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"A mathematical explication of Chomsky's Merge theory of syntax"--

A mathematical formalization of Chomsky’s theory of Merge in generative linguistics. The Minimalist Program advanced by Noam Chomsky thirty years ago, focusing on the biological nature of human language, has played a central role in our modern understanding of syntax. One key to this program is the notion that the hierarchical structure of human language syntax consists of a single operation Merge. For the first time, Mathematical Structure of Syntactic Merge presents a complete and precise mathematical formalization of Chomsky’s most recent theory of Merge. It both furnishes a new way to explore Merge’s important linguistic implications clearly while also laying to rest any fears that the Minimalist framework based on Merge might itself prove to be formally incoherent. In this book, Matilde Marcolli, Noam Chomsky, and Robert C. Berwick prove that Merge can be described as a very particular kind of highly structured algebra. Additionally, the book shows how Merge can be placed within a consistent framework that includes both a syntactic-semantic interface that realizes Chomsky’s notion of a conceptual-intentional interface, and an externalization system that realizes language-specific constraints. The syntax-semantics interface encompasses many current semantical theories and offers deep insights into the ways that modern “large language models” work, proving that these do not undermine in any way the scientific theories of language based on generative grammar.

Marcolli Matilde: Mathematical Structure
of Syntactic Merge

Mathematical Structure of Syntactic Merge

An Algebraic Model for Generative Linguistics

Contents List of Figures xiii List of Tables xv 0 Minimalism and Merge: Introduction 1 The Mathematical Structure of Syntactic Merge 2 Minimalism Old and New: a Hopf Algebra Comparison 3 The Syntax-Semantics Interface: an Algebraic Model 4 Summary of Mathematical Concepts Bibliography Index

A Hybrid Texas Style Approach

An Introduction to Point-Set Topology

A Neuroscientific Approach

The Bilingual Brain

Quantitative Biology

Bloomsbury Studies in Systemic Functional Linguistics

Modelling Paradigmatic Relations for Language Description in Systemic Functional Linguistics

A Practical Guide to System Networks

This book is the first one that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. They develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called zeroing dynamics solves time-varying problems. Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Zeroing Dynamics, Gradient Dynamics, and Newton Iterations

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

This book covers a broad range of questions related to the importance of cell geometry in many areas, including nuclear positioning, chromosome dynamics, cytoskeletal remodeling, tissue patterning, cell-matrix and multicellular contacts. It also addresses medical implications, from its implication in the development of tumors to its role in fibrosis. Together, the chapters in this book will highlight current knowledge and modern approaches to investigating the biophysical design principles underlying key biological functions, with the overall goal of elucidating the connections between cell geometry and nuclear mechanics.

This book covers a broad range of questions related to the importance of cell geometry in many areas, including nuclear positioning, chromosome dynamics, cytoskeletal remodeling, tissue patterning, cell-matrix and multicellular contacts. It also addresses medical implications, from its implication in the development of tumors to its role in fibrosis. Together, the chapters in this book will highlight current knowledge and modern approaches to investigating the biophysical design principles underlying key biological functions, with the overall goal of elucidating the connections between cell geometry and nuclear mechanics.

Cell Geometry

This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications.&nbsp;Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
&nbsp;

This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications.&nbsp;Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
&nbsp;

With Applications to Oil and Gas Development

Introduction to Continuum Mechanics

De Gruyter Studies in Mathematical Physics

Mirror symmetry is one of the most exciting ideas in mathematics to emerge in the last two decades. It was introduced in physics as a duality between superconformal field theories. This book discusses this rapidly developing aspect of string theory.

Laurent Polynomials in Mirror Symmetry

De Gruyter Series in Applied and Numerical Mathematics

Advanced Computational Approaches for Rarefied Flows

Beyond Navier-Stokes

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence empowers qualitative and mixed methods researchers in the data science movement by offering no-code, cost-free software access so that they can apply cutting-edge and innovative methods to synthetize qualitative data. The book builds on the idea that qualitative and mixed methods researchers should not have to learn to code to benefit from rigorous open-source, cost-free software that uses artificial intelligence, machine learning, and data visualization tools-just as people do not need to know C++ or TypeScript to benefit from Microsoft Word. The real barrier is the hundreds of R code lines required to apply these concepts to their databases. By removing the coding proficiency hurdle, this book will empower their research endeavors and help them become active members of and contributors to the applied data science community. The book offers a comprehensive explanation of data science and machine learning methodologies, along with access to software application tools to implement these techniques without any coding proficiency. The book addresses the need for innovative tools that enable researchers to tap into the insights that come out of cutting-edge data science tools with absolutely no computer language literacy requirements.

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

Mathematical Structure of Syntactic Merge

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