Download or read book Dimensionality Reduction of the Chemical Master Equation written by Midhun Kathanaruparambil Sukumaran and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of biochemical systems show significant variability when the reactant populations are small. Standard approaches via deterministic modeling exclude such variability. A well established stochastic model, the Chemical master equation (CME), describes the dynamics of biochemical systems by representing the time evolution of the probability distribution of species' discrete states in a well-mixed reaction volume. However, the dimension of the CME (i.e.~the number of transition states in the system) rapidly grows as the molecular population and number of reactions in the network increases. Also, the dynamics of biochemical systems typically vary over a wide range of time scales: a phenomenon referred to as stiffness. Large dimensions and stiffness pose challenges to numerical analysis of system behavior. By eliminating the fast modes, which correspond to fast time scales that are often not experimentally observed, a model reduction can be achieved. In our work, we apply such a model reduction to the CME. The slow and fast modes of the system correspond to small and large eigenvalues of the transition matrix of the CME. By a transformation, we exclude the fast modes to arrive at a truncated model. We propose a method based on eigenbasis transformations that provide efficient approximations that are accurate beyond a short initial time interval. We also present efficient algorithms for generation of the CME from a network and for computation of eigenbases. Finally, we describe how this reduction approach can be implemented to provide efficient time-step identification in a well-established scheme for an approximation of the CME (the so-called finite state projection).

Download or read book Issues in General Physics Research 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 8864 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General Physics Research / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General Physics Research. The editors have built Issues in General Physics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Physics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General Physics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book Extraction of Quantifiable Information from Complex Systems written by Stephan Dahlke and published by Springer. This book was released on 2014-11-13 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Download or read book Computer Methods Part C written by and published by Academic Press. This book was released on 2010-12-24 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: The combination of faster, more advanced computers and more quantitatively oriented biomedical researchers has recently yielded new and more precise methods for the analysis of biomedical data. These better analyses have enhanced the conclusions that can be drawn from biomedical data, and they have changed the way that experiments are designed and performed. This volume, along with the 2 previous Computer Methods volumes for the Methods in Enzymology serial, aims to inform biomedical researchers about recent applications of modern data analysis and simulation methods as applied to biomedical research. Presents step-by-step computer methods and discusses the techniques in detail to enable their implementation in solving a wide range of problems Informs biomedical researchers of the modern data analysis methods that have developed alongside computer hardware Presents methods at the "nuts and bolts" level to identify and resolve a problem and analyze what the results mean

Download or read book Chemical Kinetics Stochastic Processes and Irreversible Thermodynamics written by Moisés Santillán and published by Springer. This book was released on 2014-06-27 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry and biochemistry together in an introductory but formal and comprehensive manner. Coupled with examples, the theories are developed stepwise, starting with the simplest concepts and building upon them into a more general framework. Furthermore, each new mathematical derivation is immediately applied to one or more biological systems. The last chapters focus on applying mathematical and physical techniques to study systems such as: gene regulatory networks and molecular motors. The target audience of this book are mainly final year undergraduate and graduate students with a solid mathematical background (physicists, mathematicians and engineers), as well as with basic notions of biochemistry and cellular biology. This book can also be useful to students with a biological background who are interested in mathematical modeling and have a working knowledge of calculus, differential equations and a basic understanding of probability theory.

Download or read book Advances in Chemical Physics Volume 115 written by Ilya Prigogine and published by John Wiley & Sons. This book was released on 2009-09-09 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

Download or read book Krylov Approximation and Model Reduction Methods for Solving the Chemical Master Equation written by Huy D. Vo and published by . This book was released on 2017 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex interacting networks are prevalent across many fields of science and engineering, ranging from chemical kinetics and pharmacology to social sciences. In biochemistry, such networks arise through the reactions between the cell's components such as DNA and RNA molecules. Since these key biomolecules often appear in low copy numbers, the intrinsic randomness of their interactions becomes significant. This calls for a stochastic framework that treats the chemical populations as a continuous-time, discrete-state Markov process. The time-dependent probability distribution of this process is the solution of the chemical master equation (CME). Despite many potential benefits, the CME is notoriously difficult to solve due to the curse of dimensionality. This dissertation is about numerical methods that seek to alleviate this curse. We introduce three tools for this challenging task. The first tool aims to exploit sparsity in the solution of the CME by only keeping states that have a significant probability mass at each time step. It uses the stochastic simulation algorithm to quickly scout these important states, and advance the integration using Krylov subspace approximation techniques. The second tool applies a grid-based aggregation method that is well expressed in terms of the tensor product. It employs a residual-based error control to automatically adapt the aggregation scheme to the region that requires fine details. The third tool leverages novel results in the tensor train format. It combines the finite state projection, tensor-based linear system solvers, and the inexact uniformization method. Numerical results are conducted to show the efficiency of the proposed methods.

Download or read book Stochastic Processes Multiscale Modeling and Numerical Methods for Computational Cellular Biology written by David Holcman and published by Springer. This book was released on 2017-10-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Download or read book Handbook of Statistical Genomics written by David J. Balding and published by John Wiley & Sons. This book was released on 2019-07-02 with total page 1224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely update of a highly popular handbook on statistical genomics This new, two-volume edition of a classic text provides a thorough introduction to statistical genomics, a vital resource for advanced graduate students, early-career researchers and new entrants to the field. It introduces new and updated information on developments that have occurred since the 3rd edition. Widely regarded as the reference work in the field, it features new chapters focusing on statistical aspects of data generated by new sequencing technologies, including sequence-based functional assays. It expands on previous coverage of the many processes between genotype and phenotype, including gene expression and epigenetics, as well as metabolomics. It also examines population genetics and evolutionary models and inference, with new chapters on the multi-species coalescent, admixture and ancient DNA, as well as genetic association studies including causal analyses and variant interpretation. The Handbook of Statistical Genomics focuses on explaining the main ideas, analysis methods and algorithms, citing key recent and historic literature for further details and references. It also includes a glossary of terms, acronyms and abbreviations, and features extensive cross-referencing between chapters, tying the different areas together. With heavy use of up-to-date examples and references to web-based resources, this continues to be a must-have reference in a vital area of research. Provides much-needed, timely coverage of new developments in this expanding area of study Numerous, brand new chapters, for example covering bacterial genomics, microbiome and metagenomics Detailed coverage of application areas, with chapters on plant breeding, conservation and forensic genetics Extensive coverage of human genetic epidemiology, including ethical aspects Edited by one of the leading experts in the field along with rising stars as his co-editors Chapter authors are world-renowned experts in the field, and newly emerging leaders. The Handbook of Statistical Genomics is an excellent introductory text for advanced graduate students and early-career researchers involved in statistical genetics.

Download or read book On Reduced Models for the Chemical Master Equation written by Tobias Jahnke and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inexact Methods for the Chemical Master Equation with Constant Or Time varying Propensities and Application to Parameter Inference written by Khanh Ngoc Dinh and published by . This book was released on 2018 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex reaction networks arise in molecular biology and many other different fields of science such as ecology and social study. A familiar approach to modeling such problems is to find their master equation. In systems biology, the equation is called the chemical master equation (CME), and solving the CME is a difficult task, because of the curse of dimensionality. The goal of this dissertation is to alleviate this curse via the use of the finite state projection (FSP), in both cases where the CME matrix is constant (if the reaction rates are time-independent) or time-varying (if the reaction rates change over time). The work includes a theoretical characterization of the FSP truncation technique by showing that it can be put in the framework of inexact Krylov methods that relax matrix-vector products and compute them expediently by trading accuracy for speed. We also examine practical applications of our work in delay CME and parameter inference through local and global optimization schemes.

Download or read book 13th International Symposium on Process Systems Engineering PSE 2018 July 1 5 2018 written by Mario R. Eden and published by Elsevier. This book was released on 2018-07-19 with total page 2620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Process Systems Engineering brings together the international community of researchers and engineers interested in computing-based methods in process engineering. This conference highlights the contributions of the PSE community towards the sustainability of modern society and is based on the 13th International Symposium on Process Systems Engineering PSE 2018 event held San Diego, CA, July 1-5 2018. The book contains contributions from academia and industry, establishing the core products of PSE, defining the new and changing scope of our results, and future challenges. Plenary and keynote lectures discuss real-world challenges (globalization, energy, environment and health) and contribute to discussions on the widening scope of PSE versus the consolidation of the core topics of PSE. Highlights how the Process Systems Engineering community contributes to the sustainability of modern society Establishes the core products of Process Systems Engineering Defines the future challenges of Process Systems Engineering

Download or read book Advances in Chemical Engineering written by Guy B. Marin and published by Elsevier. This book was released on 2005-10-24 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of the present volume "Multiscale Analysis" has been introduced about a decade ago and is now reaching a stage where a first balance can be made and further research directions should be decided. Contributions have been carefully selected to ensure the reader will not be confronted with quantum mechanics at one side of the spectrum nor with chemical plants or even the environment on the other side. Maintaining a strong connection with reality i.e. experimental data was another selection criterion. Experimental validation remains the corner stone of any theoretical development and very powerful experimentel techniques are emerging.Areas covered include discussing in depth an important example of experimental techniques. Coming from the medical world, Magnetic Resonance techniques can now provide even quantitative answers to problems our community is faced with. The modeling issue is discussed further. Finally, the limitations of the classic reactor engineering models are outlined. * Original reviews* Leading chemical engineers as authors* Update on biomaterials use* Novel subject on use of biomaterials in drug delivery and gene therapy* Mathematical modeling

Download or read book Dynamics and Complexity of Molecular Networks Controlling Cell Fate Decisions written by Chunhe Li and published by Frontiers Media SA. This book was released on 2022-11-21 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Modelling for Systems Biology Second Edition written by Darren J. Wilkinson and published by CRC Press. This book was released on 2011-11-09 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Re-written to reflect this modern perspective, this second edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. Keeping with the spirit of the first edition, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. New in the Second Edition All examples have been updated to Systems Biology Markup Language Level 3 All code relating to simulation, analysis, and inference for stochastic kinetic models has been re-written and re-structured in a more modular way An ancillary website provides links, resources, errata, and up-to-date information on installation and use of the associated R package More background material on the theory of Markov processes and stochastic differential equations, providing more substance for mathematically inclined readers Discussion of some of the more advanced concepts relating to stochastic kinetic models, such as random time change representations, Kolmogorov equations, Fokker-Planck equations and the linear noise approximation Simple modelling of "extrinsic" and "intrinsic" noise An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional mathematical detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

Download or read book ISIS International Symposium on Interdisciplinary Science written by Andrei Ludu and published by American Institute of Physics. This book was released on 2005-04-07 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sponsoring organizations: Northwestern State University, The IDEAS Program, Richardson Technologies, Inc.

Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations