Generalized Minimality


Book Description

This dissertation addresses the issue of the relation between deviant behavior in agrammatic Broca's aphasia and the theory of grammar. Agrammatic Broca's aphasics have particular difficulties comprehending semantically reversible sentences in which the canonical order of arguments have been inverted.




The Grammatical Nature of Minimal Structures


Book Description

An important development in linguistic models is the shift from construction-oriented rules to elementary computations that generate complex grammatical expressions. In this monograph, the author presents a systematic linguistic examination of an Italian aphasic speaker focusing on locality conditions as configurational restrictions on syntactic computations and on functional elements as fundamental triggers for computational processes. The explanatory framework which has been adopted considers the grammar to be an integral part of language processing; it is a derivational model compatible with well-known parsing strategies such as the minimal link condition and the minimal chain principle. This approach to aphasia supports the hypothesis that linguistic deficit is an impoverishment of procedural capacities that manifests itself in reduced syntactic structures. The book is recommended for advanced undergraduates and graduate students in neurolinguistics, psycholinguistics and theoretical linguistics, as well as medical researchers and speech therapists interested in the same fields. It can be adopted as principal text for the specific domain (syntax and aphasia).




Algorithms and Theory of Computation Handbook, Volume 2


Book Description

Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems.Along with updating and revising many of




Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem


Book Description

Plateau's problem is a scientific trend in modern mathematics that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem is concerned with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional space--perhaps the best-known example of such surfaces is provided by soap films. From the mathematical point of view, such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise in many applied problems in chemistry, physics, and also in nature. In applications, one finds not only two-dimensional but also multidimensional minimal surfaces that span fixed closed ``contours'' in some multidimensional Riemannian space. An exact mathematical statement of the problem of finding a surface of least area or volume requires the formulation of definitions of such fundamental concepts as a surface, its boundary, minimality of a surface, and so on. It turns out that there are several natural definitions of these concepts, which permit the study of minimal surfaces by different, and complementary, methods. In the framework of this comparatively small book it would be almost impossible to cover all aspects of the modern problem of Plateau, to which a vast literature has been devoted. However, this book makes a unique contribution to this literature, for the authors' guiding principle was to present the material with a maximum of clarity and a minimum of formalization. Chapter 1 contains historical background on Plateau's problem, referring to the period preceding the 1930s, and a description of its connections with the natural sciences. This part is intended for a very wide circle of readers and is accessible, for example, to first-year graduate students. The next part of the book, comprising Chapters 2-5, gives a fairly complete survey of various modern trends in Plateau's problem. This section is accessible to second- and third-year students specializing in physics and mathematics. The remaining chapters present a detailed exposition of one of these trends (the homotopic version of Plateau's problem in terms of stratified multivarifolds) and the Plateau problem in homogeneous symplectic spaces. This last part is intended for specialists interested in the modern theory of minimal surfaces and can be used for special courses; a command of the concepts of functional analysis is assumed.




Contemporary and Emergent Theories of Agrammatism


Book Description

Contemporary and Emergent Theories of Agrammatism provides an in-depth review of the previous five decades of research on agrammatism focusing specifically on work which has been informed by linguistic theory. The final chapters reflect the recent turning point in the conceptualization of the underlying causes of the impairments agrammatic individuals present with. The book includes chapters on impairments to grammatical morphemes the tree pruning and trace deletion hypotheses verb deficits in sentences, and as single words generalized minimality adaptation theory and slow syntax the involvement of discourse To facilitate student reading the writing is clear and accessible, and the book includes a glossary of unfamiliar terms. Contemporary and Emergent Theories of Agrammatism will be of great interest to advanced students and researchers in areas such as psychology of language, linguistics, neurolinguistics, aphasiology and speech and language therapy.




Complete and Compact Minimal Surfaces


Book Description

'Et moi ..., si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.




Minimal Surfaces II


Book Description

Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.




Minimal Surfaces I


Book Description

Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.




Minimal Surfaces from a Complex Analytic Viewpoint


Book Description

This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.




Merge in the Mind-Brain


Book Description

Cover -- Title -- Copyright -- Contents -- Original Publication Details -- Introduction -- Part I Merge in the Mind -- 1 Merge and Bare Phrase Structure -- 2 Merge and (A)symmetry -- 3 Generalized Search and Cyclic Derivation by Phase: A Preliminary Study -- 4 Merge, Labeling, and Projection -- 5 A Note on Weak vs. Strong Generation in Human Language -- 6 0-Search and 0-Merge -- Part II Merge in the Brain -- 7 The Cortical Dynamics in Building Syntactic Structures of Sentences: An MEG Study in a Minimal-Pair Paradigm -- 8 Syntactic Computation in the Human Brain: The Degree of Merger as a Key Factor -- 9 Computational Principles of Syntax in the Regions Specialized for Language: Integrating Theoretical Linguistics and Functional Neuroimaging -- Bibliography -- Author Index -- Subject Index