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The second published collection based on a conference sponsored by the Metroplex Institute for Neural Dynamics -- the first is Motivation, Emotion, and Goal Direction in Neural Networks (LEA, 1992) -- this book addresses the controversy between symbolicist artificial intelligence and neural network theory. A particular issue is how well neural networks -- well established for statistical pattern matching -- can perform the higher cognitive functions that are more often associated with symbolic approaches. This controversy has a long history, but recently erupted with arguments against the abilities of renewed neural network developments. More broadly than other attempts, the diverse contributions presented here not only address the theory and implementation of artificial neural networks for higher cognitive functions, but also critique the history of assumed epistemologies -- both neural networks and AI -- and include several neurobiological studies of human cognition as a real system to guide the further development of artificial ones. Organized into four major sections, this volume: * outlines the history of the AI/neural network controversy, the strengths and weaknesses of both approaches, and shows the various capabilities such as generalization and discreetness as being along a broad but common continuum; * introduces several explicit, theoretical structures demonstrating the functional equivalences of neurocomputing with the staple objects of computer science and AI, such as sets and graphs; * shows variants on these types of networks that are applied in a variety of spheres, including reasoning from a geographic database, legal decision making, story comprehension, and performing arithmetic operations; * discusses knowledge representation process in living organisms, including evidence from experimental psychology, behavioral neurobiology, and electroencephalographic responses to sensory stimuli.
Ancient texts, once written by hand on parchment and papyrus, are now increasingly discoverable online in newly digitized editions, and their readers now work online as well as in traditional libraries. So what does this mean for how scholars may now engage with these texts, and for how the disciplines of biblical, Jewish and Christian studies might develop? These are the questions that contributors to this volume address. Subjects discussed include textual criticism, palaeography, philology, the nature of ancient monotheism, and how new tools and resources such as blogs, wikis, databases and digital publications may transform the ways in which contemporary scholars engage with historical sources. Contributors attest to the emergence of a conscious recognition of something new in the way that we may now study ancient writings, and the possibilities that this new awareness raises.
The Book of R is a comprehensive, beginner-friendly guide to R, the world’s most popular programming language for statistical analysis. Even if you have no programming experience and little more than a grounding in the basics of mathematics, you’ll find everything you need to begin using R effectively for statistical analysis. You’ll start with the basics, like how to handle data and write simple programs, before moving on to more advanced topics, like producing statistical summaries of your data and performing statistical tests and modeling. You’ll even learn how to create impressive data visualizations with R’s basic graphics tools and contributed packages, like ggplot2 and ggvis, as well as interactive 3D visualizations using the rgl package. Dozens of hands-on exercises (with downloadable solutions) take you from theory to practice, as you learn: –The fundamentals of programming in R, including how to write data frames, create functions, and use variables, statements, and loops –Statistical concepts like exploratory data analysis, probabilities, hypothesis tests, and regression modeling, and how to execute them in R –How to access R’s thousands of functions, libraries, and data sets –How to draw valid and useful conclusions from your data –How to create publication-quality graphics of your results Combining detailed explanations with real-world examples and exercises, this book will provide you with a solid understanding of both statistics and the depth of R’s functionality. Make The Book of R your doorway into the growing world of data analysis.
"The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix."--Jaquette.
This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
V.1. A.N. v.2. O.Z. Apendices and indexes.