On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen’s fast matrix multiplication algorithm with DNA based on an n-moduli set in the residue number system, thereby demonstrating the viability of computational mathematics with DNA. As a result, a general scalable implementation of this model in the DNA computing paradigm is presented and can be generalized to the application of all fast matrix multiplication algorithms on a DNA computer. We also discuss the practical capabilities and issues of this scalable implementation. Fast methods of matrix computations with DNA are important because they also allow for the efficient implementation of other algorithms (that is inversion, computing determinants, and graph theory) with DNA. Key words: DNA computing, residue number system, logic and arithmetic operations, Strassen algorithm.
{"title":"Fast matrix multiplication techniques based on the Adleman-Lipton model","authors":"Aran Nayebi","doi":"10.5897/IJCER10.016","DOIUrl":"https://doi.org/10.5897/IJCER10.016","url":null,"abstract":"On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen’s fast matrix multiplication algorithm with DNA based on an n-moduli set in the residue number system, thereby demonstrating the viability of computational mathematics with DNA. As a result, a general scalable implementation of this model in the DNA computing paradigm is presented and can be generalized to the application of all fast matrix multiplication algorithms on a DNA computer. We also discuss the practical capabilities and issues of this scalable implementation. Fast methods of matrix computations with DNA are important because they also allow for the efficient implementation of other algorithms (that is inversion, computing determinants, and graph theory) with DNA. \u0000 \u0000 \u0000 \u0000 Key words: DNA computing, residue number system, logic and arithmetic operations, Strassen algorithm.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125419955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-05-25DOI: 10.1007/978-0-8176-4556-4_26
Radostin D Simitev, V. N.Biktashev
{"title":"An Analytically Solvable Asymptotic Model of Atrial Excitability","authors":"Radostin D Simitev, V. N.Biktashev","doi":"10.1007/978-0-8176-4556-4_26","DOIUrl":"https://doi.org/10.1007/978-0-8176-4556-4_26","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130541860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-10-30DOI: 10.1007/978-3-540-70600-7
M. Elloumi, J. Küng, M. Linial, R. Murphy, K. Schneider, Cristian Toma
{"title":"Bioinformatics Research and Development","authors":"M. Elloumi, J. Küng, M. Linial, R. Murphy, K. Schneider, Cristian Toma","doi":"10.1007/978-3-540-70600-7","DOIUrl":"https://doi.org/10.1007/978-3-540-70600-7","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114950313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-09-22DOI: 10.1002/9780470556757.CH7
Jean-Philippe Vert
We review a recent trend in computational systems biology which aims at using pattern recognition algorithms to infer the structure of large-scale biological networks from heterogeneous genomic data. We present several strategies that have been proposed and that lead to different pattern recognition problems and algorithms. The strenght of these approaches is illustrated on the reconstruction of metabolic, protein-protein and regulatory networks of model organisms. In all cases, state-of-the-art performance is reported.
{"title":"Reconstruction of Biological Networks by Supervised Machine Learning Approaches","authors":"Jean-Philippe Vert","doi":"10.1002/9780470556757.CH7","DOIUrl":"https://doi.org/10.1002/9780470556757.CH7","url":null,"abstract":"We review a recent trend in computational systems biology which aims at using pattern recognition algorithms to infer the structure of large-scale biological networks from heterogeneous genomic data. We present several strategies that have been proposed and that lead to different pattern recognition problems and algorithms. The strenght of these approaches is illustrated on the reconstruction of metabolic, protein-protein and regulatory networks of model organisms. In all cases, state-of-the-art performance is reported.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124525329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nucleotide composition of human genes with a special emphasis on transcription-related strand asymmetries is analyzed. Such asymmetries may be associated with different mutational rates in two principal factors. The first one is transcription-coupled repair and the second one is the selective pressure related to optimization of the translation efficiency. The former factor affects both coding and noncoding regions of a gene, while the latter factor is applicable only to the coding regions. Compositional asymmetries calculated at the third position of a codon in coding (exons) and noncoding (introns, UTR, upstream and downstream) regions of human genes are compared. It is shown that the keto-skew (excess of the frequencies of G and T nucleotides over the frequencies of A and C nucleotides in the same strand) is most pronounced in intronic regions, less pronounced in coding regions, and has near zero values in untranscribed regions. The keto-skew correlates with the level of gene expression in germ-line cells in both introns and exons. We propose to use the results of our analysis to estimate the contribution of different evolutionary factors to the transcription-related compositional biases.
{"title":"Comparative analysis of the nucleotide composition biases in exons and introns of human genes","authors":"D. Duplij","doi":"10.7124/BC.0007B4","DOIUrl":"https://doi.org/10.7124/BC.0007B4","url":null,"abstract":"The nucleotide composition of human genes with a special emphasis on transcription-related strand asymmetries is analyzed. Such asymmetries may be associated with different mutational rates in two principal factors. The first one is transcription-coupled repair and the second one is the selective pressure related to optimization of the translation efficiency. The former factor affects both coding and noncoding regions of a gene, while the latter factor is applicable only to the coding regions. Compositional asymmetries calculated at the third position of a codon in coding (exons) and noncoding (introns, UTR, upstream and downstream) regions of human genes are compared. It is shown that the keto-skew (excess of the frequencies of G and T nucleotides over the frequencies of A and C nucleotides in the same strand) is most pronounced in intronic regions, less pronounced in coding regions, and has near zero values in untranscribed regions. The keto-skew correlates with the level of gene expression in germ-line cells in both introns and exons. We propose to use the results of our analysis to estimate the contribution of different evolutionary factors to the transcription-related compositional biases.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126233476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-06-19DOI: 10.1142/S0217979210054919
A. Iorio, Samik Sen, S. Sen
The classical electrostatic interaction between DNA molecules in water in the presence of counterions is reconsidered and we propose it is governed by a modified Poisson-Boltzmann equation. Quantum fluctuations are then studied and shown to lead to a vacuum interaction that is numerically computed for several configurations of many DNA strands and found to be strongly many-body. This Casimir vacuum interaction can be the ``glue'' holding together DNA molecules into aggregates.
{"title":"Do quantum effects hold together DNA condensates","authors":"A. Iorio, Samik Sen, S. Sen","doi":"10.1142/S0217979210054919","DOIUrl":"https://doi.org/10.1142/S0217979210054919","url":null,"abstract":"The classical electrostatic interaction between DNA molecules in water in the presence of counterions is reconsidered and we propose it is governed by a modified Poisson-Boltzmann equation. Quantum fluctuations are then studied and shown to lead to a vacuum interaction that is numerically computed for several configurations of many DNA strands and found to be strongly many-body. This Casimir vacuum interaction can be the ``glue'' holding together DNA molecules into aggregates.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129942553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-01-16DOI: 10.3182/20080706-5-KR-1001.02130
Diego A. Oyarz'un, B. Ingalls, R. Middleton, D. Kalamatianos
This paper deals with temporal enzyme distribution in the activation of biochemical pathways. Pathway activation arises when production of a certain biomolecule is required due to changing environmental conditions. Under the premise that biological systems have been optimized through evolutionary processes, a biologically meaningful optimal control problem is posed. In this setup, the enzyme concentrations are assumed to be time dependent and constrained by a limited overall enzyme production capacity, while the optimization criterion accounts for both time and resource usage. Using geometric arguments we establish the bang-bang nature of the solution and reveal that each reaction must be sequentially activated in the same order as they appear in the pathway. The results hold for a broad range of enzyme dynamics which includes, but is not limited to, Mass Action, Michaelis-Menten and Hill Equation kinetics.
{"title":"Optimal metabolic pathway activation","authors":"Diego A. Oyarz'un, B. Ingalls, R. Middleton, D. Kalamatianos","doi":"10.3182/20080706-5-KR-1001.02130","DOIUrl":"https://doi.org/10.3182/20080706-5-KR-1001.02130","url":null,"abstract":"This paper deals with temporal enzyme distribution in the activation of biochemical pathways. Pathway activation arises when production of a certain biomolecule is required due to changing environmental conditions. Under the premise that biological systems have been optimized through evolutionary processes, a biologically meaningful optimal control problem is posed. In this setup, the enzyme concentrations are assumed to be time dependent and constrained by a limited overall enzyme production capacity, while the optimization criterion accounts for both time and resource usage. \u0000Using geometric arguments we establish the bang-bang nature of the solution and reveal that each reaction must be sequentially activated in the same order as they appear in the pathway. The results hold for a broad range of enzyme dynamics which includes, but is not limited to, Mass Action, Michaelis-Menten and Hill Equation kinetics.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124441021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-12-27DOI: 10.1007/978-0-8176-4556-4_25
J. Claussen
{"title":"Offdiagonal Complexity: A Computationally Quick Network Complexity Measure—Application to Protein Networks and Cell Division","authors":"J. Claussen","doi":"10.1007/978-0-8176-4556-4_25","DOIUrl":"https://doi.org/10.1007/978-0-8176-4556-4_25","url":null,"abstract":"","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129211782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a maximum entropy (ME) based approach to smooth noise not only in data but also to noise amplified by second order derivative calculation of the data especially for electroencephalography (EEG) studies. The approach includes two steps, applying method of ME to generate a family of filters and minimizing noise variance after applying these filters on data selects the preferred one within the family. We examine performance of the ME filter through frequency and noise variance analysis and compare it with other well known filters developed in the EEG studies. The results show the ME filters to outperform others. Although we only demonstrate a filter design especially for second order derivative of EEG data, these studies still shed an informatic approach of systematically designing a filter for specific purposes.
{"title":"Filter Out High Frequency Noise in EEG Data Using The Method of Maximum Entropy","authors":"C. Tseng, Hc Lee","doi":"10.1063/1.2821286","DOIUrl":"https://doi.org/10.1063/1.2821286","url":null,"abstract":"We propose a maximum entropy (ME) based approach to smooth noise not only in data but also to noise amplified by second order derivative calculation of the data especially for electroencephalography (EEG) studies. The approach includes two steps, applying method of ME to generate a family of filters and minimizing noise variance after applying these filters on data selects the preferred one within the family. We examine performance of the ME filter through frequency and noise variance analysis and compare it with other well known filters developed in the EEG studies. The results show the ME filters to outperform others. Although we only demonstrate a filter design especially for second order derivative of EEG data, these studies still shed an informatic approach of systematically designing a filter for specific purposes.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116851935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Magnetoencephalography (MEG) provides dynamic spatial-temporal insight of neural activities in the cortex. Because the number of possible sources is far greater than the number of MEG detectors, the proposition to localize sources directly from MEG data is notoriously ill-posed. Here we develop an approach based on data processing procedures including clustering, forward and backward filtering, and the method of maximum entropy. We show that taking as a starting point the assumption that the sources lie in the general area of the auditory cortex (an area of about 40 mm by 15 mm), our approach is capable of achieving reasonable success in pinpointing active sources concentrated in an area of a few mm's across, while limiting the spatial distribution and number of false positives.
{"title":"Data Processing Approach for Localizing Bio-magnetic Sources in the Brain","authors":"Hung-I Pai, C. Tseng, H. C. Lee","doi":"10.1063/1.2759772","DOIUrl":"https://doi.org/10.1063/1.2759772","url":null,"abstract":"Magnetoencephalography (MEG) provides dynamic spatial-temporal insight of neural activities in the cortex. Because the number of possible sources is far greater than the number of MEG detectors, the proposition to localize sources directly from MEG data is notoriously ill-posed. Here we develop an approach based on data processing procedures including clustering, forward and backward filtering, and the method of maximum entropy. We show that taking as a starting point the assumption that the sources lie in the general area of the auditory cortex (an area of about 40 mm by 15 mm), our approach is capable of achieving reasonable success in pinpointing active sources concentrated in an area of a few mm's across, while limiting the spatial distribution and number of false positives.","PeriodicalId":119149,"journal":{"name":"arXiv: Quantitative Methods","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114577474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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