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Physical Sciences and Mathematics Commons™

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Mathematics

University of Nebraska at Omaha

Series

2016

Articles 1 - 7 of 7

Full-Text Articles in Physical Sciences and Mathematics

Logical Reduction Of Biological Networks To Their Most Determinative Components, Mihaela Teodora Matache, Valentin Matache Jul 2016

Logical Reduction Of Biological Networks To Their Most Determinative Components, Mihaela Teodora Matache, Valentin Matache

Mathematics Faculty Publications

Boolean networks have been widely used as models for gene regulatory networks, signal transduction networks, or neural networks, among many others. One of the main difficulties in analyzing the dynamics of a Boolean network and its sensitivity to perturbations or mutations is the fact that it grows exponentially with the number of nodes. Therefore, various approaches for simplifying the computations and reducing the network to a subset of relevant nodes have been proposed in the past few years. We consider a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain. …

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Systems Perturbation Analysis Of A Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates For Cancer Therapeutics, Bhanwar L. Puniya, Laura Allen, Colleen Hochfelder, Mahbubul Majumder, Tomáš Helikar Feb 2016

Systems Perturbation Analysis Of A Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates For Cancer Therapeutics, Bhanwar L. Puniya, Laura Allen, Colleen Hochfelder, Mahbubul Majumder, Tomáš Helikar

Mathematics Faculty Publications

Dysregulation in signal transduction pathways can lead to a variety of complex disorders, including cancer. Computational approaches such as network analysis are important tools to understand system dynamics as well as to identify critical components that could be further explored as therapeutic targets. Here, we performed perturbation analysis of a large-scale signal transduction model in extracellular environments that stimulate cell death, growth, motility, and quiescence. Each of the model’s components was perturbed under both loss-of-function and gain-of-function mutations. Using 1,300 simulations under both types of perturbations across various extracellular conditions, we identified the most and least influential components based on …

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Some New Refinements Of The Arithmetic, Geometric And Harmonic Mean Inequalities With Applications, Steven G. From, R. Suthakaran Jan 2016

Some New Refinements Of The Arithmetic, Geometric And Harmonic Mean Inequalities With Applications, Steven G. From, R. Suthakaran

Mathematics Faculty Publications

No abstract provided.

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Analysis Of A Posteriori Error Estimates Of The Discontinuous Galerkin Method For Nonlinear Ordinary Differential Equations, Mahboub Baccouch Jan 2016

Analysis Of A Posteriori Error Estimates Of The Discontinuous Galerkin Method For Nonlinear Ordinary Differential Equations, Mahboub Baccouch

Mathematics Faculty Publications

We develop and analyze a new residual-based a posteriori error estimator for the discontinuous Galerkin (DG) method for nonlinear ordinary differential equations (ODEs). The a posteriori DG error estimator under investigation is computationally simple, efficient, and asymptotically exact. It is obtained by solving a local residual problem with no boundary condition on each element. We first prove that the DG solution exhibits an optimal O(hp+1) convergence rate in the L2-norm when p-degree piece-wise polynomials with p ≥1 are used. We further prove that the DG solution is O(h2p+1) superconvergent at the downwind points. We …

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Analysis Of Optimal Error Estimates And Superconvergence Of The Discontinuous Galerkin Method For Convection-Diffusion Problems In One Space Dimension, Mahboub Baccouch, Helmi Temimi Jan 2016

Analysis Of Optimal Error Estimates And Superconvergence Of The Discontinuous Galerkin Method For Convection-Diffusion Problems In One Space Dimension, Mahboub Baccouch, Helmi Temimi

Mathematics Faculty Publications

In this paper, we study the convergence and superconvergence properties of the discontinuous Galerkin (DG) method for a linear convection-diffusion problem in one-dimensional setting. We prove that the DG solution and its derivative exhibit optimal O(hp+1) and O(hp) convergence rates in the L 2 -norm, respectively, when p-degree piecewise polynomials with p ≥ 1 are used. We further prove that the p-degree DG solution and its derivative are O(h2p) superconvergent at the downwind and upwind points, respectively. Numerical experiments demonstrate that the theoretical rates are optimal and that the DG …

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The Discontinuous Galerkin Finite Element Method For Ordinary Differential Equations, Mahboub Baccouch Jan 2016

The Discontinuous Galerkin Finite Element Method For Ordinary Differential Equations, Mahboub Baccouch

Mathematics Faculty Publications

We present an analysis of the discontinuous Galerkin (DG) finite element method for nonlinear ordinary differential equations (ODEs). We prove that the DG solution is $(p + 1) $th order convergent in the $L^2$-norm, when the space of piecewise polynomials of degree $p$ is used. A $ (2p+1) $th order superconvergence rate of the DG approximation at the downwind point of each element is obtained under quasi-uniform meshes. Moreover, we prove that the DG solution is superconvergent with order $p+2$ to a particular projection of the exact solution. The superconvergence results are used to show that the leading term of …

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Invertible And Normal Composition Operators On The Hilbert Hardy Space Of A Half–Plane, Valentin Matache Jan 2016

Invertible And Normal Composition Operators On The Hilbert Hardy Space Of A Half–Plane, Valentin Matache

Mathematics Faculty Publications

Operators on function spaces of form... is a fixed map are called composition operators with symbol φ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.

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