The Effect of Compression and Expansion on Stochastic Reaction Networks
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Intrinsic Noise Analyzer: a Software Package for the Exploration of Stochastic Biochemical Kinetics Using the System Size Expansion
Intrinsic Noise Analyzer: A Software Package for the Exploration of Stochastic Biochemical Kinetics Using the System Size Expansion Philipp Thomas1,2,3., Hannes Matuschek4., Ramon Grima1,2* 1 School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom, 2 SynthSys Edinburgh, University of Edinburgh, Edinburgh, United Kingdom, 3 Department of Physics, Humboldt University of Berlin, Berlin, Germany, 4 Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany Abstract The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen’s system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. -
Type Checking Physical Frames of Reference for Robotic Systems
PhysFrame: Type Checking Physical Frames of Reference for Robotic Systems Sayali Kate Michael Chinn Hongjun Choi Purdue University University of Virginia Purdue University USA USA USA [email protected] [email protected] [email protected] Xiangyu Zhang Sebastian Elbaum Purdue University University of Virginia USA USA [email protected] [email protected] ABSTRACT Engineering (ESEC/FSE ’21), August 23–27, 2021, Athens, Greece. ACM, New A robotic system continuously measures its own motions and the ex- York, NY, USA, 16 pages. https://doi.org/10.1145/3468264.3468608 ternal world during operation. Such measurements are with respect to some frame of reference, i.e., a coordinate system. A nontrivial 1 INTRODUCTION robotic system has a large number of different frames and data Robotic systems have rapidly growing applications in our daily life, have to be translated back-and-forth from a frame to another. The enabled by the advances in many areas such as AI. Engineering onus is on the developers to get such translation right. However, such systems becomes increasingly important. Due to the unique this is very challenging and error-prone, evidenced by the large characteristics of such systems, e.g., the need of modeling the phys- number of questions and issues related to frame uses on developers’ ical world and satisfying the real time and resource constraints, forum. Since any state variable can be associated with some frame, robotic system engineering poses new challenges to developers. reference frames can be naturally modeled as variable types. We One of the prominent challenges is to properly use physical frames hence develop a novel type system that can automatically infer of reference. -
Dynamic Extension of Typed Functional Languages
Dynamic Extension of Typed Functional Languages Don Stewart PhD Dissertation School of Computer Science and Engineering University of New South Wales 2010 Supervisor: Assoc. Prof. Manuel M. T. Chakravarty Co-supervisor: Dr. Gabriele Keller Abstract We present a solution to the problem of dynamic extension in statically typed functional languages with type erasure. The presented solution re- tains the benefits of static checking, including type safety, aggressive op- timizations, and native code compilation of components, while allowing extensibility of programs at runtime. Our approach is based on a framework for dynamic extension in a stat- ically typed setting, combining dynamic linking, runtime type checking, first class modules and code hot swapping. We show that this framework is sufficient to allow a broad class of dynamic extension capabilities in any statically typed functional language with type erasure semantics. Uniquely, we employ the full compile-time type system to perform run- time type checking of dynamic components, and emphasize the use of na- tive code extension to ensure that the performance benefits of static typing are retained in a dynamic environment. We also develop the concept of fully dynamic software architectures, where the static core is minimal and all code is hot swappable. Benefits of the approach include hot swappable code and sophisticated application extension via embedded domain specific languages. We instantiate the concepts of the framework via a full implementation in the Haskell programming language: providing rich mechanisms for dy- namic linking, loading, hot swapping, and runtime type checking in Haskell for the first time. We demonstrate the feasibility of this architecture through a number of novel applications: an extensible text editor; a plugin-based network chat bot; a simulator for polymer chemistry; and xmonad, an ex- tensible window manager. -
System Size Expansion Using Feynman Rules and Diagrams
System size expansion using Feynman rules and diagrams Philipp Thomas∗y, Christian Fleck,z Ramon Grimay, Nikola Popovi´c∗ October 2, 2018 Abstract Few analytical methods exist for quantitative studies of large fluctuations in stochastic systems. In this article, we develop a simple diagrammatic approach to the Chemical Master Equation that allows us to calculate multi-time correlation functions which are accurate to a any desired order in van Kampen's system size expansion. Specifically, we present a set of Feynman rules from which this diagrammatic perturbation expansion can be constructed algo- rithmically. We then apply the methodology to derive in closed form the leading order corrections to the linear noise approximation of the intrinsic noise power spectrum for general biochemical reaction networks. Finally, we illustrate our results by describing noise-induced oscillations in the Brusselator reaction scheme which are not captured by the common linear noise approximation. 1 Introduction The quantification of intrinsic fluctuations in biochemical networks is becoming increasingly important for the study of living systems, as some of the key molecular players are expressed in low numbers of molecules per cell [1]. The most commonly employed method for investigating this type of cell-to-cell variability is the stochastic simulation algorithm (SSA) [2]. While the SSA allows for the exact sampling of trajectories of discrete intracellular biochemistry, it is computationally expensive, which often prevents one from obtaining statistics for large ranges of the biological parameter space. A widely used approach to overcome these limitations has been the linear noise approximation (LNA) [3, 4, 5]. The LNA is obtained to leading order in van Kampen's system size expansion [6]. -
Approximate Probability Distributions of the Master Equation
Approximate probability distributions of the master equation Philipp Thomas∗ School of Mathematics and School of Biological Sciences, University of Edinburgh Ramon Grimay School of Biological Sciences, University of Edinburgh Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems. I. INTRODUCTION first few moments [12{14]; alternative methods are based on moment closure [15]. It is however the case that the Master equations are commonly used to describe fluc- knowledge of a limited number of moments does not al- tuations of particulate systems. In most instances, how- low to uniquely determine the underlying distribution ever, the number of reachable states is so large that their functions. Reconstruction of the probability distribution combinatorial complexity prevents one from obtaining therefore requires additional approximations such as the analytical solutions to these equations. Explicit solutions maximum entropy principle [16] or the truncated moment are known only for certain classes of linear birth-death generating function [17] which generally yield different processes [1], under detailed balance conditions [2], or results. -
Introduction to the Literature on Programming Language Design Gary T
Computer Science Technical Reports Computer Science 7-1999 Introduction to the Literature On Programming Language Design Gary T. Leavens Iowa State University Follow this and additional works at: http://lib.dr.iastate.edu/cs_techreports Part of the Programming Languages and Compilers Commons Recommended Citation Leavens, Gary T., "Introduction to the Literature On Programming Language Design" (1999). Computer Science Technical Reports. 59. http://lib.dr.iastate.edu/cs_techreports/59 This Article is brought to you for free and open access by the Computer Science at Iowa State University Digital Repository. It has been accepted for inclusion in Computer Science Technical Reports by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Introduction to the Literature On Programming Language Design Abstract This is an introduction to the literature on programming language design and related topics. It is intended to cite the most important work, and to provide a place for students to start a literature search. Keywords programming languages, semantics, type systems, polymorphism, type theory, data abstraction, functional programming, object-oriented programming, logic programming, declarative programming, parallel and distributed programming languages Disciplines Programming Languages and Compilers This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/cs_techreports/59 Intro duction to the Literature On Programming Language Design Gary T. Leavens TR 93-01c Jan. 1993, revised Jan. 1994, Feb. 1996, and July 1999 Keywords: programming languages, semantics, typ e systems, p olymorphism, typ e theory, data abstrac- tion, functional programming, ob ject-oriented programming, logic programming, declarative programming, parallel and distributed programming languages. -
How Reliable Is the Linear Noise Approximation Of
Thomas et al. BMC Genomics 2013, 14(Suppl 4):S5 http://www.biomedcentral.com/1471-2164/14/S4/S5 RESEARCH Open Access How reliable is the linear noise approximation of gene regulatory networks? Philipp Thomas1,2, Hannes Matuschek3, Ramon Grima1* From IEEE International Conference on Bioinformatics and Biomedicine 2012 Philadelphia, PA, USA. 4-7 October 2012 Abstract Background: The linear noise approximation (LNA) is commonly used to predict how noise is regulated and exploited at the cellular level. These predictions are exact for reaction networks composed exclusively of first order reactions or for networks involving bimolecular reactions and large numbers of molecules. It is however well known that gene regulation involves bimolecular interactions with molecule numbers as small as a single copy of a particular gene. It is therefore questionable how reliable are the LNA predictions for these systems. Results: We implement in the software package intrinsic Noise Analyzer (iNA), a system size expansion based method which calculates the mean concentrations and the variances of the fluctuations to an order of accuracy higher than the LNA. We then use iNA to explore the parametric dependence of the Fano factors and of the coefficients of variation of the mRNA and protein fluctuations in models of genetic networks involving nonlinear protein degradation, post-transcriptional, post-translational and negative feedback regulation. We find that the LNA can significantly underestimate the amplitude and period of noise-induced oscillations in genetic oscillators. We also identify cases where the LNA predicts that noise levels can be optimized by tuning a bimolecular rate constant whereas our method shows that no such regulation is possible. -
Computation of Biochemical Pathway Fluctuations Beyond the Linear Noise Approximation Using
Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA Philipp Thomas∗†‡ ¶, Hannes Matuschek§¶ and Ramon Grima∗† ∗School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom †SynthSys Edinburgh, University of Edinburgh, Edinburgh, United Kingdom ‡Department of Physics, Humboldt University of Berlin, Berlin, Germany §Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany ¶These authors contributed equally. Abstract—The linear noise approximation is commonly used the first software package enabling a fluctuation analysis of to obtain intrinsic noise statistics for biochemical networks. biochemical networks via the Linear Noise Approximation These estimates are accurate for networks with large numbers (LNA) and Effective Mesoscopic Rate Equation (EMRE) of molecules. However it is well known that many biochemical networks are characterized by at least one species with a approximations of the CME. The former gives the variance small number of molecules. We here describe version 0.3 of and covariance of concentration fluctuations in the limit of the software intrinsic Noise Analyzer (iNA) which allows for large molecule numbers while the latter gives the mean accurate computation of noise statistics over wide ranges of concentrations for intermediate to large molecule numbers molecule numbers. This is achieved by calculating the next and is more accurate than the conventional Rate Equations order corrections to the linear noise approximation’s estimates of variance and covariance of concentration fluctuations. The (REs). efficiency of the methods is significantly improved by auto- In this proceeding we develop and efficiently implement mated just-in-time compilation using the LLVM framework in iNA, the Inverse Omega Square (IOS) method comple- leading to a fluctuation analysis which typically outperforms menting the EMRE method by providing estimates for the that obtained by means of exact stochastic simulations. -
Incremental Type Inference for Software Engineering
Incremental Type Inference for Software Engineering Jonathan Aldrich University of Washington [email protected] Abstract The desire to use high-level language constructs while Software engineering focused type inference can enhance preserving a static type-safe guarantee drives programmer productivity in statically typed object- programmers to ask for ever-more powerful type systems. oriented languages. Type inference is a system of However, specifying a type that may be almost as long automatically inferring the argument and return types of and complicated as the function it describes can be a function. It provides considerable programming impractical. convenience, because the programmer can realize the benefits of a statically typed language without manually 1.2. Type Inference in ML entering the type annotations. We study the problem of type inference in object-oriented languages and propose In ML, it is possible for the compiler to analyze the an incremental, programmer-aided approach. Code is body of a function and infer the type of that function. For added one method at a time and missing types are example, a function that squares each of its arguments and inferred if possible. We present a specification and returns the sum of the squares clearly takes several algorithm for inferring simple object-oriented types in arguments of type int and yields an int in return (see this kind of incremental development environment. figure 1). - fun sumsqrs (x, y) = x*x + y*y; 1. Introduction val sumsqrs = fn : int * int -> int Type inference was popularized by the ML language [Milner et al., 1990]. ML is made up of functions and Figure 1. -
Luca Cardelli • Curriculum Vitae • 2014
Luca Cardelli • Curriculum Vitae • 2014 Short Bio Luca Cardelli was born near Montecatini Terme, Italy, studied at the University of Pisa (until 1978-07- 12), and has a Ph.D. in computer science from the University of Edinburgh(1982-04-01). He worked at Bell Labs, Murray Hill, from 1982-04-05 to 1985-09-20, and at Digital Equipment Corporation, Systems Research Center in Palo Alto, from 1985-09-30 to 1997-10-31, before assuming a position on 1997-11-03 at Microsoft Research, in Cambridge UK, where he was head of the Programming Principles and Tools andSecurity groups until 2012, and is currently a Principal Researcher. His main interests are in type theory and operational semantics (for applications to language design, semantics, and implementation), and in concurrency theory (for applications to computer networks and to modeling biological systems). He implemented the first compiler for ML (one of the most popular typed functional language, whose recent incarnations are Caml and F#) and one of the earliest direct-manipulation user-interface editors. He was a member of the Modula-3 design committee, and has designed a few experimental languages, including Obliq: a distributed higher- order scripting language (voted most influential POPL'95 paper 10 years later), and Polyphonic C#, a distributed extension of C#. His more protracted research activity has been in establishing the semantic and type-theoretic foundations of object-oriented languages, resulting in the 1996 book "A Theory of Objects" with Martin Abadi. More recently he has focused on modeling global and mobile computation, via the Ambient Calculus andSpatial Logics, which indirectly led to a current interest in Systems Biology , Molecular Programming, and Stochastic Systems. -
Stochastic Analysis of Biochemical Systems
ON MOMENTS AND TIMING { STOCHASTIC ANALYSIS OF BIOCHEMICAL SYSTEMS by Khem Raj Ghusinga A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering Summer 2018 c 2018 Khem Raj Ghusinga All Rights Reserved ON MOMENTS AND TIMING { STOCHASTIC ANALYSIS OF BIOCHEMICAL SYSTEMS by Khem Raj Ghusinga Approved: Kenneth E. Barner, Ph.D. Chair of the Department of Electrical and Computer Engineering Approved: Babatunde Ogunnaike, Ph.D. Dean of the College of Engineering Approved: Ann L. Ardis, Ph.D. Senior Vice Provost for Graduate and Professional Education I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Abhyudai Singh, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Ryan Zurakowski, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Gonzalo R. Arce, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. -
Nonequilibrium Critical Phenomena: Exact Langevin Equations, Erosion of Tilted Landscapes
Nonequilibrium critical phenomena : exact Langevin equations, erosion of tilted landscapes. Charlie Duclut To cite this version: Charlie Duclut. Nonequilibrium critical phenomena : exact Langevin equations, erosion of tilted landscapes.. Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2017. English. NNT : 2017PA066241. tel-01690438 HAL Id: tel-01690438 https://tel.archives-ouvertes.fr/tel-01690438 Submitted on 23 Jan 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITÉ PIERRE ET MARIE CURIE ÉCOLE DOCTORALE PHYSIQUE EN ÎLE-DE-FRANCE THÈSE pour obtenir le titre de Docteur de l’Université Pierre et Marie Curie Mention : PHYSIQUE THÉORIQUE Présentée et soutenue par Charlie DUCLUT Nonequilibrium critical phenomena: exact Langevin equations, erosion of tilted landscapes. Thèse dirigée par Bertrand DELAMOTTE préparée au Laboratoire de Physique Théorique de la Matière Condensée soutenue le 11 septembre 2017 devant le jury composé de : M. Andrea GAMBASSI Rapporteur M. Michael SCHERER Rapporteur M. Giulio BIROLI Examinateur Mme Leticia CUGLIANDOLO Présidente du jury M. Andrei FEDORENKO Examinateur M. Bertrand DELAMOTTE Directeur de thèse Remerciements First of all, I would like to thank the referees Andrea Gambassi and Michael Scherer for taking the time to carefully read the manuscript.