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Stochastic Simulation of Neurons, Axons, and Action Potentials

A. Aldo Faisal

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0011
Subject:
Mathematics, Biostatistics

Variability is inherent in neurons. To account for variability we have to make use of stochastic models. We will take a look at this biologically more rigorous approach by studying the fundamental ... More


Stochastic-Simulation Tests of Nonlinear Econometric Models

Roberto S. Mariano and Bryan W. Brown

in Comparative Performance of U.S. Econometric Models

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195057720
eISBN:
9780199854967
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195057720.003.0009
Subject:
Economics and Finance, Econometrics

Stochastic simulations of nonlinear dynamic econometric models have been used in various ways in the past. This chapter discusses how stochastic simulations can be exploited to develop appropriate ... More


Master equations and simulation algorithms for the discrete‐stochastic approach

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0006
Subject:
Physics, Soft Matter / Biological Physics

The discrete-stochastic model of diffusion introduced in the preceding chapter implies that the system state evolves in time as what is known as a jump Markov process. The time evolution of such a ... More


Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Daniel Thomas Gillespie and Effrosyni Seitaridou

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.001.0001
Subject:
Physics, Soft Matter / Biological Physics

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian ... More


Numerical Simulation for Biochemical Kinetics

Daniel T. Gillespie and Linda R. Petzold

in System Modeling in Cellular Biology: From Concepts to Nuts and Bolts

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262195485
eISBN:
9780262257060
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262195485.003.0016
Subject:
Mathematics, Mathematical Biology

This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as ... More


Mathematical and computational modelling tools

Baltazar D. Aguda and Avner Friedman

in Models of Cellular Regulation

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198570912
eISBN:
9780191718717
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570912.003.0003
Subject:
Physics, Soft Matter / Biological Physics

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ... More


Notional Defined Contribution Pension Systems in a Stochastic Context: Design and Stability

Ronald Lee

Alan J. Auerbach (ed.)

in Social Security Policy in a Changing Environment

Published in print:
2009
Published Online:
February 2013
ISBN:
9780226076485
eISBN:
9780226076508
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226076508.003.0003
Subject:
Economics and Finance, Public and Welfare

This chapter explores a new approach to Social Security reform that is known as “Notional Defined Contribution” or “Nonfinancial Defined Contribution” (NDC). This chapter uses a stochastic ... More


Computing Chemical Reactions

Wolfgang Banzhaf and Lidia Yamamoto

in Artificial Chemistries

Published in print:
2015
Published Online:
September 2016
ISBN:
9780262029438
eISBN:
9780262329460
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262029438.003.0004
Subject:
Public Health and Epidemiology, Public Health

This chapter examines various reactor algorithms that are frequently used in artificial chemistries. We contrast macroscopic, deterministic reaction algorithms and microscopic, stochastic reaction ... More


Implications and limitations of the Einstein theory of diffusion

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0004
Subject:
Physics, Soft Matter / Biological Physics

Chapter 3 showed how Einstein's analysis of Brownian motion shifted the focus of the classical diffusion equation from the average behavior of many solute molecules to the probabilistic behavior of ... More


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