Michael J. North and Charles M. Macal
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195172119
- eISBN:
- 9780199789894
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172119.003.0002
- Subject:
- Business and Management, Strategy
This chapter discusses foundational issues in modeling, such as the differences between deterministic and stochastic models as well as the strategic, tactical, and operational model guidance ...
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This chapter discusses foundational issues in modeling, such as the differences between deterministic and stochastic models as well as the strategic, tactical, and operational model guidance horizons. It also explains how agent-based modeling and simulation fits into this context.Less
This chapter discusses foundational issues in modeling, such as the differences between deterministic and stochastic models as well as the strategic, tactical, and operational model guidance horizons. It also explains how agent-based modeling and simulation fits into this context.
N. Thompson Hobbs and Mevin B. Hooten
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0002
- Subject:
- Biology, Ecology
This chapter talks about deterministic models as expressions of ecological hypotheses. These models are based on a deterministic equation or equations making predictions that can be compared with ...
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This chapter talks about deterministic models as expressions of ecological hypotheses. These models are based on a deterministic equation or equations making predictions that can be compared with observations. The nature of the model ensures that there is no uncertainty in such predictions. Hence, the chapter first discusses the different ways that deterministic models have been used in ecology; identifying three main ones: theoretical, empirical, and simulation. It then outlines a few deterministic models widely used in ecology. Rather than attempting a comprehensive treatment of the subject, the chapter instead introduces a set of core functions that are widely used to represent ecological process across all subdisciplines.Less
This chapter talks about deterministic models as expressions of ecological hypotheses. These models are based on a deterministic equation or equations making predictions that can be compared with observations. The nature of the model ensures that there is no uncertainty in such predictions. Hence, the chapter first discusses the different ways that deterministic models have been used in ecology; identifying three main ones: theoretical, empirical, and simulation. It then outlines a few deterministic models widely used in ecology. Rather than attempting a comprehensive treatment of the subject, the chapter instead introduces a set of core functions that are widely used to represent ecological process across all subdisciplines.
Domitilla Del Vecchio and Richard M. Murray
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161532
- eISBN:
- 9781400850501
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161532.003.0002
- Subject:
- Biology, Biochemistry / Molecular Biology
This chapter describes basic biological mechanisms in a way that can be represented by simple dynamical models. It begins with a discussion of the basic modeling formalisms that will be utilized to ...
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This chapter describes basic biological mechanisms in a way that can be represented by simple dynamical models. It begins with a discussion of the basic modeling formalisms that will be utilized to model biomolecular feedback systems. The focus in this chapter (as well as the next) is on deterministic models using ordinary differential equations. Here, the chapter proceeds to study a number of core processes within the cell, providing different model-based descriptions of the dynamics that will be used in later chapters to analyze and design biomolecular systems. In this chapter, emphasis is placed on dynamics with time scales measured in seconds to hours and mean behavior averaged across a large number of molecules.Less
This chapter describes basic biological mechanisms in a way that can be represented by simple dynamical models. It begins with a discussion of the basic modeling formalisms that will be utilized to model biomolecular feedback systems. The focus in this chapter (as well as the next) is on deterministic models using ordinary differential equations. Here, the chapter proceeds to study a number of core processes within the cell, providing different model-based descriptions of the dynamics that will be used in later chapters to analyze and design biomolecular systems. In this chapter, emphasis is placed on dynamics with time scales measured in seconds to hours and mean behavior averaged across a large number of molecules.
Russell Lande, Steinar Engen, and Bernt-Erik Saether
- Published in print:
- 2003
- Published Online:
- April 2010
- ISBN:
- 9780198525257
- eISBN:
- 9780191584930
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525257.001.0001
- Subject:
- Biology, Ecology
All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book ...
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All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book provides an introduction to stochastic population dynamics, combining classical background material with a variety of modern approaches, including previously unpublished results by the authors, illustrated with examples from bird and mammal populations, and insect communities. Demographic and environmental stochasticity are introduced with statistical methods for estimating them from field data. The long-run growth rate of a population is explained and extended to include age structure with both demographic and environmental stochasticity. Diffusion approximations facilitate the analysis of extinction dynamics and the duration of the final decline. Methods are developed for estimating delayed density dependence from population time series using life history data. Metapopulation viability and the spatial scale of population fluctuations and extinction risk are analyzed. Stochastic dynamics and statistical uncertainty in population parameters are incorporated in Population Viability Analysis and strategies for sustainable harvesting. Statistics of species diversity measures and species abundance distributions are described, with implications for rapid assessments of biodiversity, and methods are developed for partitioning species diversity into additive components. Analysis of the stochastic dynamics of a tropical butterfly community in space and time indicates that most of the variance in the species abundance distribution is due to ecological heterogeneity among species, so that real communities are far from neutral.Less
All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book provides an introduction to stochastic population dynamics, combining classical background material with a variety of modern approaches, including previously unpublished results by the authors, illustrated with examples from bird and mammal populations, and insect communities. Demographic and environmental stochasticity are introduced with statistical methods for estimating them from field data. The long-run growth rate of a population is explained and extended to include age structure with both demographic and environmental stochasticity. Diffusion approximations facilitate the analysis of extinction dynamics and the duration of the final decline. Methods are developed for estimating delayed density dependence from population time series using life history data. Metapopulation viability and the spatial scale of population fluctuations and extinction risk are analyzed. Stochastic dynamics and statistical uncertainty in population parameters are incorporated in Population Viability Analysis and strategies for sustainable harvesting. Statistics of species diversity measures and species abundance distributions are described, with implications for rapid assessments of biodiversity, and methods are developed for partitioning species diversity into additive components. Analysis of the stochastic dynamics of a tropical butterfly community in space and time indicates that most of the variance in the species abundance distribution is due to ecological heterogeneity among species, so that real communities are far from neutral.
Søren Johansen
- Published in print:
- 1995
- Published Online:
- November 2003
- ISBN:
- 9780198774501
- eISBN:
- 9780191596476
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774508.003.0006
- Subject:
- Economics and Finance, Econometrics
Contains the likelihood analysis of the I(1) models. The main result is the derivation of the method of reduced rank regression because of Anderson. This solves the estimation problem for the ...
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Contains the likelihood analysis of the I(1) models. The main result is the derivation of the method of reduced rank regression because of Anderson. This solves the estimation problem for the unrestricted cointegration vectors, and hence the problem of deriving a test for cointegrating rank, the so‐called trace test. The reduced rank algorithm is applied to a number of different models defined by restrictions on the deterministic terms.Less
Contains the likelihood analysis of the I(1) models. The main result is the derivation of the method of reduced rank regression because of Anderson. This solves the estimation problem for the unrestricted cointegration vectors, and hence the problem of deriving a test for cointegrating rank, the so‐called trace test. The reduced rank algorithm is applied to a number of different models defined by restrictions on the deterministic terms.
Ellen R. McGrattan
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.003.0006
- Subject:
- Economics and Finance, Macro- and Monetary Economics
Many problems in economics require the solution to a functional equation as an intermediate step, and typically, decision functions are sought that satisfy a set of Euler conditions or a value ...
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Many problems in economics require the solution to a functional equation as an intermediate step, and typically, decision functions are sought that satisfy a set of Euler conditions or a value function that satisfies Bellman's equation. However, in many cases, analytical solutions cannot be derived for these functions, and numerical methods are needed instead. Shows how to apply weighted residual and finite‐element methods to this type of problem by illustrating their application to various examples. The first type of problem involves a simple differential equation because the coefficients to be computed satisfy a linear system of equations, and no computer is needed for the solution. Weighted residual and finite‐element methods are then applied to a deterministic growth model and a stochastic growth model—two standard models used in economics; in these examples, the coefficients to be computed satisfy nonlinear systems of equations, which, fortunately, are exploitably sparse if they are derived from a finite‐element method.Less
Many problems in economics require the solution to a functional equation as an intermediate step, and typically, decision functions are sought that satisfy a set of Euler conditions or a value function that satisfies Bellman's equation. However, in many cases, analytical solutions cannot be derived for these functions, and numerical methods are needed instead. Shows how to apply weighted residual and finite‐element methods to this type of problem by illustrating their application to various examples. The first type of problem involves a simple differential equation because the coefficients to be computed satisfy a linear system of equations, and no computer is needed for the solution. Weighted residual and finite‐element methods are then applied to a deterministic growth model and a stochastic growth model—two standard models used in economics; in these examples, the coefficients to be computed satisfy nonlinear systems of equations, which, fortunately, are exploitably sparse if they are derived from a finite‐element method.
Domitilla Del Vecchio and Richard M. Murray
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161532
- eISBN:
- 9781400850501
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161532.003.0003
- Subject:
- Biology, Biochemistry / Molecular Biology
This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the ...
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This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the dynamics of a system using the input/output modeling formalism described in Chapter 1 and then studies the “robustness” of the system of a given function of the circuit. The chapter then discusses some of the underlying ideas for how to model biological oscillatory behavior, focusing on those types of oscillations that are most common in biomolecular systems. Hereafter, the chapter explores how the location of equilibrium points, their stability, their regions of attraction, and other dynamic phenomena vary based on the values of the parameters in a model. Finally, methods for reducing the complexity of the models that are introduced in this chapter are reviewed.Less
This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the dynamics of a system using the input/output modeling formalism described in Chapter 1 and then studies the “robustness” of the system of a given function of the circuit. The chapter then discusses some of the underlying ideas for how to model biological oscillatory behavior, focusing on those types of oscillations that are most common in biomolecular systems. Hereafter, the chapter explores how the location of equilibrium points, their stability, their regions of attraction, and other dynamic phenomena vary based on the values of the parameters in a model. Finally, methods for reducing the complexity of the models that are introduced in this chapter are reviewed.
Otso Ovaskainen, Henrik Johan de Knegt, and Maria del Mar Delgado
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780198714866
- eISBN:
- 9780191783210
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198714866.003.0003
- Subject:
- Biology, Ecology, Biomathematics / Statistics and Data Analysis / Complexity Studies
This chapter introduces mathematical and statistical modelling approaches in population ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends ...
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This chapter introduces mathematical and statistical modelling approaches in population ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to population ecology. The mathematical sections start by constructing an individual-based model in homogeneous space, and then simplifies the model to derive the classical model of logistic population growth. The models are then expanded to heterogeneous space in two contrasting ways, resulting in models called the plant population model and the butterfly metapopulation model. Both types of models are used to analyse the consequences of habitat loss and fragmentation at the population level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of time-series data, species distribution modelling, and metapopulation modelling.Less
This chapter introduces mathematical and statistical modelling approaches in population ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to population ecology. The mathematical sections start by constructing an individual-based model in homogeneous space, and then simplifies the model to derive the classical model of logistic population growth. The models are then expanded to heterogeneous space in two contrasting ways, resulting in models called the plant population model and the butterfly metapopulation model. Both types of models are used to analyse the consequences of habitat loss and fragmentation at the population level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of time-series data, species distribution modelling, and metapopulation modelling.
John C. Moore and Peter C. De Ruiter
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780198566182
- eISBN:
- 9780191774683
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566182.003.0002
- Subject:
- Biology, Ecology
This chapter tackles four distinct objectives. The first is that it presents the general approach to developing the models of simple and complex systems which are to be used throughout the book in ...
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This chapter tackles four distinct objectives. The first is that it presents the general approach to developing the models of simple and complex systems which are to be used throughout the book in discussing energetic food webs. These models are deterministic models in nature, but are also applicable to the study of the uncertainty of random fluctuations in the environment. The second objective is to determine whether the special configurations of model systems, as well as other dynamic properties of the models, are all inherently stable. The third objective of the chapter is to develop and assess the dynamics and stability of two models: models based on primary producers, and models based on detritus. Finally, the fourth objective is to compare the structure and dynamics of these two models, and how each contributes to further knowledge of energetic food webs.Less
This chapter tackles four distinct objectives. The first is that it presents the general approach to developing the models of simple and complex systems which are to be used throughout the book in discussing energetic food webs. These models are deterministic models in nature, but are also applicable to the study of the uncertainty of random fluctuations in the environment. The second objective is to determine whether the special configurations of model systems, as well as other dynamic properties of the models, are all inherently stable. The third objective of the chapter is to develop and assess the dynamics and stability of two models: models based on primary producers, and models based on detritus. Finally, the fourth objective is to compare the structure and dynamics of these two models, and how each contributes to further knowledge of energetic food webs.
David DeGrazia and Lester H. Hunt
- Published in print:
- 2016
- Published Online:
- October 2016
- ISBN:
- 9780190251253
- eISBN:
- 9780190629465
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190251253.003.0007
- Subject:
- Philosophy, Moral Philosophy
The empirical literature on gun ownership and gun violence is influenced by philosophical considerations. In this way, “philosophy” is logically prior to empirical evidence. More important, the ...
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The empirical literature on gun ownership and gun violence is influenced by philosophical considerations. In this way, “philosophy” is logically prior to empirical evidence. More important, the chapter argues, it affects the way in which one applies, or fails to apply, the results of empirical research to one’s own conduct. Instead, there are ethical reasons for not viewing normal human adults in this way.Less
The empirical literature on gun ownership and gun violence is influenced by philosophical considerations. In this way, “philosophy” is logically prior to empirical evidence. More important, the chapter argues, it affects the way in which one applies, or fails to apply, the results of empirical research to one’s own conduct. Instead, there are ethical reasons for not viewing normal human adults in this way.
Henry Jenkins and Adolfo Plasencia
- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780262036016
- eISBN:
- 9780262339308
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262036016.003.0012
- Subject:
- Society and Culture, Technology and Society
Henry Jenkins, former professor of humanities, MIT, is one of the leading science authorities in the analysis of New Media. Today, he is Professor of Communication, Journalism, and Cinematic Arts at ...
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Henry Jenkins, former professor of humanities, MIT, is one of the leading science authorities in the analysis of New Media. Today, he is Professor of Communication, Journalism, and Cinematic Arts at USC. In this dialogue, Jenkins explains how technology is transforming the traditional view of humanities. He outlines his vision of convergence culture in his book, Convergence Culture: Where Old and New Media Collide. He explains why he thinks the idea of copyright is an aberration. He goes on to relate the causes for conglomerates losing control of media flows and how to deal with this situation. He describes the new logic framework under which our current participatory culture is run. He defines himself in this dialogue as a critical utopian trying to demonstrate how to harness the great power that changes taking place in new media have on people. Emphasizing the ‘new social skills’, which bring about new forms of ethics, interactions, politics, types of economic activities and legal culture, in the clash between the new digital media and the old mass media.Less
Henry Jenkins, former professor of humanities, MIT, is one of the leading science authorities in the analysis of New Media. Today, he is Professor of Communication, Journalism, and Cinematic Arts at USC. In this dialogue, Jenkins explains how technology is transforming the traditional view of humanities. He outlines his vision of convergence culture in his book, Convergence Culture: Where Old and New Media Collide. He explains why he thinks the idea of copyright is an aberration. He goes on to relate the causes for conglomerates losing control of media flows and how to deal with this situation. He describes the new logic framework under which our current participatory culture is run. He defines himself in this dialogue as a critical utopian trying to demonstrate how to harness the great power that changes taking place in new media have on people. Emphasizing the ‘new social skills’, which bring about new forms of ethics, interactions, politics, types of economic activities and legal culture, in the clash between the new digital media and the old mass media.
