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Author: Bertrand Eynard Publisher: Springer Science & Business Media ISBN: 3764387971 Category : Mathematics Languages : en Pages : 427
Book Description
The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.
Author: Bertrand Eynard Publisher: Springer Science & Business Media ISBN: 3764387971 Category : Mathematics Languages : en Pages : 427
Book Description
The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.
Author: Elaine M. Keohane Publisher: Elsevier Health Sciences ISBN: 0323549632 Category : Medical Languages : en Pages : 910
Book Description
**Selected for Doody's Core Titles® 2024 in Laboratory Technology** Make sure you are thoroughly prepared to work in a clinical lab. Rodak's Hematology: Clinical Principles and Applications, 6th Edition uses hundreds of full-color photomicrographs to help you understand the essentials of hematology. This new edition shows how to accurately identify cells, simplifies hemostasis and thrombosis concepts, and covers normal hematopoiesis through diseases of erythroid, myeloid, lymphoid, and megakaryocytic origins. Easy to follow and understand, this book also covers key topics including: working in a hematology lab; complementary testing areas such as flow cytometry, cytogenetics, and molecular diagnostics; the parts and functions of the cell; and laboratory testing of blood cells and body fluid cells. - UPDATED nearly 700 full-color illustrations and photomicrographs make it easier for you to visualize hematology concepts and show what you'll encounter in the lab, with images appearing near their mentions in the text to minimize flipping pages back and forth. - UPDATED content throughout text reflects latest information on hematology. - Instructions for lab procedures include sources of possible errors along with comments. - Hematology instruments are described, compared, and contrasted. - Case studies in each chapter provide opportunities to apply hematology concepts to real-life scenarios. - Hematology/hemostasis reference ranges are listed on the inside front and back covers for quick reference. - A bulleted summary makes it easy for you to review the important points in every chapter. - Learning objectives begin each chapter and indicate what you should achieve, with review questions appearing at the end. - A glossary of key terms makes it easy to find and learn definitions. - NEW! Additional content on cell structure and receptors helps you learn to identify these organisms. - NEW! New chapter on Introduction to Hematology Malignancies provides and overview of diagnostic technology and techniques used in the lab.
Author: Sergey Fedoroff Publisher: Springer Science & Business Media ISBN: 0896039021 Category : Medical Languages : en Pages : 366
Book Description
Sergey Fedoroff and Arleen Richardson extensively revise, update, and expand their best-selling and highly praised collection of readily reproducible neural tissue culture protocols. This 3rd edition adds 11 new chapters describing important new procedures for the isolation, growth, and characterization of neural stem cells and for the manipulation of glial progenitor cells, as well as are essential procedures for hippocampal and microglial slice cultures. Protocols for Neural Cell Culture: Third Edition is a richly augmented updating of the tried and tested laboratory procedures that have made earlier editions an indispensable reference and guide to neural cell culture and its disorders.
Author: Elaine M. Keohane Publisher: Elsevier Health Sciences ISBN: 0323239064 Category : Medical Languages : en Pages : 917
Book Description
Featuring hundreds of full-color photomicrographs, Rodak's Hematology: Clinical Principles and Applications, 5th Edition prepares you for a job in the clinical lab by exploring the essential aspects of hematology. It shows how to accurately identify cells, simplifies hemostasis and thrombosis concepts, and covers normal hematopoiesis through diseases of erythroid, myeloid, lymphoid, and megakaryocytic origins. This text also makes it easy to understand complementary testing areas such as flow cytometry, cytogenetics, and molecular diagnostics. Clinical lab experts Elaine Keohane, Larry Smith, and Jeanine Walenga also cover key topics such as working in a hematology lab, the parts and functions of the cell, and laboratory testing of blood cells and body fluid cells. Instructions for lab procedures include sources of possible errors along with comments. Case studies in each chapter provide opportunities to apply hematology concepts to real-life scenarios. Hematology instruments are described, compared, and contrasted. UPDATED, full-color illustrations make it easier to visualize hematology concepts and show what you'll encounter in the lab, with images appearing near their mentions in the text so you don't have to flip pages back and forth. Hematology/hemostasis reference ranges are listed on the inside front and back covers for quick reference. A bulleted summary makes it easy to review the important points in every chapter. Learning objectives begin each chapter and indicate what you should achieve, with review questions appearing at the end. A glossary of key terms makes it easy to find and learn definitions. NEW coverage of hematogones in the chapter on pediatric and geriatric hematology helps you identify these cells, a skill that is useful in diagnosing some pediatric leukemias. UPDATED chapter on molecular diagnostics covers new technology and techniques used in the lab.
Author: Bernadette F. Rodak Publisher: Elsevier Health Sciences ISBN: 1416030069 Category : Medical Languages : en Pages : 836
Book Description
Textbook explores key aspects of hematology from normal hematopoiesis through diseases of erythroid, myeloid, lymphoid, and megakaryocytic origin. Includes a revised section on hemostasis and thrombosis. Case studies and chapter summaries are included.
Author: Bertrand Eynard
Author: Bertrand Eynard
Author: Thomas, Arthur H., Company, Philadelphia
Author: Elaine M. Keohane
Author: Hermann Sahli
Author: Sergey Fedoroff
Author: Elaine M. Keohane
Author: Francisco Ciruela
Author: Bernadette F. Rodak
Author: James Franklin Messenger
Author: Thomas Breuer