Bear and his friend Ben feel like they are living two lives: one, where native traditions--like long hair--are a crucial part of their identities, and the other, where indigenous expressions are mocked and treated with ignorance. When the boys encounter bullying because of the braids they wear, these two worlds collide. Seeking guidance from his beloved grandma, Bear confides his doubts and questions himself and his heritage. Bear's grandma knows about the strength it takes to overcome hardships, and with her help, Bear and Ben develop a plan to strengthen their connection to their roots while also bridging the gap between their schoolmates and their families. Seamlessly blending discussions of modern indigeneity and universal experiences of bullying and resilience, Bear's Braid is an essential and of-the-moment book that belongs on every bookshelf, and fits in easily with the classics of social justice children's literature.

Rivers are important agents of change that shape the Earth's surface and evolve through time in response to fluctuations in climate and other environmental conditions. They are fundamental in landscape development, and essential for water supply, irrigation, and transportation. This book provides a comprehensive overview of the geomorphological processes that shape rivers and that produce change in the form of rivers. It explores how the dynamics of rivers are being affected by anthropogenic change, including climate change, dam construction, and modification of rivers for flood control and land drainage. It discusses how concern about environmental degradation of rivers has led to the emergence of management strategies to restore and naturalize these systems, and how river management techniques work best when coordinated with the natural dynamics of rivers. This textbook provides an excellent resource for students, researchers, and professionals in fluvial geomorphology, hydrology, river science, and environmental policy.

Tutorial on the braid groups / Dale Rolfsen -- Simplicial objects and homotopy groups / Jie Wu -- Introduction to configuration spaces and their applications / Frederick R. Cohen -- Configuration spaces, braids, and robotics / Robert Ghrist -- Braids and magnetic fields / Mitchell A. Berger -- Braid group cryptography / David Garber

The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively.Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

In the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The homotopy methods of braid groups turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in Laughlin correlations. The real progress in understanding of structure and role of composite fermions in Hall system is provided. The crucial significance of carrier mobility apart from interaction in creation of the fractional quantum Hall effect (FQHE) is described and supported by recent graphene experiments. Recent progress in FQHE field including topological insulators and optical lattices was reviewed and commented in terms of braid group approach. The braid group methods are presented from more general point of view including proposition of pure braid group application.

This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids. The text uses the particular example of taffy pulling devices to represent pseudo-Anosov maps in practice. In addition, its final chapters also briefly discuss current applications in the emerging field of analyzing braids created from trajectory data. While written with beginning graduate students, advanced undergraduates, or practicing applied mathematicians in mind, the book is also suitable for pure mathematicians seeking real-world examples. Readers can benefit from some knowledge of homotopy and homology groups, but these concepts are briefly reviewed. Some familiarity with Matlab is also helpful for the computational examples.

Essays develop the elementary theory of Artin Braid groups geometrically and via homotopy theory, discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem and investigate polynomial covering maps.