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.
Reinhard B. Neder and Thomas Proffen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199233694
- eISBN:
- 9780191715563
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233694.003.0010
- Subject:
- Physics, Crystallography: Physics
This chapter addresses the question of how to visualize a large disordered structure and how to extract information describing the disorder from a large model crystal. Topics include the ...
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This chapter addresses the question of how to visualize a large disordered structure and how to extract information describing the disorder from a large model crystal. Topics include the determination of occupancies and their homogeneity, the calculation of correlations, and the concept of bond valence sums.Less
This chapter addresses the question of how to visualize a large disordered structure and how to extract information describing the disorder from a large model crystal. Topics include the determination of occupancies and their homogeneity, the calculation of correlations, and the concept of bond valence sums.
Edward A. Zelinsky
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195339352
- eISBN:
- 9780199855407
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195339352.003.0001
- Subject:
- Law, Employment Law
Traditional defined benefit pensions have four major characteristics as a matter of plan design. First, they provide income on a deferred basis at retirement and not before then. Second, they provide ...
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Traditional defined benefit pensions have four major characteristics as a matter of plan design. First, they provide income on a deferred basis at retirement and not before then. Second, they provide such retirement income as periodic, annuity-type payments, rather than as single lump sums. Third, they are funded collectively, the employer's contributions being pooled in a common trust fund from which all participants receive their benefits. Finally, the defined benefit format places on the employer (rather than the employee) the obligation to fund the benefit promised to the participating employee. In all four respects, the prototypical defined contribution retirement plan, exemplified by 401(k) arrangements, is today different. The contemporary defined contribution arrangement distributes to an employee when he leaves employment, even if the employee is well short of retirement age. Typically, the distribution takes the form of a single, lump sum payout of the employee's individual account balance.Less
Traditional defined benefit pensions have four major characteristics as a matter of plan design. First, they provide income on a deferred basis at retirement and not before then. Second, they provide such retirement income as periodic, annuity-type payments, rather than as single lump sums. Third, they are funded collectively, the employer's contributions being pooled in a common trust fund from which all participants receive their benefits. Finally, the defined benefit format places on the employer (rather than the employee) the obligation to fund the benefit promised to the participating employee. In all four respects, the prototypical defined contribution retirement plan, exemplified by 401(k) arrangements, is today different. The contemporary defined contribution arrangement distributes to an employee when he leaves employment, even if the employee is well short of retirement age. Typically, the distribution takes the form of a single, lump sum payout of the employee's individual account balance.
Todd Sinai and Nicholas Souleles
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199549108
- eISBN:
- 9780191720734
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199549108.003.0004
- Subject:
- Business and Management, Pensions and Pension Management
This chapter documents the trends in the life-cycle profiles of net worth and housing equity of older persons. During the 1993-2004 period, older households' net worth rose significantly, yet net ...
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This chapter documents the trends in the life-cycle profiles of net worth and housing equity of older persons. During the 1993-2004 period, older households' net worth rose significantly, yet net worth grew by more than housing equity, in part because other assets also appreciated at the same time. Moreover, the younger elderly offset rising house prices by increasing their housing debt and used some of the proceeds to invest in other assets. The chapter considers how much of their housing equity older households could actually tap using reverse mortgages. It shows that this fraction is lower at younger ages, such that young retirees can consume less than half of their housing equity. Their results imply that consumable net worth is smaller than standard calculations of net worth.Less
This chapter documents the trends in the life-cycle profiles of net worth and housing equity of older persons. During the 1993-2004 period, older households' net worth rose significantly, yet net worth grew by more than housing equity, in part because other assets also appreciated at the same time. Moreover, the younger elderly offset rising house prices by increasing their housing debt and used some of the proceeds to invest in other assets. The chapter considers how much of their housing equity older households could actually tap using reverse mortgages. It shows that this fraction is lower at younger ages, such that young retirees can consume less than half of their housing equity. Their results imply that consumable net worth is smaller than standard calculations of net worth.
PETER SIMONS
- Published in print:
- 2000
- Published Online:
- October 2011
- ISBN:
- 9780199241460
- eISBN:
- 9780191696930
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199241460.003.0011
- Subject:
- Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics
This book has shown that mereology was dominated by a single theory: classical extensional mereology (CEM), present in two logical guises — the Calculus of Individuals and Mereology — each in a ...
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This book has shown that mereology was dominated by a single theory: classical extensional mereology (CEM), present in two logical guises — the Calculus of Individuals and Mereology — each in a number of variants. CEM is algebraically neat: only a complete Boolean algebra is neater. It is also strong. CEM is tenseless, non-modal, upholds extensionality of parts, and upholds the conditioned existence of general sums. The first two characteristics are privative, while the last two are positive. Among approaches at variance with CEM, most retain the first three characteristics and drop the last in favour of some weaker conditional existence principle. In the face of apparent temporal and modal variation, two major strategies have been followed. The first ignores modality and attempts to retain the third characteristic by recourse to an ontology of four-dimensional objects. The second strategy, that of Roderick Chisholm, takes both time and modality seriously, but preserves the third characteristic by putting forward an ontology, opposed to common sense, of modally and temporally invariable objects.Less
This book has shown that mereology was dominated by a single theory: classical extensional mereology (CEM), present in two logical guises — the Calculus of Individuals and Mereology — each in a number of variants. CEM is algebraically neat: only a complete Boolean algebra is neater. It is also strong. CEM is tenseless, non-modal, upholds extensionality of parts, and upholds the conditioned existence of general sums. The first two characteristics are privative, while the last two are positive. Among approaches at variance with CEM, most retain the first three characteristics and drop the last in favour of some weaker conditional existence principle. In the face of apparent temporal and modal variation, two major strategies have been followed. The first ignores modality and attempts to retain the third characteristic by recourse to an ontology of four-dimensional objects. The second strategy, that of Roderick Chisholm, takes both time and modality seriously, but preserves the third characteristic by putting forward an ontology, opposed to common sense, of modally and temporally invariable objects.
Loukas Tsoukalis
- Published in print:
- 2005
- Published Online:
- October 2005
- ISBN:
- 9780199279487
- eISBN:
- 9780191602979
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199279489.003.0003
- Subject:
- Political Science, European Union
This chapter analyses the winners and losers in European integration. Integration has been perceived as a positive-sum game, involving the joint management of economic interdependence for increasing ...
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This chapter analyses the winners and losers in European integration. Integration has been perceived as a positive-sum game, involving the joint management of economic interdependence for increasing open economies, the intermeshing and interlocking of sovereign political entities as a means of consolidating peace and security on a continent with a long history of national rivalries and bloody conflict, and the strengthening of democratic institutions. However, these have gradually disappeared with the worsening economic environment, deepening integration, and increasing inability of the nation-state to redistribute internally. The division between winners and losers has become a more important issue within countries rather than between countries.Less
This chapter analyses the winners and losers in European integration. Integration has been perceived as a positive-sum game, involving the joint management of economic interdependence for increasing open economies, the intermeshing and interlocking of sovereign political entities as a means of consolidating peace and security on a continent with a long history of national rivalries and bloody conflict, and the strengthening of democratic institutions. However, these have gradually disappeared with the worsening economic environment, deepening integration, and increasing inability of the nation-state to redistribute internally. The division between winners and losers has become a more important issue within countries rather than between countries.
I. David Brown
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199298815
- eISBN:
- 9780191708879
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199298815.001.0001
- Subject:
- Physics, Crystallography: Physics
The bond valence model, which is derived from the ionic model, is expressed through a number of rules and equations that determines which acid-base bond structures can exist. Chief among these rules ...
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The bond valence model, which is derived from the ionic model, is expressed through a number of rules and equations that determines which acid-base bond structures can exist. Chief among these rules is the bond valence sum rule, which states that the sum of bond valences around an ion is equal to its atomic valence. These rules can be used to understand many of the properties of inorganic structures, such as bond lengths, coordination numbers, their structures and their solution chemistry. The unusual geometries and properties of hydrogen bonds follow naturally from these rules. Because the model describes chemically ideal structures, it allows one to quantify the role of electronic anisotropies and steric strain in observed structures, the latter frequently leading to phase transitions in crystals. In favourable cases the model can be used for structure prediction by constructing the bond network ab initio and then mapping this onto a compatible space group. The model has applications in many fields ranging from earth sciences to biology.Less
The bond valence model, which is derived from the ionic model, is expressed through a number of rules and equations that determines which acid-base bond structures can exist. Chief among these rules is the bond valence sum rule, which states that the sum of bond valences around an ion is equal to its atomic valence. These rules can be used to understand many of the properties of inorganic structures, such as bond lengths, coordination numbers, their structures and their solution chemistry. The unusual geometries and properties of hydrogen bonds follow naturally from these rules. Because the model describes chemically ideal structures, it allows one to quantify the role of electronic anisotropies and steric strain in observed structures, the latter frequently leading to phase transitions in crystals. In favourable cases the model can be used for structure prediction by constructing the bond network ab initio and then mapping this onto a compatible space group. The model has applications in many fields ranging from earth sciences to biology.
Nicholas M. Katz
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153308
- eISBN:
- 9781400842704
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153308.001.0001
- Subject:
- Mathematics, Number Theory
This book explores an important aspect of number theory—the theory of exponential sums over finite fields and their Mellin transforms—from a new, categorical point of view. The book presents ...
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This book explores an important aspect of number theory—the theory of exponential sums over finite fields and their Mellin transforms—from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.Less
This book explores an important aspect of number theory—the theory of exponential sums over finite fields and their Mellin transforms—from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
Ben Brubaker, Daniel Bump, and Solomon Friedberg
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0008
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter introduces a method of marking up a short Gelfand-Tsetlin pattern based on inequalities between its entries, that encodes the effect of the involution t 7 → t′ and the boxing and ...
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This chapter introduces a method of marking up a short Gelfand-Tsetlin pattern based on inequalities between its entries, that encodes the effect of the involution t 7 → t′ and the boxing and circling of its accordion. This will have another benefit: it will lead to the decomposition of the pattern into pieces called episodes that will ultimately lead to the reduction to the totally resonant case. The proof is easily checked using standard properties of Gauss sums. To define the cartoon, the chapter takes a slightly more formal approach to the short Gelfand-Tsetlin patterns. The vertices of the cartoon will be the elements of the substrate Θ, and the edges must be defined.Less
This chapter introduces a method of marking up a short Gelfand-Tsetlin pattern based on inequalities between its entries, that encodes the effect of the involution t 7 → t′ and the boxing and circling of its accordion. This will have another benefit: it will lead to the decomposition of the pattern into pieces called episodes that will ultimately lead to the reduction to the totally resonant case. The proof is easily checked using standard properties of Gauss sums. To define the cartoon, the chapter takes a slightly more formal approach to the short Gelfand-Tsetlin patterns. The vertices of the cartoon will be the elements of the substrate Θ, and the edges must be defined.
Ben Brubaker, Daniel Bump, and Solomon Friedberg
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0012
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter introduces the Knowability Lemma, which explains when products of Gauss sums associated to elements of a preaccordion are explicitly evaluable as polynomials in q, the order of the ...
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This chapter introduces the Knowability Lemma, which explains when products of Gauss sums associated to elements of a preaccordion are explicitly evaluable as polynomials in q, the order of the residue class field. It considers an episode in the cartoon associated to the short Gelfand-Tsetlin pattern and the three cases that apply according to the Knowability Lemma, two of which are maximality and knowability. Knowability is not important for the proof that Statement C implies Statement B. The chapter discusses the cases where ε is Class II or Class I, leaving the remaining two cases to the reader. It also describes the variant of the argument for the case that ε is of Class I, again leaving the two other cases to the reader.Less
This chapter introduces the Knowability Lemma, which explains when products of Gauss sums associated to elements of a preaccordion are explicitly evaluable as polynomials in q, the order of the residue class field. It considers an episode in the cartoon associated to the short Gelfand-Tsetlin pattern and the three cases that apply according to the Knowability Lemma, two of which are maximality and knowability. Knowability is not important for the proof that Statement C implies Statement B. The chapter discusses the cases where ε is Class II or Class I, leaving the remaining two cases to the reader. It also describes the variant of the argument for the case that ε is of Class I, again leaving the two other cases to the reader.
Pavol Hell and Jaroslav Nešetřil
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.003.0006
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter sets out certain particular classes of homomorphism problems that have been investigated as variants of graph colourings. The homomorphism perspective unifies these concepts and offers ...
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This chapter sets out certain particular classes of homomorphism problems that have been investigated as variants of graph colourings. The homomorphism perspective unifies these concepts and offers new questions. The chapter includes a discussion of the circular chromatic number, the fractional chromatic number, the $T$-span, and the oriented chromatic number. Highlights include a number of equivalent definitions of the circular chromatic number in terms of $H$-colourability; in terms of a geometric representation, in terms of orientations implying, for instance, Minty’s result on chromatic numbers; and in terms of schedule concurrency. For fractional chromatic numbers, equivalent formulations are given in terms of Kneser graphs, integer linear programs, and zero-sum games, and they are related in several ways to the circular chromatic numbers. Homomorphisms amongst Kneser graphs are investigated, and a proof of Kneser’s conjecture is given. It is shown that the span for any set $T$ of the cliques $K_n$ has a limit, which is closely related to the fractional chromatic number of an associated graph. Bounds on the oriented chromatic numbers of planar and outerplanar graphs are given, and oriented chromatic numbers are related to acyclic chromatic numbers.Less
This chapter sets out certain particular classes of homomorphism problems that have been investigated as variants of graph colourings. The homomorphism perspective unifies these concepts and offers new questions. The chapter includes a discussion of the circular chromatic number, the fractional chromatic number, the $T$-span, and the oriented chromatic number. Highlights include a number of equivalent definitions of the circular chromatic number in terms of $H$-colourability; in terms of a geometric representation, in terms of orientations implying, for instance, Minty’s result on chromatic numbers; and in terms of schedule concurrency. For fractional chromatic numbers, equivalent formulations are given in terms of Kneser graphs, integer linear programs, and zero-sum games, and they are related in several ways to the circular chromatic numbers. Homomorphisms amongst Kneser graphs are investigated, and a proof of Kneser’s conjecture is given. It is shown that the span for any set $T$ of the cliques $K_n$ has a limit, which is closely related to the fractional chromatic number of an associated graph. Bounds on the oriented chromatic numbers of planar and outerplanar graphs are given, and oriented chromatic numbers are related to acyclic chromatic numbers.
Ken Binmore
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780195300574
- eISBN:
- 9780199783748
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300574.003.0007
- Subject:
- Economics and Finance, Microeconomics
This chapter describes the theory of two-person, zero-sum games invented by John Von Neumann in 1928. It begins with an application to the computation of economic shadow prices. It shows that a ...
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This chapter describes the theory of two-person, zero-sum games invented by John Von Neumann in 1928. It begins with an application to the computation of economic shadow prices. It shows that a two-person game is strictly competitive if, and only if, it has a zero-sum representation. Such a game can be represented using only the first player's payoff matrix. The minimax and maximin values of the matrix are defined and linked to the concept of a saddle point. The ideas are then related to a player's security level in a game. An inductive proof of Von Neumann's minimax theorem is offered. The connexion between the minimax theorem and the duality theorem of linear programming is explained. The method of solving certain two-person, zero-sum games geometrically with the help of the theorem of the separating hyperplane is introduced. The Hide-and-Seek Game is used as a non-trivial example.Less
This chapter describes the theory of two-person, zero-sum games invented by John Von Neumann in 1928. It begins with an application to the computation of economic shadow prices. It shows that a two-person game is strictly competitive if, and only if, it has a zero-sum representation. Such a game can be represented using only the first player's payoff matrix. The minimax and maximin values of the matrix are defined and linked to the concept of a saddle point. The ideas are then related to a player's security level in a game. An inductive proof of Von Neumann's minimax theorem is offered. The connexion between the minimax theorem and the duality theorem of linear programming is explained. The method of solving certain two-person, zero-sum games geometrically with the help of the theorem of the separating hyperplane is introduced. The Hide-and-Seek Game is used as a non-trivial example.
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.
Donald Laming
- Published in print:
- 1997
- Published Online:
- January 2008
- ISBN:
- 9780198523420
- eISBN:
- 9780191712425
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523420.003.0007
- Subject:
- Psychology, Cognitive Neuroscience
If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The ...
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If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The experimental evidence in this chapter says ‘Not so’. A variety of ideas have been proposed in attempts to save the role of magnitude estimates as measures of sensation. These include non-extensive ratio-scale measurement, attributing a subjective value to number itself, and a two-stage model for the judgment of the combined sensation of pairs of stimuli presented both simultaneously and successively (the resultant estimates are different). The idea of the power law as a definitive measure of sensation finally founders on certain situations, in the judgment of loudness and of brightness, in which an increase in total stimulus magnitude leads to a reduction in judged sensation.Less
If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The experimental evidence in this chapter says ‘Not so’. A variety of ideas have been proposed in attempts to save the role of magnitude estimates as measures of sensation. These include non-extensive ratio-scale measurement, attributing a subjective value to number itself, and a two-stage model for the judgment of the combined sensation of pairs of stimuli presented both simultaneously and successively (the resultant estimates are different). The idea of the power law as a definitive measure of sensation finally founders on certain situations, in the judgment of loudness and of brightness, in which an increase in total stimulus magnitude leads to a reduction in judged sensation.
Michael Potter
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199215836
- eISBN:
- 9780191721243
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215836.003.0015
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter begins with a discussion of disjunctive facts, speculating on the reasons for Wittgenstein's reluctance to countenance disjunctive facts. It then discusses negative facts, summing facts, ...
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This chapter begins with a discussion of disjunctive facts, speculating on the reasons for Wittgenstein's reluctance to countenance disjunctive facts. It then discusses negative facts, summing facts, general facts, and logical data.Less
This chapter begins with a discussion of disjunctive facts, speculating on the reasons for Wittgenstein's reluctance to countenance disjunctive facts. It then discusses negative facts, summing facts, general facts, and logical data.
Lieve Van Hoof
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199583263
- eISBN:
- 9780191723131
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199583263.003.0008
- Subject:
- Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy
This chapter deals with Plutarch's ‘psychotherapeutic’ text On Curiosity, in which he strongly condemns the desire to discover other people's evils, which, he suggests, is omnipresent in the cities ...
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This chapter deals with Plutarch's ‘psychotherapeutic’ text On Curiosity, in which he strongly condemns the desire to discover other people's evils, which, he suggests, is omnipresent in the cities of the Roman Empire. In Plutarch's analysis, such malicious curiosity goes hand in hand with envy and malice: in order to win what they perceive to be a zero-sum game for reputation, people try to discover and spread scandal about others. Starting from this premiss, Plutarch demonstrates that the reader's tactics do not yield social esteem: curiosity often leads to danger, always to dishonour. By engaging in a subtle dialogue with various traditional readings of curiosity, Plutarch manages to guide the reader away from malicious curiosity, to promote himself and his own writings, and to avoid a possible rebound effect when criticizing others for criticizing others.Less
This chapter deals with Plutarch's ‘psychotherapeutic’ text On Curiosity, in which he strongly condemns the desire to discover other people's evils, which, he suggests, is omnipresent in the cities of the Roman Empire. In Plutarch's analysis, such malicious curiosity goes hand in hand with envy and malice: in order to win what they perceive to be a zero-sum game for reputation, people try to discover and spread scandal about others. Starting from this premiss, Plutarch demonstrates that the reader's tactics do not yield social esteem: curiosity often leads to danger, always to dishonour. By engaging in a subtle dialogue with various traditional readings of curiosity, Plutarch manages to guide the reader away from malicious curiosity, to promote himself and his own writings, and to avoid a possible rebound effect when criticizing others for criticizing others.
Ignacio Palacios-Huerta
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691144023
- eISBN:
- 9781400850310
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144023.003.0003
- Subject:
- Economics and Finance, History of Economic Thought
This chapter focuses on zero-sum experimental games where players are predicted to choose probability mixtures. Whereas perfectively competitive games do not represent the entire universe of ...
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This chapter focuses on zero-sum experimental games where players are predicted to choose probability mixtures. Whereas perfectively competitive games do not represent the entire universe of strategic games involving mixed strategies, they are considered a “vital cornerstone”and can be regarded as the branch of game theory with the most solid theoretical foundation. Soccer has three unique features that make it especially suitable for this purpose: (1) professional soccer players face a simple strategic interaction that is governed by very detailed rules: a penalty kick; (2) the formal structure of this interaction can be reproduced in the laboratory; and (3) when professional soccer players from European leagues play this game in the field, their behavior is consistent with the equilibrium predictions of the theory. These three distinct characteristics allow us to study whether the skills and heuristics that players may have developed in the field can be transferred to the laboratory, and hence whether laboratory findings are reliable for predicting field behavior in these strategic situations.Less
This chapter focuses on zero-sum experimental games where players are predicted to choose probability mixtures. Whereas perfectively competitive games do not represent the entire universe of strategic games involving mixed strategies, they are considered a “vital cornerstone”and can be regarded as the branch of game theory with the most solid theoretical foundation. Soccer has three unique features that make it especially suitable for this purpose: (1) professional soccer players face a simple strategic interaction that is governed by very detailed rules: a penalty kick; (2) the formal structure of this interaction can be reproduced in the laboratory; and (3) when professional soccer players from European leagues play this game in the field, their behavior is consistent with the equilibrium predictions of the theory. These three distinct characteristics allow us to study whether the skills and heuristics that players may have developed in the field can be transferred to the laboratory, and hence whether laboratory findings are reliable for predicting field behavior in these strategic situations.
João P. Hespanha
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175218
- eISBN:
- 9781400885442
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175218.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be ...
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This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to “the game” solve the original design problem? Using the fundamentals of game theory, the book explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, the book examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.Less
This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to “the game” solve the original design problem? Using the fundamentals of game theory, the book explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, the book examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.
Ben Brubaker, Daniel Bump, and Solomon Friedberg
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are ...
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This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are introduced: Φ, a reduced root system; n, a positive integer; F, an algebraic number field containing the group μ₂ₙ of 2n-th roots of unity; S, a finite set of places of F containing all the archimedean places, all places ramified over a ℚ; and an r-tuple of nonzero S-integers. In the language of representation theory, the weight of the basis vector corresponding to the Gelfand-Tsetlin pattern can be read from differences of consecutive row sums in the pattern. The chapter considers in this case expressions of the weight of the pattern up to an affine linear transformation.Less
This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are introduced: Φ, a reduced root system; n, a positive integer; F, an algebraic number field containing the group μ₂ₙ of 2n-th roots of unity; S, a finite set of places of F containing all the archimedean places, all places ramified over a ℚ; and an r-tuple of nonzero S-integers. In the language of representation theory, the weight of the basis vector corresponding to the Gelfand-Tsetlin pattern can be read from differences of consecutive row sums in the pattern. The chapter considers in this case expressions of the weight of the pattern up to an affine linear transformation.
Ben Brubaker, Daniel Bump, and Solomon Friedberg
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0006
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter presents the proof of the equivalence of the two definitions for the λ-parts in terms of Gelfand-Tsetlin patterns. The equivalence of these two descriptions is a deep fact that uses ...
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This chapter presents the proof of the equivalence of the two definitions for the λ-parts in terms of Gelfand-Tsetlin patterns. The equivalence of these two descriptions is a deep fact that uses subtle combinatorial manipulations depending in an essential way on the properties of λ-th order Gauss sums. This equivalence is the key step in demonstrating functional equations. In outlining the proof, the chapter introduces many concepts and ideas as well as several equivalent forms of the result, called Statements A through G. Each statement is an intrinsically combinatorial identity involving products of Gauss sums, but with each statement the nature of the problem changes. The first reduction, Statement B, changes the focus from Gelfand-Tsetlin patterns to “short” Gelfand-Tsetlin patterns, consisting of just three rows.Less
This chapter presents the proof of the equivalence of the two definitions for the λ-parts in terms of Gelfand-Tsetlin patterns. The equivalence of these two descriptions is a deep fact that uses subtle combinatorial manipulations depending in an essential way on the properties of λ-th order Gauss sums. This equivalence is the key step in demonstrating functional equations. In outlining the proof, the chapter introduces many concepts and ideas as well as several equivalent forms of the result, called Statements A through G. Each statement is an intrinsically combinatorial identity involving products of Gauss sums, but with each statement the nature of the problem changes. The first reduction, Statement B, changes the focus from Gelfand-Tsetlin patterns to “short” Gelfand-Tsetlin patterns, consisting of just three rows.
