Bijan Mohammadi and Olivier Pironneau
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.001.0001
- Subject:
- Mathematics, Mathematical Physics
The fields of computational fluid dynamics (CFD) and optimal shape design (OSD) have received considerable attention in the recent past, and are of practical importance for many engineering ...
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The fields of computational fluid dynamics (CFD) and optimal shape design (OSD) have received considerable attention in the recent past, and are of practical importance for many engineering applications. This book deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Strokes, but also those for microfluids) and with the numerical simulation of these problems. It presents the state of the art in shape optimization for an extended range of applications involving fluid flows. Automatic differentiation, approximate gradients, unstructured mesh adaptation, multi-model configurations, and time-dependent problems are introduced, and their implementation into the industrial environments of aerospace and automobile equipment industry explained and illustrated. With the increases in the power of computers in industry since the first edition of this book, methods which were previously unfeasible have begun giving results, namely evolutionary algorithms, topological optimization methods, and level set algorithms. In this edition, these methods have been treated in separate chapters, but the book remains primarily one on differential shape optimization.Less
The fields of computational fluid dynamics (CFD) and optimal shape design (OSD) have received considerable attention in the recent past, and are of practical importance for many engineering applications. This book deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Strokes, but also those for microfluids) and with the numerical simulation of these problems. It presents the state of the art in shape optimization for an extended range of applications involving fluid flows. Automatic differentiation, approximate gradients, unstructured mesh adaptation, multi-model configurations, and time-dependent problems are introduced, and their implementation into the industrial environments of aerospace and automobile equipment industry explained and illustrated. With the increases in the power of computers in industry since the first edition of this book, methods which were previously unfeasible have begun giving results, namely evolutionary algorithms, topological optimization methods, and level set algorithms. In this edition, these methods have been treated in separate chapters, but the book remains primarily one on differential shape optimization.
Jan Modersitzki
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0007
- Subject:
- Mathematics, Applied Mathematics
This chapter summarizes the techniques discussed so far in this book. The techniques are all based on the minimization of a certain distance measure, and the distance measure is based on image ...
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This chapter summarizes the techniques discussed so far in this book. The techniques are all based on the minimization of a certain distance measure, and the distance measure is based on image features or directly on image intensities. Image features can be user supplied (e.g., landmarks) or may be deduced automatically from the image intensities (e.g., principal axes). Typical examples of intensity-based distance measures are the sum of squared differences, correlation or mutual information. For all proposed techniques, the transformation is parametric, i.e., it can be expanded in terms of some parameters and basis functions. The desired transformation is a minimizer of the distance measure in the space spanned by the basis functions. The minimizer can be obtained from algebraic equations or by applying appropriate optimization tools.Less
This chapter summarizes the techniques discussed so far in this book. The techniques are all based on the minimization of a certain distance measure, and the distance measure is based on image features or directly on image intensities. Image features can be user supplied (e.g., landmarks) or may be deduced automatically from the image intensities (e.g., principal axes). Typical examples of intensity-based distance measures are the sum of squared differences, correlation or mutual information. For all proposed techniques, the transformation is parametric, i.e., it can be expanded in terms of some parameters and basis functions. The desired transformation is a minimizer of the distance measure in the space spanned by the basis functions. The minimizer can be obtained from algebraic equations or by applying appropriate optimization tools.
Fabio-Cesare Bagliano and Giuseppe Bertola
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199266821
- eISBN:
- 9780191601606
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199266824.001.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics
Introduces methodological tools for dynamic analysis of macroeconomic phenomena: consumption and investment choices, employment, and unemployment outcomes, and economic growth. Discrete‐time dynamic ...
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Introduces methodological tools for dynamic analysis of macroeconomic phenomena: consumption and investment choices, employment, and unemployment outcomes, and economic growth. Discrete‐time dynamic optimization under uncertainty is introduced in Ch. 1 and applied to intertemporal consumption theory, with particular attention to empirical implementation. Chapter 2 focuses on continuous‐time optimization techniques and discusses the relevant insights in the context of partial equilibrium investment models. Chapter 3 applies previous chapters’ tools to dynamic labour demand, deriving the labour market equilibrium when both firms and workers face dynamic adjustment problems. Chapter 4 studies continuous‐time equilibrium dynamics of representative‐agent economies featuring both consumption and investment choices, with applications to long‐run growth issues. The role of externalities in more recent models of endogenous growth is carefully discussed. Chapter 5 studies the determination of aggregate equilibria in markets with decentralized trading, discussing the possibility of coordination failures and multiple equilibria. A search model of the labour market, focussed on the flows into and out of unemployment, is then analyzed and the dynamics of frictional unemployment are discussed. Many exercises can be found both within and at the ends of chapters, with extended solutions.Less
Introduces methodological tools for dynamic analysis of macroeconomic phenomena: consumption and investment choices, employment, and unemployment outcomes, and economic growth. Discrete‐time dynamic optimization under uncertainty is introduced in Ch. 1 and applied to intertemporal consumption theory, with particular attention to empirical implementation. Chapter 2 focuses on continuous‐time optimization techniques and discusses the relevant insights in the context of partial equilibrium investment models. Chapter 3 applies previous chapters’ tools to dynamic labour demand, deriving the labour market equilibrium when both firms and workers face dynamic adjustment problems. Chapter 4 studies continuous‐time equilibrium dynamics of representative‐agent economies featuring both consumption and investment choices, with applications to long‐run growth issues. The role of externalities in more recent models of endogenous growth is carefully discussed. Chapter 5 studies the determination of aggregate equilibria in markets with decentralized trading, discussing the possibility of coordination failures and multiple equilibria. A search model of the labour market, focussed on the flows into and out of unemployment, is then analyzed and the dynamics of frictional unemployment are discussed. Many exercises can be found both within and at the ends of chapters, with extended solutions.
Gregory C. Chow
- Published in print:
- 1997
- Published Online:
- October 2011
- ISBN:
- 9780195101928
- eISBN:
- 9780199855032
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195101928.001.0001
- Subject:
- Economics and Finance, Financial Economics
This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The ...
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This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The book presents the optimization framework for dynamic economics to foster an understanding of the approach. Instead of using dynamic programming, the book chooses instead to use the method of Lagrange multipliers in the analysis of dynamic optimization because it is easier and more efficient than dynamic programming, and gives an understanding of the substance of dynamic economics better. The book treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance, and dynamic games. It also teaches by examples, using concepts to solve simple problems; it then moves to general propositions.Less
This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The book presents the optimization framework for dynamic economics to foster an understanding of the approach. Instead of using dynamic programming, the book chooses instead to use the method of Lagrange multipliers in the analysis of dynamic optimization because it is easier and more efficient than dynamic programming, and gives an understanding of the substance of dynamic economics better. The book treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance, and dynamic games. It also teaches by examples, using concepts to solve simple problems; it then moves to general propositions.
Jerome L. Stein
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199280575
- eISBN:
- 9780191603501
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280576.003.0002
- Subject:
- Economics and Finance, Financial Economics
Data on the credit rating of bonds issued in the first half of the 1990s suggest that investors in emerging market securities paid little attention to credit risk, or that they were comfortable with ...
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Data on the credit rating of bonds issued in the first half of the 1990s suggest that investors in emerging market securities paid little attention to credit risk, or that they were comfortable with the high level of credit risk that they were incurring. This chapter develops a paradigm for intertemporal optimization under uncertainty in a finite horizon discrete time context, with the constraint that there be no default on short-term foreign currency denominated debt. The object is to select consumption, investment, and the resulting short-term debt in the first period to maximize the expected present value of the utility of consumption over both periods. The constraint is that regardless of the state of nature in the second period, there will be no default on the debt.Less
Data on the credit rating of bonds issued in the first half of the 1990s suggest that investors in emerging market securities paid little attention to credit risk, or that they were comfortable with the high level of credit risk that they were incurring. This chapter develops a paradigm for intertemporal optimization under uncertainty in a finite horizon discrete time context, with the constraint that there be no default on short-term foreign currency denominated debt. The object is to select consumption, investment, and the resulting short-term debt in the first period to maximize the expected present value of the utility of consumption over both periods. The constraint is that regardless of the state of nature in the second period, there will be no default on the debt.
Jerome L. Stein
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199280575
- eISBN:
- 9780191603501
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280576.003.0003
- Subject:
- Economics and Finance, Financial Economics
This chapter answers the following technical questions: In a stochastic environment, where the return on capital and the interest rate are stochastic, what is an optimal (1) long-term debt, (2) ...
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This chapter answers the following technical questions: In a stochastic environment, where the return on capital and the interest rate are stochastic, what is an optimal (1) long-term debt, (2) expected current account, (3) consumption, and (4) expected growth rate. The mathematical techniques necessary to answer these questions, concerning intertemporal optimization in continuous time over an infinite horizon, involve dynamic programming. A mean-variance interpretation is given for the dynamic programming solution.Less
This chapter answers the following technical questions: In a stochastic environment, where the return on capital and the interest rate are stochastic, what is an optimal (1) long-term debt, (2) expected current account, (3) consumption, and (4) expected growth rate. The mathematical techniques necessary to answer these questions, concerning intertemporal optimization in continuous time over an infinite horizon, involve dynamic programming. A mean-variance interpretation is given for the dynamic programming solution.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0008
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter argues that the common view that believing a contradiction is the nadir of rationality should be rejected, and that rational considerations may require one to believe contradictions. An ...
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This chapter argues that the common view that believing a contradiction is the nadir of rationality should be rejected, and that rational considerations may require one to believe contradictions. An informal model of rationality as an optimization procedure under constraint is given.Less
This chapter argues that the common view that believing a contradiction is the nadir of rationality should be rejected, and that rational considerations may require one to believe contradictions. An informal model of rationality as an optimization procedure under constraint is given.
Graham Priest
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199263288
- eISBN:
- 9780191603631
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263280.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter discusses an account of belief-revision that is compatible with the rational belief of contradictions. In the process, a formal account of the model of rationality of the preceding ...
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This chapter discusses an account of belief-revision that is compatible with the rational belief of contradictions. In the process, a formal account of the model of rationality of the preceding chapter is provided. The account of belief-revision is contrasted with the familiar AGM account.Less
This chapter discusses an account of belief-revision that is compatible with the rational belief of contradictions. In the process, a formal account of the model of rationality of the preceding chapter is provided. The account of belief-revision is contrasted with the familiar AGM account.
Daniel L. Stein and Charles M. Newman
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691147338
- eISBN:
- 9781400845637
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147338.001.0001
- Subject:
- Sociology, Science, Technology and Environment
Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book ...
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Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into and modify this framework. The book then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, the book also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a useful book for students and practitioners in the natural and social sciences, with new material even for the experts.Less
Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into and modify this framework. The book then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, the book also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a useful book for students and practitioners in the natural and social sciences, with new material even for the experts.
Lars Peter Hansen and Thomas J. Sargent
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691042770
- eISBN:
- 9781400848188
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691042770.001.0001
- Subject:
- Economics and Finance, History of Economic Thought
A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. This book uses these tools to create a class of econometrically tractable models of prices and ...
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A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. This book uses these tools to create a class of econometrically tractable models of prices and quantities. The book presents examples from microeconomics, macroeconomics, and asset pricing. The models are cast in terms of a representative consumer. While the book demonstrates the analytical benefits acquired when an analysis with a representative consumer is possible, it also characterizes the restrictiveness of assumptions under which a representative household justifies a purely aggregative analysis. The book unites economic theory with a workable econometrics while going beyond and beneath demand and supply curves for dynamic economies. It constructs and applies competitive equilibria for a class of linear-quadratic-Gaussian dynamic economies with complete markets. The book, based on the 2012 Gorman lectures, stresses heterogeneity, aggregation, and how a common structure unites what superficially appear to be diverse applications. An appendix describes MATLAB programs that apply to the book's calculations.Less
A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. This book uses these tools to create a class of econometrically tractable models of prices and quantities. The book presents examples from microeconomics, macroeconomics, and asset pricing. The models are cast in terms of a representative consumer. While the book demonstrates the analytical benefits acquired when an analysis with a representative consumer is possible, it also characterizes the restrictiveness of assumptions under which a representative household justifies a purely aggregative analysis. The book unites economic theory with a workable econometrics while going beyond and beneath demand and supply curves for dynamic economies. It constructs and applies competitive equilibria for a class of linear-quadratic-Gaussian dynamic economies with complete markets. The book, based on the 2012 Gorman lectures, stresses heterogeneity, aggregation, and how a common structure unites what superficially appear to be diverse applications. An appendix describes MATLAB programs that apply to the book's calculations.
Gøsta Esping‐Andersen
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198742005
- eISBN:
- 9780191599163
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198742002.003.0009
- Subject:
- Political Science, Comparative Politics
The introduction to this chapter discusses the question of why nations respond so differently to a set of social risks that are similar over various countries, and analyses three typical homines: ...
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The introduction to this chapter discusses the question of why nations respond so differently to a set of social risks that are similar over various countries, and analyses three typical homines: Homo liberalisimus, Homo familias, and Homo socialdemocraticus. When the instincts of these ideal typical homines are combined, moral conflicts result, although a sufficient mass manages to profile itself in collective expression and sways society towards its preferred welfare regime. Old risks may fade and new ones emerge, but the response of a welfare regime will be, more likely than not, normatively path dependent. It is argued that since core institutional traits appear to be so unyielding to change, it is unlikely that the contemporary welfare state crisis will produce revolutionary change: there may be a blueprint for an ideal post‐industrial regime, but unless it is compatible with existing welfare regime practice, it may not be practicable. The author argues that, nonetheless, optimizing welfare in a post‐industrial setting will require radical departures, and these are discussed under the following headings: What is to be Optimized; Rival Reform Strategies; The Market Strategy; A Third Way?; and Equality with Inequality?Less
The introduction to this chapter discusses the question of why nations respond so differently to a set of social risks that are similar over various countries, and analyses three typical homines: Homo liberalisimus, Homo familias, and Homo socialdemocraticus. When the instincts of these ideal typical homines are combined, moral conflicts result, although a sufficient mass manages to profile itself in collective expression and sways society towards its preferred welfare regime. Old risks may fade and new ones emerge, but the response of a welfare regime will be, more likely than not, normatively path dependent. It is argued that since core institutional traits appear to be so unyielding to change, it is unlikely that the contemporary welfare state crisis will produce revolutionary change: there may be a blueprint for an ideal post‐industrial regime, but unless it is compatible with existing welfare regime practice, it may not be practicable. The author argues that, nonetheless, optimizing welfare in a post‐industrial setting will require radical departures, and these are discussed under the following headings: What is to be Optimized; Rival Reform Strategies; The Market Strategy; A Third Way?; and Equality with Inequality?
Ralph Hertwig, Ulrich Hoffrage, and ABC Research Group (eds)
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780195388435
- eISBN:
- 9780199950089
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195388435.001.0001
- Subject:
- Psychology, Social Psychology
This book invites readers to discover the simple heuristics that people use to navigate the complexities and surprises of environments populated with others. The social world is a terrain where ...
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This book invites readers to discover the simple heuristics that people use to navigate the complexities and surprises of environments populated with others. The social world is a terrain where humans and other animals compete with conspecifics for myriad resources, including food, mates, and status, and where rivals grant the decision maker little time for deep thought, protracted information search, or complex calculations. The social world also encompasses domains, however, where social animals such as humans learn from one another how to deal with the vagaries of a natural world that both inflicts unforeseeable hazards and presents useful opportunities and dare to trust and forge alliances with one another to boost their chances of success. According to the book's thesis, the undeniable complexity of the social world does not dictate cognitive complexity as many scholars of rationality argue. Rather, it entails circumstances that render optimization impossible or computationally arduous: intractability, the existence of incommensurable considerations, and competing goals. With optimization beyond reach, less can be more. That is, heuristics—simple strategies for making decisions when time is pressing and careful deliberation an unaffordable luxury—become indispensible mental tools. As accurate or even more accurate than complex methods when used in the appropriate environments, these heuristics are good descriptive models of how people make many decisions and inferences, but their impressive performance also poses a normative challenge for optimization models. In short, the homo socialis may prove to be a homo heuristicus whose intelligence reflects ecological rather than logical rationality.Less
This book invites readers to discover the simple heuristics that people use to navigate the complexities and surprises of environments populated with others. The social world is a terrain where humans and other animals compete with conspecifics for myriad resources, including food, mates, and status, and where rivals grant the decision maker little time for deep thought, protracted information search, or complex calculations. The social world also encompasses domains, however, where social animals such as humans learn from one another how to deal with the vagaries of a natural world that both inflicts unforeseeable hazards and presents useful opportunities and dare to trust and forge alliances with one another to boost their chances of success. According to the book's thesis, the undeniable complexity of the social world does not dictate cognitive complexity as many scholars of rationality argue. Rather, it entails circumstances that render optimization impossible or computationally arduous: intractability, the existence of incommensurable considerations, and competing goals. With optimization beyond reach, less can be more. That is, heuristics—simple strategies for making decisions when time is pressing and careful deliberation an unaffordable luxury—become indispensible mental tools. As accurate or even more accurate than complex methods when used in the appropriate environments, these heuristics are good descriptive models of how people make many decisions and inferences, but their impressive performance also poses a normative challenge for optimization models. In short, the homo socialis may prove to be a homo heuristicus whose intelligence reflects ecological rather than logical rationality.
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/9780195172119.003.0005
- Subject:
- Business and Management, Strategy
This chapter uses a supply chain example to compare and contrast agent-based modeling and simulation with other modeling techniques, including systems dynamics, discrete-event simulation, ...
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This chapter uses a supply chain example to compare and contrast agent-based modeling and simulation with other modeling techniques, including systems dynamics, discrete-event simulation, participatory simulation, statistical modeling, risk analysis, and optimization. It also discusses why businesses and government agencies do modeling and simulation.Less
This chapter uses a supply chain example to compare and contrast agent-based modeling and simulation with other modeling techniques, including systems dynamics, discrete-event simulation, participatory simulation, statistical modeling, risk analysis, and optimization. It also discusses why businesses and government agencies do modeling and simulation.
Vipin Narang
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159829
- eISBN:
- 9781400850402
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159829.003.0002
- Subject:
- Political Science, International Relations and Politics
This chapter identifies three main types of regional power nuclear postures, arrayed across a spectrum of capabilities and deployment procedures. This theory, the Posture Optimization Theory, ...
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This chapter identifies three main types of regional power nuclear postures, arrayed across a spectrum of capabilities and deployment procedures. This theory, the Posture Optimization Theory, explains why the existing regional nuclear powers have adopted the nuclear postures and strategies they have, and generates testable predictions about what type of nuclear posture future regional nuclear powers might adopt based on a set of readily observable variables. Because of the dearth of regional states that have acquired nuclear weapons, this exercise has inherent limitations. However, by testing the framework against the existing empirical record, we can determine whether it provides a plausible framework with which to explain the choices of existing regional powers and to predict the choices that future nuclear powers might make.Less
This chapter identifies three main types of regional power nuclear postures, arrayed across a spectrum of capabilities and deployment procedures. This theory, the Posture Optimization Theory, explains why the existing regional nuclear powers have adopted the nuclear postures and strategies they have, and generates testable predictions about what type of nuclear posture future regional nuclear powers might adopt based on a set of readily observable variables. Because of the dearth of regional states that have acquired nuclear weapons, this exercise has inherent limitations. However, by testing the framework against the existing empirical record, we can determine whether it provides a plausible framework with which to explain the choices of existing regional powers and to predict the choices that future nuclear powers might make.
Vipin Narang
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159829
- eISBN:
- 9781400850402
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159829.003.0011
- Subject:
- Political Science, International Relations and Politics
This chapter reiterates the findings explored in this book and discusses their implications. In doing so, the chapter stresses the significance of the posited optimization theory. This theory is the ...
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This chapter reiterates the findings explored in this book and discusses their implications. In doing so, the chapter stresses the significance of the posited optimization theory. This theory is the first comparative theory of regional power nuclear postures. Against the full universe of empirical cases involving selection of nuclear posture—a decision that unfolds deliberately over many years and often over many leaders—optimization theory is the most valid theory available. It is also the first broadly comparative theory for why states select the nuclear postures they do, suggesting that states may be rational to sacrifice deterrent power in certain security environments and under particular organizational and relative endowment circumstances. In addition, the chapter closes the volume by detailing some avenues for further research, as well as some concluding insights.Less
This chapter reiterates the findings explored in this book and discusses their implications. In doing so, the chapter stresses the significance of the posited optimization theory. This theory is the first comparative theory of regional power nuclear postures. Against the full universe of empirical cases involving selection of nuclear posture—a decision that unfolds deliberately over many years and often over many leaders—optimization theory is the most valid theory available. It is also the first broadly comparative theory for why states select the nuclear postures they do, suggesting that states may be rational to sacrifice deterrent power in certain security environments and under particular organizational and relative endowment circumstances. In addition, the chapter closes the volume by detailing some avenues for further research, as well as some concluding insights.
Rolf Niedermeier
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566076
- eISBN:
- 9780191713910
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566076.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter discusses three introductory examples for studying exact and fixed-parameter algorithms. It starts with the boolean Satisfiability problem and its numerous parameters, then discusses an ...
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This chapter discusses three introductory examples for studying exact and fixed-parameter algorithms. It starts with the boolean Satisfiability problem and its numerous parameters, then discusses an application problem from railway optimization, and concludes with a communication problem in tree networks (Multicut in Trees). It briefly summarizes the leitmotif of parameterized algorithm design and analysis.Less
This chapter discusses three introductory examples for studying exact and fixed-parameter algorithms. It starts with the boolean Satisfiability problem and its numerous parameters, then discusses an application problem from railway optimization, and concludes with a communication problem in tree networks (Multicut in Trees). It briefly summarizes the leitmotif of parameterized algorithm design and analysis.
Rolf Niedermeier
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566076
- eISBN:
- 9780191713910
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566076.003.0002
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter introduces the basic mathematical formalism and discusses concepts used throughout the book. Among other things, it looks at decision problems vs optimization problems, Random Access ...
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This chapter introduces the basic mathematical formalism and discusses concepts used throughout the book. Among other things, it looks at decision problems vs optimization problems, Random Access Machines, big Oh notation, strings and graphs. It concludes by looking at the basics from computational complexity theory.Less
This chapter introduces the basic mathematical formalism and discusses concepts used throughout the book. Among other things, it looks at decision problems vs optimization problems, Random Access Machines, big Oh notation, strings and graphs. It concludes by looking at the basics from computational complexity theory.
J. C. Gower and G. B. Dijksterhuis
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0009
- Subject:
- Mathematics, Probability / Statistics
This chapter is concerned with generalizations where the two sets of configurations X1 and X2 are replaced by K sets, X1 , X2 ...
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This chapter is concerned with generalizations where the two sets of configurations X1 and X2 are replaced by K sets, X1 , X2 ,..., XK , each with its own transformation matrix T1 ,..., Tk . All the variants of two-sets Procrustes problems generalize. Different choices of Tk , scaling, weighting, and the optimization criteria are discussed.Less
This chapter is concerned with generalizations where the two sets of configurations X1 and X2 are replaced by K sets, X1 , X2 ,..., XK , each with its own transformation matrix T1 ,..., Tk . All the variants of two-sets Procrustes problems generalize. Different choices of Tk , scaling, weighting, and the optimization criteria are discussed.
Moody T. Chu and Gene H. Golub
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566649
- eISBN:
- 9780191718021
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566649.003.0007
- Subject:
- Mathematics, Applied Mathematics
This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general ...
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This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general framework by using the projected gradient method is described. A broad range of applications, including the Toeplitz inverse eigenvalue problem, the simultaneous reduction problem, and the nearest normal matrix approximation, are discussed.Less
This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general framework by using the projected gradient method is described. A broad range of applications, including the Toeplitz inverse eigenvalue problem, the simultaneous reduction problem, and the nearest normal matrix approximation, are discussed.
Jan Modersitzki
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0006
- Subject:
- Mathematics, Applied Mathematics
This chapter investigates the question of how to find an optimal linear transformation based on a distance measure. Popular choices for distance measures such as the sum of squared differences, ...
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This chapter investigates the question of how to find an optimal linear transformation based on a distance measure. Popular choices for distance measures such as the sum of squared differences, correlation, and mutual information are discussed. Particular attention is paid to the differentiability of the distance measures. The desired transformation is restricted to a parameterizable space, and as such can be expanded in terms of a linear combination of some basis functions. The registration task is considered as an optimization problem, where the objective is to find the optimal coefficient in the expansion while minimizing the distance measure. The well-known Gauss-Newton method is described and used for numerical optimization. Different examples are used to identify similarities and differences of the distance measures.Less
This chapter investigates the question of how to find an optimal linear transformation based on a distance measure. Popular choices for distance measures such as the sum of squared differences, correlation, and mutual information are discussed. Particular attention is paid to the differentiability of the distance measures. The desired transformation is restricted to a parameterizable space, and as such can be expanded in terms of a linear combination of some basis functions. The registration task is considered as an optimization problem, where the objective is to find the optimal coefficient in the expansion while minimizing the distance measure. The well-known Gauss-Newton method is described and used for numerical optimization. Different examples are used to identify similarities and differences of the distance measures.
