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  • 1
    Electronic Resource
    Electronic Resource
    Hirota bilinear approach to a new integrable differential-difference system (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2001-2010 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new integrable differential-difference system is proposed. By the dependent variable transformation, the system is transformed into multilinear form. By introducing an auxiliary variable, we further transform it into the bilinear form. A corresponding Bäcklund transformation for it is obtained. Furthermore a nonlinear superposition formula is presented. As an application of the obtained results, soliton solutions to the system are derived. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532846
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  • 2
    Electronic Resource
    Electronic Resource
    Some new results on the Blaszak–Marciniak lattice: Bäcklund transformation and nonlinear superposition formula (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4766-4772 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The so-called Blaszak–Marciniak lattice is considered. By the dependent variable transformation, the Blaszak–Marciniak lattice is transformed into a quart-linear form. By introducing an auxiliary variable, we further transform it into the bilinear form. A corresponding Bäcklund transformation is obtained. Furthermore, a nonlinear superposition formula is proved rigorously. As an application of the obtained results, soliton solutions are derived. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532535
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  • 3
    Electronic Resource
    Electronic Resource
    A Bäcklund transformation and nonlinear superposition formula of a modified Korteweg–de Vries-type bilinear equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4739-4745 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A modified Korteweg–de Vries (mKdV)-type bilinear equation that has been shown to pass the three-soliton solution and the Painlevé tests [see, J. Math. Phys. 2094, 28 (1987); 2572, 31 (1990)] is considered herein. In this article, a Bäcklund transformation and a nonlinear superposition formula are proven rigorously. As an application of the obtained results, N-soliton solutions are obtained. Therefore, the integrability of this mKdV-type bilinear equation is confirmed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530811
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  • 4
    Electronic Resource
    Electronic Resource
    Erratum: "Hirota bilinear approach to a new integrable differential-difference system" [J. Math. Phys. 40, 2001 (1999)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4180-4180 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532953
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  • 5
    Electronic Resource
    Electronic Resource
    Supervised Detection of Regulatory Motifs in DNA Sequences (2003)
    Berkeley, Calif. : Berkeley Electronic Press (now: De Gruyter)
    Statistical applications in genetics and molecular biology 2.2003, 1, art5 
    Details
    ISSN: 1544-6115
    Source: Berkeley Electronic Press Academic Journals
    Topics: Biology
    Notes: Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs motif sampler) model binding sites as families of sequences described by a position weight matrix (PWM) and identify PWMs that maximize the likelihood of observed sequence data under a simple multinomial mixture model. This model assumes that the positions of the PWM correspond to independent multinomial distributions with four cell probabilities. We address supervising the search for DNA binding sites using the information derived from structural characteristics of protein-DNA interactions. We extend the simple multinomial mixture model to a constrained multinomial mixture model by incorporating constraints on the information content profiles or on specific parameters of the motif PWMs. The parameters of this extended model are estimated by maximum likelihood using a nonlinear constraint optimization method. Likelihood-based cross-validation is used to select model parameters such as motif width and constraint type. The performance of COMODE is compared with existing motif detection methods on simulated data that incorporate real motif examples from Saccharomyces cerevisiae. The proposed method is especially effective when the motif of interest appears as a weak signal in the data. Some of the transcription factor binding data of Lee et al. (2002) were also analyzed using COMODE and biologically verified sites were identified.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/sagmb/vol2/iss1/art5
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  • 6
    Electronic Resource
    Electronic Resource
    Renormalization group calculation of the critical temperature dependence on longitudinal magnetic field for a disordered superconductor model (1990)
    Springer
    The European physical journal 78 (1990), S. 485-487 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We describe a calculation ofT c (P, H) in a model of a disordered superconductor which is based on the de Gennes-Skal-Shklovskii (dGSS) picture of the large cluster in a percolation system. The calculation is done by carrying out successive decimations on the Landau-Ginzburg Hamiltonian describing the ‘links’ in the model. We calculateT c (P, H) in the presence of longitudinal magnetic field by evaluating the renormalized Landau-Ginzburg coupling when the renormalized Landau-Ginzburg length equals the percolation link length in the dGSS picture and obtain the approximate analytic form ofT c (P, H).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313331
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