Guo Shenyang
- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780195337518
- eISBN:
- 9780199864256
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195337518.003.0008
- Subject:
- Social Work, Research and Evaluation
This chapter presents some concluding thoughts from the author. It comments on criticisms of studies using survival analysis, and on directions for future development. It calls for the continuous ...
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This chapter presents some concluding thoughts from the author. It comments on criticisms of studies using survival analysis, and on directions for future development. It calls for the continuous development and improvement of approaches to handling clustered event times, the need to solidify the statistical theories of survival analysis by connecting the existing models (e.g., the Kaplan–Meier estimator and the Cox proportional hazards model) to the study of counting process and martingale theory, and a more innovative and wider application of the advanced survival models to solving research problems outside the field of biomedics.Less
This chapter presents some concluding thoughts from the author. It comments on criticisms of studies using survival analysis, and on directions for future development. It calls for the continuous development and improvement of approaches to handling clustered event times, the need to solidify the statistical theories of survival analysis by connecting the existing models (e.g., the Kaplan–Meier estimator and the Cox proportional hazards model) to the study of counting process and martingale theory, and a more innovative and wider application of the advanced survival models to solving research problems outside the field of biomedics.
Hidetoshi Nishimori and Gerardo Ortiz
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into ...
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Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.Less
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Steve Selvin
- Published in print:
- 2004
- Published Online:
- September 2009
- ISBN:
- 9780195172805
- eISBN:
- 9780199865697
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172805.001.0001
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
Analytic procedures suitable for the study of human disease are scattered throughout the statistical and epidemiologic literature. Explanations of their properties are frequently presented in ...
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Analytic procedures suitable for the study of human disease are scattered throughout the statistical and epidemiologic literature. Explanations of their properties are frequently presented in mathematical and theoretical language. This text provides a clear understanding of the statistical methods that are widely used in epidemiologic research without depending on advanced mathematical or statistical theory. By applying these methods to actual data, this book reveals the strengths and weaknesses of each analytic approach. The book combines techniques from the fields of statistics, biostatistics, demography, and epidemiology to present an overview that does not require computational details of the statistical techniques described. Throughout, the text contains illuminating discussions with new elements for this edition, including the analysis of multi-level categorical data and simple, intuitive arguments that exponential survival times cause the hazard function to be constant. There are also new applied examples to illustrate such topics as the pitfalls of proportional mortality data, the analysis of matched pair categorical data, and the age-adjustment of mortality rates based on statistical models. The most important new feature is a chapter on Poisson regression analysis. This essential statistical tool permits the multivariable analysis of rates, probabilities, and counts.Less
Analytic procedures suitable for the study of human disease are scattered throughout the statistical and epidemiologic literature. Explanations of their properties are frequently presented in mathematical and theoretical language. This text provides a clear understanding of the statistical methods that are widely used in epidemiologic research without depending on advanced mathematical or statistical theory. By applying these methods to actual data, this book reveals the strengths and weaknesses of each analytic approach. The book combines techniques from the fields of statistics, biostatistics, demography, and epidemiology to present an overview that does not require computational details of the statistical techniques described. Throughout, the text contains illuminating discussions with new elements for this edition, including the analysis of multi-level categorical data and simple, intuitive arguments that exponential survival times cause the hazard function to be constant. There are also new applied examples to illustrate such topics as the pitfalls of proportional mortality data, the analysis of matched pair categorical data, and the age-adjustment of mortality rates based on statistical models. The most important new feature is a chapter on Poisson regression analysis. This essential statistical tool permits the multivariable analysis of rates, probabilities, and counts.
A. C. Davison, Yadolah Dodge, and N. Wermuth (eds)
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566540
- eISBN:
- 9780191718038
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566540.001.0001
- Subject:
- Mathematics, Probability / Statistics
Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied ...
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Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied probability. This book contains summaries of the invited talks at a meeting held at the University of Neuchâtel in July 2004 to celebrate David Cox’s 80th birthday. The chapters describe current developments across a wide range of topics, ranging from statistical theory and methods, through applied probability and modelling, to applications in areas including finance, epidemiology, hydrology, medicine, and social science. The book contains chapters by numerous well-known statisticians. It provides a summary of current thinking across a wide front by leading statistical thinkers.Less
Sir David Cox is among the most important statisticians of the past half-century, making pioneering and highly influential contributions to a wide range of topics in statistics and applied probability. This book contains summaries of the invited talks at a meeting held at the University of Neuchâtel in July 2004 to celebrate David Cox’s 80th birthday. The chapters describe current developments across a wide range of topics, ranging from statistical theory and methods, through applied probability and modelling, to applications in areas including finance, epidemiology, hydrology, medicine, and social science. The book contains chapters by numerous well-known statisticians. It provides a summary of current thinking across a wide front by leading statistical thinkers.
Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0018
- Subject:
- Physics, Nuclear and Plasma Physics
This chapter derives formulas for gross sections of potential scattering, and shows their generalizations to nuclear reactions. A projection technique is introduced, which allows one to separate in ...
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This chapter derives formulas for gross sections of potential scattering, and shows their generalizations to nuclear reactions. A projection technique is introduced, which allows one to separate in the T-matrix the part which varies smoothly in energy from that for resonances. For the latter, general expressions are deduced which involve partial and total widths. Non-hermitean Hamiltonians for the optical model are obtained by applying suitable energy averages. The doorway mechanism is explained by which the intermediate structure in the resonances can be understood: it employs widths for decays to the continuum and to the compound states. The statistical theory is addressed, for which on the basis of general assumptions, analytic formulas for the fluctuating cross section are derived, which are in accord with N. Bohr's hypothesis of the independence of entrance and exit channels. The Weisskopf-Ewing relations and the Hauser-Feshbach theory are described, which involve branching ratios and formation probabilities. A critique of the statistical model is included.Less
This chapter derives formulas for gross sections of potential scattering, and shows their generalizations to nuclear reactions. A projection technique is introduced, which allows one to separate in the T-matrix the part which varies smoothly in energy from that for resonances. For the latter, general expressions are deduced which involve partial and total widths. Non-hermitean Hamiltonians for the optical model are obtained by applying suitable energy averages. The doorway mechanism is explained by which the intermediate structure in the resonances can be understood: it employs widths for decays to the continuum and to the compound states. The statistical theory is addressed, for which on the basis of general assumptions, analytic formulas for the fluctuating cross section are derived, which are in accord with N. Bohr's hypothesis of the independence of entrance and exit channels. The Weisskopf-Ewing relations and the Hauser-Feshbach theory are described, which involve branching ratios and formation probabilities. A critique of the statistical model is included.
Jakob Hohwy
- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780262029346
- eISBN:
- 9780262330213
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262029346.003.0012
- Subject:
- Philosophy, Moral Philosophy
Jakob Hohwy seeks to recover an approach to consciousness from a general theory of brain function, namely the prediction error minimization theory. The way this theory applies to mental and ...
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Jakob Hohwy seeks to recover an approach to consciousness from a general theory of brain function, namely the prediction error minimization theory. The way this theory applies to mental and developmental disorder demonstrates its relevance to consciousness. The resulting view is discussed in relation to a contemporary theory of consciousness, namely, the idea that conscious perception depends on Bayesian metacognition which is also supported by considerations of psychopathology. This Bayesian theory is first disconnected from the higher-order thought theory, and then, via a prediction error conception of action, connected instead to the global workspace theory. Considerations of mental and developmental disorder therefore show that a very general theory of brain function is relevant to explaining the structure of conscious perception. Furthermore, Hohwy argues that this theory can unify two contemporary approaches to consciousness in a move that seeks to elucidate the fundamental mechanism for the selection of representational content into consciousness.Less
Jakob Hohwy seeks to recover an approach to consciousness from a general theory of brain function, namely the prediction error minimization theory. The way this theory applies to mental and developmental disorder demonstrates its relevance to consciousness. The resulting view is discussed in relation to a contemporary theory of consciousness, namely, the idea that conscious perception depends on Bayesian metacognition which is also supported by considerations of psychopathology. This Bayesian theory is first disconnected from the higher-order thought theory, and then, via a prediction error conception of action, connected instead to the global workspace theory. Considerations of mental and developmental disorder therefore show that a very general theory of brain function is relevant to explaining the structure of conscious perception. Furthermore, Hohwy argues that this theory can unify two contemporary approaches to consciousness in a move that seeks to elucidate the fundamental mechanism for the selection of representational content into consciousness.
Charles F. Manski
- Published in print:
- 2019
- Published Online:
- May 2020
- ISBN:
- 9780691194738
- eISBN:
- 9780691195360
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691194738.003.0005
- Subject:
- Economics and Finance, Econometrics
This chapter considers reasonable decision making with sample data from randomized trials. It continues discussion of reasonable patient care under uncertainty. Because of its centrality to ...
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This chapter considers reasonable decision making with sample data from randomized trials. It continues discussion of reasonable patient care under uncertainty. Because of its centrality to evidence-based medicine, the chapter focuses on the use of sample trial data in treatment choice. Moreover, having already addressed identification, the chapter considers only statistical imprecision, as has been the case in the statistical literature on trials. The Wald (1950) development of statistical decision theory provides a coherent framework for use of sample data to make decisions. A body of recent research applies statistical decision theory to determine treatment choices that achieve adequate performance in all states of nature, in the sense of maximum regret. This chapter describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests.Less
This chapter considers reasonable decision making with sample data from randomized trials. It continues discussion of reasonable patient care under uncertainty. Because of its centrality to evidence-based medicine, the chapter focuses on the use of sample trial data in treatment choice. Moreover, having already addressed identification, the chapter considers only statistical imprecision, as has been the case in the statistical literature on trials. The Wald (1950) development of statistical decision theory provides a coherent framework for use of sample data to make decisions. A body of recent research applies statistical decision theory to determine treatment choices that achieve adequate performance in all states of nature, in the sense of maximum regret. This chapter describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests.
ANDRÉ AUTHIER
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0014
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are ...
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This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.Less
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.
A. Townsend Peterson, Jorge Soberón, Richard G. Pearson, Robert P. Anderson, Enrique Martínez-Meyer, Miguel Nakamura, and Miguel Bastos Araújo
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691136868
- eISBN:
- 9781400840670
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691136868.003.0016
- Subject:
- Biology, Ecology
This book has described a comprehensive framework for thinking about the geography and ecology of species distributions, arguing that such a framework is critical to further progress in the field of ...
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This book has described a comprehensive framework for thinking about the geography and ecology of species distributions, arguing that such a framework is critical to further progress in the field of ecological niches and distributions. To develop this framework, traditional concepts in ecology have been radically reworked. In this conclusion, some of the challenges for future work regarding ecological niche modeling are discussed, such as fully integrating the BAM diagram with central concepts of population biology and statistical theory; clarifying the notion of niche conservatism versus niche evolution as regards scenopoetic versus bionomic environmental dimensions; and improving the link between correlational and mechanistic approaches to estimating and understanding ecological niches. The book argues that careful conceptual thinking must be combined with detailed empirical exploration in order to address each of these challenges.Less
This book has described a comprehensive framework for thinking about the geography and ecology of species distributions, arguing that such a framework is critical to further progress in the field of ecological niches and distributions. To develop this framework, traditional concepts in ecology have been radically reworked. In this conclusion, some of the challenges for future work regarding ecological niche modeling are discussed, such as fully integrating the BAM diagram with central concepts of population biology and statistical theory; clarifying the notion of niche conservatism versus niche evolution as regards scenopoetic versus bionomic environmental dimensions; and improving the link between correlational and mechanistic approaches to estimating and understanding ecological niches. The book argues that careful conceptual thinking must be combined with detailed empirical exploration in order to address each of these challenges.
Niels E. Henriksen and Flemming Y. Hansen
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199203864
- eISBN:
- 9780191708251
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199203864.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where ...
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This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.Less
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.
James Davidson
- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.001.0001
- Subject:
- Economics and Finance, Econometrics
This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the ...
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This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.Less
This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.
Thomas D. Wickens
- Published in print:
- 2001
- Published Online:
- April 2010
- ISBN:
- 9780195092509
- eISBN:
- 9780199893812
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195092509.003.0001
- Subject:
- Psychology, Cognitive Psychology
This chapter introduces the basic detection task: an observer receives a stimulus (in any sensory domain) that may or may not contain a weak signal and must decide whether the signal is present or ...
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This chapter introduces the basic detection task: an observer receives a stimulus (in any sensory domain) that may or may not contain a weak signal and must decide whether the signal is present or not. The key elements of a mathematical model for this situation based on statistical decision theory are described.Less
This chapter introduces the basic detection task: an observer receives a stimulus (in any sensory domain) that may or may not contain a weak signal and must decide whether the signal is present or not. The key elements of a mathematical model for this situation based on statistical decision theory are described.
Jean Zinn-Justin
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed ...
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This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed point, the Gaussian fixed point, which is stable in dimension larger than four. It identifies the leading perturbation to the Gaussian fixed point in dimension = four. It discusses the possible existence of a non-Gaussian fixed point near dimension four.Less
This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed point, the Gaussian fixed point, which is stable in dimension larger than four. It identifies the leading perturbation to the Gaussian fixed point in dimension = four. It discusses the possible existence of a non-Gaussian fixed point near dimension four.
Giuseppe Mussardo
- Published in print:
- 2020
- Published Online:
- May 2020
- ISBN:
- 9780198788102
- eISBN:
- 9780191830082
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788102.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book is an introduction to statistical field theory, which is an important subject within theoretical physics and a field that has seen substantial progress in recent years. The book covers ...
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This book is an introduction to statistical field theory, which is an important subject within theoretical physics and a field that has seen substantial progress in recent years. The book covers fundamental topics in great detail and includes areas like conformal field theory, quantum integrability, S-matrices, braiding groups, Bethe ansatz, renormalization groups, Majorana fermions, form factors, the truncated conformal space approach and boundary field theory. It also provides an introduction to lattice statistical models. Many topics are discussed at a fairly advanced level but via a pedagogical approach. In particular, the book presents in a clear way non-perturbative methods of quantum field theories that have become decisive tools in many different areas of statistical and condensed matter physics, and which are currently an essential foundation of the working knowledge of a modern theoretical physicist.Less
This book is an introduction to statistical field theory, which is an important subject within theoretical physics and a field that has seen substantial progress in recent years. The book covers fundamental topics in great detail and includes areas like conformal field theory, quantum integrability, S-matrices, braiding groups, Bethe ansatz, renormalization groups, Majorana fermions, form factors, the truncated conformal space approach and boundary field theory. It also provides an introduction to lattice statistical models. Many topics are discussed at a fairly advanced level but via a pedagogical approach. In particular, the book presents in a clear way non-perturbative methods of quantum field theories that have become decisive tools in many different areas of statistical and condensed matter physics, and which are currently an essential foundation of the working knowledge of a modern theoretical physicist.
John von Neumann
Nicholas A. Wheeler (ed.)
- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780691178561
- eISBN:
- 9781400889921
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691178561.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, ...
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This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ] (∥φ∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ] is the state φ).Less
This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ] (∥φ∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ] is the state φ).
M. E. LINES and A. M. GLASS
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book looks at some concepts leading to a basic understanding of ferroelectricity. Depending on their geometry, crystals are commonly classified into seven systems: triclinic (the least ...
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This book looks at some concepts leading to a basic understanding of ferroelectricity. Depending on their geometry, crystals are commonly classified into seven systems: triclinic (the least symmetrical), monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. These systems can again be subdivided into point groups (crystal classes) according to their symmetry with respect to a point. There are 32 such crystal classes and 11 of them possess a centre of symmetry. Twenty of the 21 non-centric crystal classes exhibit electrical polarity when subjected to stress. The effect (and also its converse, the production of strain by application of an electric field) is linear, with reversal of the stimulus resulting in a reversal of the response, and is termed the piezoelectric effect. Topics in this book include statistical theory, soft modes, phase transitions, macroscopics and phenomenology, thermodynamics, structural crystallography, order-disorder ferroelectrics, nonlinear optics, and applications of ferroelectrics.Less
This book looks at some concepts leading to a basic understanding of ferroelectricity. Depending on their geometry, crystals are commonly classified into seven systems: triclinic (the least symmetrical), monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. These systems can again be subdivided into point groups (crystal classes) according to their symmetry with respect to a point. There are 32 such crystal classes and 11 of them possess a centre of symmetry. Twenty of the 21 non-centric crystal classes exhibit electrical polarity when subjected to stress. The effect (and also its converse, the production of strain by application of an electric field) is linear, with reversal of the stimulus resulting in a reversal of the response, and is termed the piezoelectric effect. Topics in this book include statistical theory, soft modes, phase transitions, macroscopics and phenomenology, thermodynamics, structural crystallography, order-disorder ferroelectrics, nonlinear optics, and applications of ferroelectrics.
Jean Zinn-Justin
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter studies a statistical field theory with an O(N) orthogonal symmetry and a (f2)2 interaction (denoted here by f = (f1, . . . , fN) the N-component field rather than s, in contrast with ...
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This chapter studies a statistical field theory with an O(N) orthogonal symmetry and a (f2)2 interaction (denoted here by f = (f1, . . . , fN) the N-component field rather than s, in contrast with previous chapters), at fixed dimension, in the framework of another approximation scheme, the N approaching the 8 limit. The results confirm the universal properties derived in the framework of the formal e-expansion.Less
This chapter studies a statistical field theory with an O(N) orthogonal symmetry and a (f2)2 interaction (denoted here by f = (f1, . . . , fN) the N-component field rather than s, in contrast with previous chapters), at fixed dimension, in the framework of another approximation scheme, the N approaching the 8 limit. The results confirm the universal properties derived in the framework of the formal e-expansion.
Steve Selvin
- Published in print:
- 2004
- Published Online:
- September 2009
- ISBN:
- 9780195172805
- eISBN:
- 9780199865697
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195172805.003.01
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
This chapter discusses rates and probabilities in epidemiological analysis. A rate is defined as an instantaneous measure of change per unit time. A rate calculated from epidemiologic data reflects ...
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This chapter discusses rates and probabilities in epidemiological analysis. A rate is defined as an instantaneous measure of change per unit time. A rate calculated from epidemiologic data reflects risk. A probability is another widely used measure of risk, distinct from a rate, but plays a similar role in epidemiologic analysis. Survival probabilities and hazard rates, statistical properties of probabilities calculated from mortality or disease data, and analysis of rates are discussed.Less
This chapter discusses rates and probabilities in epidemiological analysis. A rate is defined as an instantaneous measure of change per unit time. A rate calculated from epidemiologic data reflects risk. A probability is another widely used measure of risk, distinct from a rate, but plays a similar role in epidemiologic analysis. Survival probabilities and hazard rates, statistical properties of probabilities calculated from mortality or disease data, and analysis of rates are discussed.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0026
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
There is a rather subtle connection between quantum field theory and statistical physics, and this is explored here, where the concepts of imaginary time and the Wick rotation are introduced.
There is a rather subtle connection between quantum field theory and statistical physics, and this is explored here, where the concepts of imaginary time and the Wick rotation are introduced.
Jacob K. Goeree, Charles A. Holt, and Thomas R. Palfrey
- Published in print:
- 2016
- Published Online:
- January 2018
- ISBN:
- 9780691124230
- eISBN:
- 9781400880928
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691124230.003.0001
- Subject:
- Economics and Finance, History of Economic Thought
This introductory chapter provides an overview of the book's main themes. This book focuses on a class of general models, quantal response equilibrium (QRE) models, and its applications to economics, ...
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This introductory chapter provides an overview of the book's main themes. This book focuses on a class of general models, quantal response equilibrium (QRE) models, and its applications to economics, political science, and pure game theory. It aims to lay out for an informed reader the broad array of theoretical and experimental results based on QRE. It contains some genuinely new material, offering new directions and open issues that have not been explored in depth yet, as well as delving into a range of peripheral issues, tangencies, and more detailed data analysis than the typical journal-article format allows for. There is also a “how-to” aspect to the book, as it provides details and sample programs to show readers how to compute QRE and how to take it to the data.Less
This introductory chapter provides an overview of the book's main themes. This book focuses on a class of general models, quantal response equilibrium (QRE) models, and its applications to economics, political science, and pure game theory. It aims to lay out for an informed reader the broad array of theoretical and experimental results based on QRE. It contains some genuinely new material, offering new directions and open issues that have not been explored in depth yet, as well as delving into a range of peripheral issues, tangencies, and more detailed data analysis than the typical journal-article format allows for. There is also a “how-to” aspect to the book, as it provides details and sample programs to show readers how to compute QRE and how to take it to the data.
