E. J. Milner-Gulland and Marcus Rowcliffe
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198530367
- eISBN:
- 9780191713095
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530367.003.0005
- Subject:
- Biology, Biodiversity / Conservation Biology
The effective management of natural resources use requires a mechanistic understanding of the system, not just correlations between variables of the kind discussed in Chapter 4. Understanding may ...
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The effective management of natural resources use requires a mechanistic understanding of the system, not just correlations between variables of the kind discussed in Chapter 4. Understanding may simply be in the form of a conceptual model, but is much more powerful when formalized as a mathematical model. This chapter introduces methods for building a model of the system that can be used to predict future sustainability with or without management interventions. The emphasis is on the simulation of biological and bioeconomic dynamics, for which step-by-step worked examples are given. These examples start with conceptual models, then show how to formalize these as mathematical equations, build these into computer code; test model sensitivity, validity, and alternative structures; and finally, explore future scenarios. Methods for modelling stochasticity and human behaviour are also introduced, as well as the use of Bayesian methods for understanding dynamic systems and exploring management interventions.Less
The effective management of natural resources use requires a mechanistic understanding of the system, not just correlations between variables of the kind discussed in Chapter 4. Understanding may simply be in the form of a conceptual model, but is much more powerful when formalized as a mathematical model. This chapter introduces methods for building a model of the system that can be used to predict future sustainability with or without management interventions. The emphasis is on the simulation of biological and bioeconomic dynamics, for which step-by-step worked examples are given. These examples start with conceptual models, then show how to formalize these as mathematical equations, build these into computer code; test model sensitivity, validity, and alternative structures; and finally, explore future scenarios. Methods for modelling stochasticity and human behaviour are also introduced, as well as the use of Bayesian methods for understanding dynamic systems and exploring management interventions.
Franck Courchamp, Luděk Berec, and Joanna Gascoigne
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780198570301
- eISBN:
- 9780191717642
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570301.003.0003
- Subject:
- Biology, Biodiversity / Conservation Biology
Much of what is known about Allee effects comes from mathematical models. This chapter deals with models of demographic Allee effects. It shows what types of model are available, what their ...
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Much of what is known about Allee effects comes from mathematical models. This chapter deals with models of demographic Allee effects. It shows what types of model are available, what their underlying assumptions are, how they can be used, and how they have contributed to our understanding of the dynamical consequences of Allee effects, both in single-species populations and multiple-species communities. The chapter does not provide detailed information on how to develop and analyse any single model, nor discusses the structure and predictions of every model that has ever been used to study Allee effects. Rather, it is conceived as a sort of summary of a large amount of literature that has been published on models which address Allee effects: providing a comprehensive (if a little dense) overview of the topic.Less
Much of what is known about Allee effects comes from mathematical models. This chapter deals with models of demographic Allee effects. It shows what types of model are available, what their underlying assumptions are, how they can be used, and how they have contributed to our understanding of the dynamical consequences of Allee effects, both in single-species populations and multiple-species communities. The chapter does not provide detailed information on how to develop and analyse any single model, nor discusses the structure and predictions of every model that has ever been used to study Allee effects. Rather, it is conceived as a sort of summary of a large amount of literature that has been published on models which address Allee effects: providing a comprehensive (if a little dense) overview of the topic.
Lev Ginzburg and Mark Colyvan
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780195168167
- eISBN:
- 9780199790159
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195168167.001.0001
- Subject:
- Biology, Ecology
The main focus of the book is the presentation of the inertial view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the ...
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The main focus of the book is the presentation of the inertial view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of the account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment experienced by the previous generation.Less
The main focus of the book is the presentation of the inertial view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of the account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment experienced by the previous generation.
Ramon Marimon and Andrew Scott (eds)
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.001.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics
Macroeconomics increasingly uses stochastic dynamic general equilibrium models to understand theoretical and policy issues. Unless very strong assumptions are made, understanding the properties of ...
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Macroeconomics increasingly uses stochastic dynamic general equilibrium models to understand theoretical and policy issues. Unless very strong assumptions are made, understanding the properties of particular models requires solving the model using a computer. This volume brings together leading contributors in the field who explain in detail how to implement the computational techniques needed to solve dynamic economics models. It is based on lectures presented at the 7th Summer School of the European Economic Association on computational methods for the study of dynamic economies, held in 1996. A broad spread of techniques is covered, and their application to a wide range of subjects discussed. The book provides the basics of a tool kit that researchers and graduate students can use to solve and analyse their own theoretical models. It is oriented towards economists who already have the equivalent of a first year of graduate studies or to any advanced undergraduates or researchers with a solid mathematical background. No competence with writing computer codes is assumed. After an introduction by the editors, it is arranged in three parts: I Almost linear methods; II Nonlinear methods; and III Solving some dynamic economies.Less
Macroeconomics increasingly uses stochastic dynamic general equilibrium models to understand theoretical and policy issues. Unless very strong assumptions are made, understanding the properties of particular models requires solving the model using a computer. This volume brings together leading contributors in the field who explain in detail how to implement the computational techniques needed to solve dynamic economics models. It is based on lectures presented at the 7th Summer School of the European Economic Association on computational methods for the study of dynamic economies, held in 1996. A broad spread of techniques is covered, and their application to a wide range of subjects discussed. The book provides the basics of a tool kit that researchers and graduate students can use to solve and analyse their own theoretical models. It is oriented towards economists who already have the equivalent of a first year of graduate studies or to any advanced undergraduates or researchers with a solid mathematical background. No competence with writing computer codes is assumed. After an introduction by the editors, it is arranged in three parts: I Almost linear methods; II Nonlinear methods; and III Solving some dynamic economies.
Richard B. Codell and James O. Duguid
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780195127270
- eISBN:
- 9780199869121
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195127270.003.0005
- Subject:
- Biology, Ecology, Biochemistry / Molecular Biology
Humans can be exposed to radioactive materials released to the ground by processes such as mining and milling of uranium, disposal of radioactive waste in repositories and landfills, or through ...
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Humans can be exposed to radioactive materials released to the ground by processes such as mining and milling of uranium, disposal of radioactive waste in repositories and landfills, or through accidents. This chapter covers practical problems of release of radioactive materials from sources, current practices for the characterization of groundwater transport pathways through the unsaturated and saturated zones, and the ultimate consumption of transported radionuclides by humans. It discusses the underlying principles of groundwater flow, the transport of radioactive materials dissolved or suspended in water, and the interaction and retardation of radionuclides with soil and rock along transport pathways. Finally, the chapter discusses the formulation of mathematical models for these processes and presents simplified analytical techniques for preliminary calculations of groundwater flow, contaminant transport, and doses.Less
Humans can be exposed to radioactive materials released to the ground by processes such as mining and milling of uranium, disposal of radioactive waste in repositories and landfills, or through accidents. This chapter covers practical problems of release of radioactive materials from sources, current practices for the characterization of groundwater transport pathways through the unsaturated and saturated zones, and the ultimate consumption of transported radionuclides by humans. It discusses the underlying principles of groundwater flow, the transport of radioactive materials dissolved or suspended in water, and the interaction and retardation of radionuclides with soil and rock along transport pathways. Finally, the chapter discusses the formulation of mathematical models for these processes and presents simplified analytical techniques for preliminary calculations of groundwater flow, contaminant transport, and doses.
Alex Simpson
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.003.0003
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter advocates a pragmatic approach to constructive set theory, using axioms based solely on set-theoretic principles that are directly relevant to (constructive) mathematical practice. The ...
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This chapter advocates a pragmatic approach to constructive set theory, using axioms based solely on set-theoretic principles that are directly relevant to (constructive) mathematical practice. The aim is to leave the notion of set as unconstrained as possible, while remaining consistent with the ways in which sets are actually used in mathematical practice. Following this approach, the chapter presents theories ranging in power from weaker predicative theories to stronger impredicative ones. The theories considered all have sound and complete classes of category-theoretic models, obtained by axiomatizing the structure of an ambient category of classes together with its subcategory of sets. In certain special cases, the categories of sets have independent characterizations in familiar category-theoretic terms, and one thereby obtains a rich source of naturally occurring mathematical models for (both predicative and impredicative) constructive set theories.Less
This chapter advocates a pragmatic approach to constructive set theory, using axioms based solely on set-theoretic principles that are directly relevant to (constructive) mathematical practice. The aim is to leave the notion of set as unconstrained as possible, while remaining consistent with the ways in which sets are actually used in mathematical practice. Following this approach, the chapter presents theories ranging in power from weaker predicative theories to stronger impredicative ones. The theories considered all have sound and complete classes of category-theoretic models, obtained by axiomatizing the structure of an ambient category of classes together with its subcategory of sets. In certain special cases, the categories of sets have independent characterizations in familiar category-theoretic terms, and one thereby obtains a rich source of naturally occurring mathematical models for (both predicative and impredicative) constructive set theories.
David Herman
Apostolos Doxiadis and Barry Mazur (eds)
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0013
- Subject:
- Mathematics, History of Mathematics
This chapter considers formal models of narrative and the nature of the theory of narrative. After discussing the diachronic and synchronic approaches to investigating the role of formal models in ...
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This chapter considers formal models of narrative and the nature of the theory of narrative. After discussing the diachronic and synchronic approaches to investigating the role of formal models in narrative analysis, the chapter looks at those ideas about models and modeling as a kind of bridge between humanistic and technoscientific discourse. It then evaluates descriptive and functional classifications of models, along with a range of perspectives on mathematical models and modeling. It also presents a case study in metanarratology, with a particular focus on modeling practices that have been brought to bear on focalization. It also analyzes some instances of the confluence of the formal study of narrative and mathematics, including the use of permutation groups, as well as the synergy between mathematically based theories of structural linguistics and early work on story grammars.Less
This chapter considers formal models of narrative and the nature of the theory of narrative. After discussing the diachronic and synchronic approaches to investigating the role of formal models in narrative analysis, the chapter looks at those ideas about models and modeling as a kind of bridge between humanistic and technoscientific discourse. It then evaluates descriptive and functional classifications of models, along with a range of perspectives on mathematical models and modeling. It also presents a case study in metanarratology, with a particular focus on modeling practices that have been brought to bear on focalization. It also analyzes some instances of the confluence of the formal study of narrative and mathematics, including the use of permutation groups, as well as the synergy between mathematically based theories of structural linguistics and early work on story grammars.
Oliver Penrose
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199231256
- eISBN:
- 9780191710803
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199231256.003.0015
- Subject:
- Mathematics, History of Mathematics
Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own ...
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Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own contributions. Topics covered include Kelvin and thermoelectricity, gas modeled as a collection of molecules, the reversibility paradox, mathematical probability models, and Boltzmann's equations.Less
Kelvin played a big part in the development of statistical mechanics, both for equilibrium and non-equilibrium. This chapter reviews these developments, taking a particular interest in Kelvin's own contributions. Topics covered include Kelvin and thermoelectricity, gas modeled as a collection of molecules, the reversibility paradox, mathematical probability models, and Boltzmann's equations.
Joshua M. Epstein
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691158884
- eISBN:
- 9781400848256
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691158884.003.0002
- Subject:
- Mathematics, Applied Mathematics
This part of the book describes explicit mathematical models for the affective, cognitive, and social components of Agent_Zero. It first considers some underlying neuroscience of fear and the role of ...
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This part of the book describes explicit mathematical models for the affective, cognitive, and social components of Agent_Zero. It first considers some underlying neuroscience of fear and the role of the amygdala before turning to Rescorla–Wagner equations of conditioning. In particular, it explains how the fear circuit can be activated and how fear conditioning can occur unconsciously. It then reviews some standard nomenclature adopted by Ivan Pavlov in his study, Conditioned Reflexes: An Investigation of the Physiological Activity of the Cerebral Cortex, with emphasis on David Hume's “association of ideas,” the theory of conditioning, and the Rescorla–Wagner model. After examining “the passions,” the discussion focuses on reason, Agent_Zero's cognitive component, and the model's social component. The central case is that the agent initiates the group's behavior despite starting with the lowest disposition, with no initial emotional inclination, no evidence, the same threshold as all others, and no orders from above.Less
This part of the book describes explicit mathematical models for the affective, cognitive, and social components of Agent_Zero. It first considers some underlying neuroscience of fear and the role of the amygdala before turning to Rescorla–Wagner equations of conditioning. In particular, it explains how the fear circuit can be activated and how fear conditioning can occur unconsciously. It then reviews some standard nomenclature adopted by Ivan Pavlov in his study, Conditioned Reflexes: An Investigation of the Physiological Activity of the Cerebral Cortex, with emphasis on David Hume's “association of ideas,” the theory of conditioning, and the Rescorla–Wagner model. After examining “the passions,” the discussion focuses on reason, Agent_Zero's cognitive component, and the model's social component. The central case is that the agent initiates the group's behavior despite starting with the lowest disposition, with no initial emotional inclination, no evidence, the same threshold as all others, and no orders from above.
C. J. Brainerd and V. F. Reyna
- Published in print:
- 2005
- Published Online:
- January 2008
- ISBN:
- 9780195154054
- eISBN:
- 9780199868384
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195154054.003.0009
- Subject:
- Psychology, Cognitive Psychology
This chapter considers what the near future of the science of false memory may hold by exploring some emerging areas of experimentation. It focuses on three specific areas: mathematical models of ...
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This chapter considers what the near future of the science of false memory may hold by exploring some emerging areas of experimentation. It focuses on three specific areas: mathematical models of false memory, aging effects, and cognitive neuroscience.Less
This chapter considers what the near future of the science of false memory may hold by exploring some emerging areas of experimentation. It focuses on three specific areas: mathematical models of false memory, aging effects, and cognitive neuroscience.
Uri Margolin
Apostolos Doxiadis and Barry Mazur (eds)
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0014
- Subject:
- Mathematics, History of Mathematics
This chapter examines the manifold relations between narrative and mathematics from the point of view of narratology. In particular, it considers some of the ways in which we can speak of mathematics ...
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This chapter examines the manifold relations between narrative and mathematics from the point of view of narratology. In particular, it considers some of the ways in which we can speak of mathematics in literature; for example, the portrayal in a literary narrative of the destiny of an actual or fictional mathematician as a function of his intellectual endeavors; or the use of mathematical notions (infinity, infinite regression, branching time) as the key thematic element or basic initial situation of a narrative. The chapter also discusses the structural similarities and differences between how mathematical texts and narratives treat the creation of imaginary worlds, as well as the criteria of truth, levels and hierarchies of representation involved in this process. Finally, it explores the logical requirements for computer simulations of future scenarios, along with the mathematical concepts, models, and methods used in theories of narrative.Less
This chapter examines the manifold relations between narrative and mathematics from the point of view of narratology. In particular, it considers some of the ways in which we can speak of mathematics in literature; for example, the portrayal in a literary narrative of the destiny of an actual or fictional mathematician as a function of his intellectual endeavors; or the use of mathematical notions (infinity, infinite regression, branching time) as the key thematic element or basic initial situation of a narrative. The chapter also discusses the structural similarities and differences between how mathematical texts and narratives treat the creation of imaginary worlds, as well as the criteria of truth, levels and hierarchies of representation involved in this process. Finally, it explores the logical requirements for computer simulations of future scenarios, along with the mathematical concepts, models, and methods used in theories of narrative.
Bas C. van Fraassen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199278220
- eISBN:
- 9780191707926
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199278220.003.0003
- Subject:
- Philosophy, Philosophy of Mind, Philosophy of Science
Resemblance comes in, not when we are answering the question — What is representation? — but rather when we address How does this or that representation represent, and how does it succeed? The ...
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Resemblance comes in, not when we are answering the question — What is representation? — but rather when we address How does this or that representation represent, and how does it succeed? The various modes of representation here distinguished include imaging, picturing, and scaling. Imaging is representation that is effected through resemblance; picturing is imaging that carries the hallmarks of perspectivity. Mathematical representation of nature includes much imagery, and has so far always involved some features that, in retrospect, with hindsight, were seen as necessary failures in resemblance. Such representations can fall short through idealization, but can also achieve their success through systematic distortion.Less
Resemblance comes in, not when we are answering the question — What is representation? — but rather when we address How does this or that representation represent, and how does it succeed? The various modes of representation here distinguished include imaging, picturing, and scaling. Imaging is representation that is effected through resemblance; picturing is imaging that carries the hallmarks of perspectivity. Mathematical representation of nature includes much imagery, and has so far always involved some features that, in retrospect, with hindsight, were seen as necessary failures in resemblance. Such representations can fall short through idealization, but can also achieve their success through systematic distortion.
Baltazar D. Aguda and Avner Friedman
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198570912
- eISBN:
- 9780191718717
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570912.003.0001
- Subject:
- Physics, Soft Matter / Biological Physics
This introductory chapter begins with a brief discussion of the primary goal of this book, which is to provide an account of networks of physicochemical interactions and the cellular processes that ...
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This introductory chapter begins with a brief discussion of the primary goal of this book, which is to provide an account of networks of physicochemical interactions and the cellular processes that they regulate: cell growth and division, death, differentiation, and aging. The general aim is to illustrate how mathematical models of these processes can be developed and analyzed. An overview of the chapters is presented. This is followed by a discussion on mathematical modelling of biological phenomena and a brief note on the organization and use of the book.Less
This introductory chapter begins with a brief discussion of the primary goal of this book, which is to provide an account of networks of physicochemical interactions and the cellular processes that they regulate: cell growth and division, death, differentiation, and aging. The general aim is to illustrate how mathematical models of these processes can be developed and analyzed. An overview of the chapters is presented. This is followed by a discussion on mathematical modelling of biological phenomena and a brief note on the organization and use of the book.
Norma Van Surdam Graham
- Published in print:
- 1989
- Published Online:
- January 2008
- ISBN:
- 9780195051544
- eISBN:
- 9780199872183
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195051544.001.0001
- Subject:
- Psychology, Cognitive Neuroscience
From the light that falls on the retina, the visual system must extract meaningful information about what is where in our environment. At an early stage in this process, it analyzes the incoming ...
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From the light that falls on the retina, the visual system must extract meaningful information about what is where in our environment. At an early stage in this process, it analyzes the incoming sensory data along many dimensions of pattern vision. This book describes the current knowledge about this stage of visual processing, focusing both on psychophysical experiments measuring the detection and identification of near-threshold patterns and on the mathematical models used to draw inferences from such experimental results. Neurophysiological evidence is presented and compared critically to the psychophysical evidence. Orientation, spatial frequency, direction of motion, and eye of origin are among the many dimensions of spatiotemporal pattern vision for which experimental results and mathematical models are reviewed. Introductory material on psychophysical methods, signal detection theory, and the mathematics of Fourier analysis is also given. The preface gives a guide to the organization of the book and to what parts of the book can be read independently of one another. The last two chapters contain lists of references organized by dimensions of pattern vision. An appendix at the end of the book lists the assumptions used in the models both in order of appearance and in groups according to function.Less
From the light that falls on the retina, the visual system must extract meaningful information about what is where in our environment. At an early stage in this process, it analyzes the incoming sensory data along many dimensions of pattern vision. This book describes the current knowledge about this stage of visual processing, focusing both on psychophysical experiments measuring the detection and identification of near-threshold patterns and on the mathematical models used to draw inferences from such experimental results. Neurophysiological evidence is presented and compared critically to the psychophysical evidence. Orientation, spatial frequency, direction of motion, and eye of origin are among the many dimensions of spatiotemporal pattern vision for which experimental results and mathematical models are reviewed. Introductory material on psychophysical methods, signal detection theory, and the mathematics of Fourier analysis is also given. The preface gives a guide to the organization of the book and to what parts of the book can be read independently of one another. The last two chapters contain lists of references organized by dimensions of pattern vision. An appendix at the end of the book lists the assumptions used in the models both in order of appearance and in groups according to function.
Martine Ben Amar, Alain Goriely, Martin Michael Müller, and Leticia Cugliandolo (eds)
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199605835
- eISBN:
- 9780191729522
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605835.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics
In July 2009, many experts in the mathematical modelling of biological sciences gathered in Les Houches for a four-week summer school on the mechanics and physics of biological systems. The goal of ...
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In July 2009, many experts in the mathematical modelling of biological sciences gathered in Les Houches for a four-week summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic was very wide, the summer school focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modelling of particular systems in the biology of the cell, plants, microbes, and in physiology. The chapters in this book contain the lecture notes which are organized (as was the school) around five different main topics all connected by the common theme of continuum modelling for biological systems: bio-fluidics, bio-gels, bio-mechanics, bio-membranes, and morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction on the basic problematic in modelling biological systems from a mechanics perspective.Less
In July 2009, many experts in the mathematical modelling of biological sciences gathered in Les Houches for a four-week summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic was very wide, the summer school focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modelling of particular systems in the biology of the cell, plants, microbes, and in physiology. The chapters in this book contain the lecture notes which are organized (as was the school) around five different main topics all connected by the common theme of continuum modelling for biological systems: bio-fluidics, bio-gels, bio-mechanics, bio-membranes, and morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction on the basic problematic in modelling biological systems from a mechanics perspective.
Michael Weisberg
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199933662
- eISBN:
- 9780199333004
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199933662.003.0004
- Subject:
- Philosophy, Philosophy of Science
Chapter 3 develops a version of the maths view of mathematical models. On this view, mathematical and computational models are interpreted mathematical structures. However, in the last few years, a ...
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Chapter 3 develops a version of the maths view of mathematical models. On this view, mathematical and computational models are interpreted mathematical structures. However, in the last few years, a concrete or fictions view of mathematical models has become especially popular. Philosophers such as Roman Frigg, Peter Godfrey-Smith, and Arnon Levy have argued that the best way to understand mathematical models is as if they were more closely related to literary fictions than to bits of mathematics. This chapter argues against such accounts, but also shows how the maths view can be modified to take into account some of the insights of these philosophers.Less
Chapter 3 develops a version of the maths view of mathematical models. On this view, mathematical and computational models are interpreted mathematical structures. However, in the last few years, a concrete or fictions view of mathematical models has become especially popular. Philosophers such as Roman Frigg, Peter Godfrey-Smith, and Arnon Levy have argued that the best way to understand mathematical models is as if they were more closely related to literary fictions than to bits of mathematics. This chapter argues against such accounts, but also shows how the maths view can be modified to take into account some of the insights of these philosophers.
Baltazar D. Aguda and Avner Friedman
- 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 ...
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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 differential equations; but coupling of chemical reactions to physical processes such as diffusion requires the formulation of partial differential equations to describe the spatiotemporal evolution of the system. Mathematical analysis of the dynamical models involves basic concepts from ordinary and partial differential equations. Computational methods, including stochastic simulations and sources of computer software programs available free on the internet are also summarized.Less
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 differential equations; but coupling of chemical reactions to physical processes such as diffusion requires the formulation of partial differential equations to describe the spatiotemporal evolution of the system. Mathematical analysis of the dynamical models involves basic concepts from ordinary and partial differential equations. Computational methods, including stochastic simulations and sources of computer software programs available free on the internet are also summarized.
J. N. REDDY
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198525295
- eISBN:
- 9780191711671
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525295.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, ...
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One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, biological, chemical, geological, or mechanical. The mathematical models are developed using laws of physics and they are often described in terms of algebraic, differential, and/or integral equations relating various quantities of interest. A mathematical model of the motion of the pendulum can be constructed using the principle of conservation of linear momentum, that is, Newton's second law of motion. This chapter also discusses the traditional finite element method, nonlinear analysis, and classification of nonlinearities. The finite element method is a powerful method that can be used to perform numerical simulations of engineering problems.Less
One of the most important thing engineers and scientists do is to model natural phenomena. They develop conceptual and mathematical models to simulate physical events, whether they are aerospace, biological, chemical, geological, or mechanical. The mathematical models are developed using laws of physics and they are often described in terms of algebraic, differential, and/or integral equations relating various quantities of interest. A mathematical model of the motion of the pendulum can be constructed using the principle of conservation of linear momentum, that is, Newton's second law of motion. This chapter also discusses the traditional finite element method, nonlinear analysis, and classification of nonlinearities. The finite element method is a powerful method that can be used to perform numerical simulations of engineering problems.
Christine DeMars
- Published in print:
- 2010
- Published Online:
- March 2012
- ISBN:
- 9780195377033
- eISBN:
- 9780199847341
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195377033.001.0001
- Subject:
- Psychology, Cognitive Psychology
This book addresses an important issue for the design of survey instruments, which is rarely taught in graduate programs beyond those specifically for statisticians. Item Response Theory is used to ...
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This book addresses an important issue for the design of survey instruments, which is rarely taught in graduate programs beyond those specifically for statisticians. Item Response Theory is used to describe the application of mathematical models to data from questionnaires and tests as a basis for measuring abilities, attitudes, or other variables. It is used for statistical analysis and the development of assessments, often for high stakes tests such as the Graduate Record Examination. This volume includes examples of both good and bad write-ups for the methods sections of journal articles.Less
This book addresses an important issue for the design of survey instruments, which is rarely taught in graduate programs beyond those specifically for statisticians. Item Response Theory is used to describe the application of mathematical models to data from questionnaires and tests as a basis for measuring abilities, attitudes, or other variables. It is used for statistical analysis and the development of assessments, often for high stakes tests such as the Graduate Record Examination. This volume includes examples of both good and bad write-ups for the methods sections of journal articles.
Michael Doebeli
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128931
- eISBN:
- 9781400838936
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128931.003.0001
- Subject:
- Biology, Biodiversity / Conservation Biology
This introductory chapter provides an overview of frequency-dependent selection—the phenomenon that the evolving population is part of the changing environment determining the evolutionary ...
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This introductory chapter provides an overview of frequency-dependent selection—the phenomenon that the evolving population is part of the changing environment determining the evolutionary trajectory. Selection is frequency-dependent if the sign and magnitude of the correlations between heritable variation and reproductive variation change as a consequence of changes in the trait distribution that are themselves generated by such correlations. From the perspective of mathematical modeling, the realm of frequency dependence in evolution is larger than the realm of situations in which selection is not frequency dependent, because the absence of frequency dependence in a mathematical model of evolution essentially means that some parameters describing certain types of biological interactions are set to zero. Thus, in a suitable parameter space, frequency independence corresponds to the region around zero, while everything else corresponds to frequency dependence. In this way, frequency-dependent selection should therefore be considered the norm, not the exception, for evolutionary processes.Less
This introductory chapter provides an overview of frequency-dependent selection—the phenomenon that the evolving population is part of the changing environment determining the evolutionary trajectory. Selection is frequency-dependent if the sign and magnitude of the correlations between heritable variation and reproductive variation change as a consequence of changes in the trait distribution that are themselves generated by such correlations. From the perspective of mathematical modeling, the realm of frequency dependence in evolution is larger than the realm of situations in which selection is not frequency dependent, because the absence of frequency dependence in a mathematical model of evolution essentially means that some parameters describing certain types of biological interactions are set to zero. Thus, in a suitable parameter space, frequency independence corresponds to the region around zero, while everything else corresponds to frequency dependence. In this way, frequency-dependent selection should therefore be considered the norm, not the exception, for evolutionary processes.
