Structural Additive Theory

Structural Additive Theory

Author: David J. Grynkiewicz

Publisher: Springer Science & Business Media

Published: 2013-05-30

Total Pages: 426

ISBN-13: 3319004166

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​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.


Book Synopsis Structural Additive Theory by : David J. Grynkiewicz

Download or read book Structural Additive Theory written by David J. Grynkiewicz and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

Structural Additive Theory

Structural Additive Theory

Author: David Grynkiewicz

Publisher: Springer

Published: 2013-06-01

Total Pages: 426

ISBN-13: 9783319004174

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​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.


Book Synopsis Structural Additive Theory by : David Grynkiewicz

Download or read book Structural Additive Theory written by David Grynkiewicz and published by Springer. This book was released on 2013-06-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

Additive Combinatorics

Additive Combinatorics

Author: Terence Tao

Publisher: Cambridge University Press

Published: 2006-09-14

Total Pages: 18

ISBN-13: 1139458345

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Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.


Book Synopsis Additive Combinatorics by : Terence Tao

Download or read book Additive Combinatorics written by Terence Tao and published by Cambridge University Press. This book was released on 2006-09-14 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Combinatorial and Additive Number Theory IV

Combinatorial and Additive Number Theory IV

Author: Melvyn B. Nathanson

Publisher: Springer Nature

Published: 2021-08-12

Total Pages: 445

ISBN-13: 3030679969

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This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.


Book Synopsis Combinatorial and Additive Number Theory IV by : Melvyn B. Nathanson

Download or read book Combinatorial and Additive Number Theory IV written by Melvyn B. Nathanson and published by Springer Nature. This book was released on 2021-08-12 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Combinatorial Number Theory and Additive Group Theory

Combinatorial Number Theory and Additive Group Theory

Author: Alfred Geroldinger

Publisher: Springer Science & Business Media

Published: 2009-04-15

Total Pages: 324

ISBN-13: 3764389613

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Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.


Book Synopsis Combinatorial Number Theory and Additive Group Theory by : Alfred Geroldinger

Download or read book Combinatorial Number Theory and Additive Group Theory written by Alfred Geroldinger and published by Springer Science & Business Media. This book was released on 2009-04-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Additive Combinatorics

Additive Combinatorics

Author: Bela Bajnok

Publisher: CRC Press

Published: 2018-04-27

Total Pages: 390

ISBN-13: 1351137611

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Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods. The book is divided into five parts which are compared to a meal. The first part is called Ingredients and includes relevant background information about number theory, combinatorics, and group theory. The second part, Appetizers, introduces readers to the book’s main subject through samples. The third part, Sides, covers auxiliary functions that appear throughout different chapters. The book’s main course, so to speak, is Entrees: it thoroughly investigates a large variety of questions in additive combinatorics by discussing what is already known about them and what remains unsolved. These include maximum and minimum sumset size, spanning sets, critical numbers, and so on. The final part is Pudding and features numerous proofs and results, many of which have never been published. Features: The first book of its kind to explore the subject Students of any level can use the book as the basis for research projects The text moves gradually through five distinct parts, which is suitable both for beginners without prerequisites and for more advanced students Includes extensive proofs of propositions and theorems Each of the introductory chapters contains numerous exercises to help readers


Book Synopsis Additive Combinatorics by : Bela Bajnok

Download or read book Additive Combinatorics written by Bela Bajnok and published by CRC Press. This book was released on 2018-04-27 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods. The book is divided into five parts which are compared to a meal. The first part is called Ingredients and includes relevant background information about number theory, combinatorics, and group theory. The second part, Appetizers, introduces readers to the book’s main subject through samples. The third part, Sides, covers auxiliary functions that appear throughout different chapters. The book’s main course, so to speak, is Entrees: it thoroughly investigates a large variety of questions in additive combinatorics by discussing what is already known about them and what remains unsolved. These include maximum and minimum sumset size, spanning sets, critical numbers, and so on. The final part is Pudding and features numerous proofs and results, many of which have never been published. Features: The first book of its kind to explore the subject Students of any level can use the book as the basis for research projects The text moves gradually through five distinct parts, which is suitable both for beginners without prerequisites and for more advanced students Includes extensive proofs of propositions and theorems Each of the introductory chapters contains numerous exercises to help readers

Advancing Organizational Theory in a Complex World

Advancing Organizational Theory in a Complex World

Author: Jane Qiu

Publisher: Routledge

Published: 2016-10-14

Total Pages: 246

ISBN-13: 1317387732

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While research in organisational studies has become increasingly rich and complex, organisation researchers are constantly challenged by the growing quest for theoretical advancement and innovation. To conduct theoretically rigorous and innovative research, contemporary researchers and students must develop in-depth understanding of the theoretical traditions and future prospects of their discipline. This book provides a collection of cutting-edge research topics in the field of organisation and management and offers advanced research findings that explore the frontiers of the field. Advancing Organisational Theory in a Complex World aims to provide deep insights into many influential organisational theories, including, contingency theory, institutional theory, stewardship theory, population ecology theory, ambidexterity, and complexity theory. All these theories have been developed to explain the external and internal factors that influence organisational survival and evolvement. We focus on these theories because they represent some of the most important ways into the modern literature, counter-points to the modern literature, and a breath of fresh air to some theories which should be better known. This book shows the fruitfulness and the continuous vitality of the theoretical field of organisational studies in a critical and innovative way. Finally, this book is dedicated to Professor Lex Donaldson who is a thought leader in the field. The field owed this to Lex, for his lifelong dedication to organisational studies and for his creation and advancement of theories that have inspired several generations of researchers.


Book Synopsis Advancing Organizational Theory in a Complex World by : Jane Qiu

Download or read book Advancing Organizational Theory in a Complex World written by Jane Qiu and published by Routledge. This book was released on 2016-10-14 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: While research in organisational studies has become increasingly rich and complex, organisation researchers are constantly challenged by the growing quest for theoretical advancement and innovation. To conduct theoretically rigorous and innovative research, contemporary researchers and students must develop in-depth understanding of the theoretical traditions and future prospects of their discipline. This book provides a collection of cutting-edge research topics in the field of organisation and management and offers advanced research findings that explore the frontiers of the field. Advancing Organisational Theory in a Complex World aims to provide deep insights into many influential organisational theories, including, contingency theory, institutional theory, stewardship theory, population ecology theory, ambidexterity, and complexity theory. All these theories have been developed to explain the external and internal factors that influence organisational survival and evolvement. We focus on these theories because they represent some of the most important ways into the modern literature, counter-points to the modern literature, and a breath of fresh air to some theories which should be better known. This book shows the fruitfulness and the continuous vitality of the theoretical field of organisational studies in a critical and innovative way. Finally, this book is dedicated to Professor Lex Donaldson who is a thought leader in the field. The field owed this to Lex, for his lifelong dedication to organisational studies and for his creation and advancement of theories that have inspired several generations of researchers.

A Magneton Theory of the Structure of the Atom

A Magneton Theory of the Structure of the Atom

Author: Alfred Locke Parson

Publisher:

Published: 1915

Total Pages: 90

ISBN-13:

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Book Synopsis A Magneton Theory of the Structure of the Atom by : Alfred Locke Parson

Download or read book A Magneton Theory of the Structure of the Atom written by Alfred Locke Parson and published by . This book was released on 1915 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Environmental Modelling

Environmental Modelling

Author: Keith Beven

Publisher: CRC Press

Published: 2010-02-25

Total Pages: 329

ISBN-13: 020393248X

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Uncertainty in the predictions of science when applied to the environment is an issue of great current relevance in relation to the impacts of climate change, protecting against natural and man-made disasters, pollutant transport and sustainable resource management. However, it is often ignored both by scientists and decision makers, or interpreted as a conflict or disagreement between scientists. This is not necessarily the case, the scientists might well agree, but their predictions would still be uncertain and knowledge of that uncertainty might be important in decision making. Environmental Modelling: An Uncertain Future? introduces students, scientists and decision makers to: the different concepts and techniques of uncertainty estimation in environmental prediction the philosophical background to different concepts of uncertainty the constraint of uncertainties by the collection of observations and data assimilation in real-time forecasting techniques for decision making under uncertainty. This book will be relevant to environmental modellers, practitioners and decision makers in hydrology, hydraulics, ecology, meteorology and oceanography, geomorphology, geochemistry, soil science, pollutant transport and climate change. A companion website for the book can be found at www.uncertain-future.org.uk


Book Synopsis Environmental Modelling by : Keith Beven

Download or read book Environmental Modelling written by Keith Beven and published by CRC Press. This book was released on 2010-02-25 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty in the predictions of science when applied to the environment is an issue of great current relevance in relation to the impacts of climate change, protecting against natural and man-made disasters, pollutant transport and sustainable resource management. However, it is often ignored both by scientists and decision makers, or interpreted as a conflict or disagreement between scientists. This is not necessarily the case, the scientists might well agree, but their predictions would still be uncertain and knowledge of that uncertainty might be important in decision making. Environmental Modelling: An Uncertain Future? introduces students, scientists and decision makers to: the different concepts and techniques of uncertainty estimation in environmental prediction the philosophical background to different concepts of uncertainty the constraint of uncertainties by the collection of observations and data assimilation in real-time forecasting techniques for decision making under uncertainty. This book will be relevant to environmental modellers, practitioners and decision makers in hydrology, hydraulics, ecology, meteorology and oceanography, geomorphology, geochemistry, soil science, pollutant transport and climate change. A companion website for the book can be found at www.uncertain-future.org.uk

Personality Research, Methods, and Theory

Personality Research, Methods, and Theory

Author: Patrick E. Shrout

Publisher: Psychology Press

Published: 2014-04-04

Total Pages: 386

ISBN-13: 1317781678

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Donald W. Fiske's professional life and collaborations are themselves a textbook in the development of the field of personality. From the field's early origins in personnel selection, rating accuracy, and psychotherapy outcomes, to its current status of theoretical and methodological maturity -- complete with mid-life crises -- the field has been fundamentally changed by Fiske's work, and the changes have influenced generations of scholars. This festschrift is a celebration of Fiske's impact, but not merely of his impact on the history of personality research. Instead, the volume focuses on ongoing debates and issues that have been framed or influenced by Fiske's work. The festschrift's three sections are organized around three themes in Fiske's writings -- themes that also correspond to three periods in his career. This volume examines current thinking about what can be known about personality, how constructs relevant to personality psychology are best measured, and how to approach specific research problems in personality and related fields. The contributors create an eminent cross-section of the development and current status of personality methods. In addition to Fiske's eminent contemporaries, the contributors to this volume include Fiske's former students, collaborators, and his two children, both of whom are behavioral scientists. The accomplishments of his students, colleagues, and children testifies to the range of psychologists who have benefited from his scholarly and practical wisdom. This collection is a valuable textbook for an advanced graduate course as well as appealing as a scholarly resource. Many of the contributors are renown psychological leaders who have made available their latest original thoughts. The book concludes with an essay by Fiske offering his perspective on the central themes: behavioral and social science metatheory, methods, and strategies.


Book Synopsis Personality Research, Methods, and Theory by : Patrick E. Shrout

Download or read book Personality Research, Methods, and Theory written by Patrick E. Shrout and published by Psychology Press. This book was released on 2014-04-04 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Donald W. Fiske's professional life and collaborations are themselves a textbook in the development of the field of personality. From the field's early origins in personnel selection, rating accuracy, and psychotherapy outcomes, to its current status of theoretical and methodological maturity -- complete with mid-life crises -- the field has been fundamentally changed by Fiske's work, and the changes have influenced generations of scholars. This festschrift is a celebration of Fiske's impact, but not merely of his impact on the history of personality research. Instead, the volume focuses on ongoing debates and issues that have been framed or influenced by Fiske's work. The festschrift's three sections are organized around three themes in Fiske's writings -- themes that also correspond to three periods in his career. This volume examines current thinking about what can be known about personality, how constructs relevant to personality psychology are best measured, and how to approach specific research problems in personality and related fields. The contributors create an eminent cross-section of the development and current status of personality methods. In addition to Fiske's eminent contemporaries, the contributors to this volume include Fiske's former students, collaborators, and his two children, both of whom are behavioral scientists. The accomplishments of his students, colleagues, and children testifies to the range of psychologists who have benefited from his scholarly and practical wisdom. This collection is a valuable textbook for an advanced graduate course as well as appealing as a scholarly resource. Many of the contributors are renown psychological leaders who have made available their latest original thoughts. The book concludes with an essay by Fiske offering his perspective on the central themes: behavioral and social science metatheory, methods, and strategies.