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Michelle D Quirk - One of the best experts on this subject based on the ideXlab platform.

  • A stochastic Differential Equation Model for transcriptional regulatory networks
    BMC Bioinformatics, 2007
    Co-Authors: Adriana Climescu-haulica, Michelle D Quirk
    Abstract:

    International audienceBACKGROUND: This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets.The dynamics of the gene expression level are fitted via a stochastic Differential Equation Model, yielding a set of specific regulators and their contribution. RESULTS: We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic Differential Equation Model follows well the dynamic of the gene expression levels. CONCLUSION: When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved Models of the transcriptional regulatory networks

  • A stochastic Differential Equation Model for transcriptional regulatory networks.
    BMC bioinformatics, 2007
    Co-Authors: Adriana Climescu-haulica, Michelle D Quirk
    Abstract:

    This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic Differential Equation Model, yielding a set of specific regulators and their contribution. We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic Differential Equation Model follows well the dynamic of the gene expression levels. When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved Models of the transcriptional regulatory networks.

  • A stochastic Differential Equation Model for transcriptional regulatory networks.
    BMC Bioinformatics, 2007
    Co-Authors: Adriana Climescu-haulica, Michelle D Quirk
    Abstract:

    BACKGROUND: This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets.The dynamics of the gene expression level are fitted via a stochastic Differential Equation Model, yielding a set of specific regulators and their contribution. RESULTS: We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic Differential Equation Model follows well the dynamic of the gene expression levels. CONCLUSION: When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved Models of the transcriptional regulatory networks.

Adriana Climescu-haulica - One of the best experts on this subject based on the ideXlab platform.

  • A stochastic Differential Equation Model for transcriptional regulatory networks
    BMC Bioinformatics, 2007
    Co-Authors: Adriana Climescu-haulica, Michelle D Quirk
    Abstract:

    International audienceBACKGROUND: This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets.The dynamics of the gene expression level are fitted via a stochastic Differential Equation Model, yielding a set of specific regulators and their contribution. RESULTS: We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic Differential Equation Model follows well the dynamic of the gene expression levels. CONCLUSION: When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved Models of the transcriptional regulatory networks

  • A stochastic Differential Equation Model for transcriptional regulatory networks.
    BMC bioinformatics, 2007
    Co-Authors: Adriana Climescu-haulica, Michelle D Quirk
    Abstract:

    This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic Differential Equation Model, yielding a set of specific regulators and their contribution. We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic Differential Equation Model follows well the dynamic of the gene expression levels. When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved Models of the transcriptional regulatory networks.

  • A stochastic Differential Equation Model for transcriptional regulatory networks.
    BMC Bioinformatics, 2007
    Co-Authors: Adriana Climescu-haulica, Michelle D Quirk
    Abstract:

    BACKGROUND: This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets.The dynamics of the gene expression level are fitted via a stochastic Differential Equation Model, yielding a set of specific regulators and their contribution. RESULTS: We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic Differential Equation Model follows well the dynamic of the gene expression levels. CONCLUSION: When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved Models of the transcriptional regulatory networks.

Helen M Byrne - One of the best experts on this subject based on the ideXlab platform.

  • an ordinary Differential Equation Model for full thickness wounds and the effects of diabetes
    Journal of Theoretical Biology, 2014
    Co-Authors: L G Bowden, Philip K Maini, Derek E Moulton, J B Tang, X T Wang, P Y Liu, Helen M Byrne
    Abstract:

    Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary Differential Equation Model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting Model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the Model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The Model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment.

  • qualitative analysis of an integro Differential Equation Model of periodic chemotherapy
    Applied Mathematics Letters, 2012
    Co-Authors: Harsh Vardhan Jain, Helen M Byrne
    Abstract:

    An existing Model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.

Fengde Chen - One of the best experts on this subject based on the ideXlab platform.

  • almost periodic solution of an impulsive Differential Equation Model of plankton allelopathy
    Nonlinear Analysis-real World Applications, 2010
    Co-Authors: Fengde Chen
    Abstract:

    Abstract In this paper, we consider an impulsive Differential Equation Model of plankton allelopathy. Sufficient conditions ensuring the existence of a unique almost periodic solution of the system are obtained, by the relation between the solutions of impulsive system and the corresponding non-impulsive system.

  • Dynamic behaviors of a delay Differential Equation Model of plankton allelopathy
    Journal of Computational and Applied Mathematics, 2007
    Co-Authors: Fengde Chen, Xiaoxing Chen, Jitka Laitochová
    Abstract:

    In this paper, we consider a modified delay Differential Equation Model of the growth of n-species of plankton having competitive and allelopathic effects on each other. We first obtain the sufficient conditions which guarantee the permanence of the system. As a corollary, for periodic case, we obtain a set of delay-dependent condition which ensures the existence of at least one positive periodic solution of the system. After that, by means of a suitable Lyapunov functional, sufficient conditions are derived for the global attractivity of the system. For the two-dimensional case, under some suitable assumptions, we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic Equation. Examples show the feasibility of the main results.

Lucie Baudouin - One of the best experts on this subject based on the ideXlab platform.

  • robust control of a cable from a hyperbolic partial Differential Equation Model
    IEEE Transactions on Control Systems and Technology, 2019
    Co-Authors: Lucie Baudouin, Aude Rondepierre, Simon A Neild
    Abstract:

    This article presents a detailed study of the robust control of a cable’s vibrations, with emphasis on considering a Model of infinite dimension. Indeed, using a partial Differential Equation Model of the vibrations of an inclined cable with sag, we are interested in studying the application of $\mathcal H_{\infty }$ -robust feedback control to this infinite dimensional system. The approach relies on Riccati Equations to stabilize the system under measurement feedback when it is subjected to external disturbances. Henceforth, this article focuses on the construction of a standard linear infinite dimensional state space description of the cable under consideration before writing its approximation of finite dimension and studying the $\mathcal H_{\infty }$ feedback control of vibrations with partial observation of the state in both cases. The closed-loop system is numerically simulated to illustrate the effectiveness of the resulting control law.

  • Robust control of a cable from a hyperbolic partial Differential Equation Model
    IEEE Transactions on Control Systems Technology, 2019
    Co-Authors: Lucie Baudouin, Aude Rondepierre, Simon Neild
    Abstract:

    This paper presents a detailed study of the robust control of a cable’s vibrations, with emphasis on considering a Model of infinite dimension. Indeed, using a partial Differential Equation Model of the vibrations of an inclined cable with sag, we are interested in studying the application of H∞-robust feedback control to this infinite dimensional system. The approach relies on Riccati Equations to stabilize the system under measurement feedback when it is subjected to external disturbances. Henceforth, our study focuses on the construction of a standard linear infinite dimensional state space description of the cable under consideration before writing its approximation of finite dimension and studying the H∞ feedback control of vibrations with partial observation of the state in both cases. The closed loop system is numerically simulated to illustrate the effectiveness of the resulting control law.