“…Topics include: •an intuitive introduction to ergodic theory •an introduction to the basic notions, constructions, and standard examples of topological dynamical systems •Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem •measure-preserving dynamical systems •von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem •strongly and weakly mixing systems •an examination of notions of isomorphism for measure-preserving systems •Markov operators, and the related concept of a factor of a measure-preserving system •compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition •an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai, and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory.…”
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“…Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises. …”
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“…Two appendices cover the basics of integration in the complex plane and linear algebra. A third appendix presents a basic Matlab toolkit for computer signal analysis. …”
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“…The only pre-requisite is algebra, so it can be taken by college freshman or sophomore students or even used in Advanced Placement courses in high school. …”
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“…Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.…”
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“…Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume. …”
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“…Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. …”
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“…The text opens with a foundational section on linear algebra, then covers a variety of advanced topics, including robust regression, model selection based on bias and efficiency, nonlinear models and optimization routines, generalized linear models, and survival and time-series analysis. …”
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“…This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.…”
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“…With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. …”
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“…Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.…”
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“…Concomitantly, various areas such as topology, functional analysis, abstract algebra, logic or probability, among others, experienced exceptional development. …”
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“…Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. …”
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“…In LSMMD-MA, we reformulate the MMD-MA optimization problem using linear algebra and solve it with KeOps, a CUDA framework for symbolic matrix computation in Python. …”
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“…We show that the algebra of cylinder functions in the Wasserstein Sobolev space [Formula: see text] generated by a finite and positive Borel measure [Formula: see text] on the [Formula: see text] -Wasserstein space [Formula: see text] on a complete and separable metric space [Formula: see text] is dense in energy. …”
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“…Consequently, numerous recent studies have focused on implementing efficient dense and sparse numerical linear algebra (NLA) kernels on FPGAs. To maximize the efficiency of these kernels, a key aspect is the exploration of analytical tools to comprehend the performance of the developments and guide the optimization process. …”
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“…Knowledge of some basic linear algebra and probability theory should make the review easier to follow, although it may still have something to offer to those readers whose mathematics may be more limited.…”
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“…We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. …”
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“…In this work, we employed enhanced Boolean algebra to model biofilm formation. RESULTS: The network obtained describes biofilm formation successfully, assuming - in accordance with the literature - that when the negative regulators (RscCD and EnvZ/OmpR) are off, the positive regulator (FlhDC) is on. …”
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