Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
ACM Computing Surveys (CSUR)
Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Improved Fast Gauss Transform and Efficient Kernel Density Estimation
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Computational Modeling of Genetic and Biochemical Networks (Computational Molecular Biology)
Computational Modeling of Genetic and Biochemical Networks (Computational Molecular Biology)
Multi-Resolution-Analysis Scheme for Uncertainty Quantification in Chemical Systems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs
SIAM Journal on Scientific Computing
Multiparameter Spectral Representation of Noise-Induced Competence in Bacillus Subtilis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Preconditioned Bayesian Regression for Stochastic Chemical Kinetics
Journal of Scientific Computing
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Dynamical analysis tools are well established for deterministic models. However, for many biochemical phenomena in cells the molecule count is low, leading to stochastic behavior that causes deterministic macroscale reaction models to fail. The main mathematical framework representing these phenomena is based on jump Markov processes that model the underlying stochastic reaction network. Conventional dynamical analysis tools do not readily generalize to the stochastic setting due to nondifferentiability and absence of explicit state evolution equations. We developed a reduced order methodology for dynamical analysis that relies on the Karhunen-Loève decomposition and polynomial chaos expansions. The methodology relies on adaptive data partitioning to obtain an accurate representation of the stochastic process, especially in the case of multimodal behavior. As a result, a mixture model is obtained that represents the reduced order dynamics of the system. The Schlögl model is used as a prototype bistable process that exhibits time scale separation and leads to multimodality in the reduced order model.