Machine Learning In Pure Mathematics And Theoretical Physics
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Machine Learning In Pure Mathematics And Theoretical Physics
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Author : Yang-hui He
language : en
Publisher: World Scientific
Release Date : 2023-06-21
Machine Learning In Pure Mathematics And Theoretical Physics written by Yang-hui He and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-21 with Computers categories.
The juxtaposition of 'machine learning' and 'pure mathematics and theoretical physics' may first appear as contradictory in terms. The rigours of proofs and derivations in the latter seem to reside in a different world from the randomness of data and statistics in the former. Yet, an often under-appreciated component of mathematical discovery, typically not presented in a final draft, is experimentation: both with ideas and with mathematical data. Think of the teenage Gauss, who conjectured the Prime Number Theorem by plotting the prime-counting function, many decades before complex analysis was formalized to offer a proof.Can modern technology in part mimic Gauss's intuition? The past five years saw an explosion of activity in using AI to assist the human mind in uncovering new mathematics: finding patterns, accelerating computations, and raising conjectures via the machine learning of pure, noiseless data. The aim of this book, a first of its kind, is to collect research and survey articles from experts in this emerging dialogue between theoretical mathematics and machine learning. It does not dwell on the well-known multitude of mathematical techniques in deep learning, but focuses on the reverse relationship: how machine learning helps with mathematics. Taking a panoramic approach, the topics range from combinatorics to number theory, and from geometry to quantum field theory and string theory. Aimed at PhD students as well as seasoned researchers, each self-contained chapter offers a glimpse of an exciting future of this symbiosis.
The Calabi Yau Landscape
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Author : Yang-Hui He
language : en
Publisher: Springer Nature
Release Date : 2021-07-31
The Calabi Yau Landscape written by Yang-Hui He and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-31 with Mathematics categories.
Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.
Mathematical Theories Of Machine Learning Theory And Applications
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Author : Bin Shi
language : en
Publisher: Springer
Release Date : 2019-06-12
Mathematical Theories Of Machine Learning Theory And Applications written by Bin Shi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Technology & Engineering categories.
This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Mathematical Software Icms 2024
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Author : Kevin Buzzard
language : en
Publisher: Springer Nature
Release Date : 2024-07-16
Mathematical Software Icms 2024 written by Kevin Buzzard and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-16 with Computers categories.
This book constitutes the proceedings of the 8th International Conference on Mathematical Software, ICMS 2024, held in Durham, UK, during July 22–25, 2024. The 37 full papers presented were carefully reviewed and selected from 46 submissions. The papers are organized in subject areas as follows: plenary lectures; number theory and related areas; novel formalisations of mathematics in lean; software for the applications of group theory to combinatorics; classical algebraic geometry & modern computer algebra: innovative software design and its applications; advancing computer algebra with massively parallel methods; computer algebra applications in the life sciences; machine learning within computer algebra systems; numerical software for special functions; mathematical research data; symbolic-numeric methods in algebraic geometry; Polyhedral geometry and combinatorics; general session.
Visual Group Theory
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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-08
Visual Group Theory written by Nathan Carter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Education categories.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
De Novo Quantum Cosmology With Artificial Intelligence
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Author : Ariel Fernández
language : en
Publisher: CRC Press
Release Date : 2025-07-22
De Novo Quantum Cosmology With Artificial Intelligence written by Ariel Fernández and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-22 with Science categories.
Experiments attempting to recreate the Big Bang and measurements in deep space point to the tantalizing possibility that our universe may be the relic of something simple, powerful, and highly symmetric. The evidence suggests an entity where matter and energy cannot be told apart and the four fundamental forces are unified into one. Empowered by artificial intelligence, De Novo Quantum Cosmology with Artificial Intelligence seeks to unravel the mystery as it searches for an encompassing physical picture where it all falls into place at the aftermath of creation from a quantum void. From the outset, AI reckons that the problem cannot be tackled without proper contextualization, that is, without dealing with other intimately related problems in particle cosmology including: the nature of dark matter and dark energy, the hierarchy problem of particle masses, the incommensurably weak coupling strength of gravity, the universe topology, the cosmological constant problem, and the vacuum catastrophe. Accordingly, the book addresses the matter in its full conceptual richness. This monograph addresses a broad readership that includes a nonhuman audience involving AI systems. A background in college-level physics and computer science would be essential. Although informal in the approach, the material is presented with scientific rigor, so that readers gain hands-on experience on the subject. The book is geared at graduate students as well as professional physicists, mathematicians, cosmologists, and big data scientists that seek to venture into some of the core problems in particle cosmology empowered by AI. Notably, the book is also geared at nonhuman audiences, since AI systems may incorporate its fundamental operational tenets and take the matter to unfathomable heights. Key Features: Introduces an artificial intelligence system to tackle core problems in particle cosmology Describes a grand unification scheme to explain the common origin of the fundamental forces Identifies the origin of matter as a phase transition from the quantum vacuum.
Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition
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Author : Tristan Hubsch
language : en
Publisher: World Scientific
Release Date : 2024-12-17
Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition written by Tristan Hubsch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-17 with Science categories.
Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kähler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi-Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.The first edition of Calabi-Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi-Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.
Artificial Intelligence
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Author :
language : en
Publisher: Elsevier
Release Date : 2023-09-11
Artificial Intelligence written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-11 with Mathematics categories.
Artificial Intelligence, Volume 49 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics. Chapters in this new release include AI Teacher-Student based Adaptive Structural Deep Learning Model and Its Estimating Uncertainty of Image Data, Machine-derived Intelligence: Computations Beyond the Null Hypothesis, Object oriented basis of artificial intelligence methodologies I in Judicial Systems in India, Artificial Intelligence in Systems Biology, Machine-Learning in Geometry and Physics, Innovation and Machine Learning: Crowdsourcing Open-Source Natural Language Processing (NLP) Algorithms to Advance Public Health Surveillance, and more. Other chapters cover Learning and identity testing of Markov chains, Data privacy for machine learning and statistics, and The interface between AI and Mathematics. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Statistics series - Includes the latest information on Artificial Intelligence
Human Centric Integration Of Next Generation Data Science And Blockchain Technology
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Author : Amit Kumar Tyagi
language : en
Publisher: Academic Press
Release Date : 2025-03-17
Human Centric Integration Of Next Generation Data Science And Blockchain Technology written by Amit Kumar Tyagi and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Science categories.
Human- Centric Integration of Next Generation Data Science and Blockchain Technology: Advancing Society 5.0 Paradigms focuses on the current technological landscape, addressing the evolving integration of data science and blockchain within the context of Society 5.0. This comprehensive resource explains the convergences between data science, blockchain, and the human-centric vision of Society 5.0, while also filling the gap in understanding and navigating this transformative intersection with recent shifts towards more decentralized and data-driven paradigms.The book introduces the concept of Society 5.0, examining the historical context, and outlines the evolving technological landscape shaping our interconnected future. It discusses the fundamental principles of data science, from data collection and preprocessing to exploratory data analysis and explains the transformative impact of data science and blockchain across industries such as healthcare, finance, education, and transportation. This book is essential to understanding and shaping the future of technology and society from decentralized solutions to predictive analytics/ emerging technologies. - Addresses the evolving integration of data science and blockchain within the context of Society 5.0 - Introduces the basic architecture and taxonomy of blockchain technology - Explores the future urban lives under the concept of "Society 5.0", characterized by the key phrases of data-driven society and knowledge-intensive society - Offers a firm foundation and understanding of recent advancements in various domains such as data analytics, neural networks, computer vision, and robotics, along with practical solutions to existing problems in fields such as healthcare, manufacturing industries, security, and infrastructure management