The Experts below are selected from a list of 4278 Experts worldwide ranked by ideXlab platform

Abdul Salam Jarrah - One of the best experts on this subject based on the ideXlab platform.

  • Probabilistic Polynomial Dynamical Systems for reverse engineering of gene regulatory networks
    EURASIP Journal on Bioinformatics and Systems Biology, 2011
    Co-Authors: Elena S Dimitrova, Indranil Mitra, Abdul Salam Jarrah
    Abstract:

    Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of Systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic Polynomial Dynamical Systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic Polynomial Dynamical System. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

  • Probabilistic Polynomial Dynamical Systems for reverse engineering of gene regulatory networks
    EURASIP Journal on Bioinformatics and Systems Biology, 2011
    Co-Authors: Elena S Dimitrova, Indranil Mitra, Abdul Salam Jarrah
    Abstract:

    Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of Systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic Polynomial Dynamical Systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic Polynomial Dynamical System. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

Elena S Dimitrova - One of the best experts on this subject based on the ideXlab platform.

  • Probabilistic Polynomial Dynamical Systems for reverse engineering of gene regulatory networks
    EURASIP Journal on Bioinformatics and Systems Biology, 2011
    Co-Authors: Elena S Dimitrova, Indranil Mitra, Abdul Salam Jarrah
    Abstract:

    Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of Systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic Polynomial Dynamical Systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic Polynomial Dynamical System. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

  • Probabilistic Polynomial Dynamical Systems for reverse engineering of gene regulatory networks
    EURASIP Journal on Bioinformatics and Systems Biology, 2011
    Co-Authors: Elena S Dimitrova, Indranil Mitra, Abdul Salam Jarrah
    Abstract:

    Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of Systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic Polynomial Dynamical Systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic Polynomial Dynamical System. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

Indranil Mitra - One of the best experts on this subject based on the ideXlab platform.

  • Probabilistic Polynomial Dynamical Systems for reverse engineering of gene regulatory networks
    EURASIP Journal on Bioinformatics and Systems Biology, 2011
    Co-Authors: Elena S Dimitrova, Indranil Mitra, Abdul Salam Jarrah
    Abstract:

    Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of Systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic Polynomial Dynamical Systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic Polynomial Dynamical System. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

  • Probabilistic Polynomial Dynamical Systems for reverse engineering of gene regulatory networks
    EURASIP Journal on Bioinformatics and Systems Biology, 2011
    Co-Authors: Elena S Dimitrova, Indranil Mitra, Abdul Salam Jarrah
    Abstract:

    Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of Systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic Polynomial Dynamical Systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic Polynomial Dynamical System. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

Antoine Girard - One of the best experts on this subject based on the ideXlab platform.

  • Control of Polynomial Dynamical Systems on rectangles
    2013 European Control Conference (ECC), 2013
    Co-Authors: Mohamed Amin Ben Sassi, Antoine Girard
    Abstract:

    In this paper we focus on a particular class of nonlinear Dynamical Systems given by Polynomial vector fields in rectangular domains (boxes). This is a generalization of the work of Belta and Habets dealing with multi-affine Dynamical Systems on rectangles. The main idea is to use the blossoming principle which allows us to relate our Polynomial Dynamical System to a multi-affine one. This technique allows us to establish sufficient conditions for invariance of a rectangle or exit of a rectangle through a given facet. We extend these results to handle control synthesis. Finally, we show how our approach can be used to solve motion planning problem.

  • ECC - Control of Polynomial Dynamical Systems on rectangles
    2013 European Control Conference (ECC), 2013
    Co-Authors: Mohamed Amin Ben Sassi, Antoine Girard
    Abstract:

    In this paper we focus on a particular class of nonlinear Dynamical Systems given by Polynomial vector fields in rectangular domains (boxes). This is a generalization of the work of Belta and Habets dealing with multi-affine Dynamical Systems on rectangles. The main idea is to use the blossoming principle which allows us to relate our Polynomial Dynamical System to a multi-affine one. This technique allows us to establish sufficient conditions for invariance of a rectangle or exit of a rectangle through a given facet. We extend these results to handle control synthesis. Finally, we show how our approach can be used to solve motion planning problem.

Maria V. Demina - One of the best experts on this subject based on the ideXlab platform.

  • The method of Puiseux series and invariant algebraic curves
    arXiv: Dynamical Systems, 2018
    Co-Authors: Maria V. Demina
    Abstract:

    An explicit expression for the cofactor related to an irreducible invariant algebraic curve of a Polynomial Dynamical System in the plane is derived. A sufficient condition for a Polynomial Dynamical System in the plane to have a finite number of irreducible invariant algebraic curves is obtained. All these results are applied to Li\'enard Dynamical Systems $x_t=y$, $y_t=-f(x)y-g(x)$ with $\text{deg}\, f

  • From Puiseux series to invariant algebraic curves: the FitzHugh-Nagumo model
    arXiv: Exactly Solvable and Integrable Systems, 2018
    Co-Authors: Maria V. Demina
    Abstract:

    A relationship between Puiseux series satisfying an ordinary differential equation corresponding to a Polynomial Dynamical System and degrees of irreducible invariant algebraic curves is studied. A bound on the degrees of irreducible invariant algebraic curves for a wide class of Polynomial Dynamical Systems is obtained. It is demonstrated that the Puiseux series near infinity can be used to find irreducible algebraic curves explicitly. As an example, all irreducible invariant algebraic curves for the famous FitzHugh-Nagumo System are obtained.

  • From Puiseux series to invariant algebraic curves
    arXiv: Exactly Solvable and Integrable Systems, 2018
    Co-Authors: Maria V. Demina
    Abstract:

    A relationship between Puiseux series satisfying an ordinary differential equation corresponding to a Polynomial Dynamical System and degrees of irreducible invariant algebraic curves is studied. A bound on the degrees of irreducible invariant algebraic curves for a wide class of Polynomial Dynamical Systems is obtained. It is demonstrated that the Puiseux series near infinity can be used to find irreducible algebraic curves explicitly. As an example, all irreducible invariant algebraic curves for the famous FitzHugh-Nagumo System are obtained.

  • Novel algebraic aspects of Liouvillian integrability for two-dimensional Polynomial Dynamical Systems
    Physics Letters A, 2018
    Co-Authors: Maria V. Demina
    Abstract:

    Abstract The general structure of irreducible invariant algebraic curves for a Polynomial Dynamical System in C 2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing–van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing–van der Pol System are constructed.