When the new Young Mistress entered the palace, the Queen welcomed him. Among the dozen or so Young Mistress, the Queen treated Zhao Zhaoge as a thorn in her side. This time, the topic of the dance had already been decided. Zhao Chen had already performed the dance with the emperor's sincerity, and had been conferred the title of an everlasting existence. The Emperor was obsessed with Zhao Gang, but Zhao Gang seemed to have something on his mind. In order to let Zhao uncover his heart and pay tribute to his treasures, the emperor had drawn the mockery and ridicule of the civil and military officials. When the dynasty's Premier had the most opinions towards Zhao, he asked to be chased out of the palace, to be rude, and to provoke the Emperor's wrath. On the way back, Zhaoge also met with the Premier and had a dispute with him.
This book presents a mathematical analysis of the relationship between the cell biology idea of metabolic networks and the mathematical idea of polyhedral cones. Such cones can be used to describe the set of steady state admissible fluxes through metabolic networks, and consequently they have become important constructs in the field of microbiology. Fundamental objects called elementary flux modes (EFMs) can be described mathematically via convex cone concepts; the fundamental algorithm of this relationship is the Double Description method. While this method has an extended history in the field of computational geometry, this monograph addresses its relatively recent use in the context of cellular metabolism, providing an easy-to-read introduction to a central topic of mathematical systems biology. Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones addresses important topics in the mathematical description of metabolic activity that have not previously appeared in unified form and presents a careful study of the Double Description method in the context of metabolic analysis. It makes mathematical aspects of the material readily accessible to bioengineers and system biologists, and biological aspects readily accessible to mathematicians. This book is intended for readers from both mathematical and biological backgrounds, including mathematicians, engineers, and biologists interested in cell metabolism. It will also be helpful to mathematicians interested in applying computational geometry methods in computational biology as well as for systems biologists and modelers interested in the mathematical and algorithmic foundations of metabolic pathway analysis.
The book Control of Nonlinear Systems–Stability and Performance fills a crucial gap in the field of nonlinear control systems by providing a comprehensive yet accessible treatment of the subject. Unlike many existing texts that are either too complex for beginners or omit essential topics, this book strikes the right balance of mathematical rigor and practicality. The main objective of the book is to simplify and unify the existing techniques for designing and analyzing control systems for nonlinear systems. It aims to alleviate confusion and difficulty in understanding these methods, making it an invaluable resource for students, researchers, and practitioners in the field. By presenting the material in a tutorial manner, the book enhances the reader's understanding of the design and analysis of a wide range of control methods for nonlinear systems. The emphasis on stability and performance highlights the practical relevance of the concepts discussed in the book. Overall, Control of Nonlinear Systems–Stability and Performance is a valuable contribution to the field of nonlinear control systems. Its emphasis on practical applications and its accessible presentation make it an indispensable resource for engineers seeking to enhance their knowledge and skills in this important area of control theory.
The theme of the 2010 PCMI Summer School was Mathematics in Image Processing in a broad sense, including mathematical theory, analysis, computation algorithms and applications. In image processing, information needs to be processed, extracted and analyzed from visual content, such as photographs or videos. These demands include standard tasks such as compression and denoising, as well as high-level understanding and analysis, such as recognition and classification. Centered on the theme of mathematics in image processing, the summer school covered quite a wide spectrum of topics in this field. The summer school is particularly timely and exciting due to the very recent advances and developments in the mathematical theory and computational methods for sparse representation. This volume collects three self-contained lecture series. The topics are multi-resolution based wavelet frames and applications to image processing, sparse and redundant representation modeling of images and simulation of elasticity, biomechanics, and virtual surgery. Recent advances in image processing, compressed sensing and sparse representation are discussed.
In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics. A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.
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