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From Classical Analysis to Analysis on Fractals: A Tribute to Robert Strichartz, Volume 1 (Applied and Numerical Harmonic Analysis)
by Patricia Alonso Ruiz Michael Hinz Kasso A. Okoudjou Luke G. Rogers Alexander TeplyaevOver the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.
From Classical to Modern Algebraic Geometry
by Gianfranco Casnati Alberto Conte Letterio Gatto Livia Giacardi Marina Marchisio Alessandro VerraThis book commemorates the 150th birthday of Corrado Segre, one of the founders of the Italian School of Algebraic Geometry and a crucial figure in the history of Algebraic Geometry. It is the outcome of a conference held in Turin, Italy. One of the book's most unique features is the inclusion of a previously unpublished manuscript by Corrado Segre, together with a scientific commentary. Representing a prelude to Segre's seminal 1894 contribution on the theory of algebraic curves, this manuscript and other important archival sources included in the essays shed new light on the eminent role he played at the international level. Including both survey articles and original research papers, the book is divided into three parts: section one focuses on the implications of Segre's work in a historic light, while section two presents new results in his field, namely Algebraic Geometry. The third part features Segre's unpublished notebook: Sulla Geometria Sugli Enti Algebrici Semplicemente Infiniti (1890-1891). This volume will appeal to scholars in the History of Mathematics, as well as to researchers in the current subfields of Algebraic Geometry.
From Classical to Modern Analysis
by Rinaldo B. SchinaziThis innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis.To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuity on metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.
From Colonization to Nation-State: The Political Demography of Indonesia
by Riwanto TirtosudarmoThis book examines the history of the political demography of Indonesia. Chronologically, the book begins by introducing the colonization program as a predecessor of transmigration program after independence. The transmigration program, Indonesia’s state policy on migration, is discussed at length in the book but other migration related issues are also presented to show the complex relationship between migration and other social, economic and political issues in Indonesia. In the final chapter, the book discusses the contemporary issues and challenges of disintegration that is facing Indonesia as a nation-state. The book ends with an epilog that shows Indonesia’s political demography challenges in the 21st Century.
From Communists to Foreign Capitalists: The Social Foundations of Foreign Direct Investment in Postsocialist Europe
by Nina BandeljFrom Communists to Foreign Capitalists explores the intersections of two momentous changes in the late twentieth century: the fall of Communism and the rise of globalization. Delving into the economic change that accompanied these shifts in central and Eastern Europe, Nina Bandelj presents a pioneering sociological treatment of the process of foreign direct investment (FDI). She demonstrates how both investors and hosts rely on social networks, institutions, politics, and cultural understandings to make decisions about investment, employing practical rather than rational economic strategies to deal with the true uncertainty that plagues the postsocialist environment. The book explores how eleven postsocialist countries address the very idea of FDI as an integral part of their market transition. The inflows of foreign capital after the collapse of Communism resulted not from the withdrawal of states from the economy, as is commonly expected, but rather from the active involvement of postsocialist states in institutionalizing and legitimizing FDI. Using a wide array of data sources, and combining a macro-level account of national variation in the liberalization to foreign capital with a micro-level account of FDI transactions in the decade following the collapse of Communism in 1989, the book reveals how social forces not only constrain economic transformations but also make them possible. From Communists to Foreign Capitalists is a welcome addition to the growing literature on the social processes that shape economic life.
From Complex Analysis to Operator Theory: In Memory of Sergey Naboko (Operator Theory: Advances and Applications #291)
by Malcolm Brown Fritz Gesztesy Pavel Kurasov Ari Laptev Barry Simon Gunter Stolz Ian WoodThis volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.
From Computational Logic to Computational Biology: Essays Dedicated to Alfredo Ferro to Celebrate His Scientific Career (Lecture Notes in Computer Science #14070)
by Domenico Cantone Alfredo PulvirentiAlfredo Ferro’s impact on information technology has traversed diverse domains, encompassing Computational Logic, Data Mining, Bioinformatics, and Complex Systems. After first studying Mathematics at the University of Catania, he received a Ph.D. in Computer Science from NYU in 1981, working under the supervision of Jacob Theodor (Jack) Schwartz. He returned to the University of Catania where he established the Computer Science undergraduate program, served as the coordinator of the Ph.D. program in Computer Science, cofounded the Ph.D. program in Biology, Human Genetics, and Bioinformatics, and retired as a full professor in 2021.Alfredo’s academic career as a computer scientist is characterized by two distinct research phases: Computational Logic until approximately 1995, followed by a notable focus on Data Mining and Bioinformatics. The contributions in this volume reflect the quality and the scope of his personal and collaborative successes.He also taught andinspired many excellent scientists. A pioneering initiative was to establish summer schools for Ph.D. students in 1989, leading to the so-called Lipari School, now the J.T. Schwartz International School for Scientific Research, where Alfredo continues to serve as director. This prestigious series includes schools focused on Computer Science, Complex Systems, and Computational Biology, featuring world-class scientists as lecturers and mentors.
From Computing to Computational Thinking
by Paul WangComputational Thinking (CT) involves fundamental concepts and reasoning, distilled from computer science and other computational sciences, which become powerful general mental tools for solving problems, increasing efficiency, reducing complexity, designing procedures, or interacting with humans and machines. An easy-to-understand guidebook, From Computing to Computational Thinking gives you the tools for understanding and using CT. It does not assume experience or knowledge of programming or of a programming language, but explains concepts and methods for CT with clarity and depth. Successful applications in diverse disciplines have shown the power of CT in problem solving. The book uses puzzles, games, and everyday examples as starting points for discussion and for connecting abstract thinking patterns to real-life situations. It provides an interesting and thought-provoking way to gain general knowledge about modern computing and the concepts and thinking processes underlying modern digital technologies.
From Concepts to Code: Introduction to Data Science
by Adam P. TashmanThe breadth of problems that can be solved with data science is astonishing, and this book provides the required tools and skills fot a broad audience. The reader takes a journey into the forms, uses, and abuses of data and models, and learns how to critically examine each step. Python coding and data analysis skills are built from the ground up, with no prior coding experience assumed. The necessary background in computer science, mathematics, and statistics is provided in an approachable manner.Each step of the machine learning lifecycle is discussed, from business objective planning to monitoring a model in production. This end-to-end approach supplies the broad view necessary to sidestep many of the pitfalls that can sink a data science project. Detailed examples are provided from a wide range of applications and fields, from fraud detection in banking to breast cancer classification in healthcare. The reader will learn the techniques to accomplish tasks that include predicting outcomes, explaining observations, and detecting patterns. Improper use of data and models can introduce unwanted effects and dangers to society. A chapter on model risk provides a framework for comprehensively challenging a model and mitigating weaknesses. When data is collected, stored, and used, it may misrepresent reality and introduce bias. Strategies for addressing bias are discussed. From Concepts to Code: Introduction to Data Science leverages content developed by the author for a full-year data science course suitable for advanced high school or early undergraduate students. This course is freely available and it includes weekly lesson plans.
From Current Algebra to Quantum Chromodynamics
by Tian Yu Cao"The advent of quantum chromodynamics (QCD) in the early 1970s was one of the most important events in twentieth-century science. This book examines the conceptual steps that were crucial to the rise of QCD, placing them in historical context against the background of debates that were ongoing between the bootstrap approach and composite modeling, and between mathematical and realistic conceptions of quarks. It explains the origins of QCD in current algebra and its development through high-energy experiments, model-building, mathematical analysis and conceptual synthesis. Addressing a range of complex physical, philosophical and historiographical issues in detail, this book will interest graduate students and researchers in physics and in the history and philosophy of science"--
From Data to Decisions in Music Education Research: Data Analytics and the General Linear Model Using R
by Brian C. WesolowskiFrom Data to Decisions in Music Education Research provides a structured and hands-on approach to working with empirical data in the context of music education research. Using step-by-step tutorials with in-depth examples of music education data, this book draws upon concepts in data science and statistics to provide a comprehensive framework for working with a variety of data and solving data-driven problems. All of the skills presented here use the R programming language, a free, open-source statistical computing and graphics environment. Using R enables readers to refine their computational thinking abilities and data literacy skills while facilitating reproducibility, replication, and transparency of data analysis in the field. The book offers: A clear and comprehensive framework for thinking about data analysis processes in a music education context. An overview of common data structures and data types used in statistical programming and data analytics. Techniques for cleaning, preprocessing, manipulating, aggregating, and mining data in ways that facilitate organization and interpretation. Methods for summarizing and visualizing data to help identify structures, patterns, and trends within data sets. Detailed applications of descriptive, diagnostic, and predictive analytics processes. Step-by-step code for all concepts and analyses. Direct access to all data sets and R script files through the accompanying eResource. From Data to Decisions in Music Education Research offers a reference "cookbook" of code and programming recipes written with the graduate music education student in mind and breaks down data analysis processes and skills in an approachable fashion. It can be used across a wide range of graduate music education courses that rely on the application of empirical data analyses and will be useful to all music education scholars and professionals seeking to enhance their use of quantitative data.
From Data to Decisions in Music Education Research: Data Analytics and the General Linear Model Using R
by Brian C. WesolowskiFrom Data to Decisions in Music Education Research provides a structured and hands-on approach to working with empirical data in the context of music education research. Using step-by-step tutorials with in-depth examples of music education data, this book draws upon concepts in data science and statistics to provide a comprehensive framework for working with a variety of data and solving data-driven problems.All of the skills presented here use the R programming language, a free, open-source statistical computing and graphics environment. Using R enables readers to refine their computational thinking abilities and data literacy skills while facilitating reproducibility, replication, and transparency of data analysis in the field. The book offers: A clear and comprehensive framework for thinking about data analysis processes in a music education context. An overview of common data structures and data types used in statistical programming and data analytics. Techniques for cleaning, preprocessing, manipulating, aggregating, and mining data in ways that facilitate organization and interpretation. Methods for summarizing and visualizing data to help identify structures, patterns, and trends within data sets. Detailed applications of descriptive, diagnostic, and predictive analytics processes. Step-by-step code for all concepts and analyses. Direct access to all data sets and R script files through the accompanying eResource. From Data to Decisions in Music Education Research offers a reference "cookbook" of code and programming recipes written with the graduate music education student in mind and breaks down data analysis processes and skills in an approachable fashion. It can be used across a wide range of graduate music education courses that rely on the application of empirical data analyses and will be useful to all music education scholars and professionals seeking to enhance their use of quantitative data.
From Data To Profit: How Businesses Leverage Data to Grow Their Top and Bottom Lines
by Vin VashishtaTransform your company’s AI and data frameworks to unlock the true power of disruptive new tech In From Data to Profit: How Businesses Leverage Data to Grow Their Top and Bottom Lines, accomplished entrepreneur and AI strategist Vineet Vashishta delivers an engaging and insightful new take on making the most of data, artificial intelligence, and technology at your company. You’ll learn to change the culture, strategy, structure, and operational framework of your company to take full advantage of disruptive advances in tech. The author explores fascinating work being undertaken by firms in the real world, as well as high-value use cases and innovative projects and products made possible by realigning organizational frameworks using the capabilities of new technologies. He explains how to get everyone in your company on the same page, following a single framework, in a way that ensures individual departments get what they want and need. You’ll learn to outline a comprehensive technical vision and purpose that respects departmental autonomy over their core competencies while guaranteeing that they all get the tools they need to make technology their partner. You’ll also discover why firms that have adopted a holistic strategy toward AI and data have enjoyed results far beyond those experienced by those that have taken a piecemeal approach. From Data to Profit demonstrates the proper role of the CEO during an intensive transformation: one of maintaining culture during the change. It offers advice for organizational change, including the 3-Phase Data Organizational Development Framework, the Core Rim 3 Main People Groups Framework, and the way to implement new roles for a Chief Digital Officer and Technical Strategist. Perfect for data professionals, data organizational leaders, and data product and process owners, From Data to Profit will also benefit executives, managers, and other business leaders seeking hands-on advice for digital transformation at their firms.
From Death to Birth: Mortality Decline and Reproductive Change
by Committee on PopulationThe last 35 years or so have witnessed a dramatic shift in the demography of many developing countries. Before 1960, there were substantial improvements in life expectancy, but fertility declines were very rare. Few people used modern contraceptives, and couples had large families. Since 1960, however, fertility rates have fallen in virtually every major geographic region of the world, for almost all political, social, and economic groups. What factors are responsible for the sharp decline in fertility? What role do child survival programs or family programs play in fertility declines? Casual observation suggests that a decline in infant and child mortality is the most important cause, but there is surprisingly little hard evidence for this conclusion. The papers in this volume explore the theoretical, methodological, and empirical dimensions of the fertility-mortality relationship. It includes several detailed case studies based on contemporary data from developing countries and on historical data from Europe and the United States.
From Differential Geometry to Non-commutative Geometry and Topology
by Neculai S. TelemanThis book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
From Domination to Coloring: Stephen Hedetniemi's Graph Theory and Beyond (SpringerBriefs in Mathematics)
by Gary Chartrand Teresa W. Haynes Michael A. Henning Ping ZhangThis book is in honor of the 80th birthday of Stephen Hedetniemi. It describes advanced material in graph theory in the areas of domination, coloring, spanning cycles and circuits, and distance that grew out of research topics investigated by Stephen Hedetniemi. The purpose of this book is to provide background and principal results on these topics, along with same related problems and conjectures, for researchers in these areas. The most important features deal with material, results, and problems that researchers may not be aware of but may find of interest. Each chapter contains results, methods and information that will give readers the necessary background to investigate each topic in more detail.
From Electrons to Elephants and Elections: Exploring the Role of Content and Context (The Frontiers Collection)
by Shyam Wuppuluri Ian StewartThis highly interdisciplinary book, covering more than six fields, from philosophy and sciences all the way up to the humanities and with contributions from eminent authors, addresses the interplay between content and context, reductionism and holism and their meeting point: the notion of emergence. Much of today’s science is reductionist (bottom-up); in other words, behaviour on one level is explained by reducing it to components on a lower level. Chemistry is reduced to atoms, ecosystems are explained in terms of DNA and proteins, etc. This approach fails quickly since we can’t cannot extrapolate to the properties of atoms solely from Schrödinger's equation, nor figure out protein folding from an amino acid sequence or obtain the phenotype of an organism from its genotype. An alternative approach to this is holism (top-down). Consider an ecosystem or an organism as a whole: seek patterns on the same scale. Model a galaxy not as 400 billion-point masses (stars) but as an object in its own right with its own properties (spiral, elliptic). Or a hurricane as a structured form of moist air and water vapour. Reductionism is largely about content, whereas holistic models are more attuned to context. Reductionism (content) and holism (context) are not opposing philosophies — in fact, they work best in tandem. Join us on a journey to understand the multifaceted dialectic concerning this duo and how they shape the foundations of sciences and humanities, our thoughts and, the very nature of reality itself.
From Euclidean to Hilbert Spaces: Introduction to Functional Analysis and its Applications
by Edoardo ProvenziFrom Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces.The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations.The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.
From Experimental Network to Meta-analysis: Methods and Applications with R for Agronomic and Environmental Sciences
by David Makowski François Piraux François BrunThis book has been designed as a methodological guide and shows the interests and limitations of different statistical methods to analyze data from experimental networks and to perform meta-analyses. It is intended for engineers, students and researchers involved in data analysis in agronomy and environmental science.
From Fourier Analysis and Number Theory to Radon Transforms and Geometry
by Hershel M. Farkas Robert C. Gunning Marvin I. Knopp B. A. TaylorA memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis's contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore. A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.
From Fourier Analysis to Wavelets
by Jonas Gomes Luiz VelhoThis text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
From Frechet Differentials to Firing Tables: The Scope and Sources of Gilbert Ames Bliss' Contributions to World War I Era Ballistics
by Alan GluchoffThis monograph explores the history of the contribution to ballistics by the American mathematician Gilbert Ames Bliss during World War I. Drawing on the then-evolving calculus of variations, Bliss pioneered a novel technique for solving the problem of differential variations in ballistic trajectory. Called Bliss’ adjoint method, this technique was both hailed and criticized at the time: it was seen as both a triumphant application of pure mathematics to an applied problem and as a complex intrusion of higher mathematics into the jobs of military personnel not particularly interested in these matters. Although he received much praise immediately after the War, the details of Bliss’ work, its furthering of pure mathematical thought, and its absorption into mainstream ballistic work and instruction have never been adequately examined. Gluchoff explores the mathematics of Bliss’ work and the strands from which his technique was developed. He then documents the efforts to make the adjoint method accessible to military officers and the conflicts that emerged as a result both between mathematicians and officers and among mathematicians themselves. The eventual absorption of the adjoint method into range firing table construction is considered by looking at later technical books which incorporate it, and, finally, its influence on the ongoing development of functional calculus is detailed. From Frechet Differentials to Firing Tables will appeal to historians of mathematics, physics, engineering, and warfare, as well as current researchers, professors, and students in these areas.
From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931
by Jean Van HeijenoortThe fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege’s Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory. <p><p> Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and König mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Löwenheim’s theorem, and he and Fraenkel amend Zermelo’s axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gödel, including the latter’s famous incompleteness paper. <p> Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.
From Galileo to Modern Economics: The Italian Origins of Econophysics
by Gianfranco TussetEmpirical laws are rare in economics. This book describes efforts to anchor economic knowledge to invariant empirical laws. It links 17th and 18th century Galilean monetary economists to econophysics, a field that emerged in the mid-1990s. This virtual journey from past to present is charted by episodes on aggregates and empirical primacy. It includes the virtually unknown story of 19th century scholars who, by searching for a stricter mathematical approach, paved the way to an ‘engineering’ view of economics. Then there are celebrities like Pareto and his first empirical law governing the distribution of wealth. Pareto and Amoroso sparked a debate on the skewed distribution that spanned decades, ranging from finance to market transformations, to econophysics, with its concepts and tools inherited from statistical physics. The last stage of the journey goes through econophysics and the recent gradual advances it has made, which show how its position vis-à-vis economics has been changing.
From Generation to Generation: The Health and Well-Being of Children in Immigrant Families
by Adjustment of Immigrant Families Committee on the HealthImmigrant children and youth are the fastest growing segment of the U.S. population, and so their prospects bear heavily on the well-being of the country. However, relevant public policy is shaped less by informed discussion than by politicized contention over welfare reform and immigration limits.From Generation to Generation explores what we know about the development of white, black, Hispanic, and Asian children and youth from numerous countries of origin. Describing the status of immigrant children and youth as "severely understudied," the committee both draws on and supplements existing research to characterize the current status and outlook of immigrant children.The book discusses the many factors--family size, fluency in English, parent employment, acculturation, delivery of health and social services, and public policies--that shape the outlook for the lives of these children and youth. The committee makes recommendations for improved research and data collection designed to advance knowledge about these children and, as a result, their visibility in current policy debates.