Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.
This book pursues a nonlinear approach in considering both chaotic dynamical models and agent-based simulation models of economics, as well as their dynamical behaviors. Three key concepts arising in this context are “nonlinearity,” “bounded rationality” and “heterogeneity,” which also make up the title of the book. Nonlinearity is the warp that runs throughout all models because systems that exhibit chaotic or other complex behavior in the absence of any exogenous disturbances are absolutely nonlinear. Bounded rationality constitutes the woof, because economic systems do not exhibit complex behavior if all agents are perfectly rational, as is usually assumed in neoclassical economics. Agents who are boundedly rational have to struggle to do their best with limited information and tend to adapt to their economic environment without knowing what is the best. Furthermore, the heterogeneity of firms or consumers dyes the fabric of complex dynamics woven from the warp and woof.
“The projects are easy (not to mention fun) . . . Beginners or experienced quilters will love 9-Patch Pizzazz. It’s a keeper for your quilt book library.” —Armchair Interviews They’ll never believe you made it in a day! Talk about bang for the buck: combining a special fabric with a few easy nine-patches yields captivating quilts ranging from sassy to sophisticated. You’ll get hooked on this technique! Judy provides sixteen different layouts for unlimited project potential. A beginner book without that “beginner look!” It’s been called the “potato chip quilt”—no one can make just one Use your favorite fabrics including large-scale, novelty, and panels “Most quilts only use three or four fabrics and only squares and rectangles are used in their design but the results look much more complex than that would suggest . . . The choice of fabrics and design guidelines at the beginning of the book are well illustrated, simple to comprehend and can be adapted to produce quilts of any size . . . The six projects given in the second part are for small quilts which can be used as large wall-hangings or lap quilts.” —Popular Patchwork “A great way to use large scale fabrics, and it’s also a design that leaves a lot of room for your own sense of color and artistic layouts.” —Quilting . . . for the Rest of Us
Magnetoencephalography (MEG) is an invaluable functional brain imaging technique that provides direct, real-time monitoring of neuronal activity necessary for gaining insight into dynamic cortical networks. Our intentions with this book are to cover the richness and transdisciplinary nature of the MEG field, make it more accessible to newcomers and experienced researchers and to stimulate growth in the MEG area. The book presents a comprehensive overview of MEG basics and the latest developments in methodological, empirical and clinical research, directed toward master and doctoral students, as well as researchers. There are three levels of contributions: 1) tutorials on instrumentation, measurements, modeling, and experimental design; 2) topical reviews providing extensive coverage of relevant research topics; and 3) short contributions on open, challenging issues, future developments and novel applications. The topics range from neuromagnetic measurements, signal processing and source localization techniques to dynamic functional networks underlying perception and cognition in both health and disease. Topical reviews cover, among others: development on SQUID-based and novel sensors, multi-modal integration (low field MRI and MEG; EEG and fMRI), Bayesian approaches to multi-modal integration, direct neuronal imaging, novel noise reduction methods, source-space functional analysis, decoding of brain states, dynamic brain connectivity, sensory-motor integration, MEG studies on perception and cognition, thalamocortical oscillations, fetal and neonatal MEG, pediatric MEG studies, cognitive development, clinical applications of MEG in epilepsy, pre-surgical mapping, stroke, schizophrenia, stuttering, traumatic brain injury, post-traumatic stress disorder, depression, autism, aging and neurodegeneration, MEG applications in cognitive neuropharmacology and an overview of the major open-source analysis tools.
A Publishers Weekly Best Book of the Year From an obesity and neuroscience researcher with a knack for engaging, humorous storytelling, The Hungry Brain uses cutting-edge science to answer the questions: why do we overeat, and what can we do about it? No one wants to overeat. And certainly no one wants to overeat for years, become overweight, and end up with a high risk of diabetes or heart disease--yet two thirds of Americans do precisely that. Even though we know better, we often eat too much. Why does our behavior betray our own intentions to be lean and healthy? The problem, argues obesity and neuroscience researcher Stephan J. Guyenet, is not necessarily a lack of willpower or an incorrect understanding of what to eat. Rather, our appetites and food choices are led astray by ancient, instinctive brain circuits that play by the rules of a survival game that no longer exists. And these circuits don’t care about how you look in a bathing suit next summer. To make the case, The Hungry Brain takes readers on an eye-opening journey through cutting-edge neuroscience that has never before been available to a general audience. The Hungry Brain delivers profound insights into why the brain undermines our weight goals and transforms these insights into practical guidelines for eating well and staying slim. Along the way, it explores how the human brain works, revealing how this mysterious organ makes us who we are.
This textbook is designed for a one-year graduate course in real algebraic geometry, with a particular focus on positivity and sums of squares of polynomials. The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski-Seidenberg projection theorem and transfer principle. Classical results such as Artin's solution to Hilbert's 17th problem and Hilbert's theorems on sums of squares of polynomials are presented in detail. Other features include careful introductions to the real spectrum and to the geometry of semialgebraic sets. The second part studies Archimedean positivstellensätze in great detail and in various settings, together with important applications. The techniques and results presented here are fundamental to contemporary approaches to polynomial optimization. Important results on sums of squares on projective varieties are covered as well. The last part highlights applications to semidefinite programming and polynomial optimization, including recent research on semidefinite representation of convex sets. Written by a leading expert and based on courses taught for several years, the book assumes familiarity with the basics of commutative algebra and algebraic varieties, as can be covered in a one-semester first course. Over 350 exercises, of all levels of difficulty, are included in the book.
An experimental approach to the study and teaching of color is comprised of exercises in seeing color action and feeling color relatedness before arriving at color theory.
