ray diffraction spectroscopy (XRD), Raman spectroscopy, Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Electrochemical impedance spectroscopy analysis revealed that the charge transfer resistance of rGO modified glassy carbon (GC) electrode was much lower than that of the GC electrode. The electrochemical behavior of dihydronicotinamide adenine dinucleotide (NADH) on rGO modified GC electrode was investigated by cyclic voltammetry and amperometry. Electrochemical experiments indicated that rGO/GC electrode exhibited excellent electrocatalytic activity toward the NADH, which can be attributed to excellent electrical conductivity and high specific surface area of the rGO composite. The resulting biosensor showed highly sensitive amperometric response to NADH with a low detection limit (0.33μM). Copyright © 2014 Elsevier Inc. All rights reserved.
On the origin of multiexponential fluorescence decays from 2-aminopurine-labeled dinucleotides.
Remington, Jacob M; Philip, Abbey M; Hariharan, Mahesh; Kohler, Bern
2016-10-21
The fluorescent probe 2-aminopurine (2Ap) has been used for decades to study local conformational fluctuations in DNA. Steady-state and time-resolved measurements of 2Ap fluorescence have been used to predict specific conformational states through suitable modeling of the quenching of the fluorescence of a 2Ap residue incorporated site-specifically into a DNA strand. The success of this approach has been limited by a lack of understanding of the precise factors responsible for the complex, multiexponential decays observed experimentally. In this study, dinucleotides composed of 2Ap and adenine were studied by the time-correlated single-photon counting technique to investigate the causes of heterogeneous emission kinetics. Contrary to previous reports, we argue that emission from 2Ap that is stacked with a neighboring base contributes negligibly to the emission signals recorded more than 50 ps after excitation, which are instead dominated by emission from unstacked 2Ap. We find that the decay kinetics can be modeled using a continuous lifetime distribution, which arises from the inherent distance dependence of electron transfer rates without the need to postulate a small number of discrete states with decay times derived from multiexponential fits. These results offer a new perspective on the quenching of 2Ap fluorescence and expand the information that can be obtained from experiments.
High resolution detection and analysis of CpG dinucleotides methylation using MBD-Seq technology.
Xun Lan
Full Text Available Methyl-CpG binding domain protein sequencing (MBD-seq is widely used to survey DNA methylation patterns. However, the optimal experimental parameters for MBD-seq remain unclear and the data analysis remains challenging. In this study, we generated high depth MBD-seq data in MCF-7 cell and developed a bi-asymmetric-Laplace model (BALM to perform data analysis. We found that optimal efficiency of MBD-seq experiments was achieved by sequencing ∼100 million unique mapped tags from a combination of 500 mM and 1000 mM salt concentration elution in MCF-7 cells. Clonal bisulfite sequencing results showed that the methylation status of each CpG dinucleotides in the tested regions was accurately detected with high resolution using the proposed model. These results demonstrated the combination of MBD-seq and BALM could serve as a useful tool to investigate DNA methylome due to its low cost, high specificity, efficiency and resolution.
Wang, Yiheng; Liu, Tong; Xu, Dong; Shi, Huidong; Zhang, Chaoyang; Mo, Yin-Yuan; Wang, Zheng
2016-01-22
The hypo- or hyper-methylation of the human genome is one of the epigenetic features of leukemia. However, experimental approaches have only determined the methylation state of a small portion of the human genome. We developed deep learning based (stacked denoising autoencoders, or SdAs) software named "DeepMethyl" to predict the methylation state of DNA CpG dinucleotides using features inferred from three-dimensional genome topology (based on Hi-C) and DNA sequence patterns. We used the experimental data from immortalised myelogenous leukemia (K562) and healthy lymphoblastoid (GM12878) cell lines to train the learning models and assess prediction performance. We have tested various SdA architectures with different configurations of hidden layer(s) and amount of pre-training data and compared the performance of deep networks relative to support vector machines (SVMs). Using the methylation states of sequentially neighboring regions as one of the learning features, an SdA achieved a blind test accuracy of 89.7% for GM12878 and 88.6% for K562. When the methylation states of sequentially neighboring regions are unknown, the accuracies are 84.82% for GM12878 and 72.01% for K562. We also analyzed the contribution of genome topological features inferred from Hi-C. DeepMethyl can be accessed at http://dna.cs.usm.edu/deepmethyl/.
Interaction of flavin adenine dinucleotide (FAD) with a glassy carbon electrode surface.
Wei, Haizhen; Omanovic, Sasha
2008-08-01
The interaction of flavin adenine dinucleotide (FAD) with a glassy carbon electrode (GCE) surface was investigated in terms of the FAD adsorption thermodynamics and kinetics, the subsequent electroreduction mechanism, and the corresponding electron-transfer rate. The kinetics of FAD electroreduction at the GCE was found to be an adsorption-controlled process. A set of electroreduction kinetic parameters was calculated: the true number of electrons involved in the FAD reduction, n=1.76, the apparent transfer coefficient, alpha(app)=0.41, and the apparent heterogeneous electron-transfer rate constant, k(app)=1.4 s(-1). The deviation of the number of exchanged electrons from the theoretical value for the complete reduction of FAD to FADH(2) (n=2) indicates that a small portion of FAD goes to a semiquinone state during the redox process. The FAD adsorption was well described by the Langmuir adsorption isotherm. The large negative apparent Gibbs energy of adsorption (DeltaG(ads)=-39.7 +/-0.4 kJ mol(-1)) indicated a highly spontaneous and strong adsorption of FAD on the GCE. The energetics of the adsorption process was found to be independent of the electrode surface charge in the electrochemical double-layer region. The kinetics of FAD adsorption was modeled using a pseudo-first-order kinetic model.
Yoshimoto, Makoto; Yamashita, Takayuki; Kinoshita, Satoshi
2011-07-10
The thermal stability of formaldehyde dehydrogenase (FaDH) from Pseudomonas sp. was examined and controlled by encapsulation in liposomes with β-reduced nicotinamide adenine dinucleotide (NADH). The activity of 4.8 μg/mL free FaDH at pH 8.5 in catalyzing the oxidation of 50mM formaldehyde was highly dependent on temperature so that the activity at 60 °C was 27 times larger than that at 25 °C. Thermal stability of the FaDH activity was examined with and without liposomes composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). Rapid deactivation of free FaDH was observed at 60 °C because of its dissociation into two subunits. The rate of dissociative deactivation of POPC liposome-encapsulated FaDH was smaller than that of the free enzyme. The liposomal FaDH was however progressively deactivated for the incubation period of 60 min eventually leading to complete loss of its activity. The free FaDH and NADH molecules were revealed to form the thermostable binary complex. The thermal stability of POPC liposome-encapsulated FaDH and NADH system was significantly higher than the liposomal enzyme without cofactor. The above results clearly show that NADH is a key molecule that controls the activity and stability of FaDH in liposomes at high temperatures.
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On Decompositions of Matrices over Distributive Lattices
Yizhi Chen
2014-01-01
Full Text Available Let L be a distributive lattice and Mn,q (L(Mn(L, resp. the semigroup (semiring, resp. of n × q (n × n, resp. matrices over L. In this paper, we show that if there is a subdirect embedding from distributive lattice L to the direct product ∏i=1mLi of distributive lattices L1,L2, …,Lm, then there will be a corresponding subdirect embedding from the matrix semigroup Mn,q(L (semiring Mn(L, resp. to semigroup ∏i=1mMn,q(Li (semiring ∏i=1mMn(Li, resp.. Further, it is proved that a matrix over a distributive lattice can be decomposed into the sum of matrices over some of its special subchains. This generalizes and extends the decomposition theorems of matrices over finite distributive lattices, chain semirings, fuzzy semirings, and so forth. Finally, as some applications, we present a method to calculate the indices and periods of the matrices over a distributive lattice and characterize the structures of idempotent and nilpotent matrices over it. We translate the characterizations of idempotent and nilpotent matrices over a distributive lattice into the corresponding ones of the binary Boolean cases, which also generalize the corresponding structures of idempotent and nilpotent matrices over general Boolean algebras, chain semirings, fuzzy semirings, and so forth.
Compressed Adjacency Matrices: Untangling Gene Regulatory Networks.
Dinkla, K; Westenberg, M A; van Wijk, J J
2012-12-01
We present a novel technique-Compressed Adjacency Matrices-for visualizing gene regulatory networks. These directed networks have strong structural characteristics: out-degrees with a scale-free distribution, in-degrees bound by a low maximum, and few and small cycles. Standard visualization techniques, such as node-link diagrams and adjacency matrices, are impeded by these network characteristics. The scale-free distribution of out-degrees causes a high number of intersecting edges in node-link diagrams. Adjacency matrices become space-inefficient due to the low in-degrees and the resulting sparse network. Compressed adjacency matrices, however, exploit these structural characteristics. By cutting open and rearranging an adjacency matrix, we achieve a compact and neatly-arranged visualization. Compressed adjacency matrices allow for easy detection of subnetworks with a specific structure, so-called motifs, which provide important knowledge about gene regulatory networks to domain experts. We summarize motifs commonly referred to in the literature, and relate them to network analysis tasks common to the visualization domain. We show that a user can easily find the important motifs in compressed adjacency matrices, and that this is hard in standard adjacency matrix and node-link diagrams. We also demonstrate that interaction techniques for standard adjacency matrices can be used for our compressed variant. These techniques include rearrangement clustering, highlighting, and filtering.
McClatchey, Andrea I.; Trofatter, James; McKenna-Yasek, Diane; Raskind, Wendy; Bird, Thomas; Pericak-Vance, Margaret; Gilchrist, James; Arahata, Kiichi; Radosavljevic, Danica; Worthen, Hilary G.; Van den Bergh, Peter; Haines, Jonathan L.; Gusella, James F.; Brown, Robert H.
1992-01-01
Two polymorphic dinucleotide repeats–one (dGdA)n and one (dGdT)n –have been identified at the SCN4A locus, encoding the α-subunit of the adult skeletal muscle sodium channel. When typed using PCR, the dinucleotide repeats display 4 and 10 alleles, respectively, with a predicted heterozygosity of .81 for the combined haplotype. We have applied these polymorphisms to the investigation of hyperkalemic periodic paralysis and paramyotonia congenita, distinct neuromuscular disorders both of which are thought to involve mutation at SCN4A. Our data confirm the genetic linkage of both disorders with SCN4A. Haplotype analysis also indicates the strong likelihood of allelic heterogeneity in both disorders. ImagesFigure 1Figure 2 PMID:1315122
Tzedakis, Theodore, E-mail: tzedakis@chimie.ups-tlse.f [Laboratoire de Genie Chimique, UMR 5503, Universite Paul Sabatier, 31062 Toulouse cedex 04 (France); Cheikhou, Kane [Ecole Superieure Polytechnique de Dakar BP: 16263 Dakar-Fann (Senegal); Jerome, Roche; Karine, Groenen Serrano; Olivier, Reynes [Laboratoire de Genie Chimique, UMR 5503, Universite Paul Sabatier, 31062 Toulouse cedex 04 (France)
2010-02-28
The electrochemical reduction of flavin adenine dinucleotide (FAD) is studied in a classical electrochemical cell as well as in two types of microreactors: the first one is a one-channel reactor and the other one, a multichannel filter-press reactor. The ultimate goal is to use the reduced form of flavin (FADH{sub 2}), in the presence of formate dehydrogenase (FDH), in order to continuously regenerate the reduced form of nicotinamide adenine dinucleotide (NADH) for chiral syntheses. Various voltammetric and adsorption measurements were carried out for a better understanding of the redox behavior of the FAD as well as its adsorption on gold. Diffusivity and kinetic electrochemical parameters of FAD were determined.
Marina Arav
2009-01-01
Full Text Available Let H be an m×n real matrix and let Zi be the set of column indices of the zero entries of row i of H. Then the conditions |Zk∩(∪i=1k−1Zi|≤1 for all k (2≤k≤m are called the (row Zero Position Conditions (ZPCs. If H satisfies the ZPC, then H is said to be a (row ZPC matrix. If HT satisfies the ZPC, then H is said to be a column ZPC matrix. The real matrix H is said to have a zero cycle if H has a sequence of at least four zero entries of the form hi1j1,hi1j2,hi2j2,hi2j3,…,hikjk,hikj1 in which the consecutive entries alternatively share the same row or column index (but not both, and the last entry has one common index with the first entry. Several connections between the ZPC and the nonexistence of zero cycles are established. In particular, it is proved that a matrix H has no zero cycle if and only if there are permutation matrices P and Q such that PHQ is a row ZPC matrix and a column ZPC matrix.
Random Matrices and Lyapunov Coefficients Regularity
Gallavotti, Giovanni
2017-02-01
Analyticity and other properties of the largest or smallest Lyapunov exponent of a product of real matrices with a "cone property" are studied as functions of the matrices entries, as long as they vary without destroying the cone property. The result is applied to stability directions, Lyapunov coefficients and Lyapunov exponents of a class of products of random matrices and to dynamical systems. The results are not new and the method is the main point of this work: it is is based on the classical theory of the Mayer series in Statistical Mechanics of rarefied gases.
Statistical properties of random density matrices
Sommers, H J; Sommers, Hans-Juergen; Zyczkowski, Karol
2004-01-01
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analyzed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter--circle distribution characteristic of the Hilbert--Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.
Statistical properties of random density matrices
Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Essen, 45117 Essen (Germany); Zyczkowski, Karol [Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Cracow (Poland)
2004-09-03
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analysed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter-circle distribution characteristic of the Hilbert-Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.
Direct dialling of Haar random unitary matrices
Russell, Nicholas J.; Chakhmakhchyan, Levon; O’Brien, Jeremy L.; Laing, Anthony
2017-03-01
Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits.
A method for generating realistic correlation matrices
Garcia, Stephan Ramon
2011-01-01
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating normal data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating normal data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Finally, using our results with an existing clustering algorithm, we show that simulating correlation matrices can help assess statistical methodology.
The Antitriangular Factorization of Saddle Point Matrices
Pestana, J.
2014-01-01
Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.
Elie J. Diner
2013-05-01
Full Text Available The presence of foreign DNA in the cytosol of mammalian cells elicits a potent antiviral interferon response. Recently, cytosolic DNA was proposed to induce the synthesis of cyclic GMP-AMP (cGAMP upon binding to an enzyme called cGAMP synthase (cGAS. cGAMP activates an interferon response by binding to a downstream receptor called STING. Here, we identify natural variants of human STING (hSTING that are poorly responsive to cGAMP yet, unexpectedly, are normally responsive to DNA and cGAS signaling. We explain this paradox by demonstrating that the cGAS product is actually a noncanonical cyclic dinucleotide, cyclic [G(2′-5′pA(3′-5′p], which contains a single 2′-5′ phosphodiester bond. Cyclic [G(2′-5′pA(3′-5′p] potently activates diverse hSTING receptors and, therefore, may be a useful adjuvant or immunotherapeutic. Our results indicate that hSTING variants have evolved to distinguish conventional (3′-5′ cyclic dinucleotides, known to be produced mainly by bacteria, from the noncanonical cyclic dinucleotide produced by mammalian cGAS.
Drew, Janice E; Farquharson, Andrew J; Horgan, Graham W; Williams, Lynda M
2016-11-01
The sirtuin (SIRT)/nicotinamide adenine dinucleotide (NAD) system is implicated in development of type 2 diabetes (T2D) and diet-induced obesity, a major risk factor for T2D. Mechanistic links have not yet been defined. SIRT/NAD system gene expression and NAD/NADH levels were measured in liver, white adipose tissue (WAT) and skeletal muscle from mice fed either a low-fat diet or high-fat diet (HFD) for 3 days up to 16 weeks. An in-house custom-designed multiplex gene expression assay assessed all 7 mouse SIRTs (SIRT1-7) and 16 enzymes involved in conversion of tryptophan, niacin, nicotinamide riboside and metabolic precursors to NAD. Significantly altered transcription was correlated with body weight, fat mass, plasma lipids and hormones. Regulation of the SIRT/NAD system was associated with early (SIRT4, SIRT7, NAPRT1 and NMNAT2) and late phases (NMNAT3, NMRK2, ABCA1 and CD38) of glucose intolerance. TDO2 and NNMT were identified as markers of HFD consumption. Altered regulation of the SIRT/NAD system in response to HFD was prominent in liver compared with WAT or muscle. Multiple components of the SIRTs and NAD biosynthetic enzymes network respond to consumption of dietary fat. Novel molecular targets identified above could direct strategies for dietary/therapeutic interventions to limit metabolic dysfunction and development of T2D.
Helary, Christophe; Abed, Aicha; Mosser, Gervaise; Louedec, Liliane; Letourneur, Didier; Coradin, Thibaud; Giraud-Guille, Marie Madeleine; Meddahi-Pellé, Anne
2015-02-01
Cutaneous chronic wounds are characterized by an impaired wound healing which may lead to infection and amputation. When current treatments are not effective enough, the application of wound dressings is required. To date, no ideal biomaterial is available. In this study, highly dense collagen matrices have been evaluated as novel medicated wound dressings for the treatment of chronic wounds. For this purpose, the structure, mechanical properties, swelling ability and in vivo stability of matrices concentrated from 5 to 40 mg mL(-1) were tested. The matrix stiffness increased with the collagen concentration and was associated with the fibril density and thickness. Increased collagen concentration also enhanced the material resistance against accelerated digestion by collagenase. After subcutaneous implantation in rats, dense collagen matrices exhibited high stability without any degradation after 15 days. The absence of macrophages and neutrophils evidenced their biocompatibility. Subsequently, dense matrices at 40 mg mL(-1) were evaluated as drug delivery system for ampicillin release. More concentrated matrices exhibited the best swelling abilities and could absorb 20 times their dry weight in water, allowing for an efficient antibiotic loading from their dried form. They released efficient doses of antibiotics that inhibited the bacterial growth of Staphylococcus Aureus over 3 days. In parallel, they show no cytotoxicity towards human fibroblasts. These results show that dense collagen matrices are promising materials to develop medicated wound dressings for the treatment of chronic wounds.
Role of adenine in thymine-dimer repair by reduced flavin-adenine dinucleotide.
Li, Guifeng; Sichula, Vincent; Glusac, Ksenija D
2008-08-28
We present a study of excited-state behavior of reduced flavin cofactors using femtosecond optical transient absorption spectroscopy. The reduced flavin cofactors studied were in two protonation states: flavin-adenine dinucleotide (FADH2 and FADH-) and flavin-mononucleotide (FMNH2 and FMNH-). We find that FMNH- exhibits multiexponential decay dynamics due to the presence of two bent conformers of the isoalloxazine ring. FMNH2 exhibits an additional fast deactivation component that is assigned to an iminol tautomer. Reduced flavin cofactors also exhibit a long-lived component that is attributed to the semiquinone and the hydrated electron that are produced in photoinduced electron transfer to the solvent. The presence of adenine in FADH2 and FADH- further changes the excited-state dynamics due to intramolecular electron transfer from the isoalloxazine to the adenine moiety of cofactors. This electron transfer is more pronounced in FADH2 due to pi-stacking interactions between two moieties. We further studied cyclobutane thymine dimer (TT-dimer) repair via FADH- and FMNH- and found that the repair is much more efficient in the case of FADH-. These results suggest that the adenine moiety plays a significant role in the TT-dimer repair dynamics. Two possible explanations for the adenine mediation are presented: (i) a two-step electron transfer process, with the initial electron transfer occurring from flavin to adenine moiety of FADH-, followed by a second electron transfer from adenine to TT-dimer; (ii) the preconcentration of TT-dimer molecules around the flavin cofactor due to the hydrophobic nature of the adenine moiety.
THE ROWWISE CORRELATION BETWEEN 2 PROXIMITY MATRICES AND THE PARTIAL ROWWISE CORRELATION
de Vries, Han
1993-01-01
This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearma
THE ROWWISE CORRELATION BETWEEN 2 PROXIMITY MATRICES AND THE PARTIAL ROWWISE CORRELATION
de Vries, Han
This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson,
Synchronous correlation matrices and Connes’ embedding conjecture
Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, Texas 77843-3368 (United States); Paulsen, Vern, E-mail: vern@math.uh.edu [Department of Mathematics, University of Houston, Houston, Texas 77204 (United States)
2016-01-15
In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove that if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.
THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES
Wen Li; Jian-xin Chen
2006-01-01
In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
Sufficient Conditions of Nonsingular H-matrices
王广彬; 洪振杰; 高中喜
2004-01-01
From the concept of a diagonally dominant matrix, two sufficient conditions of nonsingular H-matrices were obtained in this paper. An example was given to show that these results improve the known results.
Optimizing the Evaluation of Finite Element Matrices
Kirby, Robert C; Logg, Anders; Scott, L Ridgway; 10.1137/040607824
2012-01-01
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space dimensions, we have developed a heuristic graph algorithm that searches for such redundancies and generates code for computing the local stiffness matrices. Up to cubics, we are able to build the stiffness matrix on any triangle in less than one multiply-add pair per entry. Up to sixth degree, we can do it in less than about two. Preliminary low-degree results for Poisson and Navier-Stokes operators in three dimensions are also promising.
Orthogonal Polynomials from Hermitian Matrices II
Odake, Satoru
2016-01-01
This is the second part of the project `unified theory of classical orthogonal polynomials of a discrete variable derived from the eigenvalue problems of hermitian matrices.' In a previous paper, orthogonal polynomials having Jackson integral measures were not included, since such measures cannot be obtained from single infinite dimensional hermitian matrices. Here we show that Jackson integral measures for the polynomials of the big $q$-Jacobi family are the consequence of the recovery of self-adjointness of the unbounded Jacobi matrices governing the difference equations of these polynomials. The recovery of self-adjointness is achieved in an extended $\\ell^2$ Hilbert space on which a direct sum of two unbounded Jacobi matrices acts as a Hamiltonian or a difference Schr\\"odinger operator for an infinite dimensional eigenvalue problem. The polynomial appearing in the upper/lower end of Jackson integral constitutes the eigenvector of each of the two unbounded Jacobi matrix of the direct sum. We also point out...
A Few Applications of Imprecise Matrices
Sahalad Borgoyary
2015-07-01
Full Text Available This article introduces generalized form of extension definition of the Fuzzy set and its complement in the sense of reference function namely in imprecise set and its complement. Discuss Partial presence of element, Membership value of an imprecise number in the normal and subnormal imprecise numbers. Further on the basis of reference function define usual matrix into imprecise form with new notation. And with the help of maximum and minimum operators, obtain some new matrices like reducing imprecise matrices, complement of reducing imprecise matrix etc. Along with discuss some of the classical matrix properties which are hold good in the imprecise matrix also. Further bring out examples of application of the addition of imprecise matrices, subtraction of imprecise matrices etc. in the field of transportation problems.
Balanced random Toeplitz and Hankel Matrices
Basak, Anirban
2010-01-01
Except the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist, share a common property--the number of times each random variable appears in the matrix is (more or less) same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is scaled by the square root of the number of times that entry appears in the matrix instead of the uniform scaling by $n^{-1/2}$. We show that the LSD of these balanced matrices exist and derive integral formulae for the moments of the limit distribution. Curiously, it is not clear if these moments define a unique distribution.
Boolean Inner product Spaces and Boolean Matrices
Gudder, Stan; Latremoliere, Frederic
2009-01-01
This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary Boolean matrices are studied. A dimension theorem for orthonormal bases of a Boolean space is proven. We characterize the invariant stochastic Boolean vectors for a Boolean stochastic matrix and show that they can be used to reduce a unitary m...
Generalized Inverses of Matrices over Rings
韩瑞珠; 陈建龙
1992-01-01
Let R be a ring,*be an involutory function of the set of all finite matrices over R. In this pa-per,necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse,(1,4)-inverse,or Morre-Penrose inverse,relative to *.Some results about generalized inverses of matrices over division rings are generalized and improved.
A Euclidean algorithm for integer matrices
Lauritzen, Niels; Thomsen, Jesper Funch
2015-01-01
We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers.......We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers....
Infinite Products of Random Isotropically Distributed Matrices
Il'yn, A S; Zybin, K P
2016-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
A Wegner estimate for Wigner matrices
Maltsev, Anna
2011-01-01
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of Wigner matrices. The Wegner estimate gives an upper bound for the probability to find an eigenvalue in an interval $I$, proportional to the size $|I|$ of the interval.
Matrices related to some Fock space operators
Krzysztof Rudol
2011-01-01
Full Text Available Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.
Linear algebra for skew-polynomial matrices
Abramov, Sergei; Bronstein, Manuel
2002-01-01
We describe an algorithm for transforming skew-polynomial matrices over an Ore domain in row-reduced form, and show that this algorithm can be used to perform the standard calculations of linear algebra on such matrices (ranks, kernels, linear dependences, inhomogeneous solving). The main application of our algorithm is to desingularize recurrences and to compute the rational solutions of a large class of linear functional systems. It also turns out to be efficient when applied to ordinary co...
Moment matrices, border bases and radical computation
Mourrain, B.; J. B. Lasserre; Laurent, Monique; Rostalski, P.; Trebuchet, Philippe
2013-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-denite programming. While the border basis algorithms of [17] are ecient and numerically stable for computing complex roots, algorithms based on moment matrices [12] allow the incorporation of additional polynomials, ...
Infinite Products of Random Isotropically Distributed Matrices
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2017-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD
N. A. Balonin
2014-05-01
Full Text Available Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets.; calculation methods for the quasi-orthogonal local maximum determinant Mersenne matrices are not studied enough sufficiently. The goal of this paper is to develop the theory of Mersenne and Hadamard matrices on the base of generalized Scarpis method research. Methods. Extreme solutions are found in general by minimization of maximum for absolute values of the elements of studied matrices followed by their subsequent classification according to the quantity of levels and their values depending on orders. Less universal but more effective methods are based on structural invariants of quasi-orthogonal matrices (Silvester, Paley, Scarpis methods, ets.. Results. Generalizations of Hadamard and Belevitch matrices as a family of quasi-orthogonal matrices of odd orders are observed; they include, in particular, two-level Mersenne matrices. Definitions of section and layer on the set of generalized matrices are proposed. Calculation algorithms for matrices of adjacent layers and sections by matrices of lower orders are described. Approximation examples of the Belevitch matrix structures up to 22-nd critical order by Mersenne matrix of the third order are given. New formulation of the modified Scarpis method to approximate Hadamard matrices of high orders by lower order Mersenne matrices is proposed. Williamson method is described by example of one modular level matrices approximation by matrices with a small number of levels. Practical relevance. The efficiency of developing direction for the band-pass filters creation is justified. Algorithms for Mersenne matrices design by Scarpis method are used in developing software of the research program complex. Mersenne filters are based on the suboptimal by
A Brief Historical Introduction to Matrices and Their Applications
Debnath, L.
2014-01-01
This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…
A Brief Historical Introduction to Matrices and Their Applications
Debnath, L.
2014-01-01
This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…
Representation-independent manipulations with Dirac matrices and spinors
2007-01-01
Dirac matrices, also known as gamma matrices, are defined only up to a similarity transformation. Usually, some explicit representation of these matrices is assumed in order to deal with them. In this article, we show how it is possible to proceed without any such assumption. Various important identities involving Dirac matrices and spinors have been derived without assuming any representation at any stage.
Condition number estimation of preconditioned matrices.
Kushida, Noriyuki
2015-01-01
The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Condition number estimation of preconditioned matrices.
Noriyuki Kushida
Full Text Available The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Bayesian Nonparametric Clustering for Positive Definite Matrices.
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2016-05-01
Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.
Using Elimination Theory to construct Rigid Matrices
Kumar, Abhinav; Patankar, Vijay M; N, Jayalal Sarma M
2009-01-01
The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r=Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an nxn matrix in this family are distinct primitive roots of unity of orders roughly exp(n^4 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination...
Mirror-Symmetric Matrices and Their Application
李国林; 冯正和
2002-01-01
The well-known centrosymmetric matrices correctly reflect mirror-symmetry with no component or only one component on the mirror plane. Mirror-symmetric matrices defined in this paper can represent mirror-symmetric structures with various components on the mirror plane. Some basic properties of mirror-symmetric matrices were studied and applied to interconnection analysis. A generalized odd/even-mode decomposition scheme was developed based on the mirror reflection relationship for mirror-symmetric multiconductor transmission lines (MTLs). The per-unit-length (PUL) impedance matrix Z and admittance matrix Y can be divided into odd-mode and even-mode PUL matrices. Thus the order of the MTL system is reduced from n to k and k+p, where p(≥0)is the conductor number on the mirror plane. The analysis of mirror-symmetric matrices is related to the theory of symmetric group, which is the most effective tool for the study of symmetry.
Shu, Chang; Yi, Guanghui; Watts, Tylan; Kao, C Cheng; Li, Pingwei
2012-06-24
STING (stimulator of interferon genes) is an innate immune sensor of cyclic dinucleotides that regulates the induction of type I interferons. STING's C-terminal domain forms a V-shaped dimer and binds a cyclic diguanylate monophosphate (c-di-GMP) at the dimer interface by both direct and solvent-mediated hydrogen bonds. Guanines of c-di-GMP stack against the phenolic rings of a conserved tyrosine, and mutations at the c-di-GMP binding surface reduce nucleotide binding and affect signaling.
Symmetries of the Kac-Peterson modular matrices of affine algebras
Gannon, T
1994-01-01
The characters \\chi_\\mu of nontwisted affine algebras at fixed level define in a natural way a representation R of the modular group SL_2(Z). The matrices in the image R(SL_2(Z)) are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of (A_{r_1}\\oplus\\cdots\\oplus A_{r_s})^{(1)}, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.
Geometry of 2×2 hermitian matrices
HUANG; Liping(黄礼平); WAN; Zhexian(万哲先)
2002-01-01
Let D be a division ring which possesses an involution a→ā. Assume that F = {a∈D|a=ā} is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D→F,hermitian matrices over D when n≥3 and now can be deleted. When D is a field, the fundamental theorem of 2×2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two.
INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES
无
2001-01-01
A sign pattern matrix is a matrixwhose entries are from the set {+ ,- ,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative fri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
Generalized Inverse Eigenvalue Problem for Centrohermitian Matrices
刘仲云; 谭艳祥; 田兆录
2004-01-01
In this paper we first consider the existence and the general form of solution to the following generalized inverse eigenvalue problem(GIEP) : given a set of n-dimension complex vectors { xj }jm = 1 and a set of complex numbers { λj} jm = 1, find two n × n centrohermitian matrices A, B such that { xj }jm = 1 and { λj }jm= 1 are the generalized eigenvectors and generalized eigenvalues of Ax = λBx, respectively. We then discuss the optimal approximation problem for the GIEP. More concretely, given two arbitrary matrices, A-, B- ∈Cn×n , we find two matrices A* and B* such that the matrix (A* ,B* ) is closest to (A- ,B-) in the Frobenius norm, where the matrix (A*, B* ) is the solution to the GIEP. We show that the expression of the solution of the optimal approximation is unique and derive the expression for it.
PRM: A database of planetary reflection matrices
Stam, D. M.; Batista, S. F. A.
2014-04-01
We present the PRM database with reflection matrices of various types of planets. With the matrices, users can calculate the total, and the linearly and circularly polarized fluxes of incident unpolarized light that is reflected by a planet for arbitrary illumination and viewing geometries. To allow for flexibility in these geometries, the database does not contain the elements of reflection matrices, but the coefficients of their Fourier series expansion. We describe how to sum these coefficients for given illumination and viewing geometries to obtain the local reflection matrix. The coefficients in the database can also be used to calculate flux and polarization signals of exoplanets, by integrating, for a given planetary phase angle, locally reflected fluxes across the visible part of the planetary disk. Algorithms for evaluating the summation for locally reflected fluxes, as applicable to spatially resolved observations of planets, and the subsequent integration for the disk-integrated fluxes, as applicable to spatially unresolved exoplanets are also in the database
On classification of dynamical r-matrices
Schiffmann, O
1997-01-01
Using recent results of P. Etingof and A. Varchenko on the Classical Dynamical Yang-Baxter equation, we reduce the classification of dynamical r-matrices on a commutative subalgebra l of a Lie algebra g to a purely algebraic problem when l admits a g^l-invariant complement, where g^l is the centralizer of l in g. Using this, we then classify all non skew-symmetric dynamical r-matrices when g is a simple Lie algebra and l a commutative subalgebra containing a regular semisimple element. This partially answers an open problem in [EV] q-alg/9703040, and generalizes the Belavin-Drinfled classification of constant r-matrices. This classification is similar and in some sense simpler than the Belavin-Drinfled classification.
Octonion generalization of Pauli and Dirac matrices
Chanyal, B. C.
2015-10-01
Starting with octonion algebra and its 4 × 4 matrix representation, we have made an attempt to write the extension of Pauli's matrices in terms of division algebra (octonion). The octonion generalization of Pauli's matrices shows the counterpart of Pauli's spin and isospin matrices. In this paper, we also have obtained the relationship between Clifford algebras and the division algebras, i.e. a relation between octonion basis elements with Dirac (gamma), Weyl and Majorana representations. The division algebra structure leads to nice representations of the corresponding Clifford algebras. We have made an attempt to investigate the octonion formulation of Dirac wave equations, conserved current and weak isospin in simple, compact, consistent and manifestly covariant manner.
A Multipath Connection Model for Traffic Matrices
Mr. M. V. Prabhakaran
2015-02-01
Full Text Available Peer-to-Peer (P2P applications have witnessed an increasing popularity in recent years, which brings new challenges to network management and traffic engineering (TE. As basic input information, P2P traffic matrices are of significant importance for TE. Because of the excessively high cost of direct measurement. In this paper,A multipath connection model for traffic matrices in operational networks. Media files can share the peer to peer, the localization ratio of peer to peer traffic. This evaluates its performance using traffic traces collected from both the real peer to peer video-on-demand and file-sharing applications. The estimation of the general traffic matrices (TM then used for sending the media file without traffic. Share the media file, source to destination traffic is not occur. So it give high performance and short time process.
Block TERM factorization of block matrices
SHE Yiyuan; HAO Pengwei
2004-01-01
Reversible integer mapping (or integer transform) is a useful way to realize Iossless coding, and this technique has been used for multi-component image compression in the new international image compression standard JPEG 2000. For any nonsingular linear transform of finite dimension, its integer transform can be implemented by factorizing the transform matrix into 3 triangular elementary reversible matrices (TERMs) or a series of single-row elementary reversible matrices (SERMs). To speed up and parallelize integer transforms, we study block TERM and SERM factorizations in this paper. First, to guarantee flexible scaling manners, the classical determinant (det) is generalized to a matrix function, DET, which is shown to have many important properties analogous to those of det. Then based on DET, a generic block TERM factorization,BLUS, is presented for any nonsingular block matrix. Our conclusions can cover the early optimal point factorizations and provide an efficient way to implement integer transforms for large matrices.
Advanced incomplete factorization algorithms for Stiltijes matrices
Il`in, V.P. [Siberian Division RAS, Novosibirsk (Russian Federation)
1996-12-31
The modern numerical methods for solving the linear algebraic systems Au = f with high order sparse matrices A, which arise in grid approximations of multidimensional boundary value problems, are based mainly on accelerated iterative processes with easily invertible preconditioning matrices presented in the form of approximate (incomplete) factorization of the original matrix A. We consider some recent algorithmic approaches, theoretical foundations, experimental data and open questions for incomplete factorization of Stiltijes matrices which are {open_quotes}the best{close_quotes} ones in the sense that they have the most advanced results. Special attention is given to solving the elliptic differential equations with strongly variable coefficients, singular perturbated diffusion-convection and parabolic equations.
Infinite matrices and their recent applications
Shivakumar, P N; Zhang, Yang
2016-01-01
This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such ...
Recursive Estimation of the Stein Center of SPD Matrices & its Applications.
Salehian, Hesamoddin; Cheng, Guang; Vemuri, Baba C; Ho, Jeffrey
2013-12-01
Symmetric positive-definite (SPD) matrices are ubiquitous in Computer Vision, Machine Learning and Medical Image Analysis. Finding the center/average of a population of such matrices is a common theme in many algorithms such as clustering, segmentation, principal geodesic analysis, etc. The center of a population of such matrices can be defined using a variety of distance/divergence measures as the minimizer of the sum of squared distances/divergences from the unknown center to the members of the population. It is well known that the computation of the Karcher mean for the space of SPD matrices which is a negatively-curved Riemannian manifold is computationally expensive. Recently, the LogDet divergence-based center was shown to be a computationally attractive alternative. However, the LogDet-based mean of more than two matrices can not be computed in closed form, which makes it computationally less attractive for large populations. In this paper we present a novel recursive estimator for center based on the Stein distance - which is the square root of the LogDet divergence - that is significantly faster than the batch mode computation of this center. The key theoretical contribution is a closed-form solution for the weighted Stein center of two SPD matrices, which is used in the recursive computation of the Stein center for a population of SPD matrices. Additionally, we show experimental evidence of the convergence of our recursive Stein center estimator to the batch mode Stein center. We present applications of our recursive estimator to K-means clustering and image indexing depicting significant time gains over corresponding algorithms that use the batch mode computations. For the latter application, we develop novel hashing functions using the Stein distance and apply it to publicly available data sets, and experimental results have shown favorable comparisons to other competing methods.
... Health Information Weight Management English English Español Weight Management Obesity is a chronic condition that affects more ... Liver (NASH) Heart Disease & Stroke Sleep Apnea Weight Management Topics About Food Portions Bariatric Surgery for Severe ...
Edge fluctuations of eigenvalues of Wigner matrices
Döring, Hanna
2012-01-01
We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval close to the edge of the spectrum. Moreover we prove a MDP for the $i$th largest eigenvalue close to the edge. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem. Possible extensions to other random matrix ensembles are commented.
Forecasting Covariance Matrices: A Mixed Frequency Approach
Halbleib, Roxana; Voev, Valeri
This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...... matrix dynamics. Our empirical results show that the new mixing approach provides superior forecasts compared to multivariate volatility specifications using single sources of information....
Almost Hadamard matrices: general theory and examples
Banica, Teodor; Zyczkowski, Karol
2012-01-01
We develop a general theory of "almost Hadamard matrices". These are by definition the matrices $H\\in M_N(\\mathbb R)$ having the property that $U=H/\\sqrt{N}$ is orthogonal, and is a local maximum of the 1-norm on O(N). Our study includes a detailed discussion of the circulant case ($H_{ij}=\\gamma_{j-i}$) and of the two-entry case ($H_{ij}\\in\\{x,y\\}$), with the construction of several families of examples, and some 1-norm computations.
Extremal spacings of random unitary matrices
Smaczynski, Marek; Kus, Marek; Zyczkowski, Karol
2012-01-01
Extremal spacings between unimodular eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Probability distributions for the minimal spacing for various ensembles are derived for N=4. We show that for large matrices the average minimal spacing s_min of a random unitary matrix behaves as N^(-1/(1+B)) for B equal to 0,1 and 2 for circular Poisson, orthogonal and unitary ensembles, respectively. For these ensembles also asymptotic probability distributions P(s_min) are obtained and the statistics of the largest spacing s_max are investigated.
Age differences on Raven's Coloured Progressive Matrices.
Panek, P E; Stoner, S B
1980-06-01
Raven's Coloured Progressive Matrices was administered to 150 subjects (75 males, 75 females) ranging in age from 20 to 86 yr. Subjects were placed into one of three age groups: adult (M age = 27.04 yr.), middle-age (M age = 53.36 yr.), old (M age = 73.78 yr.), with 25 males and 25 females in each age group. Significant differences between age groups on the matrices were obtained after partialing out the effects of educational level, while sex of subject was not significant.
Super Special Codes using Super Matrices
Kandasamy, W B Vasantha; Ilanthenral, K
2010-01-01
The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes. This book has four chapters. In chapter one basic properties of codes and super matrices are given. A new type of super special vector space is constructed in chapter two of this book. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced in chapter three. Applications of these codes are given in the final chapter.
Martin del Campo, Julia S. [Departamento de Fisica Aplicada, Centro de Investigacion y de Estudios Avanzados - Unidad Merida, Carretera antigua a Progreso Km. 6, A.P. 73 Cordemex, 97310, Merida, Yucatan (Mexico); Patino, Rodrigo, E-mail: rtarkus@mda.cinvestav.mx [Departamento de Fisica Aplicada, Centro de Investigacion y de Estudios Avanzados - Unidad Merida, Carretera antigua a Progreso Km. 6, A.P. 73 Cordemex, 97310, Merida, Yucatan (Mexico)
2011-04-20
Research highlights: {yields} The reaction catalyzed by one enzyme of the pentose phosphate pathway was studied. {yields} A spectrophotometric method is proposed for kinetic and thermodynamic analysis. {yields} The pH and the temperature influences are reported on physical chemical properties. {yields} Relative concentrations of substrates are also important in the catalytic process. - Abstract: The enzyme glucose-6-phosphate dehydrogenase (G6PD, EC 1.1.1.49) from Leuconostoc mesenteroides has a dual coenzyme specificity with oxidized nicotinamide adenine dinucleotide (NAD{sub ox}) and oxidized nicotinamide adenine dinucleotide phosphate as electron acceptors. The G6PD coenzyme selection is determined by the metabolic cellular prevailing conditions. In this study a kinetic and thermodynamic analysis is presented for the reaction catalyzed by G6PD from L. mesenteroides with NAD{sub ox} as coenzyme in phosphate buffer. For this work, an in situ spectrophotometric technique was employed based on the detection of one product of the reaction. Substrate and coenzyme concentrations as well as temperature and pH effects were evaluated. The apparent equilibrium constant, the Michaelis constant, and the turnover number were determined as a function of each experimental condition. The standard transformed Gibbs energy of reaction was determined from equilibrium constants at different initial conditions. For the product 6-phospho-D-glucono-1,5-lactone, a value of the standard Gibbs energy of formation is proposed, {Delta}{sub f}G{sup o} = -1784 {+-} 5 kJ mol{sup -1}.
Determinación y propiedades de H-matrices
SCOTT GUILLEARD, JOSÉ ANTONIO
2015-01-01
[EN] The essential topic of this memory is the study of H-matrices as they were introduced by Ostrowski and hereinafter extended and developed by different authors. In this study three slopes are outlined: 1) the iterative or automatic determination of H-matrices, 2) the properties inherent in the H-matrices and 3) the matrices related to H-matrices. H-matrices acquire every time major relevancy due to the fact that they arise in numerous applications so much in Mathematics,...
Universal portfolios generated by Toeplitz matrices
Tan, Choon Peng; Chu, Sin Yen; Pan, Wei Yeing
2014-06-01
Performance of universal portfolios generated by Toeplitz matrices is studied in this paper. The general structure of the companion matrix of the generating Toeplitz matrix is determined. Empirical performance of the threeband and nine-band Toeplitz universal portfolios on real stock data is presented. Pseudo Toeplitz universal portfolios are studied with promising empirical achievement of wealth demonstrated.
Parametrizations of Positive Matrices With Applications
Tseng, M C; Ramakrishna, V; Zhou, Hong
2006-01-01
This paper reviews some characterizations of positive matrices and discusses which lead to useful parametrizations. It is argued that one of them, which we dub the Schur-Constantinescu parametrization is particularly useful. Two new applications of it are given. One shows all block-Toeplitz states are PPT. The other application is to relaxation rates.
Generation Speed in Raven's Progressive Matrices Test.
Verguts, Tom; De Boeck, Paul; Maris, Eric
1999-01-01
Studied the role of response fluency on results of the Raven's Advanced Progressive Matrices (APM) Test by comparing scores on a test of generation speed (speed of generating rules that govern the items) with APM test performance for 127 Belgian undergraduates. Discusses the importance of generation speed in intelligence. (SLD)
Deconvolution and Regularization with Toeplitz Matrices
Hansen, Per Christian
2002-01-01
of these discretized deconvolution problems, with emphasis on methods that take the special structure of the matrix into account. Wherever possible, analogies to classical DFT-based deconvolution problems are drawn. Among other things, we present direct methods for regularization with Toeplitz matrices, and we show...
Extremal norms of graphs and matrices
Nikiforov, Vladimir
2010-01-01
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. In this paper some of this research is extended to more general matrix norms, like the Schatten p-norms and the Ky Fan k-norms. Whenever possible the results are given both for graphs and general matrices.
Numerical Methods for Structured Matrices and Applications
Bini, Dario A; Olshevsky, Vadim; Tyrtsyhnikov, Eugene; van Barel, Marc
2010-01-01
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.
Generation speed in Raven's Progressive Matrices Test
Verguts, T.; Boeck, P. De; Maris, E.G.G.
1999-01-01
In this paper, we investigate the role of response fluency on a well-known intelligence test, Raven's (1962) Advanced Progressive Matrices (APM) test. Critical in solving this test is finding rules that govern the items. Response fluency is conceptualized as generation speed or the speed at which a
Positivity of Matrices with Generalized Matrix Functions
Fuzhen ZHANG
2012-01-01
Using an elementary fact on matrices we show by a unified approach the positivity of a partitioned positive semidefinite matrix with each square block replaced by a compound matrix,an elementary symmetric function or a generalized matrix function.In addition,we present a refined version of the Thompson determinant compression theorem.
Robust stability of interval parameter matrices
无
2000-01-01
This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrix inequality and Hamilton matrix, several test conditions with parameter perturbation bounds are obtained.
Constructing random matrices to represent real ecosystems.
James, Alex; Plank, Michael J; Rossberg, Axel G; Beecham, Jonathan; Emmerson, Mark; Pitchford, Jonathan W
2015-05-01
Models of complex systems with n components typically have order n(2) parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species' trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.
Spectral averaging techniques for Jacobi matrices
del Rio, Rafael; Schulz-Baldes, Hermann
2008-01-01
Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Correspondence Analysis of Archeological Abundance Matrices
de Leeuw, Jan
2007-01-01
In this chapter we discuss the Correspondence Analysis (CA) techniques used in other chapters of this book. CA is presented as a multivariate exploratory technique, as a proximity analysis technique based on Benzecri distances, as a technique to decompose the total chi-square of frequency matrices, and as a least squares method to ﬁt association or ordination models.
Moment matrices, border bases and radical computation
Mourrain, B.; Lasserre, J.B.; Laurent, M.; Rostalski, P.; Trebuchet, P.
2011-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-denite programming.
Moment matrices, border bases and radical computation
Mourrain, B.; Lasserre, J.B.; Laurent, M.; Rostalski, P.; Trebuchet, P.
2013-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-denite programming.
Spectral properties of random triangular matrices
Basu, Riddhipratim; Ganguly, Shirshendu; Hazra, Rajat Subhra
2011-01-01
We provide a relatively elementary proof of the existence of the limiting spectral distribution (LSD) of symmetric triangular patterned matrices and also show their joint convergence. We also derive the expressions for the moments of the LSD of the symmetric triangular Wigner matrix using properties of Catalan words.
Affine processes on positive semidefinite matrices
Cuchiero, Christa; Mayerhofer, Eberhard; Teichmann, Josef
2009-01-01
This paper provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. These matrix-valued affine processes have arisen from a large and growing range of useful applications in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.
Malware Analysis Using Visualized Image Matrices
KyoungSoo Han
2014-01-01
Full Text Available This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.
An efficient algorithm for weighted PCA
Krijnen, W.P.; Kiers, H.A.L.
1995-01-01
The method for analyzing three-way data where one of the three components matrices in TUCKALS3 is chosen to have one column is called Replicated PCA. The corresponding algorithm is relatively inefficient. This is shown by offering an alternative algorithm called Weighted PCA. Specifically it is prov
Ackerman, Margareta; Branzei, Simina; Loker, David
2011-01-01
In this paper we investigate clustering in the weighted setting, in which every data point is assigned a real valued weight. We conduct a theoretical analysis on the influence of weighted data on standard clustering algorithms in each of the partitional and hierarchical settings, characterising the precise conditions under which such algorithms react to weights, and classifying clustering methods into three broad categories: weight-responsive, weight-considering, and weight-robust. Our analysis raises several interesting questions and can be directly mapped to the classical unweighted setting.
Karoui, Noureddine El
2009-01-01
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the asymptotic properties of correlation and covariance matrices, in the setting where $p/n\\to\\rho\\in(0,\\infty),$ for general population covariance. We show that, for a large class of models studied in random matrix theory, spectral properties of large-dimensional correlation matrices are similar to those of large-dimensional covarance matrices. We also derive a Mar\\u{c}enko--Pastur-type system of equations for the limiting spectral distribution of covariance matrices computed from data with elliptical distributions and generalizations of this family. The motivation for this study comes partly from the possible relevance of such distributional assumptions to problems in econometrics and portfolio optimization, as well as robustness questions for certain classical random matrix result...
The primitive matrices of sandwich semigroups of generalized circulant Boolean matrices
LIU Jian-ping; CHEN Jin-song
2013-01-01
Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and GC (Jn) the set of all primitive matrices in Gn(C). In this paper, some necessary and suﬃ cient conditions for A in the semigroup Gn(C) to be primitive are given. We also show that GC (Jn) is a subsemigroup of Gn(C).
Detailed assessment of homology detection using different substitution matrices
LI Jing; WANG Wei
2006-01-01
Homology detection plays a key role in bioinformatics, whereas substitution matrix is one of the most important components in homology detection. Thus, besides the improvement of alignment algorithms, another effective way to enhance the accuracy of homology detection is to use proper substitution matrices or even construct new matrices.A study on the features of various matrices and on the comparison of the performances between different matrices in homology detection enable us to choose the most proper or optimal matrix for some specific applications. In this paper, by taking BLOSUM matrices as an example, some detailed features of matrices in homology detection are studied by calculating the distributions of numbers of recognized proteins over different sequence identities and sequence lengths. Our results clearly showed that different matrices have different preferences and abilities to the recognition of remote homologous proteins. Furthermore, detailed features of the various matrices can be used to improve the accuracy of homology detection.
The complex Laguerre symplectic ensemble of non-Hermitian matrices
Akemann, G. [Department of Mathematical Sciences, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom)]. E-mail: gernot.akemann@brunel.ac.uk
2005-12-12
We solve the complex extension of the chiral Gaussian symplectic ensemble, defined as a Gaussian two-matrix model of chiral non-Hermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex eigenvalue representation of this ensemble is given for general weight functions. All k-point correlation functions of complex eigenvalues are given in terms of the corresponding skew orthogonal polynomials in the complex plane for finite-N, where N is the matrix size or number of eigenvalues, respectively. We also allow for an arbitrary number of complex conjugate pairs of characteristic polynomials in the weight function, corresponding to massive quark flavours in applications to field theory. Explicit expressions are given in the large-N limit at both weak and strong non-Hermiticity for the weight of the Gaussian two-matrix model. This model can be mapped to the complex Dirac operator spectrum with non-vanishing chemical potential. It belongs to the symmetry class of either the adjoint representation or two colours in the fundamental representation using staggered lattice fermions.
Rathore, Anurag; Carpenter, Michael A; Demir, Özlem; Ikeda, Terumasa; Li, Ming; Shaban, Nadine; Law, Emily K.; Anokhin, Dmitry; Brown, William L.; Amaro, Rommie E.; Harris, Reuben S.
2013-01-01
APOBEC3A and APOBEC3G are DNA cytosine deaminases with biological functions in foreign DNA and retrovirus restriction, respectively. APOBEC3A has an intrinsic preference for cytosine preceded by thymine (5′-TC) in single-stranded DNA substrates, whereas APOBEC3G prefers the target cytosine to be preceded by another cytosine (5′-CC). To determine the amino acids responsible for these strong dinucleotide preferences, we analyzed a series of chimeras in which putative DNA binding loop regions of APOBEC3G were replaced with the corresponding regions from APOBEC3A. Loop 3 replacement enhanced APOBEC3G catalytic activity but did not alter its intrinsic 5′-CC dinucleotide substrate preference. Loop 7 replacement caused APOBEC3G to become APOBEC3A-like and strongly prefer 5′-TC substrates. Simultaneous loop 3/7 replacement resulted in a hyperactive APOBEC3G variant that also preferred 5′-TC dinucleotides. Single amino acid exchanges revealed D317 as a critical determinant of dinucleotide substrate specificity. Multi-copy explicitly solvated all-atom molecular dynamics simulations suggested a model in which D317 acts as a helix-capping residue by constraining the mobility of loop 7, forming a novel binding pocket that favorably accommodates cytosine. All catalytically active APOBEC3G variants, regardless of dinucleotide preference, retained HIV-1 restriction activity. These data support a model in which the loop 7 region governs the selection of local dinucleotide substrates for deamination but is unlikely to be part of the higher level targeting mechanisms that direct these enzymes to biological substrates such as HIV-1 cDNA. PMID:23938202
Higher-Order Singular Systems and Polynomial Matrices
2005-01-01
There is a one-to-one correspondence between the set of quadruples of matrices defining singular linear time-invariant dynamical systems and a subset of the set of polynomial matrices. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedback-equivalent if, and only if, the polynomial matrices associated to them are also strictly equivalent. Los sistemas lineales singulares...
Decision Matrices: Tools to Enhance Middle School Engineering Instruction
Gonczi, Amanda L.; Bergman, Brenda G.; Huntoon, Jackie; Allen, Robin; McIntyre, Barb; Turner, Sheri; Davis, Jen; Handler, Rob
2017-01-01
Decision matrices are valuable engineering tools. They allow engineers to objectively examine solution options. Decision matrices can be incorporated in K-12 classrooms to support authentic engineering instruction. In this article we provide examples of how decision matrices have been incorporated into 6th and 7th grade classrooms as part of an…
19 CFR 10.90 - Master records and metal matrices.
2010-04-01
... 19 Customs Duties 1 2010-04-01 2010-04-01 false Master records and metal matrices. 10.90 Section... Master Records, and Metal Matrices § 10.90 Master records and metal matrices. (a) Consumption entries... made, of each master record or metal matrix covered thereby. (c) A bond on Customs Form 301,...
Decision Matrices: Tools to Enhance Middle School Engineering Instruction
Gonczi, Amanda L.; Bergman, Brenda G.; Huntoon, Jackie; Allen, Robin; McIntyre, Barb; Turner, Sheri; Davis, Jen; Handler, Rob
2017-01-01
Decision matrices are valuable engineering tools. They allow engineers to objectively examine solution options. Decision matrices can be incorporated in K-12 classrooms to support authentic engineering instruction. In this article we provide examples of how decision matrices have been incorporated into 6th and 7th grade classrooms as part of an…
On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers
Zhaolin Jiang
2014-01-01
inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.
Waller, Niels G
2016-01-01
For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.
Almeida, A; Brabant, L; Siepmann, F; De Beer, T; Bouquet, W; Van Hoorebeke, L; Siepmann, J; Remon, J P; Vervaet, C
2012-11-01
The aim of the present study was to evaluate the importance of matrix flexibility of hot-melt extruded (HME) ethylene vinyl acetate (EVA) matrices (with vinyl acetate (VA) contents of 9%, 15%, 28% and 40%), through the addition of hydrophilic polymers with distinct swelling capacity. Polyethylene oxide (PEO 100K, 1M and 7M) was used as swelling agent and metoprolol tartrate (MPT) as model drug. The processability via HME and drug release profiles of EVA/MPT/PEO formulations were assessed. Solid state characteristics, porosity and polymer miscibility of EVA/PEO matrices were evaluated by means of DSC, X-ray tomography and Raman spectroscopy. The processability via HME varied according to the VA content: EVA 40 and 28 were extruded at 90°C, whereas higher viscosity EVA grades (EVA 15 and 9) required a minimum extrusion temperature of 110°C to obtain high-quality extrudates. Drug release from EVA matrices depended on the VA content, PEO molecular weight and PEO content, matrix porosity as well as pore size distribution. Interestingly, the interplay of PEO leaching, matrix swelling, water influx and changes in matrix porosity influenced drug release: EVA 40- and 28-based matrices extruded with PEO of higher MW accelerated drug release, whereas for EVA 15- and 9-based matrices, drug release slowed down. These differences were related to the distinct polymer flexibility imposed by the VA content (lower VA content presents higher crystallinity and less free movement of the amorphous segments resulting in a higher rigidity). In all cases, diffusional mass transport seems to play a major role, as demonstrated by mathematical modeling using an analytical solution of Fick's second law. The bioavailability of EVA 40 and 28 matrices in dogs was not significantly different, independent of PEO 7M concentration.
... obese. Achieving a healthy weight can help you control your cholesterol, blood pressure and blood sugar. It ... use more calories than you eat. A weight-control strategy might include Choosing low-fat, low-calorie ...
Diana Aviles
2015-10-01
Full Text Available The domestic guinea pig is a valuable genetic resource because it is part of local folklore and food tradition in many South American countries. The economic importance of the guinea pig is due to its high feed efficiency and the quality of animal protein produced. For these reasons, our study is aimed to design a complete dinucleotide microsatellite marker set following international recommendation to assess the genetic diversity and genealogy management of guinea pigs. We selected a total of 20 microsatellites, looking for laboratory efficiency and good statistical parameters. The set was tested in 100 unrelated individuals of guinea pigs from Ecuador, Peru, Colombia, Bolivia and Spain. Our results show a high degree of polymorphisms with a total of 216 alleles and a mean number of 10.80±3.49 for markers with a combined exclusion probability of 0.99.
Ummarino, Simone; Mozzon, Massimo; Zamporlini, Federica; Amici, Adolfo; Mazzola, Francesca; Orsomando, Giuseppe; Ruggieri, Silverio; Raffaelli, Nadia
2017-04-15
Nicotinamide riboside, the most recently discovered form of vitamin B3, and its phosphorylated form nicotinamide mononucleotide, have been shown to be potent supplements boosting intracellular nicotinamide adenine dinucleotide (NAD) levels, thus preventing or ameliorating metabolic and mitochondrial diseases in mouse models. Here we report for the first time on the simultaneous quantitation of nicotinamide riboside, nicotinamide mononucleotide and NAD in milk by means of a fluorometric, enzyme-coupled assay. Application of this assay to milk from different species revealed that the three vitamers were present in human and donkey milk, while being selectively distributed in the other milks. Human milk was the richest source of nicotinamide mononucleotide. Overall, the three vitamers accounted for a significant fraction of total vitamin B3 content. Pasteurization did not affect the bovine milk content of nicotinamide riboside, whereas UHT processing fully destroyed the vitamin. In human milk, NAD levels were significantly affected by the lactation time.
Kirkensgaard, Kristine Groth; Hägglund, Per; Shahpiri, Azar;
2013-01-01
dinucleotide (FAD)-binding domain of HvNTR2 to strongly affect the interaction with Trx. In particular, Trp42 and Met43 play key roles for recognition of the endogenous HvTrxh2. Trx from Arabidopsis thaliana is also efficiently recycled by HvNTR2 but turnover in this case appears to be less dependent...... on these two residues, suggesting a distinct mode for NTR:Trx recognition. Comparison between the HvNTR2:HvTrxh2 model and the crystal structure of the Escherichia coli NTR:Trx complex reveals major differences in interactions involving the FAD- and NADPH-binding domains as supported by our experiments...
Ackerman, Margareta; Ben-David, Shai; Branzei, Simina
2012-01-01
We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights.We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both...... the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify...
Lectures on S-matrices and Integrability
Bombardelli, Diego
2016-01-01
In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the 2-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU(2), SU(3) chiral Gross-Neveu models. This is part of a collection of lecture notes for the Young Researchers Integrability School, organised by the GATIS network at Durham University on 6-10 July 2015.
Inferring Passenger Type from Commuter Eigentravel Matrices
Legara, Erika Fille
2015-01-01
A sufficient knowledge of the demographics of a commuting public is essential in formulating and implementing more targeted transportation policies, as commuters exhibit different ways of traveling. With the advent of the Automated Fare Collection system (AFC), probing the travel patterns of commuters has become less invasive and more accessible. Consequently, numerous transport studies related to human mobility have shown that these observed patterns allow one to pair individuals with locations and/or activities at certain times of the day. However, classifying commuters using their travel signatures is yet to be thoroughly examined. Here, we contribute to the literature by demonstrating a procedure to characterize passenger types (Adult, Child/Student, and Senior Citizen) based on their three-month travel patterns taken from a smart fare card system. We first establish a method to construct distinct commuter matrices, which we refer to as eigentravel matrices, that capture the characteristic travel routines...
Astronomical Receiver Modelling Using Scattering Matrices
King, O G; Copley, C; Davis, R J; Leahy, J P; Leech, J; Muchovej, S J C; Pearson, T J; Taylor, Angela C
2014-01-01
Proper modelling of astronomical receivers is vital: it describes the systematic errors in the raw data, guides the receiver design process, and assists data calibration. In this paper we describe a method of analytically modelling the full signal and noise behaviour of arbitrarily complex radio receivers. We use electrical scattering matrices to describe the signal behaviour of individual components in the receiver, and noise correlation matrices to describe their noise behaviour. These are combined to produce the full receiver model. We apply this approach to a specified receiver architecture: a hybrid of a continous comparison radiometer and correlation polarimeter designed for the C-Band All-Sky Survey. We produce analytic descriptions of the receiver Mueller matrix and noise temperature, and discuss how imperfections in crucial components affect the raw data. Many of the conclusions drawn are generally applicable to correlation polarimeters and continuous comparison radiometers.
Approximate inverse preconditioners for general sparse matrices
Chow, E.; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
Asymptotic properties of random matrices and pseudomatrices
Lenczewski, Romuald
2010-01-01
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.
Non-Hermitean Wishart random matrices (I)
Kanzieper, Eugene
2010-01-01
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great emphasis is placed on an asymptotic analysis of the mean eigenvalue density for which we derive, among other results, a complex-plane analogue of the Marchenko-Pastur law. A surprising connection with a class of matrix models previously invented in the context of quantum chromodynamics is pointed out. This provides one more evidence of the ubiquity of Random Matrix Theory.
Determinants of adjacency matrices of graphs
Alireza Abdollahi
2012-12-01
Full Text Available We study the set of all determinants of adjacency matrices of graphs with a given number of vertices. Using Brendan McKay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. Using an idea of M. Newman, it is proved that if $G$ is a graph with $n$ vertices and ${d_1,dots,d_n}$ is the set of vertex degrees of $G$, then $gcd(2m,d^2$ divides the determinant of the adjacency matrix of $G$, where $d=gcd(d_1,dots,d_n$. Possible determinants of adjacency matrices of graphs with exactly two cycles are obtained.
... baby, taken just after he or she is born. A low birth weight is less than 5.5 pounds. A high ... weight is more than 8.8 pounds. A low birth weight baby can be born too small, too early (premature), or both. This ...
MULTIFRACTAL STRUCTURE AND PRODUCT OF MATRICES
Lau Ka-sing
2003-01-01
There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes.Our report here concerns those with overlaps.In particular we restrict our attention to the important classes of self-similar measures that have matrix representations.The dimension spectra and the Lq-spectra are analyzed through the product of matrices.There are abnormal behaviors on the multifrac-tal structure and they will be discussed in detail.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Connection matrices for ultradiscrete linear problems
Ormerod, Chris [School of Mathematics and Statistics F07, The University of Sydney, Sydney (Australia)
2007-10-19
We present theory outlining associated linear problems for ultradiscrete equations. The appropriate domain for these problems is the max-plus semiring. Our main result is that despite the restrictive nature of the max-plus semiring, it is still possible to define a theory of connection matrices analogous to that of Birkhoff and his school for systems of linear difference equations. We use such theory to provide evidence for the integrability of an ultradiscrete difference equation.
Functional CLT for sample covariance matrices
Bai, Zhidong; Zhou, Wang; 10.3150/10-BEJ250
2010-01-01
Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including $[(1-\\sqrt{y})^2,(1+\\sqrt{y})^2]$, the support of the Mar\\u{c}enko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.
Index matrices towards an augmented matrix calculus
Atanassov, Krassimir T
2014-01-01
This book presents the very concept of an index matrix and its related augmented matrix calculus in a comprehensive form. It mostly illustrates the exposition with examples related to the generalized nets and intuitionistic fuzzy sets which are examples of an extremely wide array of possible application areas. The present book contains the basic results of the author over index matrices and some of its open problems with the aim to stimulating more researchers to start working in this area.
On the exponentials of some structured matrices
Ramakrishna, Viswanath; Costa, F [Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, PO Box 830688, Richardson, TX 75083 (United States)
2004-12-03
This paper provides explicit techniques to compute the exponentials of a variety of structured 4 x 4 matrices. The procedures are fully algorithmic and can be used to find the desired exponentials in closed form. With one exception, they require no spectral information about the matrix being exponentiated. They rely on a mixture of Lie theory and one particular Clifford algebra isomorphism. These can be extended, in some cases, to higher dimensions when combined with techniques such as Givens rotations.
2008-03-01
Rueden (lead software developer at LOCI) using Image J, VisBio, and SlimPlotter. The goal is to create an efficient and accurate method to translate...MPLSM imaging of en- dogenous signals from collagen and fluorophores such as nicotinamide adenine dinucleotide NADH or flavin ad- enine ...phores imaged with MPLSM are tryptophan, nicotinamide ad- enine dinucleotide NADH and flavin adenine dinucleotide FAD, as well as endogenous SHG
The spectrum of kernel random matrices
Karoui, Noureddine El
2010-01-01
We place ourselves in the setting of high-dimensional statistical inference where the number of variables $p$ in a dataset of interest is of the same order of magnitude as the number of observations $n$. We consider the spectrum of certain kernel random matrices, in particular $n\\times n$ matrices whose $(i,j)$th entry is $f(X_i'X_j/p)$ or $f(\\Vert X_i-X_j\\Vert^2/p)$ where $p$ is the dimension of the data, and $X_i$ are independent data vectors. Here $f$ is assumed to be a locally smooth function. The study is motivated by questions arising in statistics and computer science where these matrices are used to perform, among other things, nonlinear versions of principal component analysis. Surprisingly, we show that in high-dimensions, and for the models we analyze, the problem becomes essentially linear--which is at odds with heuristics sometimes used to justify the usage of these methods. The analysis also highlights certain peculiarities of models widely studied in random matrix theory and raises some questio...
Quark flavor mixings from hierarchical mass matrices
Verma, Rohit [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China); Rayat Institute of Engineering and Information Technology, Ropar (India); Zhou, Shun [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China); Peking University, Center for High Energy Physics, Beijing (China)
2016-05-15
In this paper, we extend the Fritzsch ansatz of quark mass matrices while retaining their hierarchical structures and show that the main features of the Cabibbo-Kobayashi-Maskawa (CKM) matrix V, including vertical stroke V{sub us} vertical stroke ≅ vertical stroke V{sub cd} vertical stroke, vertical stroke V{sub cb} vertical stroke ≅ vertical stroke V{sub ts} vertical stroke and vertical stroke V{sub ub} vertical stroke / vertical stroke V{sub cb} vertical stroke < vertical stroke V{sub td} vertical stroke / vertical stroke V{sub ts} vertical stroke can be well understood. This agreement is observed especially when the mass matrices have non-vanishing (1, 3) and (3, 1) off-diagonal elements. The phenomenological consequences of these for the allowed texture content and gross structural features of 'hierarchical' quark mass matrices are addressed from a model-independent prospective under the assumption of factorizable phases in these. The approximate and analytical expressions of the CKM matrix elements are derived and a detailed analysis reveals that such structures are in good agreement with the observed quark flavor mixing angles and the CP-violating phase at the 1σ level and call upon a further investigation of the realization of these structures from a top-down prospective. (orig.)
Scattering Matrices and Conductances of Leaky Tori
Pnueli, A.
1994-04-01
Leaky tori are two-dimensional surfaces that extend to infinity but which have finite area. It is a tempting idea to regard them as models of mesoscopic systems connected to very long leads. Because of this analogy-scattering matrices on leaky tori are potentially interesting, and indeed-the scattering matrix on one such object-"the" leaky torus-was studied by M. Gutzwiller, who showed that it has chaotic behavior. M. Antoine, A. Comtet and S. Ouvry generalized Gutzwiller‧s result by calculating the scattering matrix in the presence of a constant magnetic field B perpendicular to the surface. Motivated by these results-we generalize them further. We define scattering matrices for spinless electrons on a general leaky torus in the presence of a constant magnetic field "perpendicular" to the surface. From the properties of these matrices we show the following: (a) For integer values of B, Tij (the transition probability from cusp i to cusp j), and hence also the Büttiker conductances of the surfaces, are B-independent (this cannot be interpreted as a kind of Aharonov-Bohm effect since a magnetic force is acting on the electrons). (b) The Wigner time-delay is a monotonically increasing function of B.
On the Construction of Jointly Superregular Lower Triangular Toeplitz Matrices
Hansen, Jonas; Østergaard, Jan; Kudahl, Johnny
2016-01-01
superregular and product preserving jointly superregular matrices, and extend our explicit constructions of superregular matrices to these cases. Jointly superregular matrices are necessary to achieve optimal decoding capabilities for the case of codes with a rate lower than 1/2, and the product preserving......Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential) network codes. In this work, we provide an explicit design...
The modern origin of matrices and their applications
Debnath, L.
2014-05-01
This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show that matrices form a ring in abstract algebra. Some special matrices, including Hilbert's matrix, Toeplitz's matrix, Pauli's and Dirac's matrices in quantum mechanics, and Einstein's Pythagorean formula are discussed to illustrate diverse applications of matrix algebra. Included also is a modern piece of information that puts mathematics, science and mathematics education professionals at the forefront of advanced study and research on linear algebra and its applications.
Deterministic sensing matrices in compressive sensing: a survey.
Nguyen, Thu L N; Shin, Yoan
2013-01-01
Compressive sensing is a sampling method which provides a new approach to efficient signal compression and recovery by exploiting the fact that a sparse signal can be suitably reconstructed from very few measurements. One of the most concerns in compressive sensing is the construction of the sensing matrices. While random sensing matrices have been widely studied, only a few deterministic sensing matrices have been considered. These matrices are highly desirable on structure which allows fast implementation with reduced storage requirements. In this paper, a survey of deterministic sensing matrices for compressive sensing is presented. We introduce a basic problem in compressive sensing and some disadvantage of the random sensing matrices. Some recent results on construction of the deterministic sensing matrices are discussed.
Matrices with restricted entries and q-analogues of permutations
Lewis, Joel Brewster; Morales, Alejandro H; Panova, Greta; Sam, Steven V; Zhang, Yan
2010-01-01
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restricted values. We obtain a simple closed formula for the number of invertible matrices with zero diagonal, a $q$-analogue of derangements, and a curious relationship between invertible skew-symmetric matrices and invertible symmetric matrices with zero diagonal. In addition, we provide recursions to enumerate matrices and symmetric matrices with zero diagonal by rank, and we frame some of our results in the context of Lie theory. Finally, we provide a brief exposition of polynomiality results for enumeration questions related to those mentioned, and give several open questions.
Kavanagh, Nicole; Corrigan, Owen I
2004-07-26
The effect of dissolution medium variables, such as medium composition, ionic strength and agitation rate, on the swelling and erosion of Hypromellose (hydroxypropylmethylcellulose, HPMC) matrices of different molecular weights was examined. Swelling and erosion of HPMC polymers was determined by measuring the wet and subsequent dry weights of matrices. It was possible to describe the rate of dissolution medium uptake in terms of a square root relationship and the erosion of the polymer in terms of the cube root law. The extent of swelling increased with increasing molecular weight, and decreased with increasing agitation rate. The erosion rate was seen to increase with decrease in polymer molecular weight, with a decrease in ionic strength and with increasing agitation rate. The sensitivity of polymer erosion to the degree of agitation may influence the ability of these polymers to give reproducible, agitation-independent release, compared to more rigid non-eroding matrix materials, in the complex hydrodynamic environment of the gastrointestinal tract.
Zhao, Jingjin; Zhang, Liangliang; Jiang, Jianhui; Shen, Guoli; Yu, Ruqin
2012-05-11
A simple label-free fluorescent sensing scheme for sensitive and selective detection of nicotinamide adenine dinucleotide (NAD(+)) has been developed based on DNA ligation reaction with ligand-responsive quadruplex formation. This approach can detect 0.5 nM NAD(+) with high selectivity against other NAD(+) analogs.
Quantum Racah matrices and 3-strand braids in representation [3,3
Shakirov, Sh
2016-01-01
This paper is a next step in the project of systematic description of colored knot polynomials started in arXiv:1506.00339. In this paper, we managed to explicitly find the $\\textit{inclusive}$ Racah matrices, i.e. the whole set of mixing matrices in channels $R^{\\otimes 3}\\longrightarrow Q$ with all possible $Q$, for $R=[3,3]$. The case $R=[3,3]$ is a multiplicity free case as well as $R=[2,2]$ obtained in arXiv:1605.03098. The calculation is made possible by the use of highest weight method with the help of Gelfand-Tseitlin tables. The result allows one to evaluate and investigate $[3,3]$-colored polynomials for arbitrary 3-strand knots, and this confirms many previous conjectures on various factorizations, universality, and differential expansions. With the help of a method developed in arXiv:1605.04881 we manage to calculate {\\it exclusive} Racah matrices $S$ and $\\bar S$ in $R=[3,3]$. Our results confirm a calculation of these matrices in arXiv:1606.06015, which was based on the conjecture of explicit fo...
Bickel, Peter J
2010-01-01
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix $A$, which is invertible as a bounded operator on $\\ell^2$, can be uniformly approximated by banded matrices then so can the inverse of $A$. We give explicit formulas for the banded approximations of $A^{-1}$ as well as bounds on their accuracy and speed of convergence in terms of their band-width. In the second part we apply these results to covariance matrices $\\Sigma$ of Gaussian processes and study mixing and beta mixing of processes in terms of properties of $\\Sigma$. Finally, we note some applications of our results to statistics.
Victor Augusto Moraes da Silva
2015-01-01
Full Text Available Schizophrenia (SZ is a debilitating mental disorder characterized by psychotic events, abnormal social behavior, false beliefs, and auditory hallucinations. Hypermethylation of the promoter region of reelin (RELN, a gene involved in regulation of neuronal positioning during telencephalic development, is strongly associated with low protein expression in several cortical structures and promoter hypermethylation in brain from postmortem SZ subjects. Recent experimental data suggests that testosterone is able to promote RELN demethylation, although no direct evidence of hormonal influence on reelin promoter methylation was obtained. We investigated if reduced levels of plasma testosterone in adult male mice lead to Reln promoter demethylation. Animals were administered with flutamide, an antiandrogenic compound, and reelin promoter methylation was assessed using methylationspecific PCR using bisulfite DNA from cerebellum. We found that flutamide was able to significantly lower plasma testosterone when compared to control mice, and treatment did not influence animal survival and body weight. We also show that low plasma testosterone was associated with demethylation of a cytosine residue located at −860 in reelin promoter region. These preliminary data suggest that androgenic hormones can influence cerebral reelin demethylation. To our knowledge, this is the first experimental approach directly linking testosterone depletion and RELN promoter methylation.
da Silva, Victor Augusto Moraes; Dantas, Marília de Souza; Silva, Leonardo Agostinho de Castro; Carneiro, Juliana Garcia; Schamber-Reis, Bruno Luiz Fonseca
2015-01-01
Schizophrenia (SZ) is a debilitating mental disorder characterized by psychotic events, abnormal social behavior, false beliefs, and auditory hallucinations. Hypermethylation of the promoter region of reelin (RELN), a gene involved in regulation of neuronal positioning during telencephalic development, is strongly associated with low protein expression in several cortical structures and promoter hypermethylation in brain from postmortem SZ subjects. Recent experimental data suggests that testosterone is able to promote RELN demethylation, although no direct evidence of hormonal influence on reelin promoter methylation was obtained. We investigated if reduced levels of plasma testosterone in adult male mice lead to Reln promoter demethylation. Animals were administered with flutamide, an antiandrogenic compound, and reelin promoter methylation was assessed using methylationspecific PCR using bisulfite DNA from cerebellum. We found that flutamide was able to significantly lower plasma testosterone when compared to control mice, and treatment did not influence animal survival and body weight. We also show that low plasma testosterone was associated with demethylation of a cytosine residue located at -860 in reelin promoter region. These preliminary data suggest that androgenic hormones can influence cerebral reelin demethylation. To our knowledge, this is the first experimental approach directly linking testosterone depletion and RELN promoter methylation.
Factor structure of Raven's Coloured Progressive Matrices
Muniz, Monalisa; Gomes, Cristiano Mauro Assis; Pasian, Sonia Regina
2016-01-01
Abstract This study's objective was to verify the factor structure of Raven's Coloured Progressive Matrices (CPM). The database used included the responses of 1,279 children, 50.2% of which were males with an average age of 8.48 years old and a standard deviation of 1.49 yrs. Confirmatory factor analyses were run to test seven models based on CPM theory and on a Brazilian study addressing the test's structure. The results did not confirm the CPM theoretical proposition concerning the scales b...
Generalized Jones matrices for anisotropic media.
Ortega-Quijano, Noé; Arce-Diego, José Luis
2013-03-25
The interaction of arbitrary three-dimensional light beams with optical elements is described by the generalized Jones calculus, which has been formally proposed recently [Azzam, J. Opt. Soc. Am. A 28, 2279 (2011)]. In this work we obtain the parametric expression of the 3×3 differential generalized Jones matrix (dGJM) for arbitrary optical media assuming transverse light waves. The dGJM is intimately connected to the Gell-Mann matrices, and we show that it provides a versatile method for obtaining the macroscopic GJM of media with either sequential or simultaneous anisotropic effects. Explicit parametric expressions of the GJM for some relevant optical elements are provided.
Jones matrices of perfectly conducting metallic polarizers
Boyer, Philippe
2014-01-01
We deduce from Monomode Modal Method the analytical expressions of transmission and reflexion Jones matrices of an infinitely conducting metallic screen periodically pierced by subwavelength holes. The study is restricted to normal incidence and to the case of neglected evanescent fields (far-field) which covers many common cases. When only one non-degenerate mode propagates in cavities, they take identical forms to those of a polarizer, with Fabry-Perot-like spectral resonant factors depending on bigrating parameters. The isotropic or birefringent properties are then obtained when holes support two orthogonal polarization modes. This basic formalism is finally applied to design compact and efficient metallic half-wave plates.
Algebraic Graph Theory Morphisms, Monoids and Matrices
Knauer, Ulrich
2011-01-01
This is a highly self-contained book about algebraic graph theory which iswritten with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures -like roads, computers, telephones -instances of abstract data structures -likelists, stacks, trees -and functional or object orient
Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach.
Oña, Ofelia B; De Clercq, Olivier; Alcoba, Diego R; Torre, Alicia; Lain, Luis; Van Neck, Dimitri; Bultinck, Patrick
2016-09-19
The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.
Wagner, C.
1996-12-31
In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.
APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS
SHAO Xin-hui; SHEN Hai-long; LI Chang-jun
2006-01-01
Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.
A CLASS OF DETERMINISTIC CONSTRUCTION OF BINARY COMPRESSED SENSING MATRICES
Li Dandan; Liu Xinji; Xia Shutao; Jiang Yong
2012-01-01
Compressed Sensing (CS) is an emerging technology in the field of signal processing,which can recover a sparse signal by taking very few samples and solving a linear programming problem.In this paper,we study the application of Low-Density Parity-Check (LDPC) Codes in CS.Firstly,we find a sufficient condition for a binary matrix to satisfy the Restricted Isometric Property (RIP).Then,by employing the LDPC codes based on Berlekamp-Justesen (B-J) codes,we construct two classes of binary structured matrices and show that these matrices satisfy RIP.Thus,the proposed matrices could be used as sensing matrices for CS.Finally,simulation results show that the performance of the Droposed matrices can be comparable with the widely used random sensing matrices.
Asymmetric random matrices: What do we need them for?
Drozdz, Stanislaw; Ioannides, Andreas A; 10.5506/APhysPolB.42.987
2011-01-01
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of activity that are reproducible with statistically significant frequency compared to a reference chance probability, usually provided by random matrices as fundamental reference. The character of the problem and especially the symmetries involved must guide the choice of random matrices to be used for the definition of a baseline reference. For standard correlation matrices this is the Wishart ensemble of symmetric random matrices. The real world complexity however often shows asymmetric information flows and therefore more general correlation matrices are required to adequately capture the asymmetry. Here we first summarize the relevant theoretical concepts. We then present some examples of human brain activity where asymmetric time-lagged correlations are evident and hence...
Tensor Dictionary Learning for Positive Definite Matrices.
Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2015-11-01
Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.
Bromination of selected pharmaceuticals in water matrices.
Benitez, F Javier; Acero, Juan L; Real, Francisco J; Roldan, Gloria; Casas, Francisco
2011-11-01
The bromination of five selected pharmaceuticals (metoprolol, naproxen, amoxicillin, phenacetin, and hydrochlorothiazide) was studied with these compounds individually dissolved in ultra-pure water. The apparent rate constants for the bromination reaction were determined as a function of the pH, obtaining the sequence amoxicillin>naproxen>hydrochlorothiazide≈phenacetin≈metoprolol. A kinetic mechanism specifying the dissociation reactions and the species formed for each compound according to its pK(a) value and the pH allowed the intrinsic rate constants to be determined for each elementary reaction. There was fairly good agreement between the experimental and calculated values of the apparent rate constants, confirming the goodness of the proposed reaction mechanism. In a second stage, the bromination of the selected pharmaceuticals simultaneously dissolved in three water matrices (a groundwater, a surface water from a public reservoir, and a secondary effluent from a WWTP) was investigated. The pharmaceutical elimination trend agreed with the previously determined rate constants. The influence of the main operating conditions (pH, initial bromine dose, and characteristics of the water matrix) on the degradation of the pharmaceuticals was established. An elimination concentration profile for each pharmaceutical in the water matrices was proposed based on the use of the previously evaluated apparent rate constants, and the theoretical results agreed satisfactorily with experiment. Finally, chlorination experiments performed in the presence of bromide showed that low bromide concentrations slightly accelerate the oxidation of the selected pharmaceuticals during chlorine disinfection.
Moderate deviations for the eigenvalue counting function of Wigner matrices
Doering, Hanna
2011-01-01
We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem and applies localization results by Erd\\"os, Yau and Yin. Moreover we investigate families of covariance matrices as well.
Symmetric texture-zero mass matrices and its eigenvalues
Criollo, A
2012-01-01
Within the texture-zeros mechanism, first we provide necessary and sufficient conditions on the characteristic polynomial coefficients so that it has real, simple and positive roots, we traduce these conditions in terms to the invariants of the congruent matrices. Next all symmetric texture-zero mass matrices are counted and classified. Finally we apply in a systematic way the result from the first part to analyze the six, four and two zeros texture matrices presented in the second part.
Wick's theorem and reconstruction schemes for reduced density matrices
CHEN Feiwu
2006-01-01
We first obtained a closed form of the Wick's theorem expressed in Grassman wedge product, which is similar to a binomial expansion. With this new expansion, new reconstruction schemes for reduced density matrices are derived rigorously. The higher order reduced density matrices are systematically decomposed into a sum of the lower order reduced density matrices which could be used to solve the contracted Schr(o)dinger equation.
Xiang, Lei; Chen, Lei; Xiao, Tao; Mo, Ce-Hui; Li, Yan-Wen; Cai, Quan-Ying; Li, Hui; Zhou, Dong-Mei; Wong, Ming-Hung
2017-10-04
A robust method was developed for simultaneous determination of nine trace perfluoroalkyl carboxylic acids (PFCAs) in various edible crop matrices including cereal (grain), root vegetable (carrot), leafy vegetable (lettuce), and melon vegetable (pumpkin) using ultrasonic extraction followed by solid-phase extraction cleanup and high liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). The varieties of extractants and cleanup cartridges, the usage of Supelclean graphitized carbon, and the matrix effect and its potential influencing factors were estimated to gain an optimal extraction procedure. The developed method presented high sensitivity and accuracy with the method detection limits and the recoveries at four fortification levels in various matrices ranging from 0.017 to 0.180 ng/g (dry weight) and from 70% to 114%, respectively. The successful application of the developed method to determine PFCAs in various crops sampled from several farms demonstrated its practicability for regular monitoring of PFCAs in real crops.
The cyclic di-nucleotide c-di-AMP is an allosteric regulator of metabolic enzyme function
Precit, Mimi; Delince, Matthieu; Pensinger, Daniel; Huynh, TuAnh Ngoc; Jurado, Ashley R.; Goo, Young Ah; Sadilek, Martin; Iavarone, Anthony T.; Sauer, John-Demian; Tong, Liang; Woodward, Joshua J.
2014-01-01
SUMMARY Cyclic di-adenosine monophosphate (c-di-AMP) is a broadly conserved second messenger required for bacterial growth and infection. However, the molecular mechanisms of c-di-AMP signaling are still poorly understood. Using a chemical proteomics screen for c-di-AMP interacting proteins in the pathogen Listeria monocytogenes, we identified several broadly conserved protein receptors, including the central metabolic enzyme pyruvate carboxylase (LmPC). Biochemical and crystallographic studies of the LmPC-c-di-AMP interaction revealed a previously unrecognized allosteric regulatory site 25 Å from the active site. Mutations in this site disrupted c-di-AMP binding and affected enzyme catalysis of LmPC as well as PC from pathogenic Enterococcus faecalis. C-di-AMP depletion resulted in altered metabolic activity in L. monocytogenes. Correction of this metabolic imbalance rescued bacterial growth, reduced bacterial lysis, and resulted in enhanced bacterial burdens during infection. These findings greatly expand the c-di-AMP signaling repertoire and reveal a central metabolic regulatory role for a cyclic di-nucleotide. PMID:25215494
Hirakawa, Kazutaka; Murata, Atsushi
2017-07-31
Water-soluble porphyrins, diethoxyphosphorus(V)tetraphenylporphyrin (EtP(V)TPP) and its fluorinated analogue (FEtP(V)TPP), decreased the typical absorption around 340nm of nicotinamide adenine dinucleotide (NADH) under visible light irradiation, indicating oxidative decomposition. A singlet oxygen quencher, sodium azide, and a triplet quencher, potassium iodide, slightly inhibited photosensitized NADH oxidation. However, these inhibitory effects were very small. Furthermore, the fluorescence lifetime of these P(V)porphyrins was decreased by NADH, suggesting the contribution of electron transfer to the singlet excited (S1) state of P(V)porphyrin. The redox potential measurement supports the electron transfer-mediated oxidation of NADH. The quantum yields of NADH photodecomposition by P(V)porphyrins could be estimated from the kinetic data and the effect of these quenchers on NADH oxidation. The obtained values suggest that the electron accepting by the S1 states of P(V)porphyrins triggers a chain reaction of NADH oxidation. This photosensitized reaction may play an important role in the photocytotoxicity of P(V)porphyrins. The axial ligand fluorination of P(V)porphyrins improved electron accepting ability. However, fluorination slightly suppressed static interaction with NADH, resulting in decreased oxidation quantum yield. Copyright © 2017 Elsevier B.V. All rights reserved.
Chataporn Chunwongse
2015-04-01
Full Text Available Forty-two di-nucleotide microsatellite, or simple-sequence repeat (SSR, markers were developed using CA and CTenriched genomic libraries of Mangifera indica L. Six cultivated mangoes and two wild species were tested for primer amplifications. Most loci could amplify M. caloneura Kruz and M. foetida. The average number of alleles per locus was 4.4. The average expected heterozygosity and the maximum polymorphism information content value were 0.57 and 0.53, respectively. The SSRs developed in this study together with 65 SSRs and 145 restriction fragment length polymorphism (RFLP markers reported previously were used in the genetic linkage analysis. A partial genetic linkage map was constructed based on 31 F1 progenies from a cross between ‘Alphonso’ and ‘Palmer’. The map spanned a distance of 529.9 centiMorgan (cM and consisted of 9 microsatellite markers (6 from this study and 67 RFLP markers. The new SSR markers and the present map will be useful for mango genetic studies and breeding applications in the future.
Ali, Thanaa Hamed; El-Ghonemy, Dina Helmy
2016-06-01
The present study was conducted to investigate a new pathway for the degradation of nicotinamide adenine dinucleotide (NAD) by Penicillium brevicompactum NRC 829 extracts. Enzymes involved in the hydrolysis of NAD, i.e. alkaline phosphatase, aminohydrolase and glycohydrolase were determined. Alkaline phosphatase was found to catalyse the sequential hydrolysis of two phosphate moieties of NAD molecule to nicotinamide riboside plus adenosine. Adenosine was then deaminated by aminohydrolase to inosine and ammonia. While glycohydrolase catalyzed the hydrolysis of the nicotinamide-ribosidic bond of NAD+ to produce nicotinamide and ADP-ribose in equimolar amounts, enzyme purification through a 3-step purification procedure revealed the existence of two peaks of alkaline phosphatases, and one peak contained deaminase and glycohydrolase activities. NAD deaminase was purified to homogeneity as estimated by sodium dodecyl sulphate-polyacrylamide gel electrophoresis with an apparent molecular mass of 91 kDa. Characterization and determination of some of NAD aminohydrolase kinetic properties were conducted due to its biological role in the regulation of cellular NAD level. The results also revealed that NAD did not exert its feedback control on nicotinamide amidase produced by P. brevicompactum.
Chen, Yan; Li, Yiwei; Ma, Yaohong; Meng, Qingjun; Yan, Yan; Shi, Jianguo
2015-01-01
A nanocomposite platform built with multi-walled carbon nanotubes (MWCNTs) and nicotinamide adenine dinucleotide (NAD(+)) via a noncovalent interaction between the large π systems in NAD(+) molecules and MWCNTs on a glassy carbon substrate was successfully developed for the sensitive and selective detection of uric acid (UA) in the presence of ascorbic acid (AA), dopamine (DA). NAD(+) has an adenine subunit and a nicotinamide subunit, which enabled interaction with the purine subunit of UA through a strong π-π interaction to enhance the specificity of UA. Compared with a bare glassy carbon electrode (GCE) and MWCNTs/GCE, the MWCNTs-NAD(+)/GCE showed a low background current and a remarkable enhancement of the oxidation peak current of UA. Using differential pulse voltammetry (DPV), a high sensitivity for the determination of UA was explored for the MWCNTs-NAD(+) modified electrode. A linear relationship between the DPV peak current of UA and its concentration could be obtained in the range of 0.05 - 10 μM with the detection limit as low as 10 nM (S/N = 3). This present strategy provides a novel and promising platform for the detection of UA in human urine and serum samples.
Maeda, Kensaku; Yasunari, Kenichi; Sato, Eisuke F; Yoshikawa, Junichi; Inoue, Masayasu
2003-12-01
The involvement of oxidative stress in polymorphonuclear leukocytes (PMN) in the pathogenesis of hypertension remains to be elucidated. We analyzed the generation of reactive oxygen species (ROS) by the circulating and peritoneally infiltrating PMN from spontaneously hypertensive rats (SHR) and Wistar Kyoto rats (WKY). Flow cytometric analysis revealed that ROS generation by PMN from SHR was higher than that from WKY before (at 6 weeks of age) and after (at 16 weeks of age) the onset of hypertension. In vivo, ROS generation by PMN from SHR, but not that by PMN from WKY, was significantly suppressed by 10-week treatment with 50 mg/kg/day carvedilol, and this treatment did not affect blood pressure. Western blotting analysis revealed that protein kinase C alpha (PKCalpha), but not PKCbetaI or betaII, was activated more strongly in PMN from SHR than in PMN from WKY. Furthermore, expression of p47phox of nicotinamide adenine dinucleotide phosphate oxidase, but not of p67phox, in PMN from SHR was higher than that in PMN from WKY. These results suggest that ROS generation by PMN is principally enhanced in SHR through activation of PKCalpha and p47phox.
Yáñez-Cuna, J Omar; Arnold, Cosmas D; Stampfel, Gerald; Boryń, Lukasz M; Gerlach, Daniel; Rath, Martina; Stark, Alexander
2014-07-01
Gene expression is determined by genomic elements called enhancers, which contain short motifs bound by different transcription factors (TFs). However, how enhancer sequences and TF motifs relate to enhancer activity is unknown, and general sequence requirements for enhancers or comprehensive sets of important enhancer sequence elements have remained elusive. Here, we computationally dissect thousands of functional enhancer sequences from three different Drosophila cell lines. We find that the enhancers display distinct cis-regulatory sequence signatures, which are predictive of the enhancers' cell type-specific or broad activities. These signatures contain transcription factor motifs and a novel class of enhancer sequence elements, dinucleotide repeat motifs (DRMs). DRMs are highly enriched in enhancers, particularly in enhancers that are broadly active across different cell types. We experimentally validate the importance of the identified TF motifs and DRMs for enhancer function and show that they can be sufficient to create an active enhancer de novo from a nonfunctional sequence. The function of DRMs as a novel class of general enhancer features that are also enriched in human regulatory regions might explain their implication in several diseases and provides important insights into gene regulation.
Tachikawa, Hiroto; Kawabata, Hiroshi
2008-06-19
The interaction between the fully reduced flavin-adenine dinucleotide (FADH (-)) and thymine dimer (T) 2 has been investigated by means of density functional theory (DFT) calculations. The charges of FADH (-) and (T) 2 were calculated to be -0.9 and -0.1, respectively, at the ground state. By photoirradiation, an electron transfer occurred from FADH (-) to (T) 2 at the first excited state. Next, the reaction dynamics of electron capture of (T) 2 have been investigated by means of the direct ab initio molecular dynamics (MD) method (HF/3-21G(d) and B3LYP/6-31G(d) levels) in order to elucidate the mechanism of the repair process of thymine dimer caused by the photoenzyme. The thymine dimer has two C-C single bonds between thymine rings (C 5-C 5' and C 6-C 6' bonds) at the neutral state, which is expressed by (T) 2. After the electron capture of (T) 2, the C 5-C 5' bond was gradually elongated and then it was preferentially broken. The time scale of the C-C bond breaking and formation of the intermediate with a single bond (T) 2 (-) was estimated to be 100-150 fs. The present calculations confirmed that the repair reaction of thymine dimer takes place efficiently via an electron-transfer process from the FADH (-) enzyme.
Racah matrices and hidden integrability in evolution of knots
Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A.
2016-09-01
We construct a general procedure to extract the exclusive Racah matrices S and S bar from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R = [ 1 ], [2], [3] and [ 2 , 2 ]. The matrices S and S bar relate respectively the maps (R ⊗ R) ⊗ R bar ⟶ R with R ⊗ (R ⊗ R bar) ⟶ R and (R ⊗ R bar) ⊗ R ⟶ R with R ⊗ (R bar ⊗ R) ⟶ R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices.
Inverse Eigenvalue Problems for Two Special Acyclic Matrices
Debashish Sharma
2016-03-01
Full Text Available In this paper, we study two inverse eigenvalue problems (IEPs of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix and one eigenvalue of each of its leading principal submatrices. The second problem involves reconstruction of matrices whose graph is a broom, the eigen data being the maximum and minimum eigenvalues of each of the leading principal submatrices of the required matrix. In order to solve the problems, we use the recurrence relations among leading principal minors and the property of simplicity of the extremal eigenvalues of acyclic matrices.
Self-dual interval orders and row-Fishburn matrices
Yan, Sherry H F
2011-01-01
Recently, Jel\\'{i}nek derived that the number of self-dual interval orders of reduced size $n$ is twice the number of row-Fishburn matrices of size $n$ by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of the refined relations between self-dual Fishburn matrices and row-Fishburn matrices in answer to a problem proposed by Jel\\'{i}nek.
Applications of combinatorial matrix theory to Laplacian matrices of graphs
Molitierno, Jason J
2012-01-01
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs. Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs is a compilation of many of the exciting results concerning Laplacian matrices developed since the mid 1970s by well-known mathematicians such as Fallat, Fiedler, Grone, Kirkland, Merris, Mohar, Neumann, Shader, Sunder, and more. The text i
Matrices generadas por adición de díadas (matrices de rango 1): propiedades y aplicaciones
Ortigueira, Manuel D.
1996-01-01
Se estudian las matrices elementales de rango 1 (díadas). Para estas matrices se presentan fórmulas para su factorización, inversión, descomposición en valores propios y valores singulares. Estos resultados son aplicados en análisis recursivo a cualquier matriz, siempre que se descomponga en una suma de matrices de rango 1. Peer Reviewed
Matrices generadas por adición de díadas (matrices de rango 1): propiedades y aplicaciones
Ortigueira, Manuel D.
1996-01-01
Se estudian las matrices elementales de rango 1 (díadas). Para estas matrices se presentan fórmulas para su factorización, inversión, descomposición en valores propios y valores singulares. Estos resultados son aplicados en análisis recursivo a cualquier matriz, siempre que se descomponga en una suma de matrices de rango 1. Peer Reviewed
Investigation of degradation mechanisms in composite matrices
Giori, C.; Yamauchi, T.
1982-01-01
Degradation mechanisms were investigated for graphite/polysulfone and graphite/epoxy laminates exposed to ultraviolet and high-energy electron radiations in vacuum up to 960 equivalent sun hours and 10 to the ninth power rads respectively. Based on GC and combined GC/MS analysis of volatile by-products evolved during irradiation, several free radical mechanisms of composite degradation were identified. The radiation resistance of different matrices was compared in terms of G values and quantum yields for gas formation. All the composite materials evaluated show high electron radiation stability and relatively low ultraviolet stability as indicated by low G values and high quantum for gas formation. Mechanical property measurements of irradiated samples did not reveal significant changes, with the possible exception of UV exposed polysulfone laminates. Hydrogen and methane were identified as the main by-products of irradiation, along with unexpectedly high levels of CO and CO2.
Diameter Preserving Surjection on Alternate Matrices
Li Ping HUANG
2009-01-01
Let F be a field with |F| ≥ 3, Km be the set of all m × m (m ≥ 4) alternate matrices over F. The arithmetic distance of A, B ∈ Km is d(A, B) := rank(A- B). If d(A, B) = 2, then A and B are said to be adjacent. The diameter of Km is max{d(A, B) : A, B ∈ Km}. Assume that ψ : Km→ Km is a map. We prove the following are equivalent: (a) ψ is a diameter preserving surjection in both directions, (b) ψ is both an adjacency preserving surjection and a diameter preserving map, (c) ψ is a bijective map which preserves the arithmetic distance.
Spirooxazine Photoisomerization and Relaxation in Polymer Matrices
Maria Larkowska
2011-01-01
Full Text Available 9′-Hydroxy-1,3,3-trimethylspiro[indoline-2,3′[3H]naphtha[2,1-b]-1,4oxazine] (SPO-7OH was used in studies of photochromic transformations in polymer matrices. Illumination with UV lamp caused opening the spirostructure of the oxazine with formation of open merocyanine species absorbing at ca. 610 nm. The kinetic studies of thermal relaxation of the open form showed that this process can be described with a biexponential function including both photochemical reaction and rheological behaviour of the polymeric environment. Basing on Arrhenius plot of the rate constant ascribed to the photochemical reaction, the activation energy was determined, which was 66.1 and 84.7 kJ/mole for poly(methyl methacrylate-co-butyl methacrylate and poly(vinylpyrrolidone matrix, respectively.
Carbon nanomaterials in silica aerogel matrices
Hamilton, Christopher E [Los Alamos National Laboratory; Chavez, Manuel E [Los Alamos National Laboratory; Duque, Juan G [Los Alamos National Laboratory; Gupta, Gautam [Los Alamos National Laboratory; Doorn, Stephen K [Los Alamos National Laboratory; Dattelbaum, Andrew M [Los Alamos National Laboratory; Obrey, Kimberly A D [Los Alamos National Laboratory
2010-01-01
Silica aerogels are ultra low-density, high surface area materials that are extremely good thermal insulators and have numerous technical applications. However, their mechanical properties are not ideal, as they are brittle and prone to shattering. Conversely, single-walled carbon nanotubes (SWCNTs) and graphene-based materials, such as graphene oxide, have extremely high tensile strength and possess novel electronic properties. By introducing SWCNTs or graphene-based materials into aerogel matrices, it is possible to produce composites with the desirable properties of both constituents. We have successfully dispersed SWCNTs and graphene-based materials into silica gels. Subsequent supercritical drying results in monolithic low-density composites having improved mechanical properties. These nanocomposite aerogels have great potential for use in a wide range of applications.
Momentum representation for equilibrium reduced density matrices
Golovko, V A
2011-01-01
The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of the momentum representation opens up new opportunities in studies of macroscopic quantum systems both nonsuperfluid and superfluid. It is found that the distribution over momenta in a quantum fluid is not a Bose or Fermi distribution even in the limit of practically noninteracting particles. The distribution looks like a Maxwellian one although, strictly speaking, it is not Maxwellian. The momentum distribution in a quantum crystal depends upon the interaction potential and the crystalline structure. The momentum distribution in a superfluid contains a delta function. The momentum distribution for the condensate in a superfluid crystal consists of delta peaks that are arranged periodically in momentum space. The periodical structure remains if the condensate crystal is not su...
Statistical properties of random scattering matrices
Seba, P; Zakrzewski, J A; Seba, Petr; Zyczkowski, Karol; Zakrzewski, Jakub
1996-01-01
We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are obtained both theoretically and numerically. A simple formula describing the velocity distribution (and hence the distribution of the Wigner time delay) is derived, which is capable to explain the algebraic tail of the time delay distribution observed recently in microwave experiments. A dependence of the eigenphases on other external parameters is also discussed. We show that in the semiclassical limit (large number of channels) the curvature distribution of S--matrix eigenphases is the same as that corresponding to the curvature distribution of the underlying Hamiltonian and is given by the generalized Cauchy distribution.
Matrices over runtime systems at exascale
Agullo, Emmanuel
2012-11-01
The goal of Matrices Over Runtime Systems at Exascale (MORSE) project is to design dense and sparse linear algebra methods that achieve the fastest possible time to an accurate solution on large-scale multicore systems with GPU accelerators, using all the processing power that future high end systems can make available. In this poster, we propose a framework for describing linear algebra algorithms at a high level of abstraction and delegating the actual execution to a runtime system in order to design software whose performance is portable accross architectures. We illustrate our methodology on three classes of problems: dense linear algebra, sparse direct methods and fast multipole methods. The resulting codes have been incorporated into Magma, Pastix and ScalFMM solvers, respectively. © 2012 IEEE.
Unbiased community detection for correlation matrices
MacMahon, Mel
2013-01-01
A challenging problem in the study of large complex systems is that of resolving, without prior information, the emergent mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented at identifying such modules and suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, the attempts made so far have merely replaced network data with correlation matrices, a procedure that we show to be fundamentally biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on Random Matrix Theory, the unbiased correlation-based counterparts of the most popular community detection techniques. After successfully benchmarking our methods, we apply them to s...
Moreadith, R W; Batshaw, M L; Ohnishi, T; Kerr, D.; Knox, B; Jackson, D.; Hruban, R; Olson, J.; Reynafarje, B; Lehninger, A L
1984-01-01
We report the case of an infant with hypoglycemia, progressive lactic acidosis, an increased serum lactate/pyruvate ratio, and elevated plasma alanine, who had a moderate to profound decrease in the ability of mitochondria from four organs to oxidize pyruvate, malate plus glutamate, citrate, and other NAD+-linked respiratory substrates. The capacity to oxidize the flavin adenine dinucleotide-linked substrate, succinate, was normal. The most pronounced deficiency was in skeletal muscle, the le...
A convergence analysis of SOR iterative methods for linear systems with weak H-matrices
Zhang Cheng-yi
2016-01-01
Full Text Available It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices. However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices. This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramírez, Ricardo; Rodríguez, Eduardo
2012-10-01
A genuine gauge theory for the Poincaré, de Sitter or anti-de Sitter algebras can be constructed in (2n - 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices Γab in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices Γab can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient αs. We then give a general algorithm that computes the α-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors Bab with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, "minimal" algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Robust Generalized Low Rank Approximations of Matrices.
Jiarong Shi
Full Text Available In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM. We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods.
Robust Generalized Low Rank Approximations of Matrices.
Shi, Jiarong; Yang, Wei; Zheng, Xiuyun
2015-01-01
In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM). We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM) to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods.
A Lex-BFS-based recognition algorithm for Robinsonian matrices
Laurent, M.; Seminaroti, M.; Paschos, V.; Widmayer, P.
2015-01-01
Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be re- ordered. We present a new polynomial time algorithm to recognize Robinsonian matrices based on a new characterization of
A Lex-BFS-based recognition algorithm for Robinsonian matrices
M. Laurent (Monique); M. Seminaroti (Matteo); V. Paschos; P. Widmayer
2015-01-01
htmlabstractRobinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be re- ordered. We present a new polynomial time algorithm to recognize Robinsonian matrices based on a new characte
Mutation classes of skew-symmetrizable 3x3 matrices
Seven, Ahmet
2010-01-01
In this paper, we determine representatives for the mutation classes of skew-symmetrizable 3x3 matrices and associated graphs using a natural minimality condition, generalizing and strengthening results of Beineke-Brustle-Hille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new numerical invariant for the mutation operation on skew-symmetrizable matrices of arbitrary size.
The Exponent Set of Central Symmetric Primitive Matrices
陈佘喜; 胡亚辉
2004-01-01
This paper first establishes a distance inequality of the associated diagraph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exponent set of central symmetric primitive matrices of order n is {1, 2,… ,n-1}. There is no gap in it.
The Modern Origin of Matrices and Their Applications
Debnath, L.
2014-01-01
This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…
A Lex-BFS-based recognition algorithm for Robinsonian matrices
M. Laurent (Monique); M. Seminaroti (Matteo); V. Paschos; P. Widmayer
2015-01-01
htmlabstractRobinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be re- ordered. We present a new polynomial time algorithm to recognize Robinsonian matrices based on a new
The determinants of some multilevel Vandermonde and Toeplitz matrices
Cervellino, A [Laboratory for Neutron Scattering, PSI Villigen and ETH Zuerich, CH-5232 Villigen PSI (Switzerland); Ciccariello, S [Dipartimento di Fisica ' G. Galilei' and Unita INFM, Universita di Padova, Via Marzolo 8, I-35131 Padova (Italy)
2005-11-11
The closed algebraic expressions of the determinants of some multivariate (multilevel) Vandermonde matrices and the associated Toeplitz/Karle-Hauptman matrices are worked out. The formula can usefully be applied to evaluate the determinant of the Karle-Hauptman matrix generated by a principal basic set of reflections, the knowledge of which determines the full diffraction pattern of an ideal crystal.
Fusion for AdS/CFT boundary S-matrices
Nepomechie, Rafael I. [Physics Department, University of Miami,P.O. Box 248046, Coral Gables, FL 33124 (United States); Pimenta, Rodrigo A. [Physics Department, University of Miami,P.O. Box 248046, Coral Gables, FL 33124 (United States); Departamento de Física, Universidade Federal de São Carlos,Caixa Postal 676, CEP 13569-905, São Carlos (Brazil)
2015-11-24
We propose a fusion formula for AdS/CFT worldsheet boundary S-matrices. We show that, starting from the fundamental Y=0 boundary S-matrix, this formula correctly reproduces the two-particle bound-state boundary S-matrices.
Revisiting amino acid substitution matrices for identifying distantly related proteins.
Yamada, Kazunori; Tomii, Kentaro
2014-02-01
Although many amino acid substitution matrices have been developed, it has not been well understood which is the best for similarity searches, especially for remote homology detection. Therefore, we collected information related to existing matrices, condensed it and derived a novel matrix that can detect more remote homology than ever. Using principal component analysis with existing matrices and benchmarks, we developed a novel matrix, which we designate as MIQS. The detection performance of MIQS is validated and compared with that of existing general purpose matrices using SSEARCH with optimized gap penalties for each matrix. Results show that MIQS is able to detect more remote homology than the existing matrices on an independent dataset. In addition, the performance of our developed matrix was superior to that of CS-BLAST, which was a novel similarity search method with no amino acid matrix. We also evaluated the alignment quality of matrices and methods, which revealed that MIQS shows higher alignment sensitivity than that with the existing matrix series and CS-BLAST. Fundamentally, these results are expected to constitute good proof of the availability and/or importance of amino acid matrices in sequence analysis. Moreover, with our developed matrix, sophisticated similarity search methods such as sequence-profile and profile-profile comparison methods can be improved further. Newly developed matrices and datasets used for this study are available at http://csas.cbrc.jp/Ssearch/.
The Modern Origin of Matrices and Their Applications
Debnath, L.
2014-01-01
This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…
Reprint of Testing scattering matrices: a compendium of recipes
Hovenier, J.W.; van der Mee, C.V.M.
2010-01-01
Scattering matrices describe the transformation of the Stokes parameters of a beam of radiation upon scattering of that beam. The problems of testing scattering matrices for scattering by one particle and for single scattering by an assembly of particles are addressed. The treatment concerns
Sarymsakov matrices and coordination tasks for multi-agent systems
Xia, Weiguo; Cao, Ming
2012-01-01
The convergence of products of stochastic matrices has proven to be critical in establishing the effectiveness of distributed coordination algorithms for multi-agent systems. After reviewing some classic and recent results on infinite backward products of stochastic matrices, we provide a new
Random Matrices, Combinatorics, Numerical Linear Algebra and Complex Networks
2012-02-16
Littlewood-Offord theorems and the condition number of random discrete matrices, Annals of Mathematics , to appear. [29] T. Tao and V. Vu, The condition...Wigner. On the distribution of the roots of certain symmetric matrices. Annals of Mathematics , 67(2):325327, 1958. Department of Mathematics, Yale, New Haven, CT 06520 E-mail address: van.vu@yale.edu
On Factorization of Coupled Channel Scattering S Matrices
无
2007-01-01
We investigate the problem on how to factorize a coupled channel scattering S matrix into a product of simple S matrices. Simple S matrix solutions are found, respecting unitarity, analyticity and being real analytic. The phase shift and its physical meaning produced by these simple S matrices are discussed.
Pavel Etingof
2007-03-01
Full Text Available Following the works by Wiegmann-Zabrodin, Elbau-Felder, Hedenmalm-Makarov, and others, we consider the normal matrix model with an arbitrary potential function, and explain how the problem of finding the support domain for the asymptotic eigenvalue density of such matrices (when the size of the matrices goes to infinity is related to the problem of Hele-Shaw flows on curved surfaces, considered by Entov and the first author in 1990-s. In the case when the potential function is the sum of a rotationally invariant function and the real part of a polynomial of the complex coordinate, we use this relation and the conformal mapping method developed by Entov and the first author to find the shape of the support domain explicitly (up to finitely many undetermined parameters, which are to be found from a finite system of equations. In the case when the rotationally invariant function is βz^2, this is done by Wiegmann-Zabrodin and Elbau-Felder. We apply our results to the generalized normal matrix model, which deals with random block matrices that give rise to *-representations of the deformed preprojective algebra of the affine quiver of type Â_{m-1}. We show that this model is equivalent to the usual normal matrix model in the large N limit. Thus the conformal mapping method can be applied to find explicitly the support domain for the generalized normal matrix model.
Time series, correlation matrices and random matrix models
Vinayak [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca (Mexico); Seligman, Thomas H. [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México and Centro Internacional de Ciencias, C.P. 62210 Cuernavaca (Mexico)
2014-01-08
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.
The semi-dynamical reflection equation: solutions and structure matrices
Avan, J; Zambon, C [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise (CNRS UMR 8089), Saint-Martin 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex (France)], E-mail: avan@u-cergy.fr, E-mail: cristina.zambon@u-cergy.fr
2008-05-16
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant Arutyunov-Chekhov-Frolov structure matrices, and a specific meromorphic ansatz, it is found that only two sets of the previously found constant solutions are extendible to the non-constant case. In order to simplify future constructions of spin-chain Hamiltonians, a parametrization procedure is applied explicitly to all elements of the semi-dynamical reflection equation available. Interesting expressions for 'twists' and R-matrices entering the parametrization procedure are found. In particular, some expressions for the R-matrices seem to appear here for the first time. In addition, a new set of consistent structure matrices for the semi-dynamical reflection equation is obtained.
Pinelli, Claudia; Rastogi, Rakesh K; Scandurra, Anna; Jadhao, Arun G; Aria, Massimo; D'Aniello, Biagio
2014-09-01
Nicotinamide adenine dinucleotide phosphate-diaphorase (NADPH-d) is a key enzyme in the synthesis of the gaseous neurotransmitter nitric oxide. We compare the distribution of NADPH-d in the brain of four species of hylid frogs. NADPH-d-positive fibers are present throughout much of the brain, whereas stained cell groups are distributed in well-defined regions. Whereas most brain areas consistently show positive neurons in all species, in some areas species-specific differences occur. We analyzed our data and those available for other amphibian species to build a matrix on NADPH-d brain distribution for a multivariate analysis. Brain dissimilarities were quantified by using the Jaccard index in a hierarchical clustering procedure. The whole brain dendrogram was compared with that of its main subdivisions by applying the Fowlkes-Mallows index for dendrogram similarity, followed by bootstrap replications and a permutation test. Despite the differences in the distribution map of the NADPH-d system among species, cluster analysis of data from the whole brain and hindbrain faithfully reflected the evolutionary history (framework) of amphibians. Dendrograms from the secondary prosencephalon, diencephalon, mesencephalon, and isthmus showed some deviation from the main scheme. Thus, the present analysis supports the major evolutionary stability of the hindbrain. We provide evidence that the NADPH-d system in main brain subdivisions should be cautiously approached for comparative purposes because specific adaptations of a single species could occur and may affect the NADPH-d distribution pattern in a brain subdivision. The minor differences in staining pattern of particular subdivisions apparently do not affect the general patterns of staining across species. © 2014 Wiley Periodicals, Inc.
Tomita Motowo
2001-01-01
Full Text Available Abstract Background The autoimmune thyroid diseases (AITDs, such as Graves' disease (GD and Hashimoto's thyroiditis (HT, appear to develop as a result of complex interactions between predisposing genes and environmental triggers. Susceptibility to AITDs is conferred by genes in the human leukocyte antigen (HLA and genes unlinked to HLA, including the CTLA-4 gene. Recently, estrogen receptor (ER β, located at human chromosome 14q23-24.1, was identifed. We analyzed a dinucleotide (CAn repeat polymorphism located in the flanking region of ERβ gene in patients with AITDs and in normal subjects. High heterozygosity makes this polymorphism a useful marker in the genetic study of disorders affecting female endocrine systems. We also correlated a ERβ gene microsatellite polymorphism with bone mineral density (BMD in the distal radius and biochemical markers of bone turnover in patients with GD in remission. Results Fourteen different alleles were found in 133 patients with GD, 114 patients with HT, and 179 controls subjects. The various alleles were designated as allele*1 through allele*14 according to the number of the repeats, from 18 to 30. There was no significant difference in the distributions of ERβ alleles between patient groups and controls. Although recent study demonstrated a significant relation between a allele*9 in the ERβ gene and BMD in postmenopausal Japanese women, there were no statistically significant interaction between this allele and BMD in the distal radius, nor biochemical markers in patients with GD in remission. Conclusions The present results do not support an association between the ERβ microsatellite marker and AITD in the Japanese population. We also suggest that the ERβ microsatellite polymorphism has at most a minor pathogenic importance in predicting the risk of osteoporosis as a complication of GD.
无
2007-01-01
AIM: To elucidate the mechanisms of hepatocyte preconditioning by H2O2 to better understand the pathophysiology of ischemic preconditioning.METHODS: The in vitro effect of H2O2 pretreatment was investigated in rat isolated hepatocytes subjected to anoxia/reoxygenation. Cell viability was assessed with propidium iodide fluorometry. In other experiments, rat livers were excised and subjected to warm ischemia/reperfusion in an isolated perfused liver system to determine leakage of liver enzymes. Preconditioning was performed by H2O2 perfusion, or by stopping the perfusion for 10 min followed by 10 min of reperfusion.To inhibit Kupffer cell function or reduced nicotinamide adenine dinucleotide phosphate (NADPH) oxidase,gadolinium chloride was injected prior to liver excision, or diphenyleneiodonium, an inhibitor of NADPH oxidase, was added to the perfusate, respectively. Histological detection of o~gen radical formation in Kupffer cells was performed by perfusion with nitro blue tetrazolium.RESULTS: Anoxia/reoxygenation decreased hepatocyte viability compared to the controls. Pretreatment with H2O2 did not improve such hepatocyte injury. In liver perfusion experiments, however, H2O2 preconditioning reduced warm ischemia/reperfusion injury, which was reversed by inhibition of Kupffer cell function or NADPH oxidase. Histological examination revealed that H2O2 preconditioning induced oxygen radical formation in Kupffer cells. NADPH oxidase inhibition also reversed hepatoprotection by ischemic preconditioning.CONCLUSION: H2O2 preconditioning protects hepatocytes against warm ischemia/reperfusion injury via NADPH oxidase in Kupffer cells, and not directly. NADPH oxidase also mediates hepatoprotection by ischemic preconditioning.
LIU Tong-tao; WANG Li-li; FANG Sheng-xia; JIA Chong-qi
2012-01-01
Background The p22phox is a critical component of the superoxide-generating vascular nicotinamide adenine dinucleotide phosphate (NADPH) oxidase.Several polymorphisms in p22phox gene are studied for their association with cardiovascular diseases.However,no publication is available to assess the relation of 549C＞T polymorphism in p22phox gene to coronary artery disease (CAD) risk.This study was to investigate the effect of the p22phox gene 549C＞T polymorphism on CAD risk.Methods Hospital-based case-control study was conducted with 297 CAD patients and 343 healthy persons as the control group.Polymerase chain reaction and pyrosequencing using PSQ 96 MA Pyrosequencer (Biotage AB) were used to detect the polymorphisms.Multiple Logistic regression model was used to adjust the potential confounders and to estimate odds ratio (OR) with 95％ confidence intervals (Cls).Results The observed genotype frequencies of this polymorphism obeyed the Hardy-Weinberg equilibrium in both cases (P=0.439) and controls (P=0.668).The frequency of mutant genotypes (TT+CT) in cases (41.08％) was higher than that in controls (36.73％) with an OR=-1.20 (95％ CI=0.87-1.65).After the adjustment of the potential confounders,there was a significant association of the mutant genotypes with increased risk of CAD (OR=1.57,95％ CI=1.01-2.46,P=0.047).Conclusions The mutant genotypes of the p22phox gene 549C＞T polymorphism had a significant effect on the increased risk of CAD in this studied population.
H-MATRICES AND S-DOUBLY DIAGONALLY DOMINANT MATRICES%H-矩阵和S-双对角占优矩阵
杨月婷; 徐成贤
2004-01-01
In this paper, the concept of the s-doubly diagonally dominant matrices is introduced and the properties of these matrices are discussed. With the properties of the s-doubly diagonally dominant matrices and the properties of comparison matrices, some equivalent conditions for H-matrices are presented. These conditions generalize and improve existing results about the equivalent conditions for H-matrices. Applications and examples using these new equivalent conditions are also presented, and a new inclusion region of k-multiple eigenvalues of matrices is obtained.
Tetrodotoxin Detection by a Surface Plasmon Resonance Sensor in Pufferfish Matrices and Urine
Allen D. Taylor
2011-01-01
Full Text Available Tetrodotoxin (TTX poisoning is most commonly associated with consumption of pufferfish. TTX is a low molecular weight (~319 Da neurotoxin that selectively blocks voltage-sensitive Na+-gated ion channels. The standard method accepted worldwide for monitoring TTX toxicity in food matrices is the mouse bioassay. Ethical concerns from live animal testing, low sample throughput, and analytical inaccuracies have led to the need for an alternative method. We have previously established that surface plasmon resonance (SPR sensors can quantify TTX in aqueous buffer samples by an antibody-based inhibition assay. In this paper, we report the extension of the assay for the detection of TTX in both clinical- and food-relevant matrices. The assay was optimized for application to three relevant complex matrices: pufferfish liver extract, pufferfish muscle extract, and human urine. Matrix effects are discussed and calibration curves are presented. Naturally contaminated pufferfish liver and muscle extracts were analyzed by the SPR method, and the data is compared to liquid-chromatography electrospray-ionization multiple reactions monitoring mass spectrometry (LC/ESI/MRM/MS data. Ten samples, including three from a poisoning incident, two control monkfish samples, and five toxic pufferfish samples, were analyzed using this method, and the data is compared to LC/ESI/MRM/MS analysis of the samples.
Davor Dolar; Arna Vukovi(c); Danijela A(a)perger; Kre(s)imir Ko(s)ulti(c)
2011-01-01
This study explored the removal of five veterinary pharmaceuticals (VPs) (sulfamethoxazole (SMETOX),trimethopfim (TMP),ciprofloxacin (CIPRO),dexamethasone (DEXA) and febantel (FEBA)) from different water matrices (Milli-Q water,model water,tap water and real pharmaceutical wastewater using four types of nanofiltration (NF) membranes (NF90,NF270,NF and HL) and two reverse osmosis (RO) membranes (LFC-1 and XLE).All VPs were added to different water matrices at a concentration of 10 mg/L.Rejections of VPs and water flux were measured.The rejection increased with increase of molecular weight.The highest rejections were obtained with RO membranes (LFC-1,XLE) and tight NF (NF90) membrane.In general,the rejection of VPs was higher in model water and tap water than in Milli-Q water,but the water flux was lower.This was mainly explained by ion adsorption inside the membranes pores.Narrower pore size counteracted the effect of presence of low concentration of natural organic matter (NOM) in tap water.The NOM was assumed to enhance the adsorption of VPs onto membrane surface,increased the size exclusion and electrostatic repulsion also appeared during the transport.Investigated water matrices had influence on water flux decline due to their complexity.
Karaca, Gizem; Tasdemir, Yücel
2014-08-01
In the present study, removal of polycyclic aromatic hydrocarbons (PAHs) from synthetic solid matrices with various methods was investigated. PAH removal experiments were conducted in a specifically designed UV apparatus for this study. Polyurethane foams (PUF) cartridges were used to remove PAHs from the incoming air and to capture PAHs from the evaporated gases. Sodium sulphate (Na2SO4) was used as a synthetic solid matrices. The effects of temperature, UV radiation, titanium dioxide (TiO2) and diethylamine (DEA) dose on the PAH removal were determined. TiO2and DEA were added to the Na2SO4 sample at the rate of 5% and 20% of dry weight of samples. PAHs' removal from the Na2SO4 enhanced with increasing temperature. Sigma12 PAH content in the Na2SO4 reduced up to 95% during UV light application. Moreover, the Sigma12 PAH removal ratio was calculated as 95% with using 5% of TiO2, and increasing of TiO2 dose negatively affected PAH removal. PAH concentration in the samples decreased by 93% and 99% with addition of 5% and 20% DEA, respectively. Especially, 3- and 4-ring PAH compounds evaporated during the PAH removal applications. As expected, evaporation mechanism became more effective at high temperature for light PAH compounds. It was concluded that PAHs can successfully be removed from synthetic solid matrices such as Na2 SO4 with the applications of UV light and UV-photocatalysts.
Investigation of Drug Release from PEO Tablet Matrices in the Presence of Vitamin E as Antioxidant.
Shojaee, Saeed; Nokhodchi, Ali; Cumming, Iain; Alhalaweh, Amjad; Kaialy, Waseem
2015-01-01
The objective of this study was to investigate the influence of drug type on the release of drug from PEO matrix tablets accompanied with the impact of vitamin E succinate as antioxidant. The result showed that the presence of vitamin E promoted a stable release rate of soluble drug propranolol HCl from aged PEO matrix tablets, which was similar to fresh sample, regardless of molecular weight (MW) of PEO. However, the influence of the presence of vitamin E on the release rate of partially soluble drug, theophylline, was dependent on the MW of PEO; i.e., fast and unstable drug release was obtained in the case of low MW PEO 750 whereas stable drug release was obtained in the case of high MW PEO 303. The release of low water-soluble drug zonisamide was stable regardless of both the presence of vitamin E and the MW of PEO. The presence of vitamin E slightly slowed the release of zonisamide from aged PEO 303 matrices but not PEO 750 matrices. Therefore, in order to achieve a suitable controlled release profile from PEO matrices, not only the presence of vitamin E but also the solubility of the drug and the MW of polyox should be considered.
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Study of the optimum haplotype length to build genomic relationship matrices.
Ferdosi, Mohammad H; Henshall, John; Tier, Bruce
2016-09-29
As genomic data becomes more abundant, genomic prediction is more routinely used to estimate breeding values. In genomic prediction, the relationship matrix ([Formula: see text]), which is traditionally used in genetic evaluations is replaced by the genomic relationship matrix ([Formula: see text]). This paper considers alternative ways of building relationship matrices either using single markers or haplotypes of different lengths. We compared the prediction accuracies and log-likelihoods when using these alternative relationship matrices and the traditional [Formula: see text] matrix, for real and simulated data. For real data, we built relationship matrices using 50k genotype data for a population of Brahman cattle to analyze three traits: scrotal circumference (SC), age at puberty (AGECL) and weight at first corpus luteum (WTCL). Haplotypes were phased with hsphase and imputed with BEAGLE. The relationship matrices were built using three methods based on haplotypes of different lengths. The log-likelihood was considered to define the optimum haplotype lengths for each trait and each haplotype-based relationship matrix. Based on simulated data, we showed that the inverse of [Formula: see text] matrix and the inverse of the haplotype relationship matrices for methods using one-single nucleotide polymorphism (SNP) phased haplotypes provided coefficients of determination (R(2)) close to 1, although the estimated genetic variances differed across methods. Using real data and multiple SNPs in the haplotype segments to build the relationship matrices provided better results than the [Formula: see text] matrix based on one-SNP haplotypes. However, the optimal haplotype length to achieve the highest log-likelihood depended on the method used and the trait. The optimal haplotype length (7 to 8 SNPs) was similar for SC and AGECL. One of the haplotype-based methods achieved the largest increase in log-likelihood for SC, i.e. from -1330 when using [Formula: see text] to
Sums of Ramdom Matrices and the Potts Model on Random Planar Maps
Atkin, Max R; Wheater, John F
2015-01-01
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with $p$ and $q-p$ colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when $0\\leq q\\leq 4$ and comment on the conformal field theory description of the critical points.
Sums of random matrices and the Potts model on random planar maps
Atkin, Max R.; Niedner, Benjamin; Wheater, John F.
2016-05-01
We compute the partition function of the q-states Potts model on a random planar lattice with p≤slant q allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit, generalising a result by Voiculescu for the addition of random matrices to a situation beyond free probability theory. We show that the partition functions with p and q - p colours on the boundary are related algebraically. Finally, we investigate the phase diagram of the model when 0≤slant q≤slant 4 and comment on the conformal field theory description of the critical points.
Mechanically implementable accommodation matrices for passive force control
Goswami, A. [Univ. of Pennsylvania, Philadelphia, PA (United States). Center for Human Modeling and Simulation; Peshkin, M. [Northwestern Univ., Evanston, IL (United States). Dept. of Mechanical Engineering
1999-08-01
Robot force control implemented by means of passive mechanical devices has inherent advantages over active implementations with regard to stability, response rapidity, and physical robustness. The class of devices considered in this paper consists of a Stewart platform-type mechanism interconnected with a network of adjustable mechanical elements such as springs and dampers. The control law repertoire of such a device, imagined as a robot wrist, is given by the range of admittance matrices that it may be programmed to possess. This paper focuses on wrists incorporating damper networks for which the admittance matrices reduce to accommodation or inverse-damping matrices. The authors show that a hydraulic network of fully adjustable damper elements may attain any diagonally dominant accommodation matrix. They describe the technique of selecting the individual damping coefficients to design a desired matrix. They identify the set of dominant matrices as a polyhedral convex cone in the space of matrix entries, and show that each dominant matrix can be composed of a positive linear combination of a fixed set of basis matrices. The overall wrist-accommodation matrix is obtained by projecting the accommodation matrix of the damper network through the wrist kinematics. The linear combination of the dominant basis matrices projected through the wrist kinematics generates the entire space of mechanically implementable force-control laws. The authors quantify the versatility of mechanically implementable force-control laws by comparing this space to the space of all matrices.
Kumar, Prasoon; Gandhi, Prasanna S.; Majumder, Mainak
2016-04-01
Gills are one of the most primitive gas, solute exchange organs available in fishes. They facilitate exchange of gases, solutes and ions with a surrounding water medium through their functional unit called secondary lamella. These lamellae through their extraordinary morphometric features and peculiar arrangement in gills, achieve remarkable mass transport properties. Therefore, in the current study, modeling and simulation of convection-diffusion transport through a two dimensional model of secondary lamella and theoretical analysis of morphometric features of fish gills were carried out. Such study suggested an evolutionary conservation of parametric ratios across fishes of different weights. Further, we have also fabricated a thin microvascularised PDMS matrices mimicking secondary lamella by use of micro-technologies like electrospinning. In addition, we have also demonstrated the fluid flow by capillary action through these thin microvascularised PDMS matrices. Eventually, we also illustrated the application of these thin microvascularied PDMS matrices in solute exchange process under capillary flow conditions. Thus, our study suggested that fish gills have optimized parameteric ratios, at multiple length scale, throughout an evolution to achieve an organ with enhanced mass transport capabilities. Thus, these defined parametric ratios could be exploited to design and develop efficient, scaled-up gas/solute exchange microdevices. We also proposed an inexpensive and scalable method of fabrication of thin microvascularised polymer matrices and demonstrated its solute exchange capabilities under capillary flow conditions. Thus, mimicking the microstructures of secondary lamella will enable fabrication of microvascularised thin polymer systems through micro manufacturing technologies for potential applications in filtration, self-healing/cooling materials and bioengineering.
Limits of spiked random matrices II
Bloemendal, Alex
2011-01-01
The top eigenvalues of rank r spiked real Wishart matrices and additively perturbed Gaussian orthogonal ensembles are known to exhibit a phase transition in the large size limit. We show that they have limiting distributions for near-critical perturbations, fully resolving the conjecture of Baik, Ben Arous and P\\'ech\\'e (2005). The starting point is a new (2r+1)-diagonal form that is algebraically natural to the problem; for both models it converges to a certain random Schr\\"odinger operator on the half-line with r x r matrix-valued potential. The perturbation determines the boundary condition, and the low-lying eigenvalues describe the limit jointly over all perturbations in a fixed subspace. We treat the real, complex and quaternion (beta = 1,2,4) cases simultaneously. We also characterize the limit laws in terms of a diffusion related to Dyson's Brownian motion, and further in terms of a linear parabolic PDE; here beta is simply a parameter. At beta = 2 the PDE appears to reconcile with known Painlev\\'e fo...
NOTE ON REGULAR D-OPTIMAL MATRICES
李乔良
2003-01-01
Let A be aj ×d (0,1) matrix. It is known that ifj = 2k-1is odd, then det(AAT) ≤(j+1)((j+1)d/4j)j; ifj is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regularD-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved thatifj = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrixof a (2k - 1, k, (j + 1)d/4j)-BIBD; if j ＝ 2k is even, then A is a regular D-optimal matrix ifand only if A can be obtained from the adjacent matrix B of a (2k + 1, k + 1, (j + 2)d/4(j + 1))-BIBD by deleting any one row from B. Three 21 × 42 regular D-optimal matrices, which wereunknown in [11], are also provided.
Generalized graph states based on Hadamard matrices
Cui, Shawn X. [Department of Mathematics, University of California, Santa Barbara, California 93106 (United States); Yu, Nengkun [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China); Zeng, Bei [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8 (Canada)
2015-07-15
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.
Striations in PageRank-Ordered Matrices
Pennycuff, Corey
2016-01-01
Patterns often appear in a variety of large, real-world networks, and interesting physical phenomena are often explained by network topology as in the case of the bow-tie structure of the World Wide Web, or the small world phenomenon in social networks. The discovery and modelling of such regular patterns has a wide application from disease propagation to financial markets. In this work we describe a newly discovered regularly occurring striation pattern found in the PageRank ordering of adjacency matrices that encode real-world networks. We demonstrate that these striations are the result of well-known graph generation processes resulting in regularities that are manifest in the typical neighborhood distribution. The spectral view explored in this paper encodes a tremendous amount about the explicit and implicit topology of a given network, so we also discuss the interesting network properties, outliers and anomalies that a viewer can determine from a brief look at the re-ordered matrix.
On some Toeplitz matrices and their inversions
S. Dutta
2014-10-01
Full Text Available In this article, using the difference operator B(a[m], we introduce a lower triangular Toeplitz matrix T which includes several difference matrices such as Δ(1,Δ(m,B(r,s,B(r,s,t, and B(r̃,s̃,t̃,ũ in different special cases. For any x ∈ w and m∈N0={0,1,2,…}, the difference operator B(a[m] is defined by (B(a[m]xk=ak(0xk+ak-1(1xk-1+ak-2(2xk-2+⋯+ak-m(mxk-m,(k∈N0 where a[m] = {a(0, a(1, …, a(m} and a(i = (ak(i for 0 ⩽ i ⩽ m are convergent sequences of real numbers. We use the convention that any term with negative subscript is equal to zero. The main results of this article relate to the determination and applications of the inverse of the Toeplitz matrix T.
Visualizing complex (hydrological) systems with correlation matrices
Haas, J. C.
2016-12-01
When trying to understand or visualize the connections of different aspects of a complex system, this often requires deeper understanding to start with, or - in the case of geo data - complicated GIS software. To our knowledge, correlation matrices have rarely been used in hydrology (e.g. Stoll et al., 2011; van Loon and Laaha, 2015), yet they do provide an interesting option for data visualization and analysis. We present a simple, python based way - using a river catchment as an example - to visualize correlations and similarities in an easy and colorful way. We apply existing and easy to use python packages from various disciplines not necessarily linked to the Earth sciences and can thus quickly show how different aquifers work or react, and identify outliers, enabling this system to also be used for quality control of large datasets. Going beyond earlier work, we add a temporal and spatial element, enabling us to visualize how a system reacts to local phenomena such as for example a river, or changes over time, by visualizing the passing of time in an animated movie. References: van Loon, A.F., Laaha, G.: Hydrological drought severity explained by climate and catchment characteristics, Journal of Hydrology 526, 3-14, 2015, Drought processes, modeling, and mitigation Stoll, S., Hendricks Franssen, H. J., Barthel, R., Kinzelbach, W.: What can we learn from long-term groundwater data to improve climate change impact studies?, Hydrology and Earth System Sciences 15(12), 3861-3875, 2011
Collar, Concha; Jiménez, Teresa; Conte, Paola; Piga, Antonio
2015-01-01
The impact of wheat (WT) flour replacement up to 45% (weight basis) by incorporation of ternary blends of teff (T), green pea (GP) and buckwheat (BW) flours on the thermal profiles of quaternary blended dough matrices have been investigated by simulating baking, cooling, and storage in differential scanning calorimeter (DSC) pans. Endothermal transitions related to suitable patterns for low and slow starch hydrolysis, softer crumb and retarded firming kinetics in blended breads include delaye...
Random matrices as models for the statistics of quantum mechanics
Casati, Giulio; Guarneri, Italo; Mantica, Giorgio
1986-05-01
Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit. Permanent address: Dipartimento di Fisica, Via Celoria 16, 20133 Milano, Italy.
On the asymptotic distribution of block-modified random matrices
Arizmendi, Octavio, E-mail: octavius@cimat.mx [Department of Probability and Statistics, CIMAT, Guanajuato (Mexico); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany and CNRS, Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France); Vargas, Carlos, E-mail: obieta@math.tugraz.at [Department of Mathematical Structure Theory, Technische Universität Graz, Steyrergasse 30/III, 8010 Graz (Austria)
2016-01-15
We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations.
Kerov's interlacing sequences and random matrices
Bufetov, Alexey, E-mail: alexey.bufetov@gmail.com [Institute for Information Transmission Problems, Independent University of Moscow and Higher School of Economics, Moscow (Russian Federation)
2013-11-15
To a N × N real symmetric matrix Kerov assigns a piecewise linear function whose local minima are the eigenvalues of this matrix and whose local maxima are the eigenvalues of its (N − 1) × (N − 1) submatrix. We study the scaling limit of Kerov's piecewise linear functions for Wigner and Wishart matrices. For Wigner matrices the scaling limit is given by the Verhik-Kerov-Logan-Shepp curve which is known from asymptotic representation theory. For Wishart matrices the scaling limit is also explicitly found, and we explain its relation to the Marchenko-Pastur limit spectral law.
ANOVA like analysis for structured families of stochastic matrices
Dias, Cristina; Santos, Carla; Varadinov, Maria; Mexia, João T.
2016-12-01
Symmetric stochastic matrices width a width a dominant eigenvalue λ and the corresponding eigenvector α appears in many applications. Such matrices can be written as M =λ α αt+E¯. Thus β = λ α will be the structure vector. When the matrices in such families correspond to the treatments of a base design we can carry out a ANOVA like analysis of the action of the treatments in the model on the structured vectors. This analysis can be transversal-when we worked width homologous components and - longitudinal when we consider contrast on the components of each structure vector. The analysis will be briefly considered at the end of our presentation.
Lipschitz correspondence between metric measure spaces and random distance matrices
Gadgil, Siddhartha
2011-01-01
Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points chosen indepenedently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.
侯素梅
2002-01-01
实矩阵A称为是almostP-矩阵,如果A的行列式是正的,而所有真主子式是负的.本文给出了almostP-矩阵的一些性质以及almostP-矩阵与弱almostP-矩阵之间的关系.%An almost P-matrix A is one with real entries whose determinant is negative and all proper minors are positive. Obtain some properties for almost P-matrices, and the relationship between almost P-matrices and weak almost P-matrices.
User-Friendly Tools for Random Matrices: An Introduction
2012-12-03
The set of positive-semidefinite matrices with size d forms a closed, convex cone in the real- linear space of Hermitian matrices of dimension d...valued function h on matrices that is concave or convex. The expectation of a random matrix can be viewed as a convex combination, and the cone of...hope shatters when we subject it to interrogation. It is not hard to find the reason that (3.3.2) fails. Note that the identity (3.3.1) depends on the
Kotzian, Petr; Janku, Tereza [Department of Analytical Chemistry, University of Pardubice, Nam. Cs. Legii 565, CZ-532 10 Pardubice (Czech Republic); Kalcher, Kurt [Institute of Chemistry - Analytical Chemistry, Karl-Franzens University, Universitaetsplatz 1, A-8010 Graz (Austria); Vytras, Karel [Department of Analytical Chemistry, University of Pardubice, Nam. Cs. Legii 565, CZ-532 10 Pardubice (Czech Republic)], E-mail: karel.vytras@upce.cz
2007-09-19
Hydrogen peroxide and nicotinamide adenine dinucleotide (NADH) may be determined amperometrically using screen-printed electrodes chemically modified with iron(III) hexacyanoosmate(II) (Osmium purple) in flow injection analysis (FIA). The determination is based on the exploitation of catalytic currents resulting from the oxidation/reduction of the modifier. The performance of the sensor was characterized and optimized by controlling several operational parameters (applied potential, pH and flow rate of the phosphate buffer). Comparison has been made with analogous complexes of ruthenium (Ruthenium purple) and iron (Prussian blue). Taking into account the sensitivity and stability of corresponding sensors, the best results were obtained with the use of Osmium purple. The sensor exhibited a linear increase of the amperometric signal with the concentration of hydrogen peroxide in the range of 0.1-100 mg L{sup -1} with a detection limit (evaluated as 3{sigma}) of 0.024 mg L{sup -1} with a R.S.D. 1.5% for 10 mg L{sup -1} H{sub 2}O{sub 2} under optimized flow rate of 0.4 mL min{sup -1} in 0.1 M phosphate buffer carrier (pH 6) and a working potential of +0.15 V versus Ag/AgCl. Afterwards, a biological recognition element - either glucose oxidase or ethanol dehydrogenase - was incorporated to achieve a sensor facilitating the determination of glucose or ethanol, respectively. The glucose sensor gave linearity between current and concentration in the range from 1 to 250 mg L{sup -1} with a R.S.D. 2.4% for 100 mg L{sup -1} glucose, detection limit 0.02 mg L{sup -1} (3{sigma}) and retained its original activity after 3 weeks when stored at 6 deg. C. Optimal parameters in the determination of ethanol were selected as: applied potential +0.45 V versus Ag/AgCl, flow rate 0.2 mL min{sup -1} in 0.1 M phosphate buffer carrier (pH 7). Different structural designs of the ethanol sensor were tested and linearity obtained was up to 1000 mg L{sup -1} with a maximum R.S.D. of 5
Flach, Joost; van der Waal, Mark B; van den Nieuwboer, Maurits; Claassen, Eric; Larsen, Olaf F A
2017-06-13
Probiotic microorganisms are increasingly incorporated into food matrices in order to confer proposed health benefits on the consumer. It is important that the health benefits, sensory properties, shelf-life and probiotic gastrointestinal tract (GIT) survival of these products are carefully balanced as they determine functionality and drive consumer acceptance. The strain-specific effects of probiotic species are imperative in this process but carrier matrices may play a pivotal role as well. This study therefore recapitulates the wealth of knowledge on carrier matrices and their interaction with probiotic strains. The most substantiated carrier matrices, factors that influence probiotic functionality and matrix effects on shelf-life, GIT survival and clinical efficacy are reviewed. Results indicate that carrier matrices have a significant impact on the quality of probiotic products. Matrix components, such as proteins, carbohydrates and flavoring agents are shown to alter probiotic efficacy and viability. In vivo studies furthermore revealed strain-dependent matrix effects on the GIT survival of probiotic bacteria. However, only a limited number of studies have specifically addressed the effects of carrier matrices on the aforementioned product-parameters; most studies seem to focus solely on the strain-specific effects of probiotic microorganisms. This hampers the innovation of probiotic products. More human studies, comparing not only different probiotic strains but different carrier matrices as well, are needed to drive the innovation cycle.
ON THE STIFFNESS OF DEMINERALIZED DENTIN MATRICES
Ryou, Heonjune; Turco, Gianluca; Breschi, Lorenzo; Tay, Franklin R.; Pashley, David H.; Arola, Dwayne
2015-01-01
Resin bonding to dentin requires the use of self-etching primers or acid etching to decalcify the surface and expose a layer of collagen fibrils of the dentin matrix. Acid-etching reduces the stiffness of demineralized dentin from approximately 19 GPa to 1 MPa, requiring that it floats in water to prevent it from collapsing during bonding procedures. Several publications show that crosslinking agents like gluteraladehyde, carbodiimide or grape seed extract can stiffen collagen and improve resin-dentin bond strength. Objective The objective was to assess a new approach for evaluating the changes in stiffness of decalcified dentin by polar solvents and a collagen cross-linker. Methods Fully demineralized dentin beams and sections of etched coronal dentin were subjected to indentation loading using a cylindrical flat indenter in water, and after treatment with ethanol or ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC). The stiffness was measured as a function of strain and as a function of loading rate from 1 to 50 µm/sec. Results At a strain of 0.25% the elastic modulus of the fully demineralized dentin was approximately 0.20 MPa. It increased to over 0.90 MPa at strains of 1%. Exposure to ethanol caused an increase in elastic modulus of up to four times. Increasing the loading rate from 1 to 50 µm/sec caused an increase in the apparent modulus of up to three times in both water and ethanol. EDC treatment caused increases in the stiffness in fully demineralized samples and in acid-etched demineralized dentin surfaces in situ. Significance Changes in the mechanical behavior of demineralized collagen matrices can be measured effectively under hydration via indentation with cylindrical flat indenters. This approach can be used for quantifying the effects of bonding treatments on the properties of decalcified dentin after acid etching, as well as to follow the loss of stiffness over time due to enzymatic degradation. PMID:26747822
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
Kandasamy, W B Vasantha; Amal, K
2008-01-01
This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.
Transfer matrices of dipoles with bending radius variation
无
2011-01-01
With the increasing demand of high brightness in light source, the uniform dipole can not meet the needs of low emittance, and thus the dipole with bending radius variation is introduced in this paper. The transfer matrix of a non-uniform dipole whose bending radius is linearly changed is chosen as an example and a very simple calculation formula of non-uniform dipole transfer matrices is given. The transfer matrices of some common profile non-uniform dipoles are also listed. The comparison of these transfer matrices and the matrices calculated with slices method verifies the numerical accuracy of this formula. This method can make the non-uniform beam dynamic problem simpler, very helpful for emittance research and lattice design with non-uniform dipoles.
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Hopf monoids from class functions on unitriangular matrices
Aguiar, Marcelo; Thiem, Nathaniel
2012-01-01
We build, from the collection of all groups of unitriangular matrices, Hopf monoids in Joyal's category of species. Such structure is carried by the collection of class function spaces on those groups, and also by the collection of superclass function spaces, in the sense of Diaconis and Isaacs. Superclasses of unitriangular matrices admit a simple description from which we deduce a combinatorial model for the Hopf monoid of superclass functions, in terms of the Hadamard product of the Hopf monoids of linear orders and of set partitions. This implies a recent result relating the Hopf algebra of superclass functions on unitriangular matrices to symmetric functions in noncommuting variables. We determine the algebraic structure of the Hopf monoid: it is a free monoid in species, with the canonical Hopf structure. As an application, we derive certain estimates on the number of conjugacy classes of unitriangular matrices.
矩阵逆半群%Inverse Semigroups of Matrices
朱用文
2008-01-01
We discuss some fundamental properties of inverse semigroups of matrices, and prove that the idempotents of such a semigroup constitute a subsemilattice of a finite Boolean lattice,and that the inverse semigroups of some matrices with the same rank are groups. At last, we determine completely the construction of the inverse semigroups of some 2 x 2 matrices: such a semigroup is isomorphic to a linear group of dimension 2 or a null-adjoined group, or is afinite semilattice of Abelian linear groups of finite dimension, or satisfies some other properties.The necessary and sufficient conditions are given that the sets consisting of some 2 × 2 matrices become inverse semigroups.
Large deviations of the maximal eigenvalue of random matrices
Borot, Gaëtan; Majumdar, Satya; Nadal, Céline
2011-01-01
We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Racah matrices and hidden integrability in evolution of knots
Mironov, A; Morozov, An; Sleptsov, A
2016-01-01
We construct a general procedure to extract the exclusive Racah matrices S and \\bar S from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R =[1], [2], [3] and [2,2]. The matrices S and \\bar S relate respectively the maps (R\\otimes R)\\otimes \\bar R\\longrightarrow R with R\\otimes (R \\otimes \\bar R) \\longrightarrow R and (R\\otimes \\bar R) \\otimes R \\longrightarrow R with R\\otimes (\\bar R \\otimes R) \\longrightarrow R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices.
Determinant and inverse of join matrices on two sets
Mattila, Mika
2011-01-01
Let $(P,\\preceq)$ be a lattice and $f$ a complex-valued function on $P$. We define meet and join matrices on two arbitrary subsets $X$ and $Y$ of $P$ by $(X,Y)_f=(f(x_i\\wedge y_j))$ and $[X,Y]_f=(f(x_i\\vee x_j))$ respectively. Here we present expressions for the determinant and the inverse of $[X,Y]_f$. Our main goal is to cover the case when $f$ is not semimultiplicative since the formulas presented earlier for $[X,Y]_f$ cannot be applied in this situation. In cases when $f$ is semimultiplicative we obtain several new and known formulas for the determinant and inverse of $(X,Y)_f$ and the usual meet and join matrices $(S)_f$ and $[S]_f$. We also apply these formulas to LCM, MAX, GCD and MIN matrices, which are special cases of join and meet matrices.
Automorphisms of sl(2) and dynamical r-matrices
Tsiganov, A V
1996-01-01
Two outer automorphisms of infinite-dimensional representations of $sl(2)$ algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear and quadratic $R$-brackets include the dynamical $r$-matrices.
The Dirac operator and gamma matrices for quantum Minkowski spaces
1997-01-01
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
Synbiotic matrices derived from plant oligosaccharides and polysaccharides
A porous synbiotic matrix was prepared by lyophilization of alginate and pectin or fructan oligosaccharides and polysaccharides cross-linked with calcium. These synbiotic matrices were excellent physical structures to support the growth of Lactobacillus acidophilus (1426) and Lactobacillus reuteri (...
Morphic images of binary words and Parikh matrices
Isawasan, Pradeep; Venkat, Ibrahim; Subramanian, K. G.; Sarmin, Nor Haniza
2014-07-01
A word is a finite sequence of symbols. Parikh matrix of a word, introduced by Mateescu et al (2000), has become an effective tool in the study of certain numerical properties of words based on subwords. There have been several investigations on various properties of Parikh matrices such as M-ambiguity, M-equivalence, subword equalities and inequalities, commutativity and so on. Recently, Parikh matrices of words that are images under certain morphisms have been studied for their properties. On the other hand, Parikh matrices of words involving a certain ratio property called weak-ratio property have been investigated by Subramanian et al (2009). Here we consider two special morphisms called Fibonacci and Tribonacci morphisms and obtain properties of Parikh matrices of images of binary words under these morphisms, utilizing the notion of weak-ratio property.
A SURVEY ON SEMI-TENSOR PRODUCT OF MATRICES
Daizhan CHENG; Hongsheng QI; Ancheng XUE
2007-01-01
Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields.In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.
Maximum-likelihood estimation prevents unphysical Mueller matrices
Aiello, A; Voigt, D; Woerdman, J P
2005-01-01
We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical optical systems. Contrary to linear reconstruction algorithms, the proposed method yields physically acceptable Mueller matrices even in presence of uncontrolled experimental errors. We illustrate the method on the case of an unphysical measured Mueller matrix taken from the literature.
Embedding cocyclic D-optimal designs in cocyclic Hadamard matrices
Álvarez, Víctor; Frau, María-Dolores; Gudiel, Félix
2012-01-01
In this paper a method for embedding cocyclic submatrices with ``large'' determinants of orders 2t in certain cocyclic Hadamard matrices of orders 4t is described (t an odd integer). If these determinants attain the largest possible value, we are embedding D-optimal designs. Applications to the pivot values that appear when Gaussian Elimination with complete pivoting is performed on these cocyclic Hadamard matrices are studied.
An introduction to the theory of canonical matrices
Turnbull, H W
2004-01-01
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Remarks on a one-parameter family of singular matrices
Sharma, Ramesh; Pariso, Chris; Duda, Michelle
2015-01-01
This short article will present to the reader a family of matrices that form an algebra over the reals. This presentation provides both current and former students of modern abstract algebra a better illustration of the concepts of rings, fields, and algebra itself. In addition, this article relates eigenspaces of 3×3 matrices with the arithmetic-geometric mean equality, an attribute that teachers might enjoy utilizing as a teaching tool in their classes.
Local Law of Addition of Random Matrices on Optimal Scale
Bao, Zhigang; Erdős, László; Schnelli, Kevin
2016-11-01
The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.
Boundary transfer matrices and boundary quantum KZ equations
Vlaar, Bart, E-mail: Bart.Vlaar@nottingham.ac.uk [School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
2015-07-15
A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.
A method of diagonalization for sfermion mass matrices
Aranda, Alfredo; Noriega-Papaqui, R
2009-01-01
We present a method of diagonalization for the sfermion mass matrices of the minimal supersymmetric standard model (MSSM). It provides analytical expressions for the masses and mixing angles of rather general hermitian sfermion mass matrices, and allows the study of scenarios that extend the usual constrained - MSSM. Three signature cases are presented explicitly and a general study of flavor changing neutral current processes is outlined in the discussion.
Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices
Juan Yang
2013-01-01
Full Text Available The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.
Moment Matrices, Border Bases and Real Radical Computation
Lasserre, Jean-Bernard; Laurent, Monique; Mourrain, Bernard; Rostalski, Philipp; Trébuchet, Philippe
2013-01-01
International audience; In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite programming. While the border basis algorithms of [17] are efficient and numerically stable for computing complex roots, algorithms based on moment matrices [12] allow the incorpora...
Preliminary Analysis on Matric Suction for Barren Soil
Azhar, A. T. S.; Fazlina, M. I. S.; Aziman, M.; Fairus, Y. M.; Azman, K.; Hazreek, Z. A. M.
2016-11-01
Most research conducted on slope failures can broadly be attributed to the convergence of three factors, i.e. rainfall, steepness of slope, and soil geological profile. The mechanism of the failures is mainly due to the loss of matric suction of soils by rainwater. When rainwater infiltrates into the slopes, it will start to saturate the soil, i.e., reduce the matric suction. A good understanding of landslide mechanisms and the characteristics of unsaturated soil and rock in tropical areas is crucial in landslide hazard formulation. Most of the slope failures in unsaturated tropical residual soil in Malaysia are mainly due to infiltration, especially during intense and prolonged rainfall, which reduces the soil matric suction and hence decreases the stability of the slope. Therefore, the aim of this research is to determine the matric suction for barren soil and to model an unsaturated slope with natural rainfall to evaluate the effects of matric suction on rainfall intensity. A field test was carried out using the Watermark Soil Moisture Sensor to determine the matric suction. The sensor was connected to a program called SpecWare 9 Basic which also used Data Logging Rain gauge Watermark 1120 to measure the intensity and duration of rainfall. This study was conducted at the Research Centre for Soft Soil which is a new Research and Development (R & D) initiative by Universiti Tun Hussein Onn Malaysia, Parit Raja. Field observation showed that the highest daily suction was recorded during noon while the lowest suction was obtained at night and early morning. The highest matric suction for loose condition was 31.0 kPa while the highest matric suction for compacted condition was 32.4 kPa. The results implied that the field suction variation was not only governed by the rainfall, but also the cyclic evaporation process. The findings clearly indicated that the changes in soil suction distribution patterns occurred due to different weather conditions.
Kore, Anilkumar R; Bugarin, Alejandro; Shanmugasundaram, Muthian
2015-01-01
The first example of the synthesis of new dinucleotide cap analog containing 2('),3(')-diacetyl group on m(7)guanosine moiety is described. The desired modified cap analog, m(7,2)(')(,3)(')(-diacetyl)G[5(')]ppp[5(')]G has been obtained by the coupling reaction of triethylamine salt of m(7,2)(')(,3)(')(-diacetyl)GDP with ImGMP in presence of ZnCl2 as a catalyst in 62% yield with high purity. The structure of new cap analog has been confirmed by (1)H and (31)P NMR and mass data.
Pu, Yang; Wang, Wubao; Tang, Guichen; Alfano, Robert R.
2010-07-01
The fluorescence spectra of human cancerous and normal prostate tissues obtained by the selective excitation wavelength of 340 nm were measured. The contributions of principle biochemical components to tissue fluorescence spectra were investigated using the method of multivariate curve resolution with alternating least squares. The results show that there is a reduced contribution from the emission of collagen and increased contribution from nicotinamide adenine dinucleotide (NADH) in cancerous tissues as compared with normal tissue. This difference is attributed to the changes of relative contents of NADH and collagen during cancer development. This research may present a potential native biomarker for prostate cancer detection.
2000-01-01
4-Hydroxyphenylacetate 3-hydroxylase (HpaB and HpaC) of Escherichia coli W has been reported as a two-component flavin adenine dinucleotide (FAD)-dependent monooxygenase that attacks a broad spectrum of phenolic compounds. However, the function of each component in catalysis is unclear. The large component (HpaB) was demonstrated here to be a reduced FAD (FADH2)-utilizing monooxygenase. When an E. coli flavin reductase (Fre) having no apparent homology with HpaC was used to generate FADH2 in ...
Inference for High-dimensional Differential Correlation Matrices.
Cai, T Tony; Zhang, Anru
2016-01-01
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.
Symmetry classes of alternating sign matrices in a nineteen-vertex model
Hagendorf, Christian; Morin-Duchesne, Alexi
2016-05-01
The nineteen-vertex model of Fateev and Zamolodchikov on a periodic lattice with an anti-diagonal twist is investigated. Its inhomogeneous transfer matrix is shown to have a simple eigenvalue, with the corresponding eigenstate displaying intriguing combinatorial features. Similar results were previously found for the same model with a diagonal twist. The eigenstate for the anti-diagonal twist is explicitly constructed using the quantum separation of variables technique. A number of sum rules and special components are computed and expressed in terms of Kuperberg’s determinants for partition functions of the inhomogeneous six-vertex model. The computations of some components of the special eigenstate for the diagonal twist are also presented. In the homogeneous limit, the special eigenstates become eigenvectors of the Hamiltonians of the integrable spin-one XXZ chain with twisted boundary conditions. Their sum rules and special components for both twists are expressed in terms of generating functions arising in the weighted enumeration of various symmetry classes of alternating sign matrices (ASMs). These include half-turn symmetric ASMs, quarter-turn symmetric ASMs, vertically symmetric ASMs, vertically and horizontally perverse ASMs and double U-turn ASMs. As side results, new determinant and pfaffian formulas for the weighted enumeration of various symmetry classes of alternating sign matrices are obtained.
On consistency of the weighted arithmetical mean complex judgement matrix
无
2007-01-01
The weighted arithmetical mean complex judgement matrix(WAMCJM)is the most common method for aggregating group opinions,but it has a shortcoming,namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency.An upper bound of the WAMCJM's consistency is presented.Simultaneously,a compatibility index of judging the aggregating extent of group opinions is also introduced.The WAMCJM is of acceptable consistency and is proved provided the compatibilities of all judgement matrices given by experts are smaller than the threshold value of acceptable consistency.These conclusions are important to group decision making.
Estimated correlation matrices and portfolio optimization
Pafka, Szilárd; Kondor, Imre
2004-11-01
Correlations of returns on various assets play a central role in financial theory and also in many practical applications. From a theoretical point of view, the main interest lies in the proper description of the structure and dynamics of correlations, whereas for the practitioner the emphasis is on the ability of the models to provide adequate inputs for the numerous portfolio and risk management procedures used in the financial industry. The theory of portfolios, initiated by Markowitz, has suffered from the “curse of dimensions” from the very outset. Over the past decades a large number of different techniques have been developed to tackle this problem and reduce the effective dimension of large bank portfolios, but the efficiency and reliability of these procedures are extremely hard to assess or compare. In this paper, we propose a model (simulation)-based approach which can be used for the systematical testing of all these dimensional reduction techniques. To illustrate the usefulness of our framework, we develop several toy models that display some of the main characteristic features of empirical correlations and generate artificial time series from them. Then, we regard these time series as empirical data and reconstruct the corresponding correlation matrices which will inevitably contain a certain amount of noise, due to the finiteness of the time series. Next, we apply several correlation matrix estimators and dimension reduction techniques introduced in the literature and/or applied in practice. As in our artificial world the only source of error is the finite length of the time series and, in addition, the “true” model, hence also the “true” correlation matrix, are precisely known, therefore in sharp contrast with empirical studies, we can precisely compare the performance of the various noise reduction techniques. One of our recurrent observations is that the recently introduced filtering technique based on random matrix theory performs
Inorganic Nanoparticle Nucleation on Polymer Matrices
Kosteleski, Adrian John
dressing applications. PAA's ability to nucleate nanoparticles in a solid matrix was displayed. Interestingly enough PAA retains its ability to nucleate nanoparticle even when its reactive functional groups are used in the crosslinking process. Silver nanoparticle composition and size on the solid polymer matrices was controlled by varying the composition of PAA. PAA and silver nanoparticles effect on the mechanical properties of the calcium alginate hydrogels were also studied. Physically crosslinking PAA with calcium alginate gels enables the development of intricate gel structures that are decorated with nucleated silver; yielding a composite biomaterial with improved and enhanced antimicrobial properties.
Sinclair, Christopher D
2011-01-01
We investigate a two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged compact region K whose charge density is determined by its equilibrium potential at an inverse temperature corresponding to \\beta = 2. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a determinantal point process on the complex plane. We investigate the scaling limit, as N \\to \\infty, of the associated kernel in the neighborhood of a point on the boundary under the assumption that the boundary is sufficiently smooth. We find that the limiting kernel depends on the limiting value of N/s, and prove universality for these kernels. That is, we show that, the scaled kernel in a neighborhood of a point \\zeta \\in \\partial K can be succinctly expressed in terms of the scaled kernel for the closed unit disk, and the exterior conformal map which carries the complement K to the complement of ...
On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices
Pestana, Jennifer
2014-01-01
Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related. © 2014 Society for Industrial and Applied Mathematics.
CMV matrices in random matrix theory and integrable systems: a survey
Nenciu, Irina [Courant Institute, 251 Mercer St, New York, NY 10012 (United States)
2006-07-14
We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.
Roembke, Benjamin T; Zhou, Jie; Zheng, Yue; Sayre, David; Lizardo, Allan; Bernard, Laurentee; Sintim, Herman O
2014-06-01
Cyclic dinucleotides have emerged as second messengers that regulate diverse processes in bacteria, as well as regulating the production of type I interferons in metazoans. Fluorescent sensors for these important second messengers are highly sought-after for high-throughput inhibitor discovery, yet most sensors reported to date are not amenable for high-throughput screening purposes. Herein, we demonstrate that a new analog, 3',3'-cG(d2AP)MP, which is a 2-aminopurine (2AP)-containing cyclic dinucleotide, self-associates in the presence of Mn(2+) with an association constant of 120,000 M(-1). 3'3'-cG(d2AP)MP can also form a heterodimer with cGAMP, activator of immune regulator, STING, or the bacterial biofilm regulator, c-di-GMP in the presence of Mn(II). Upon dimer formation, the fluorescence of 3',3'-cG(d2AP)MP is quenched and this provides a convenient method to monitor the enzymatic processing of both DGC and PDE enzymes, opening up several opportunities for the discovery of inhibitors of nucleotide signaling.
Rose, Nicholas D; Regan, John M
2015-12-01
Geobacter sulfurreducens is one of the dominant bacterial species found in biofilms growing on anodes in bioelectrochemical systems. The intracellular concentrations of reduced and oxidized forms of nicotinamide-adenine dinucleotide (NADH and NAD(+), respectively) and nicotinamide-adenine dinucleotide phosphate (NADPH and NADP(+), respectively) as well as adenosine triphosphate (ATP), adenosine diphosphate (ADP), and adenosine monophosphate (AMP) were measured in G. sulfurreducens using fumarate, Fe(III)-citrate, or anodes poised at different potentials (110, 10, -90, and -190 mV (vs. SHE)) as the electron acceptor. The ratios of CNADH/CNAD+ (0.088±0.022) and CNADPH/CNADP+ (0.268±0.098) were similar under all anode potentials tested and with Fe(III)-citrate (reduced extracellularly). Both ratios significantly increased with fumarate as the electron acceptor (0.331±0.094 for NAD and 1.96±0.37 for NADP). The adenylate energy charge (the fraction of phosphorylation in intracellular adenosine phosphates) was maintained near 0.47 under almost all conditions. Anode-growing biofilms demonstrated a significantly higher molar ratio of ATP/ADP relative to suspended cultures grown on fumarate or Fe(III)-citrate. These results provide evidence that the cellular location of reduction and not the redox potential of the electron acceptor controls the intracellular redox potential in G. sulfurreducens and that biofilm growth alters adenylate phosphorylation.
Bansal Manju
2011-01-01
Full Text Available Abstract Background A nucleosome is the fundamental repeating unit of the eukaryotic chromosome. It has been shown that the positioning of a majority of nucleosomes is primarily controlled by factors other than the intrinsic preference of the DNA sequence. One of the key questions in this context is the role, if any, that can be played by the variability of nucleosomal DNA structure. Results In this study, we have addressed this question by analysing the variability at the dinucleotide and trinucleotide as well as longer length scales in a dataset of nucleosome X-ray crystal structures. We observe that the nucleosome structure displays remarkable local level structural versatility within the B-DNA family. The nucleosomal DNA also incorporates a large number of kinks. Conclusions Based on our results, we propose that the local and global level versatility of B-DNA structure may be a significant factor modulating the formation of nucleosomes in the vicinity of high-plasticity genes, and in varying the probability of binding by regulatory proteins. Hence, these factors should be incorporated in the prediction algorithms and there may not be a unique 'template' for predicting putative nucleosome sequences. In addition, the multimodal distribution of dinucleotide parameters for some steps and the presence of a large number of kinks in the nucleosomal DNA structure indicate that the linear elastic model, used by several algorithms to predict the energetic cost of nucleosome formation, may lead to incorrect results.
Rose, Nicholas D.
2015-12-01
© 2015 Elsevier B.V. Geobacter sulfurreducens is one of the dominant bacterial species found in biofilms growing on anodes in bioelectrochemical systems. The intracellular concentrations of reduced and oxidized forms of nicotinamide-adenine dinucleotide (NADH and NAD^{+}, respectively) and nicotinamide-adenine dinucleotide phosphate (NADPH and NADP^{+}, respectively) as well as adenosine triphosphate (ATP), adenosine diphosphate (ADP), and adenosine monophosphate (AMP) were measured in G. sulfurreducens using fumarate, Fe(III)-citrate, or anodes poised at different potentials (110, 10, -90, and -190mV (vs. SHE)) as the electron acceptor. The ratios of CNADH/CNAD+ (0.088±0.022) and CNADPH/CNADP+ (0.268±0.098) were similar under all anode potentials tested and with Fe(III)-citrate (reduced extracellularly). Both ratios significantly increased with fumarate as the electron acceptor (0.331±0.094 for NAD and 1.96±0.37 for NADP). The adenylate energy charge (the fraction of phosphorylation in intracellular adenosine phosphates) was maintained near 0.47 under almost all conditions. Anode-growing biofilms demonstrated a significantly higher molar ratio of ATP/ADP relative to suspended cultures grown on fumarate or Fe(III)-citrate. These results provide evidence that the cellular location of reduction and not the redox potential of the electron acceptor controls the intracellular redox potential in G. sulfurreducens and that biofilm growth alters adenylate phosphorylation.
Bioinspired matrices assembled by polysaccharide-protein interactions
Zhang, Le
Bioinspired matrices assembled on the basis of noncovalent interactions between proteins and polysaccharides have been proved suitable to deliver therapeutically relevant proteins or DNAs. Our initial efforts were dedicated to the relationship between mechanical properties of hydrogels assembled based on specific interactions between low molecular weight heparin (LMWH) and heparin binding peptides (HBPs) such as HIP, ATIII, and PF4ZIP peptides. The measured differences in affinity and kinetics for LMWH-HBP binding likely lead to observed differences in the phase separation behavior of the poly (ethylene glycol) (PEG)-LMWH/PEG-HIP hydrogels versus the PEG-LMWH/PEG-ATIII hydrogels. More attention has been given to the PF4ZIP peptide employed for the noncovalent assembly of heparinized hydrogels. Multifunctional star PEG-PF4ZIP bioconjugates complexed with star PEG-LMWH form hydrogels that exhibit increasing elastic moduli with increasing mole ratio of PEG-PF4ZIP. The viscoelastic properties of the hydrogels can be controlled via alterations in the ratio between LMWH and PF4ZIP peptide, and comparisons with other PEG-LMWH/PEG-HBP hydrogels suggest the importance of both LMWH/HBP binding kinetics and the binding capacity of LMWH in determining rheological properties in these hydrogels. Characterization of the PEG-LMWH/PEG-PF4ZIP hydrogels suggests that useful moduli for soft tissue engineering applications are obtained at physiological temperatures and after applying high shear. Furthermore, in the basic fibroblast growth factor (bFGF) release, bFGF/vascular endothelial growth factor (VEGF) co-release, and hydrogel erosion results, the combination of growth factor (GF) release profiles and hydrogel erosion profiles suggests that GF delivery from the assembled hydrogels is mainly an erosion-controlled process that may permit co-release of GF with PEG-LMWH and may therefore also improve the bioactivity of GF delivered from these matrices. Hydrogels with such engineered
Retinal pigment epithelium cell alignment on nanostructured collagen matrices.
Ulbrich, Stefan; Friedrichs, Jens; Valtink, Monika; Murovski, Simo; Franz, Clemens M; Müller, Daniel J; Funk, Richard H W; Engelmann, Katrin
2011-01-01
We investigated attachment and migration of human retinal pigment epithelial cells (primary, SV40-transfected and ARPE-19) on nanoscopically defined, two-dimensional matrices composed of parallel-aligned collagen type I fibrils. These matrices were used non-cross-linked (native) or after riboflavin/UV-A cross-linking to study cell attachment and migration by time-lapse video microscopy. Expression of collagen type I and IV, MMP-2 and of the collagen-binding integrin subunit α(2) were examined by immunofluorescence and Western blotting. SV40-RPE cells quickly attached to the nanostructured collagen matrices and aligned along the collagen fibrils. However, they disrupted both native and cross-linked collagen matrices within 5 h. Primary RPE cells aligned more slowly without destroying either native or cross-linked substrates. Compared to primary RPE cells, ARPE-19 cells showed reduced alignment but partially disrupted the matrices within 20 h after seeding. Expression of the collagen type I-binding integrin subunit α(2) was highest in SV40-RPE cells, lower in primary RPE cells and almost undetectable in ARPE-19 cells. Thus, integrin α(2) expression levels directly correlated with the degree of cell alignment in all examined RPE cell types. Specific integrin subunit α(2)-mediated matrix binding was verified by preincubation with an α(2)-function-blocking antibody, which impaired cell adhesion and alignment to varying degrees in primary and SV40-RPE cells. Since native matrices supported extended and directed primary RPE cell growth, optimizing the matrix production procedure may in the future yield nanostructured collagen matrices serving as transferable cell sheet carriers.
An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
Tongsong Jiang
2014-01-01
Full Text Available This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of consimilarity of quaternion matrices into that of ordinary similarity of complex matrices. This paper also gives algebraic methods for finding coneigenvalues and coneigenvectors of quaternion matrices by means of complex representation of a quaternion matrix.
Kumare Vinodh
2016-03-01
Full Text Available This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.
Randomized Algorithms for Matrices and Data
Mahoney, Michael W.
2012-03-01
This chapter reviews recent work on randomized matrix algorithms. By “randomized matrix algorithms,” we refer to a class of recently developed random sampling and random projection algorithms for ubiquitous linear algebra problems such as least-squares (LS) regression and low-rank matrix approximation. These developments have been driven by applications in large-scale data analysis—applications which place very different demands on matrices than traditional scientific computing applications. Thus, in this review, we will focus on highlighting the simplicity and generality of several core ideas that underlie the usefulness of these randomized algorithms in scientific applications such as genetics (where these algorithms have already been applied) and astronomy (where, hopefully, in part due to this review they will soon be applied). The work we will review here had its origins within theoretical computer science (TCS). An important feature in the use of randomized algorithms in TCS more generally is that one must identify and then algorithmically deal with relevant “nonuniformity structure” in the data. For the randomized matrix algorithms to be reviewed here and that have proven useful recently in numerical linear algebra (NLA) and large-scale data analysis applications, the relevant nonuniformity structure is defined by the so-called statistical leverage scores. Defined more precisely below, these leverage scores are basically the diagonal elements of the projection matrix onto the dominant part of the spectrum of the input matrix. As such, they have a long history in statistical data analysis, where they have been used for outlier detection in regression diagnostics. More generally, these scores often have a very natural interpretation in terms of the data and processes generating the data. For example, they can be interpreted in terms of the leverage or influence that a given data point has on, say, the best low-rank matrix approximation; and this
Macromolecular crowding for tailoring tissue-derived fibrillated matrices.
Magno, Valentina; Friedrichs, Jens; Weber, Heather M; Prewitz, Marina C; Tsurkan, Mikhail V; Werner, Carsten
2017-06-01
Tissue-derived fibrillated matrices can be instrumental for the in vitro reconstitution of multiphasic extracellular microenvironments. However, despite of several advantages, the obtained scaffolds so far offer a rather narrow range of materials characteristics only. In this work, we demonstrate how macromolecular crowding (MMC) - the supplementation of matrix reconstitution media with synthetic or natural macromolecules in ways to create excluded volume effects (EVE) - can be employed for tailoring important structural and biophysical characteristics of kidney-derived fibrillated matrices. Porcine kidneys were decellularized, ground and the obtained extracellular matrix (ECM) preparations were reconstituted under varied MMC conditions. We show that MMC strongly influences the fibrillogenesis kinetics and impacts the architecture and the elastic modulus of the reconstituted matrices, with diameters and relative alignment of fibrils increasing at elevated concentrations of the crowding agent Ficoll400, a nonionic synthetic polymer of sucrose. Furthermore, we demonstrate how MMC modulates the distribution of key ECM molecules within the reconstituted matrix scaffolds. As a proof of concept, we compared different variants of kidney-derived fibrillated matrices in cell culture experiments referring to specific requirements of kidney tissue engineering approaches. The results revealed that MMC-tailored matrices support the morphogenesis of human umbilical vein endothelial cells (HUVECs) into capillary networks and of murine kidney stem cells (KSCs) into highly branched aggregates. The established methodology is concluded to provide generally applicable new options for tailoring tissue-specific multiphasic matrices in vitro. Tissue-derived fibrillated matrices can be instrumental for the in vitro reconstitution of multiphasic extracellular microenvironments. However, despite of several advantages, the obtained scaffolds so far offer a rather narrow range of materials
Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
Han Guo
2012-01-01
Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.
Osteocalcin/fibronectin-functionalized collagen matrices for bone tissue engineering.
Kim, S G; Lee, D S; Lee, S; Jang, J-H
2015-06-01
Collagen is the most abundant protein found in the extracellular matrix and is widely used to build scaffolds for biomedical applications which are the result of its biocompatibility and biodegradability. In the present study, we constructed a rhOCN/FNIII9-10 fusion protein and rhOCN/FNIII9-10-functionalized collagen matrices and investigated the potential value for bone tissue engineering. In vitro studies carried out with preosteoblastic MC3T3-E1 cells showed that rhOCN/FNIII9-10 fusion protein promoted cell adhesion and the mRNA levels of osteogenic markers including osteocalcin, runt-related transcription factor 2, alkaline phosphatase (ALP), and collagen type I. In addition, rhOCN/FNIII9-10-functionalized collagen matrices showed significant induction of the ALP activity more than rhFNIII9-10-functionalized collagen matrices or collagen matrices alone. These results suggested that rhOCN/FNIII9-10-functionalized collagen matrices have potential for bone tissue engineering.
Learning Discriminative Stein Kernel for SPD Matrices and Its Applications.
Zhang, Jianjia; Wang, Lei; Zhou, Luping; Li, Wanqing
2016-05-01
Stein kernel (SK) has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: 1) eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation, and 2) more importantly, eigenvalues reflect only the property of an individual SPD matrix. They are not necessarily optimal for computing SK when the goal is to discriminate different classes of SPD matrices. To address the two issues, we propose a discriminative SK (DSK), in which an extra parameter vector is defined to adjust the eigenvalues of input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three kernel learning criteria that are commonly used in the literature are employed as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare the proposed DSK with the original SK and other methods for evaluating the similarity between SPD matrices. The results demonstrate that the DSK can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original SK and other commonly used methods.
The MATRICS Consensus Cognitive Battery (MCCB): performance and functional correlates.
Lystad, June Ullevoldsæter; Falkum, Erik; Mohn, Christine; Haaland, Vegard Øksendal; Bull, Helen; Evensen, Stig; Rund, Bjørn Rishovd; Ueland, Torill
2014-12-30
Neurocognitive impairment is a core feature in psychotic disorders and the MATRICS Consensus Cognitive Battery (MCCB) is now widely used to assess neurocognition in this group. The MATRICS has been translated into several languages, including Norwegian; although this version has yet to be investigated in an adult clinical population. Further, the relationship between the MATRICS and different measures of functioning needs examination. The purpose of this study was to describe neurocognition assessed with the Norwegian version of the MATRICS battery in a sample of patients with psychotic disorders compared to age and gender matched healthy controls and to examine the association with educational-, occupational- and social-functioning in the patient group. One hundred and thirty one patients and 137 healthy controls completed the battery. The Norwegian version of the MATRICS was sensitive to the magnitude of neurocognitive impairments in patients with psychotic disorders, with patients displaying significant impairments on all domains relative to healthy controls. Neurocognition was also related to both self-rated and objective functional measures such as social functioning, educational- and employment-history.
Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices
A. F. Antippa
2004-01-01
Full Text Available We introduce the hypersymmetric functions of 2×2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions, and for a specific class of 2×2 matrices, having a high degree of symmetry, they reduce to these latter functions. This class of matrices includes rotations, Lorentz boosts, and discrete time generators for the harmonic oscillators. The hypersymmetric functions are defined over four sets of independent indeterminates using a triplet of interrelated binary partitions. We work out the algebra of this triplet of partitions and then make use of the results in order to simplify the expressions for the hypersymmetric functions for a special class of matrices. In addition to their obvious applications in matrix theory, in coupled difference equations, and in the theory of symmetric functions, the results obtained here also have useful applications in problems involving successive rotations, successive Lorentz transformations, discrete harmonic oscillators, and linear two-state systems.
Dirac Matrices and Feynman's Rest of the Universe
Kim, Young S
2012-01-01
There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four $\\gamma$ matrices. These fifteen matrices can also serve as the generators of the group $SL(4,r)$. The second set consists of ten generators of the $Sp(4)$ group which he derived from two coupled harmonic oscillators. In classical mechanics, it is possible to extend the symmetry of the coupled oscillators to the SL(4,r) regime with fifteen Majorana matrices, while quantum mechanics allows only ten generators. This difference can serve as an illustrative example of Feynman's rest of the universe. The universe of the coupled oscillators consists of fifteen generators, and the ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups $SL(4,r)$ and $Sp(4)$ are locally isomorphic to the Lorentz groups O(3,3) and O(3,2) respectively. This allows us to interpret Feynman's rest...
Maize Arabinoxylan Gels as Protein Delivery Matrices
Ana Luisa Martínez-López
2009-04-01
Full Text Available The laccase induced gelation of maize bran arabinoxylans at 2.5% (w/v in the presence of insulin or β-lactoglobulin at 0.1% (w/v was investigated. Insulin and β-lacto-globulin did not modify either the gel elasticity (9 Pa or the cross-links content (0.03 and 0.015 mg di- and triferulic acids/mg arabinoxylan, respectively. The protein release capability of the gel was also investigated. The rate of protein release from gels was dependent on the protein molecular weight. The apparent diffusion coefficient was 0.99 × 10-7 and 0.79 × 10-7 cm2/s for insulin (5 kDa and β-lactoglobulin (18 kDa, respectively. The results suggest that maize bran arabinoxylan gels can be potential candidates for the controlled release of proteins.
k-控制阵%k-dominating Fuzzy Matrices
孙华春
2006-01-01
The definition of k-dominating fuzzy matrices has been introduced. The relation between k-dominating fuzzy matrices and circularly k-dominating fuzzy matrices is discussed. We point out that the convergence or oscillating index of the power sequence of an n × n k-dominating matrix is bounded by (n-1)k+m from above; and if it is oscillating, then the period index is a factor of k.%给出k-控制阵的定义,讨论k-控制阵与k-圈控制阵的关系,指出k-控制阵的周期是k的一个因子,指数不大于(n-1)k+m.
Square matrices of order 2 theory, applications, and problems
Pop, Vasile
2017-01-01
This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem. Matrices have a vast practical importance to mathematics, science, a...
Microscale extraction method for HPLC carotenoid analysis in vegetable matrices
Sidney Pacheco
2014-10-01
Full Text Available In order to generate simple, efficient analytical methods that are also fast, clean, and economical, and are capable of producing reliable results for a large number of samples, a micro scale extraction method for analysis of carotenoids in vegetable matrices was developed. The efficiency of this adapted method was checked by comparing the results obtained from vegetable matrices, based on extraction equivalence, time required and reagents. Six matrices were used: tomato (Solanum lycopersicum L., carrot (Daucus carota L., sweet potato with orange pulp (Ipomoea batatas (L. Lam., pumpkin (Cucurbita moschata Duch., watermelon (Citrullus lanatus (Thunb. Matsum. & Nakai and sweet potato (Ipomoea batatas (L. Lam. flour. Quantification of the total carotenoids was made by spectrophotometry. Quantification and determination of carotenoid profiles were formulated by High Performance Liquid Chromatography with photodiode array detection. Microscale extraction was faster, cheaper and cleaner than the commonly used one, and advantageous for analytical laboratories.
Scattering matrices in non-uniformly lined ducts
Demir, Ahmet
2017-02-01
Sudden area expansion and sudden area contraction in an infinitely long duct with discontinuous locally reacting lining are defined by respective mixed boundary value problems. In the absence of a sudden area change, a separate problem with an infinite duct having bifid lining on its wall is described. Introducing Fourier transform along the duct axis boundary value problems is solved by the well-known Wiener-Hopf technique, and then, corresponding scattering matrices are constructed. To show the proper use of scattering matrices in the case of several discontinuities and also validation and comparison purposes, transmitted field in a duct with an inserted expansion chamber whose walls are treated by acoustically absorbent material is derived by the help of the relevant scattering matrices. A perfect agreement is observed when the transmitted fields are compared numerically with a similar work exists in the literature.
Opening the Rome-Southampton window for operator mixing matrices
Arthur, R; Garron, N; Kelly, C; Lytle, A T
2011-01-01
We show that the running of operators which mix under renormalization can be computed fully non-perturbatively as a product of continuum step scaling matrices. These step scaling matrices are obtained by taking the "ratio" of Z matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD collaborations. To illustrate our method, using n_f=2+1 domain-wall fermions, we compute the non-perturbative running matrix of four-quark operators needed in K->pipi decay and neutral kaon mixing. Our results are then compared to perturbation theory.
Convex Optimization methods for computing the Lyapunov Exponent of matrices
Protasov, Vladimir Yu
2012-01-01
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for the Lyapunov exponent. They improve previously known bounds and converge to the real value. The rate of convergence is estimated and the efficiency of the algorithm is demonstrated on several problems from applications (in functional analysis, combinatorics, and lan- guage theory) and on numerical examples with randomly generated matrices. The method computes the Lyapunov exponent with a prescribed accuracy in relatively high dimensions (up to 60). We generalize this approach to all matrices, not necessar- ily nonnegative, derive a new universal upper bound for the Lyapunov exponent, and show that such a lower bound, in general, does not exist.
Asymmetric correlation matrices: an analysis of financial data
Livan, G.; Rebecchi, L.
2012-06-01
We analyse the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non-symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrix to distinguish between noise and non-trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non-symmetric correlation matrix. We find several non trivial results when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.
Inverse of invertible standard multi-companion matrices with applications
Hazem I. El Shekh Ahmed
2015-01-01
Full Text Available The inverse of invertible standard multi-companion matrices will be derived and introduced as a new technique for generation of periodic autoregression models to get the desired spectrum and extract the parameters of the model from it when the information of the standard multi-companion matrices is not enough for the extracting of the parameters of the model. We will find explicit expressions for the generalized eigenvectors of the inverse of invertible standard multi-companion matrices such that each generalized eigenvector depends on the corresponding eigenvalue therefore we obtain a parameterization of the inverse of invertible standard multi-companion matrix through the eigenvalues and these additional quantities. The results can be applied to statistical estimation, simulation and theoretical studies of periodically correlated and multivariate time series in both discrete and continuous-time series.
Composition of quantum operations and products of random matrices
Roga, Wojciech; Zyczkowski, Karol
2011-01-01
Spectral properties of evolution operators corresponding to random maps and quantized chaotic systems strongly interacting with an environment can be described by the ensemble of non-hermitian random matrices from the real Ginibre ensemble. We analyze evolution operators Psi=Psi_s...Psi_1 representing the composition of s random maps and demonstrate that their complex eigenvalues are asymptotically described by the law of Burda et al. obtained for a product of s independent random complex Ginibre matrices. Numerical data support the conjecture that the same results are applicable to characterize the distribution of eigenvalues of the s-th power of a random Ginibre matrix. Squared singular values of Psi are shown to be described by the Fuss-Catalan distribution of order s. Results obtained for products of random Ginibre matrices are also capable to describe the s-step evolution operator for a model deterministic dynamical system - a generalized quantum baker map subjected to strong interaction with an environm...
Induced Ginibre ensemble of random matrices and quantum operations
Fischmann, J; Khoruzhenko, B A; Sommers, H -J; Zyczkowski, K
2011-01-01
A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.
Formation of complex anodic films on porous alumina matrices
Alexander Zahariev; Assen Girginov
2003-04-01
The kinetics of growth of complex anodic alumina films was investigated. These films were formed by filling porous oxide films (matrices) having deep pores. The porous films (matrices) were obtained voltastatically in (COOH)2 aqueous solution under various voltages. The filling was done by re-anodization in an electrolyte solution not dissolving the film. Data about the kinetics of re-anodization depending on the porosity of the matrices were obtained. On the other hand, the slopes of the kinetic curves during reanodization were calculated by two equations expressing the dependence of these slopes on the ionic current density. A discrepancy was ascertained between the values of the calculated slopes and those experimentally found. For this discrepancy a possible explanation is proposed, related to the temperature increase in the film, because of that the real current density significantly increases during re-anodization.
Nano-Fiber Reinforced Enhancements in Composite Polymer Matrices
Chamis, Christos C.
2009-01-01
Nano-fibers are used to reinforce polymer matrices to enhance the matrix dependent properties that are subsequently used in conventional structural composites. A quasi isotropic configuration is used in arranging like nano-fibers through the thickness to ascertain equiaxial enhanced matrix behavior. The nano-fiber volume ratios are used to obtain the enhanced matrix strength properties for 0.01,0.03, and 0.05 nano-fiber volume rates. These enhanced nano-fiber matrices are used with conventional fiber volume ratios of 0.3 and 0.5 to obtain the composite properties. Results show that nano-fiber enhanced matrices of higher than 0.3 nano-fiber volume ratio are degrading the composite properties.
A Workshop on Algebraic Design Theory and Hadamard Matrices
2015-01-01
This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions. The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important ap...
The road to deterministic matrices with the restricted isometry property
Bandeira, Afonso S; Mixon, Dustin G; Wong, Percy
2012-01-01
The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are R...
Asymmetric matrices in an analysis of financial correlations
Kwapien, J; Górski, A Z; Oswiecimka, P
2006-01-01
Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and correlation matrices for rich multivariate data. In the latter case one constructs a real symmetric matrix with real non-negative eigenvalues describing the correlation structure of the data. However, if one performs a correlation-function-like analysis of multivariate data, when a stress is put on investigation of delayed dependencies among different types of signals, one can calculate an asymmetric correlation matrix with complex eigenspectrum. From the Random Matrix Theory point of view this kind of matrices is closely related to Ginibre Orthogonal Ensemble (GinOE). We present an example of practical application of such matrices in correlation analyses of empirical data. By introducing the time lag, we are able to identify temporal structure of the inter-market correlation...
Limiting Spectral Distribution of Block Matrices with Toeplitz Block Structure
Basu, Riddhipratim; Ganguly, Shirshendu; Hazra, Rajat Subhra
2011-01-01
We study two specific symmetric random block Toeplitz (of dimension $k \\times k$) matrices: where the blocks (of size $n \\times n$) are (i) matrices with i.i.d. entries, and (ii) asymmetric Toeplitz matrices. Under suitable assumptions on the entries, their limiting spectral distributions (LSDs) exist (after scaling by $\\sqrt{nk}$) when (a) $k$ is fixed and $n \\to\\infty$ (b) $n$ is fixed and $k\\rightarrow \\infty$ (c) $n$ and $k$ go to $\\infty$ simultaneously. Further the LSD's obtained in (a) and (b) coincide with those in (c) when $n$ or respectively $k$ tends to infinity. This limit in (c) is the semicircle law in case (i). In Case (ii) the limit is related to the limit of the random symmetric Toepiltz matrix as obtained by Bryc et al.(2006) and Hammond and Miller(2005).
On the exponential of matrices in su(4)
Ramakrishna, Viswanath; Zhou, Hong [Department of Mathematical Sciences and Center for Signals, Systems and Communications, University of Texas at Dallas, PO Box 830688, Richardson, TX 75083 (United States)
2006-03-24
This paper provides explicit techniques to compute the exponentials of a variety of anti-Hermitian matrices in dimension 4. Many of these formulae can be written down directly from the entries of the matrix. Whenever any spectral calculations are required, these can be done in closed form. In many instances only 2 x 2 spectral calculations are required. These formulae cover a wide variety of applications. Conditions on the matrix which render it to admit one of three minimal polynomials are also given. Matrices with these minimal polynomials admit simple and tractable representations for their exponentials. One of these is the Euler-Rodrigues formula. The key technique is the relation between real 4 x 4 matrices and the quaternions.
Non-invasive matrices in human biomonitoring: a review.
Esteban, Marta; Castaño, Argelia
2009-02-01
Humans and other living organisms are exposed to a variety of chemical pollutants that are released into the environment as a consequence of anthropogenic activities. Environmental pollutants are incorporated into the organism by different routes and can then be stored and distributed in different tissues, which leads to an internal concentration that can induce different alterations, adverse effects and/or diseases. Control measures should be taken to avoid these effects and human biomonitoring is a very useful tool that can contribute to this aim. Human biomonitoring uses different matrices to measure the target chemicals depending on the chemical, the amount of matrix necessary for the analysis and the detection limit (LOD) of the analytical technique. Blood is the ideal matrix for most chemicals due to its contact with the whole organism and its equilibrium with organs and tissues where chemicals are stored. However, it has an important disadvantage of being an invasive matrix. The development of new methodology and modern analytical techniques has allowed the use of other matrices that are less or non-invasive, such as saliva, urine, meconium, nails, hair, and semen or breast milk. The presence of a chemical in these matrices reflects an exposure, but correlations between levels in non-invasive matrices and blood must be established to ensure that these levels are related to the total body burden. The development of new biomarkers that are measurable in these matrices will improve non-invasive biomonitoring. This paper reviews studies that measure Cd, Pb, Hg, polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins (PCDDs), polychlorinated dibenzofurans (PCDFs), polycyclic aromatic hydrocarbons (PAHs), polybrominated diphenyl ethers (PBDEs), organochlorine pesticides and phthalates in non-invasive matrices, the most used techniques for measurements and what alternative techniques are available.
Matric variate Pearson type II-Riesz distribution
José A. Díaz-García
2016-10-01
Full Text Available The Pearson type II distribution is well known and is used in the general framework of real normed division algebras and Riesz distribution theory. Also, the so called Pearson type II-Riesz distribution, based on the Kotz–Riesz distribution, is presented in a unified way valid in the context of real, complex, quaternion and octonion random matrices. Specifically, the central nonsingular matric variate generalised Pearson type II-Riesz distribution and beta-Riesz type I distributions are derived in the addressed multiple numerical field settings.
A Class of Transformation Matrices and Its Applications
Wenhui Liu
2014-01-01
Full Text Available This paper studies a class of transformation matrices and its applications. Firstly, we introduce a class of transformation matrices between two different vector operators and give some important properties of it. Secondly, we consider its two applications. The first one is to improve Qian Jiling's formula. And the second one is to deal with the observability of discrete-time stochastic linear systems with Markovian jump and multiplicative noises. A new necessary and sufficient condition for the weak observability will be given in the second application.
Quantum hidden Markov models based on transition operation matrices
Cholewa, Michał; Gawron, Piotr; Głomb, Przemysław; Kurzyk, Dariusz
2017-04-01
In this work, we extend the idea of quantum Markov chains (Gudder in J Math Phys 49(7):072105 [3]) in order to propose quantum hidden Markov models (QHMMs). For that, we use the notions of transition operation matrices and vector states, which are an extension of classical stochastic matrices and probability distributions. Our main result is the Mealy QHMM formulation and proofs of algorithms needed for application of this model: Forward for general case and Vitterbi for a restricted class of QHMMs. We show the relations of the proposed model to other quantum HMM propositions and present an example of application.
Recommendations on the use and design of risk matrices
Duijm, Nijs Jan
2015-01-01
Risk matrices are widely used in risk management. They are a regular feature in various risk management standards and guidelines and are also used as formal corporate risk acceptance criteria. It is only recently, however, that scientific publications have appeared that discuss the weaknesses...... of the risk matrix. The objective of this paper is to explore these weaknesses, and provide recommendations for the use and design of risk matrices. The paper reviews the few relevant publications and adds some observations of its own in order to emphasize existing recommendations and add some suggestions...
UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES
A. AIZPURU; A. GUTIERREZ-DAVILA
2004-01-01
The authors obtain new characterizations of unconditional Cauchy series in terms of separation properties of subfamilies of p(N), and a generalization of the Orlicz-Pettis Theorem is also obtained. New results on the uniform convergence on matrices and a new version of the Hahn-Schur summation theorem are proved. For matrices whose rows define unconditional Cauchy series, a better sufficient condition for the basic Matrix Theorem of Antosik and Swartz, new necessary conditions and a new proof of that theorem are given.
Matrices con entradas enteras e inversa con entradas enteras
Mora, Walter
2004-01-01
Algunos artículos publicados en The American Mathematical Monthly discuten acerca de la construcción de matrices con entradas enteras, valores propios enteros y vectores propios con componentes enteras, en particular en [1] se hace una construcción que además permite construir, de manera sencilla, matrices con entradas enteras cuya inversa también tiene entradas enteras. Este artículo trata de estas últimas construcciones e incluye software en Java para generar y modificar ejemplos y para hac...
Singularity of Sparse Circulant Matrices is NP-complete
Toli, Ilia
2009-01-01
It is shown by Karp reduction that deciding the singularity of $(2^n - 1) \\times (2^n - 1)$ sparse circulant matrices (SC problem) is NP-complete. We can write them only implicitly, by indicating values of the $2 + n(n + 1)/2$ eventually nonzero entries of the first row and can make all matrix operations with them. The positions are $0, 1, 2^{i} + 2^{j}$. The complexity parameter is $n$. Mulmuley's work on the rank of matrices \\cite{Mulmuley87} makes SC stand alone in a list of 3,000 and growing NP-complete problems.
Matrices con entradas enteras e inversa con entradas enteras
Mora, Walter
2004-01-01
Algunos artículos publicados en The American Mathematical Monthly discuten acerca de la construcción de matrices con entradas enteras, valores propios enteros y vectores propios con componentes enteras, en particular en [1] se hace una construcción que además permite construir, de manera sencilla, matrices con entradas enteras cuya inversa también tiene entradas enteras. Este artículo trata de estas últimas construcciones e incluye software en Java para generar y modificar ejemplos y para hac...
Retinal Pigment Epithelium Cell Alignment on Nanostructured Collagen Matrices
Ulbrich, Stefan; Friedrichs, Jens; Valtink, Monika; Murovski, Simo; Franz, Clemens M.; Müller, Daniel J.; Richard H. W. Funk; Engelmann, Katrin
2014-01-01
We investigated attachment and migration of human retinal pigment epithelial cells (primary, SV40-transfected and ARPE-19) on nanoscopically defined, two-dimensional matrices composed of parallel-aligned collagen type I fibrils. These matrices were used non-cross-linked (native) or after riboflavin/UV-A cross-linking to study cell attachment and migration by time-lapse video microscopy. Expression of collagen type I and IV, MMP-2 and of the collagen-binding integrin subunit α2 were examined b...
[Ecotoxicological bioassays on aquatic sediments: experimental problems of exposure matrices].
Miniero, Roberto; Dellatte, Elena; Lupi, Carlo; Di Domenico, Alessandro
2005-01-01
In this review a discussion on some factors influencing the exposure matrices which, in turn, influences the reliability of ecotoxicological bioassays on aquatic sediments, has been carried out. These factors include the variability induced on sediments by the sampling, storage, handling, and preparative operations. The exposure matrices-sediments in toto, interstitial water and elutriate, can be deeply modified by these actions, which alter the chemicals bioavailability and, therefore, the bioassay meaning. In order to obtain reproducible and scientifically valid data, to be used in the ecological risk assessment, all these factors need to be considered and kept under control.
Positive projections of symmetric matrices and Jordan algebras
Fuglede, Bent; Jensen, Søren Tolver
2013-01-01
An elementary proof is given that the projection from the space of all symmetric p×p matrices onto a linear subspace is positive if and only if the subspace is a Jordan algebra. This solves a problem in a statistical model.......An elementary proof is given that the projection from the space of all symmetric p×p matrices onto a linear subspace is positive if and only if the subspace is a Jordan algebra. This solves a problem in a statistical model....
Random Matrices for Information Processing – A Democratic Vision
Cakmak, Burak
The thesis studies three important applications of random matrices to information processing. Our main contribution is that we consider probabilistic systems involving more general random matrix ensembles than the classical ensembles with iid entries, i.e. models that account for statistical...... dependence between the entries. Specifically, the involved matrices are invariant or fulfill a certain asymptotic freeness condition as their dimensions grow to infinity. Informally speaking, all latent variables contribute to the system model in a democratic fashion – there are no preferred latent variables...
Precise Asymptotics for Random Matrices and Random Growth Models
Zhong Gen SU
2008-01-01
The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models.We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.