Journeys in the Mind: On the Origins and Structure of Subjectivity (2版)

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This book presents a systematic exploration of the subjective experience, keeping the investigation for the most part within a subjectivefirst person perspective through the use of “vignettes” as sources of data. It also uses incorporates a ‘"third person” objective approach when that is relevant. The goal of Journeys in the Mind is to capture and convey the operations of the mind: both the shared blueprints common to the elaboration of subjective knowledge as well as the immense fishnet ofpersonalized variables that operate in each mental phase-space and act upon the blueprints to continuously recategorize them into sets of coherent, dynamic outcomes, or mental landscapes. Dr. Sanguineti's meditative perspective holds the promise to enrich the way we understand the workings of the human mind.

Graph Theory and Additive Combinatorics: Exploring Structure and Randomness (1版)

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【簡介】 Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra. 【目錄】

Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms

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The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems. This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience. The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, stochastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.