Diagrams 2000 is dedicated to the memory of Jon Barwise. Diagrams 2000 was the ?rst event in a new interdisciplinary conference series on the Theory and Application of Diagrams. It was held at the University of Edinburgh, Scotland, September 1-3, 2000. Driven by the pervasiveness of diagrams in human communication and by the increasing availability of graphical environments in computerized work, the study of diagrammatic notations is emerging as a research ?eld in its own right. This development has simultaneously taken place in several scienti?c disciplines, including, amongst others: cognitive science, arti?cial intelligence, and computer science. Consequently, a number of di?erent workshop series on this topic have been successfully organized during the last few years: Thinking with Diagrams, Theory of Visual Languages, Reasoning with Diagrammatic Representations, and Formalizing Reasoning with Visual and Diagrammatic Representations. Diagrams are simultaneously complex cognitive phenonema and sophis- cated computational artifacts. So, to be successful and relevant the study of diagrams must as a whole be interdisciplinary in nature. Thus, the workshop series mentioned above decided to merge into Diagrams 2000, as the single - terdisciplinary conference for this exciting new ?eld. It is intended that Diagrams 2000 should become the premier international conference series in this area and provide a forum with su?cient breadth of scope to encompass researchers from all academic areas who are studying the nature of diagrammatic representations and their use by humans and in machines.

The Boundary Theory of Phase Diagrams and Its Application -- Rules for Phase Diagram Construction with Phase Regions and Their Boundaries presents a novel theory of phase diagrams. Thoroughly revised on the basis of the Chinese edition and rigorously reviewed, this book inspects the general feature and structure of phase diagrams, and reveals that there exist actually two categories of boundaries. This innovative boundary theory has solved many difficulties in understanding phase diagrams, and also finds its application in constructing multi-component phase diagrams or in calculating high-pressure phase diagrams. Researchers and engineers as well as graduate students in the areas of chemistry, metallurgy and materials science will benefit from this book. Prof. Muyu Zhao was the recipient of the 1998 Prize for Progress in Science and Technology (for his work on the boundary theory of phase diagrams) awarded by the National Commission of Education, China, and many other prizes.

Finite functions (in particular, Boolean functions) play a fundamental role in computer science and discrete mathematics. This book describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. The representation size of important and selected functions is estimated, upper and lower bound techniques are studied, efficient algorithms for operations on these representations are presented, and the limits of those techniques are considered. This book is the first comprehensive description of theory and applications. Research areas like complexity theory, efficient algorithms, data structures, and discrete mathematics will benefit from the theory described in this book. The results described within have applications in verification, computer-aided design, model checking, and discrete mathematics. This is the only book to investigate the representation size of Boolean functions and efficient algorithms on these representations.

Winner of the 2007 Pfizer Prize from the History of Science Society. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process. Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calculational skills, David Kaiser frames his story around the crafting and stabilizing of the basic tools in the physicist's kit—thus offering the first book to follow the diagrams once they left Feynman's hands and entered the physics vernacular.

This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.

This book constitutes the refereed proceedings of the 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, held in Tallinn, Estonia, in August 2020.* The 20 full papers and 16 short papers presented together with 18 posters were carefully reviewed and selected from 82 submissions. The papers are organized in the following topical sections: diagrams in mathematics; diagram design, principles, and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; logic and diagrams; and posters. *The conference was held virtually due to the COVID-19 pandemic. The chapters ‘Modality and Uncertainty in Data Visualization: A Corpus Approach to the Use of Connecting Lines,’ ‘On Effects of Changing Multi-Attribute Table Design on Decision Making: An Eye Tracking Study,’ ‘Truth Graph: A Novel Method for Minimizing Boolean Algebra Expressions by Using Graphs,’ ‘The DNA Framework of Visualization’ and ‘Visualizing Curricula’ are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021. The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation systems; analysis of diagrams; diagrams and computation; cognitive analysis; diagrams as structural tools; formal diagrams; and understanding thought processes. 10 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This book constitutes the refereed proceedings of the 8th International Conference on the Theory and Application of Diagrams, Diagrams 2014, held in Melbourne, VIC, Australia in July/August 2014. The 15 revised full papers and 9 short papers presented together with 6 posters were carefully reviewed and selected from 40 submissions. The papers have been organized in the following topical sections: diagram layout, diagram notations, diagramming tools, diagrams in education, empirical studies and logic and diagrams.

For someone with a hammer the whole world looks like a nail. Within the last 10-13 years Binar·y Decision Diagmms (BDDs) have become the state-of-the-art data structure in VLSI CAD for representation and ma nipulation of Boolean functions. Today, BDDs are widely used and in the meantime have also been integrated in commercial tools, especially in the area of verijication and synthesis. The interest in BDDs results from the fact that the data structure is generally accepted as providing a good compromise between conciseness of representation and efficiency of manipulation. With increasing number of applications, also in non CAD areas, classical methods to handle BDDs are being improved and new questions and problems evolve and have to be solved. The book should help the reader who is not familiar with BDDs (or DDs in general) to get a quick start. On the other hand it will discuss several new aspects of BDDs, e.g. with respect to minimization and implementation of a package. This will help people working with BDDs (in industry or academia) to keep informed about recent developments in this area.

A renewal of immanent metaphysics through diagrammatic methods and the tools of category theorySpinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuzes philosophy of difference in conjunction with the formal operations of category theory. Category theory reveals deep structural connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work. Gangle introduces the methods of category theory from a philosophical and diagrammatic perspective, allowing philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.