John C Gower and Garmt B Dijksterhuis
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.001.0001
- Subject:
- Mathematics, Probability / Statistics
Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It ...
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Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It focuses on matching two or more configurations by using orthogonal, projection, and oblique axes transformations. Group-average summaries play an important part, and links with other group-average methods are discussed. The text is multi-disciplinary and also presents a unifying ANOVA framework.Less
Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It focuses on matching two or more configurations by using orthogonal, projection, and oblique axes transformations. Group-average summaries play an important part, and links with other group-average methods are discussed. The text is multi-disciplinary and also presents a unifying ANOVA framework.
Ian G. Roberts
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780195168211
- eISBN:
- 9780199788453
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195168211.001.0001
- Subject:
- Linguistics, Syntax and Morphology
This work provides an analysis of word order and clause structure in Welsh, within the context of a minimalist version of principles and parameters theory. The central issue is the analysis of VSO ...
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This work provides an analysis of word order and clause structure in Welsh, within the context of a minimalist version of principles and parameters theory. The central issue is the analysis of VSO order, the only unmarked clausal order in Welsh. The question is: which values of which parameters of Universal Grammar determine VSO order? Behind this basic descriptive goal, there are two theoretical questions. The first has to do with the conditions of adequacy on parameters: these must be both typologizable and learnable. The second concerns the Extended Projection Principle (EPP). Developing the conception of this principle in Chomsky (2000, 2001), it is concluded that it is a parametrized property of the C-system and/or the I-system, and that it seems to be intrinsically connected to the defective nature of certain functional heads. Successive chapters deal with the analysis of VSO orders, the Welsh Case-agreement system as it applies to both subjects and objects, the ‘verbal noun’, and the nature of the C-system. The last chapter takes up the related but distinct question of the theoretical status of head-movement, arguing that this may be construed as movement to a specifier position followed by morphological reanalysis of adjacent heads. Throughout, Welsh is compared to the other Celtic languages, and to the Romance and Germanic languages. Comparison with Romance is particularly revealing in relation to the agreement system, and comparison with Germanic in relation to C-system.Less
This work provides an analysis of word order and clause structure in Welsh, within the context of a minimalist version of principles and parameters theory. The central issue is the analysis of VSO order, the only unmarked clausal order in Welsh. The question is: which values of which parameters of Universal Grammar determine VSO order? Behind this basic descriptive goal, there are two theoretical questions. The first has to do with the conditions of adequacy on parameters: these must be both typologizable and learnable. The second concerns the Extended Projection Principle (EPP). Developing the conception of this principle in Chomsky (2000, 2001), it is concluded that it is a parametrized property of the C-system and/or the I-system, and that it seems to be intrinsically connected to the defective nature of certain functional heads. Successive chapters deal with the analysis of VSO orders, the Welsh Case-agreement system as it applies to both subjects and objects, the ‘verbal noun’, and the nature of the C-system. The last chapter takes up the related but distinct question of the theoretical status of head-movement, arguing that this may be construed as movement to a specifier position followed by morphological reanalysis of adjacent heads. Throughout, Welsh is compared to the other Celtic languages, and to the Romance and Germanic languages. Comparison with Romance is particularly revealing in relation to the agreement system, and comparison with Germanic in relation to C-system.
John V. Kulvicki
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199290758
- eISBN:
- 9780191604010
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019929075X.003.0005
- Subject:
- Philosophy, Aesthetics
This chapter explores the range of pictorial representation. It considers many kinds of projective systems and shows how they all manage to satisfy the conditions set forth in Chapters 2 and 3 for ...
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This chapter explores the range of pictorial representation. It considers many kinds of projective systems and shows how they all manage to satisfy the conditions set forth in Chapters 2 and 3 for being pictures. In addition, common systems of auditory representation turn out to be pictorial according to this view; this is surprising but not terribly counterintuitive. Tactile line drawings sometimes used by the blind also turn out to be pictorial on the account offered herein, and the discussion of bare-bones content suggests some new avenues of research on tactile pictures. The chapter closes by considering how well the structural account fares with respect to a list of explananda offered by Robert Hopkins as the gold standard for a theory of depiction.Less
This chapter explores the range of pictorial representation. It considers many kinds of projective systems and shows how they all manage to satisfy the conditions set forth in Chapters 2 and 3 for being pictures. In addition, common systems of auditory representation turn out to be pictorial according to this view; this is surprising but not terribly counterintuitive. Tactile line drawings sometimes used by the blind also turn out to be pictorial on the account offered herein, and the discussion of bare-bones content suggests some new avenues of research on tactile pictures. The chapter closes by considering how well the structural account fares with respect to a list of explananda offered by Robert Hopkins as the gold standard for a theory of depiction.
Mark Turner
- Published in print:
- 1998
- Published Online:
- October 2011
- ISBN:
- 9780195126679
- eISBN:
- 9780199853007
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195126679.001.0001
- Subject:
- Philosophy, Philosophy of Mind
This book ranges from the tools of modern linguistics, to the recent work of neuroscientists such as Antonio Damasio and Gerald Edelman, to literary masterpieces by Homer, Dante, Shakespeare, and ...
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This book ranges from the tools of modern linguistics, to the recent work of neuroscientists such as Antonio Damasio and Gerald Edelman, to literary masterpieces by Homer, Dante, Shakespeare, and Proust, to explain how story and projection — and their powerful combination in parable — are fundamental to everyday thought. In simple and traditional English, the author reveals how we use parable to understand space and time, to grasp what it means to be located in space and time, and to conceive of ourselves, other selves, other lives, and other viewpoints. He explains the role of parable in reasoning, in categorizing, and in solving problems. He develops a powerful model of conceptual construction and, in a far-reaching final chapter, extends it to a new conception of the origin of language that contradicts proposals by such thinkers as Noam Chomsky and Steven Pinker. This book argues that story, projection, and parable precede grammar, and that language follows from these mental capacities as a consequence. The author concludes that language is the child of the literary mind. Offering revisions to our understanding of thought, conceptual activity, and the origin and nature of language, The Literary Mind presents a unified theory of central problems in cognitive science, linguistics, neuroscience, psychology, and philosophy.Less
This book ranges from the tools of modern linguistics, to the recent work of neuroscientists such as Antonio Damasio and Gerald Edelman, to literary masterpieces by Homer, Dante, Shakespeare, and Proust, to explain how story and projection — and their powerful combination in parable — are fundamental to everyday thought. In simple and traditional English, the author reveals how we use parable to understand space and time, to grasp what it means to be located in space and time, and to conceive of ourselves, other selves, other lives, and other viewpoints. He explains the role of parable in reasoning, in categorizing, and in solving problems. He develops a powerful model of conceptual construction and, in a far-reaching final chapter, extends it to a new conception of the origin of language that contradicts proposals by such thinkers as Noam Chomsky and Steven Pinker. This book argues that story, projection, and parable precede grammar, and that language follows from these mental capacities as a consequence. The author concludes that language is the child of the literary mind. Offering revisions to our understanding of thought, conceptual activity, and the origin and nature of language, The Literary Mind presents a unified theory of central problems in cognitive science, linguistics, neuroscience, psychology, and philosophy.
Austen Clark
- Published in print:
- 2000
- Published Online:
- October 2011
- ISBN:
- 9780198238515
- eISBN:
- 9780191679650
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198238515.001.0001
- Subject:
- Philosophy, Philosophy of Mind
This book offers a general account of the forms of mental representation that we call ‘sensory’. To sense something, one must have some capacity to discriminate among sensory qualities; but there are ...
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This book offers a general account of the forms of mental representation that we call ‘sensory’. To sense something, one must have some capacity to discriminate among sensory qualities; but there are other requirements. What are they, and how can they be put together to yield full-blown sensing? Drawing on the findings of current neuroscience, the author proposes and defends the hypothesis that the various modalities of sensation share a generic form that he calls ‘feature-placing’. Sensing proceeds by picking out place-times in or around the body of the sentient organism, and characterizing qualities (features) that appear at those place-times. Such feature-placing is a primitive kind — probably the most primitive kind — of mental representation. Once its peculiarities have been described, many of the puzzles about the intentionality of sensation, and the phenomena that lead some to label it ‘pseudo-intentional’, can be resolved. The hypothesis casts light on many other troublesome phenomena, including the varieties of illusion, the problem of projection, the notion of a visual field, the location of after-images, the existence of sense-data, and the role of perceptual demonstratives.Less
This book offers a general account of the forms of mental representation that we call ‘sensory’. To sense something, one must have some capacity to discriminate among sensory qualities; but there are other requirements. What are they, and how can they be put together to yield full-blown sensing? Drawing on the findings of current neuroscience, the author proposes and defends the hypothesis that the various modalities of sensation share a generic form that he calls ‘feature-placing’. Sensing proceeds by picking out place-times in or around the body of the sentient organism, and characterizing qualities (features) that appear at those place-times. Such feature-placing is a primitive kind — probably the most primitive kind — of mental representation. Once its peculiarities have been described, many of the puzzles about the intentionality of sensation, and the phenomena that lead some to label it ‘pseudo-intentional’, can be resolved. The hypothesis casts light on many other troublesome phenomena, including the varieties of illusion, the problem of projection, the notion of a visual field, the location of after-images, the existence of sense-data, and the role of perceptual demonstratives.
Sarah Holden and Jack VanDerhei
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199204656
- eISBN:
- 9780191603822
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199204659.003.0003
- Subject:
- Economics and Finance, Financial Economics
As defined contribution plans are increasingly being offered as the primary employer-sponsored pension, it is of interest to ask whether these accumulations are likely to yield sufficient retirement ...
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As defined contribution plans are increasingly being offered as the primary employer-sponsored pension, it is of interest to ask whether these accumulations are likely to yield sufficient retirement income. This chapter uses a projection model to explore alternative future scenarios for retirees who had 401(k) plans available to them over their full working careers. It also assesses the impact of ‘catch-up’ contributions, saving through an individual retirement account when an employer does not offer a 401(k) plan, and changing retirement ages.Less
As defined contribution plans are increasingly being offered as the primary employer-sponsored pension, it is of interest to ask whether these accumulations are likely to yield sufficient retirement income. This chapter uses a projection model to explore alternative future scenarios for retirees who had 401(k) plans available to them over their full working careers. It also assesses the impact of ‘catch-up’ contributions, saving through an individual retirement account when an employer does not offer a 401(k) plan, and changing retirement ages.
John V. Kulvicki
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199290758
- eISBN:
- 9780191604010
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019929075X.003.0003
- Subject:
- Philosophy, Aesthetics
Transparency, when combined with repleteness, sensitivity, and richness, yields a set of necessary and sufficient conditions for a representational system to be pictorial. Like the other three ...
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Transparency, when combined with repleteness, sensitivity, and richness, yields a set of necessary and sufficient conditions for a representational system to be pictorial. Like the other three conditions, transparency makes no mention of picture perception. This structural account intuitively captures pictorial representation without appealing to perception, which is the main goal of Part I. The following chapters unpack some ramifications of the view. Understanding transparency requires drawing a distinction between pictures’ bare-bones contents and their fleshed-out contents (Haugeland, 1991). This distinction becomes very important in Part II as well.Less
Transparency, when combined with repleteness, sensitivity, and richness, yields a set of necessary and sufficient conditions for a representational system to be pictorial. Like the other three conditions, transparency makes no mention of picture perception. This structural account intuitively captures pictorial representation without appealing to perception, which is the main goal of Part I. The following chapters unpack some ramifications of the view. Understanding transparency requires drawing a distinction between pictures’ bare-bones contents and their fleshed-out contents (Haugeland, 1991). This distinction becomes very important in Part II as well.
Edmund Cannon and Ian Tonks
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199216994
- eISBN:
- 9780191711978
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199216994.003.0011
- Subject:
- Business and Management, Pensions and Pension Management
This chapter summarizes the conclusions on annuity pricing. While annuity products continue to be an important component of a number of pensions systems, there are a number of public policy questions ...
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This chapter summarizes the conclusions on annuity pricing. While annuity products continue to be an important component of a number of pensions systems, there are a number of public policy questions relating to both the supply and demand side of annuities. These include more sophisticated mortality projections, annuity products that appeal to particular clienteles, the bulk buy-out market, and the demand for long-term care. The chapter ends by suggesting possible explanations for the recent slight decline in the money's worth numbers.Less
This chapter summarizes the conclusions on annuity pricing. While annuity products continue to be an important component of a number of pensions systems, there are a number of public policy questions relating to both the supply and demand side of annuities. These include more sophisticated mortality projections, annuity products that appeal to particular clienteles, the bulk buy-out market, and the demand for long-term care. The chapter ends by suggesting possible explanations for the recent slight decline in the money's worth numbers.
Robert P. Gephart, Cagri Topal, and Zhen Zhang
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199594566
- eISBN:
- 9780191595721
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199594566.003.0013
- Subject:
- Business and Management, Organization Studies
Sensemaking is the process by which people construct, interpret, and recognize meaningful features of the world. Although retrospective sensemaking is a key property of the Weickian approach, ...
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Sensemaking is the process by which people construct, interpret, and recognize meaningful features of the world. Although retrospective sensemaking is a key property of the Weickian approach, sensemaking can also orient to the future. This chapter explores the social processes and practices of future‐oriented sensemaking to understand how it is accomplished, how it relates to other temporal dimensions, and how it legitimates institutions. To do so, we discuss five sensemaking perspectives relevant to temporality: Weickian sensemaking, post‐Weickian sensemaking, institutional rhetoric, agentivity, and ethnomethodology. We use the ideas in these perspectives as a means to conceptualize future-oriented sensemaking and to understand the potential influence that temporal modalities of sensemaking hold for legitimation. Next, we conduct an ethnomethodological investigation of future‐oriented sensemaking in a public hearing where future‐oriented sensemaking was a primary focus. Our investigation of inquiry discourse finds that the construction of plans, expertise, hypothetical entities, institutionalized sequences, and conventional histories are important practices in future‐oriented sensemaking that produce and sustain institutional legitimation.Less
Sensemaking is the process by which people construct, interpret, and recognize meaningful features of the world. Although retrospective sensemaking is a key property of the Weickian approach, sensemaking can also orient to the future. This chapter explores the social processes and practices of future‐oriented sensemaking to understand how it is accomplished, how it relates to other temporal dimensions, and how it legitimates institutions. To do so, we discuss five sensemaking perspectives relevant to temporality: Weickian sensemaking, post‐Weickian sensemaking, institutional rhetoric, agentivity, and ethnomethodology. We use the ideas in these perspectives as a means to conceptualize future-oriented sensemaking and to understand the potential influence that temporal modalities of sensemaking hold for legitimation. Next, we conduct an ethnomethodological investigation of future‐oriented sensemaking in a public hearing where future‐oriented sensemaking was a primary focus. Our investigation of inquiry discourse finds that the construction of plans, expertise, hypothetical entities, institutionalized sequences, and conventional histories are important practices in future‐oriented sensemaking that produce and sustain institutional legitimation.
Mark Wilson
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199269259
- eISBN:
- 9780191710155
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269259.003.0005
- Subject:
- Philosophy, Philosophy of Language
Many ‘pre-pragmatist’ opponents of the classical picture begin with a suspicion that such doctrines place unrealistic demands upon human capacity: that when we grasp a collection of vocabulary, its ...
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Many ‘pre-pragmatist’ opponents of the classical picture begin with a suspicion that such doctrines place unrealistic demands upon human capacity: that when we grasp a collection of vocabulary, its syntax rarely becomes as firmly attached to the world as the classical story promises. In overreaction, thinkers such as W. V. Quine frequently become sceptical that the world independently possesses attributes to which language might potentially attach at all. Such doubts are impossibly radical, but a pre-pragmatist can plausibly argue on engineering grounds that it is not easy to set classical-style semantic attachments in place. Confronted with these practical impediments, over time language often develops into more complicated forms of semantic arrangement than classical thinking anticipates.Less
Many ‘pre-pragmatist’ opponents of the classical picture begin with a suspicion that such doctrines place unrealistic demands upon human capacity: that when we grasp a collection of vocabulary, its syntax rarely becomes as firmly attached to the world as the classical story promises. In overreaction, thinkers such as W. V. Quine frequently become sceptical that the world independently possesses attributes to which language might potentially attach at all. Such doubts are impossibly radical, but a pre-pragmatist can plausibly argue on engineering grounds that it is not easy to set classical-style semantic attachments in place. Confronted with these practical impediments, over time language often develops into more complicated forms of semantic arrangement than classical thinking anticipates.
Johan Rooryck and Guido Vanden Wyngaerd
- Published in print:
- 2011
- Published Online:
- May 2012
- ISBN:
- 9780199691326
- eISBN:
- 9780191731785
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691326.003.0008
- Subject:
- Linguistics, Theoretical Linguistics, Syntax and Morphology
This chapter wraps up the main results of the book. These are as follows. Absence of Principle B effects can be elegantly accounted for in terms of Distributed Morphology. Simplex reflexives are ...
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This chapter wraps up the main results of the book. These are as follows. Absence of Principle B effects can be elegantly accounted for in terms of Distributed Morphology. Simplex reflexives are merged in a configuration of inalienable possession under unaccusative syntax, and their binding properties are derived by Agree. Self-reflexives share the syntax of floating quantifiers, raising to an adjoined position from which they probe their antecedent under Agree. Simplex and complex reflexives in PPs behave differently, depending on the adjunction site of the PP. French, Italian, German, and Swedish se reflexives are morphologically complex, and can figure in both the configurations of simplex zich and complex zichzelf in Dutch. The simple reflexive zich represents a spatiotemporal stage of its antecedent, thus disallowing dissociation readings that are available for the complex self-reflexive. The apparent lack of complementarity between pronoun and self-form in snake-sentences is related to the double-faced syntactic behavior of the Axpart projection of the locative preposition.Less
This chapter wraps up the main results of the book. These are as follows. Absence of Principle B effects can be elegantly accounted for in terms of Distributed Morphology. Simplex reflexives are merged in a configuration of inalienable possession under unaccusative syntax, and their binding properties are derived by Agree. Self-reflexives share the syntax of floating quantifiers, raising to an adjoined position from which they probe their antecedent under Agree. Simplex and complex reflexives in PPs behave differently, depending on the adjunction site of the PP. French, Italian, German, and Swedish se reflexives are morphologically complex, and can figure in both the configurations of simplex zich and complex zichzelf in Dutch. The simple reflexive zich represents a spatiotemporal stage of its antecedent, thus disallowing dissociation readings that are available for the complex self-reflexive. The apparent lack of complementarity between pronoun and self-form in snake-sentences is related to the double-faced syntactic behavior of the Axpart projection of the locative preposition.
P. J. E. Kail
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199229505
- eISBN:
- 9780191710728
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199229505.003.0005
- Subject:
- Philosophy, History of Philosophy
This chapter describes Hume's positive account of our idea of necessity, the perceptual nature of the metaphor of ‘spreading the mind’, and revisits realism. It is argued that Hume's account is ...
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This chapter describes Hume's positive account of our idea of necessity, the perceptual nature of the metaphor of ‘spreading the mind’, and revisits realism. It is argued that Hume's account is projective in two senses. The first is explanatory, whereby the modal element of causal thought is explained non-detectively. The second is feature projective, whereby we attribute a feature of mind to an external object. The chapter argues that Hume's account is better than commentators have thought.Less
This chapter describes Hume's positive account of our idea of necessity, the perceptual nature of the metaphor of ‘spreading the mind’, and revisits realism. It is argued that Hume's account is projective in two senses. The first is explanatory, whereby the modal element of causal thought is explained non-detectively. The second is feature projective, whereby we attribute a feature of mind to an external object. The chapter argues that Hume's account is better than commentators have thought.
P. J. E. Kail
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199229505
- eISBN:
- 9780191710728
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199229505.003.0006
- Subject:
- Philosophy, History of Philosophy
This chapter examines two subjects. The first is Hume's account of the fictional idea of substantial self and the sense in which it is projective. The second is an attempt to locate the source of ...
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This chapter examines two subjects. The first is Hume's account of the fictional idea of substantial self and the sense in which it is projective. The second is an attempt to locate the source of Hume's famous disquiet with his account of personal identity. It is argued that an otherwise recalcitrant feature of Hume's texts becomes perspicuous when viewed from the perspective of realism about necessary connection.Less
This chapter examines two subjects. The first is Hume's account of the fictional idea of substantial self and the sense in which it is projective. The second is an attempt to locate the source of Hume's famous disquiet with his account of personal identity. It is argued that an otherwise recalcitrant feature of Hume's texts becomes perspicuous when viewed from the perspective of realism about necessary connection.
Frederick J. Newmeyer
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780199274338
- eISBN:
- 9780191706479
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199274338.003.0003
- Subject:
- Linguistics, Language Families
This chapter launches a frontal assault not just on the parametric approach to grammar, but also on the very idea that it is the job of Universal Grammar (UG) per se to account for typological ...
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This chapter launches a frontal assault not just on the parametric approach to grammar, but also on the very idea that it is the job of Universal Grammar (UG) per se to account for typological generalizations. It contrasts two approaches to typological variation in grammar within the general envelope of formal theory. In one approach, variation is captured largely by means of parameters, either directly tied to principles of UG or to functional projections provided by UG. In the other approach, variation is captured by means of extragrammatical principles. The chapter concludes that the second approach is better supported than the first.Less
This chapter launches a frontal assault not just on the parametric approach to grammar, but also on the very idea that it is the job of Universal Grammar (UG) per se to account for typological generalizations. It contrasts two approaches to typological variation in grammar within the general envelope of formal theory. In one approach, variation is captured largely by means of parameters, either directly tied to principles of UG or to functional projections provided by UG. In the other approach, variation is captured by means of extragrammatical principles. The chapter concludes that the second approach is better supported than the first.
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/9780198510581.003.0005
- Subject:
- Mathematics, Probability / Statistics
This chapter considers projection Procrustes where T is an orthonormal matrix P, which has an interpretation of rotating an orthogonal projection of the P 1-dimensional ...
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This chapter considers projection Procrustes where T is an orthonormal matrix P, which has an interpretation of rotating an orthogonal projection of the P 1-dimensional configuration X1 to match a P 2-dimensional configuration X2 . In the two-sided version, T1 and T2 may have Q columns where Q P 1 P 2; often, Q = min(P 1, P 2).Less
This chapter considers projection Procrustes where T is an orthonormal matrix P, which has an interpretation of rotating an orthogonal projection of the P 1-dimensional configuration X1 to match a P 2-dimensional configuration X2 . In the two-sided version, T1 and T2 may have Q columns where Q P 1 P 2; often, Q = min(P 1, P 2).
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/9780198510581.003.0006
- Subject:
- Mathematics, Probability / Statistics
This chapter considers oblique Procrustes problems where T is, or is a function of, a direction cosine matrix C. There are four possibilities and a new unified approach is developed, which determines ...
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This chapter considers oblique Procrustes problems where T is, or is a function of, a direction cosine matrix C. There are four possibilities and a new unified approach is developed, which determines the optimal direction of one axis conditional on the directions of the other axes. For all four methods, one iterates over all axes until convergence. All the cases have clear geometrical interpretations.Less
This chapter considers oblique Procrustes problems where T is, or is a function of, a direction cosine matrix C. There are four possibilities and a new unified approach is developed, which determines the optimal direction of one axis conditional on the directions of the other axes. For all four methods, one iterates over all axes until convergence. All the cases have clear geometrical interpretations.
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.
George Em Karniadakis and Spencer J. Sherwin
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.003.0004
- Subject:
- Mathematics, Numerical Analysis
This chapter completes the multi-dimensional formulation by explaining how the two- and three-dimensional expansions developed in Chapter 3 can be extended into a tessellation of multiple domains. ...
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This chapter completes the multi-dimensional formulation by explaining how the two- and three-dimensional expansions developed in Chapter 3 can be extended into a tessellation of multiple domains. These extensions are decomposed into three sections: local operations such as integration and differentiation; global operations such as the construction of global matrix systems; and pre- and post-processing issues such as boundary representation, high-order mesh generation, and particle tracking. A matrix formulation is introduced to help illustrate the algebraic systems that need to be constructed when computationally implementing the spectral/hp method. Formulation of both Galerkin and collocation projections are considered in this manner. The exercises at the end of the chapter include implementation of a two-dimensional spectral/hp element solver for a multi-element Galerkin projection.Less
This chapter completes the multi-dimensional formulation by explaining how the two- and three-dimensional expansions developed in Chapter 3 can be extended into a tessellation of multiple domains. These extensions are decomposed into three sections: local operations such as integration and differentiation; global operations such as the construction of global matrix systems; and pre- and post-processing issues such as boundary representation, high-order mesh generation, and particle tracking. A matrix formulation is introduced to help illustrate the algebraic systems that need to be constructed when computationally implementing the spectral/hp method. Formulation of both Galerkin and collocation projections are considered in this manner. The exercises at the end of the chapter include implementation of a two-dimensional spectral/hp element solver for a multi-element Galerkin projection.
John L. Bell
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568520
- eISBN:
- 9780191717581
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568520.003.0008
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter gives a brief account of real analysis in Boolean-valued models arising from measure algebras and algebras of projections on Hilbert space. The latter is applied, following Martin Davis, ...
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This chapter gives a brief account of real analysis in Boolean-valued models arising from measure algebras and algebras of projections on Hilbert space. The latter is applied, following Martin Davis, to provide a novel interpretation of the formalism of quantum theory.Less
This chapter gives a brief account of real analysis in Boolean-valued models arising from measure algebras and algebras of projections on Hilbert space. The latter is applied, following Martin Davis, to provide a novel interpretation of the formalism of quantum theory.
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/9780198566649.003.0006
- Subject:
- Mathematics, Applied Mathematics
Every inverse eigenvalue problem has a natural generalization to a least squares formulation, which sometimes does carry significant purposes in applications. The least squares approximation can be ...
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Every inverse eigenvalue problem has a natural generalization to a least squares formulation, which sometimes does carry significant purposes in applications. The least squares approximation can be applied to either the spectral constraint or the structural constraint. This chapter highlights some of the main notions when considering a least squares inverse problem, and describes a hybrid lift and projection method.Less
Every inverse eigenvalue problem has a natural generalization to a least squares formulation, which sometimes does carry significant purposes in applications. The least squares approximation can be applied to either the spectral constraint or the structural constraint. This chapter highlights some of the main notions when considering a least squares inverse problem, and describes a hybrid lift and projection method.
