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\"Practical Linear Algebra covers all the concepts in a traditional undergraduate-level linear algebra course, but with a focus on practical applications. The book develops these fundamental concepts in 2D and 3D with a strong emphasis on geometric understanding before presenting the general (n-dimensional) concept. The book does not employ a theorem/proof structure, and it spends very little time on tedious, by-hand calculations (e.g., reduction to row-echelon form), which in most job applications are performed by products such as Mathematica. Instead the book presents concepts through examples and applications. \"-- Provided by publisher.

Exploring Linear Algebra: Labs and Projects with MATLAB® is a hands-on lab manual that can be used by students and instructors in classrooms every day to guide the exploration of the theory and applications of linear algebra. For the most part, labs discussed in the book can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with a browser with Java capabilities) and MATLAB® coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way. Features: The book’s inquiry-based approach promotes student interaction Each chapter contains a project set which consists of application-driven projects emphasizing the chapter’s materials Adds a project component to any Linear Algebra course Explores many applications to a variety of fields that can promote research projects Employs MATLAB® to calculate and explore concepts and theories of linear algebra Preface ix; 1 Limits and Continuity 1; 2 Derivatives and Their Applications;3 Areas, Integrals, and Accumulation; 4 Applications of AntiderivativesMathematica Demonstrations and References; Index Dr. Crista Arangala holds a PhD in mathematics from the University of Cincinnati. She is now at Elon University in North Carolina teaching and researching in a variety of fields including mathematical modeling and service learning education. She was chosen to be a Fulbright Scholar in 2014. She runs a traveling science museum with her Elon University students in Kerala, India. She is also the author of Exploring Calculus: Labs and Projects with Mathematica published by CRC Press.

\"The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem\"-- Provided by publisher.

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations.Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

\"The Final Volume of the Groundbreaking Trilogy on Agent-Based ModelingIn this pioneering synthesis, Joshua Epstein introduces a new theoretical entity: Agent Zero. This software individual, or \"agent,\" is endowed with distinct emotional/affective, cognitive/deliberative, and social modules. Grounded in contemporary neuroscience, these internal components interact to generate observed, often far-from-rational, individual behavior. When multiple agents of this new type move and interact spatially, they collectively generate an astonishing range of dynamics spanning the fields of social conflict, psychology, public health, law, network science, and economics.Epstein weaves a computational tapestry with threads from Plato, Hume, Darwin, Pavlov, Smith, Tolstoy, Marx, James, and Dostoevsky, among others. This transformative synthesis of social philosophy, cognitive neuroscience, and agent-based modeling will fascinate scholars and students of every stripe. Epstein's computer programs are provided in the book or on its Princeton University Press website, along with movies of his \"computational parables.\" Agent Zero is a signal departure in what it includes (e.g., a new synthesis of neurally grounded internal modules), what it eschews (e.g., standard behavioral imitation), the phenomena it generates (from genocide to financial panic), and the modeling arsenal it offers the scientific community. For generative social science, Agent Zero presents a groundbreaking vision and the tools to realize it\"-- Provided by publisher.

In this study, we devised a method for the design of continuous phase-only holographic masks that map laser light to arbitrary target illumination patterns, which have a wide range of applications. In this method, the discrete gradient of a holographic mask is obtained by combining geometric optics and the linear assignment problem (LAP) methods, and then the entire problem is transformed into an integral problem with a discrete gradient. Finally, the least squares method is used to solve the gradient integral to complete the construction of a phase holographic mask. Due to its good continuity, this mask design method can also be applied to the production of diffractive optical elements. We discussed the effectiveness of this method by constructing two holographic masks with uniform illumination. At the same time, we successfully constructed an Einstein face holographic mask with non-uniform illumination using the LAP method for the first time. It is believed that this method can be widely used in illumination mode, ion capture and other directions.

We reviewed our clinical experience of using a computer-powered right angle linear cutter (CPRALC) for Collis–Nissen fundoplication (CNF) in three children with gastroesophageal reflux (GER) or failed Nissen associated with short esophagus. Case 1 was a 13-month-old female with persistent GER after type-C esophageal atresia repair. Case 2 was a 2-year-old female with dysphagia secondary to fundic wrap migration after laparoscopic Nissen. Case 3 was a 3-year-old male with post type-C esophageal atresia repair, dysphagia secondary to fundic wrap migration after open Nissen. All had short esophagus confirmed pre- or intra-operatively. After the esophagus was mobilized, Collis vertical gastroplasty was performed using CPRALC parallel to the lesser curve to elongate the esophagus. Nissen fundoplication was performed loosely around the neo-esophagus. There were no intra- or post-operative complications, although case 3 still has mild dysphagia, requiring dilatation. This is the first report of CNF performed using CPRALC in children. It would appear to be safe and effective for treating children with GER or failed Nissen associated with short esophagus.

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

A comprehensive introduction to the foundations of model checking, a fully automated technique for finding flaws in hardware and software; with extensive examples and both practical and theoretical exercises.