This is a book about the "Halting Problem", arguably the most (in)famous computer-related problem: can an algorithm decide in finite time whether an arbitrary computer program eventually stops? This seems a dull, petty question: after all, you run the program and wait till it stops. However, what if the program does not stop in a reasonable time, a week, a year, or a decade? Can you infer that it will never stop? The answer is negative. Does this raise your interest? If not, consider these questions: Can mathematics be done by computers only? Can software testing be fully automated? Can you write an anti-virus program which never needs any updates? Can we make the Internet perfectly secure? Your guess is correct: the answer to each question is negative. The Halting Problem is "hidden" in many subjects, from logic (is mathematics free of contradictions?), physics (is quantum randomness perfect?), to philosophy (do humans have free will, or do our brains generate our thoughts and decisions in a deterministic way?) and quantum computing (why we don't have a quantum Halting Problem?) - this book will visit each of them.Written in an informal and thought-provoking language, supported with suggestive illustrations and applications and almost free of arcane mathematics (formal arguments are relegated to particular parts dedicated to the mathematically-oriented reader), the book will stimulate the curiosity and participation of the reader interested in the consequences of the limits of computing and in various attempts to cope with them.
Soon after their publication (1905, 1915), Einstein's special and general theories of relativity received attention by a wide variety of British scholars (astronomers, physicists, mathematicians and philosophers). That reaction varied from deep acceptance (as was the case of Arthur Eddington) to straightforward opposition. This book analyzes those reactions, which involved a large number of important scientists as well as philosophers, like Bertrand Russell or Alfred N. Whitehead. The study will cover from the 1910s till the 1960s, when the work of a group of relativists centered in London and Oxford (Penrose), Cambridge (Sciama and Hawking) as well as the Bondi's group at King's College London, who finally introduced a new, global approach to general relativity.
The ancient Greeks were the first to seriously ask for scientific explanations of the panorama of the heavens based on mathematical ideas. Ever since, mathematics has played a major role for human perception and description of the outside physical world, and in a larger perspective for comprehending the universe. This second edition pays tribute to this line of thought and takes the reader on a journey in the mathematical universe from conic sections to mathematical modelling of planetary systems.In the second edition, the four chapters in the first edition on conic sections (two chapters), isoperimetric problems for plane figures, and non-Euclidean geometry, are treated in four revised chapters with many new exercises added. In three new chapters, the reader is taken through mathematics in curves, mathematics in a Nautilus shell, and mathematics in the panorama of the heavens. In all chapters of the book, the circle plays a prominent role.This book is addressed to undergraduate and graduate students as well as researchers interested in the geometry of conic sections, including the historical background and mathematical methods used. It features selected important results, and proofs that not only proves but also 'explains' the results.
Frontiers in Entropy Across the Disciplines presents a panorama of entropy emphasizing mathematical theory, physical and scientific significance, computational methods, and applications in mathematics, physics, statistics, engineering, biomedical signals, and signal processing.In the last century classical concepts of entropy were introduced in the areas of thermodynamics, information theory, probability theory, statistics, dynamical systems, and ergodic theory. During the past 50 years, dozens of new concepts of entropy have been introduced and studied in many disciplines. This volume captures significant developments in this arena. It features expository, review, and research papers by distinguished mathematicians and scientists from many disciplines. The level of mathematics ranges from intermediate level to research level. Each chapter contains a comprehensive list of references. Topics include entropy and society, entropy and time, Souriau entropy on symplectic model of statistical physics, new definitions of entropy, geometric theory of heat and information, maximum entropy in Bayesian networks, maximum entropy methods, entropy analysis of biomedical signals (review and comparison of methods), spectral entropy and its application to video coding and speech coding, a comprehensive review of 50 years of entropy in dynamics, a comprehensive review on entropy, entropy-like quantities and applications, topological entropy of multimodal maps, entropy production in complex systems, entropy production and convergence to equilibrium, reversibility and irreversibility in entropy, nonequilibrium entropy, index of various entropy, entropy and the greatest blunder ever.
Henry Kissinger observed, 'Everybody wants to be a China hawk.' China is a bully. China is Nazi Germany. China commits genocide. China disrupts the 'international rules-based order.' Responding to such uninformed generalization on the nature of China's regime and its lack of human values, the Western Liberal Democracies have created their own 'China Problem' by clinging to Cold War anachronism. The clash of values is not nearly as deep and extensive as is often claimed. Furthermore, the contemporary public discourse on China needs a complete assessment of the values that have emerged in Xi Jinping's China. Xi is regarded as 'red' like Mao. Xi, however, has abandoned Mao's view of class struggle and his notion of a 'rejuvenated China' embraces traditional core principles that Mao bitterly condemned. 'Ren', or 'benevolence', for example, now informs entwined domestic and foreign policy as 'moderate prosperity in all respects'. 'Ren', or 'benevolence' is aligned with 'common security' and 'common development'. The question is whether this is a positive restoration of traditional values that will contribute to domestic development and international peace, or restorationist Middle-Kingdom-ism designed to assert Chinese values worldwide. This book's analysis of Chinese values argues that the current interpretation of the 'China Threat' is predicated in a serious misunderstanding of Chinese values.It is often commented that China is 'the defining geopolitical issues of our time'. This book is an especially timely contribution to the currently limited public policy debate on China as a threat to Western values and the 'international rules-based system'. Correction is long overdue with reference to speculative assumptions that Xi Jinping's regime represents a return to Mao's regime. 'Socialism with Chinese characteristics' has significantly moved on under Xi's leadership. Hyperbole about China has presumed the continuation of Chinese Cold War ideology and has either lightly commented on, or ignored altogether the resurgence of core traditional ideas in Chinese policy formation. This book provides detailed research of 'Xi Jinping Thought' and 'Xi Jinping Diplomatic Thought'. It adopts a widely construed, but serious interdisciplinary, approach towards the 'China Problem', drawing on both the social sciences and humanities. This wide-angled approach includes 'new sinology' in its recent review of 'translated China', synthesizing tradition and culture with the development of modern Chinese ideology, politics and policy formation. The book's significant topicality is presented within an unconventional approach and formatted contents designed to reach out to the biggest circle of general and advanced, China-interested readers in the time of great debate.
Water is an indispensable resource for our society. Essential to sustaining life and economic prosperity, water is also the basic component for manufacturing almost everything to keep society alive, including energy, food, clothing, cars, and electronics, among many other examples. It is, thus, an integral part of our lives beyond simply quenching our thirst. In addition, our future economy and security highly depend upon the availability of clean water. Yet given its critical importance, there is a limited supply of renewable freshwater across the globe and there is no substitute. Global population and economic growth, urbanization, and climate change further exacerbate the increasing stress on freshwater supplies. As such, society urgently needs to find the scientific and engineering solutions to more efficiently manage our precious water resources. The volumes of this multi-volume reference cover the latest scientific advancements and solutions in managing and treating this crucial resource.Related Link(s)
The Handbook on Computer Learning and Intelligence is a second edition which aims to be a one-stop-shop for the various aspects of the broad research area of computer learning and intelligence. This field of research evolved so much in the last five years that it necessitates this new edition of the earlier Handbook on Computational Intelligence. This two-volume handbook is divided into five parts. Volume 1 covers Explainable AI and Supervised Learning. Volume 2 covers three parts: Deep Learning, Intelligent Control, and Evolutionary Computation. The chapters detail the theory, methodology and applications of computer learning and intelligence, and are authored by some of the leading experts in the respective areas. The fifteen core chapters of the previous edition have been written and significantly refreshed by the same authors. Parts of the handbook have evolved to keep pace with the latest developments in computational intelligence in the areas that span across Machine Learning and Artificial Intelligence. The Handbook remains dedicated to applications and engineering-orientated aspects of these areas over abstract theories.
Volume 1: Biofabrication aims to produce artificially manufactured tissues and organs, potentially revolutionizing conventional paradigm of clinical practice in treating diseases and extending the life span and quality of human beings. In this volume, we invite notable experts in the field of biofabrication and biomanufacturing to summarize recent rapid progress in this field from multifaceted aspects covering biofabrication techniques and building materials such as scaffold and living cells. Specifically, a focus is placed on a variety of techniques derived from 3D bioprinting and bioassembly strategies, such as acoustic assembly and electrofabrication. Moreover, principles and strategies for choosing hydrogels and polymers for biofabrication are also heavily discussed. Overall, this book creates a good opportunity for undergraduate and postgraduate students as well as bioengineers and medical researchers who wish to gain a fundamental understanding of current status and future trends in biofabrication and biomanufacturing.Volume 2: Infertility has become a significant psychosocial burden affecting the lives of couples who cannot reproduce naturally. Advanced reproductive technologies (ARTs) are being developed to treat infertility. This handbook explores significant development of ARTs for fertility testing, selection of sperm, oocyte and embryo, reproductive monitors, automation in embryology, and fertility preservation. This volume provides a comprehensive overview of the myriad of emerging technologies and systems that are being utilized or will be utilized in near future in reproductive clinics. Overall this book creates a good opportunity for undergraduate and postgraduate students as well as scientists and medical researchers who wish to gain fundamental understanding of current status and future trends in fertility and reproductive medicine.Volume 3: Healthcare industry has a notable paradigm transition from centralized care to the point-of-care (POC). During this metamorphosis, a number of new technologies and strategies have been adapted to the current practice, addressing the existing challenges in the fields of medicine and biology. All the efforts aim to improve the clinical management and the effectiveness and quality of care. In particular, diagnostics has pivotal roles in guiding clinical management for the most effective treatment to control and cure the disease. In contrast to the existing diagnostic strategies employing bulky-sized tools, expensive infrastructure, laborious protocols, and lengthy processing steps, the contribution of biosensors to current healthcare system, especially to diagnostics, is paramount. The unprecedented and admirable characteristics of biosensing strategies have expanded our knowledge on medicine and biology by harmonizing materials science, chemistry, physics, and engineering. We believe that biosensors applied to disease diagnostics will not only garner more attention in clinical research to decipher disease biology and mechanism, and also, stimulate innovative perspectives in artificial intelligence (AI) and internet of things (IoT) synergistically, thereby their more facile adaptation to daily-use. Overall this book creates a good opportunity for undergraduate and postgraduate students as well as scientists and medical researchers who wish to gain fundamental understanding of current status and future trends in diagnostic technologies.
Recent discoveries in astronomy and relativistic astrophysics as well as experiments on particle and nuclear physics have blurred the traditional boundaries of physics. It is believed that at the birth of the Universe, a whirlwind of matter and antimatter, of quarks and exotic leptons, briefly appeared and merged into a sea of energy. The new phenomena and new states of matter in the Universe revealed the deep connection between quarks and the Cosmos. Motivated by these themes, this book discusses different topics: gravitational waves, dark matter, dark energy, exotic contents of compact stars, high-energy and gamma-ray astrophysics, heavy ion collisions and the formation of the quark - gluon plasma in the early Universe. The book presents some of the latest researches on these fascinating themes and is useful for experts and students in the field.
This edited volume covers the development of egg freezing over the last few decades since the pioneering work of Chen in 1986, addressing both the scientific breakthroughs that have occurred and the social and demographic changes that are currently driving an increased demand for 'social' egg freezing and a recognition of the important role of 'medical' egg freezing for women facing potentially sterilizing oncology therapy. It presents the latest research in egg vitrification, methodologies for optimizing laboratory performance and contemporary clinical management of patients seeking oocyte cryopreservation. Audited international data on access, take-up, use and birth outcomes for women undertaking egg freezing are included. The book also discusses the ethical issues related to access and funding and considers how different legal jurisdictions have approached matters such as storage duration, ownership, donation, anonymity and identification. Such wide-ranging contents will bridge the gap between the highly technical laboratory handbooks and the 'popular' tabloid accounts directed at young women considering egg freezing. Drawing on the different approaches to fertility preservation prevailing around the world, with chapters written by leading international experts and edited by Gillian Lockwood, a pioneer of the field whose clinic produced the UK's first 'frozen egg' baby in 2002, Egg Freezing in the 21st Century will have an authoritative and global appeal, and may hopefully encourage a change of attitude in some jurisdictions.
This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. It treats the dynamics of ray optics, resonant oscillators and the elastic spherical pendulum from a unified geometric viewpoint, by formulating their solutions using reduction by Lie-group symmetries. The only prerequisites are linear algebra, calculus and some familiarity with the Euler-Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie-Poisson Hamiltonian formulations and momentum maps in physical applications.The many Exercises and Worked Answers aid the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.The book's many worked exercises make it ideal for both classroom use and self-study. In particular, a substantial appendix containing both introductory examples and enhanced coursework problems with worked answers is included to help the student develop proficiency in using the powerful methods of geometric mechanics.
This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition.Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages. The diagrams correspond to integrals in momentum space. They are evaluated in 4-ε dimensions, where they possess pole terms in 1/ε. The pole terms are collected into renormalization constants.The theory of the renormalization group is used to find the critical scaling laws. They contain critical exponents which are obtained from the renormalization constants in the form of power series. These are divergent, due to factorially growing expansion coefficients. The evaluation requires resummation procedures, which are performed in two ways: (1) using traditional methods based on Padé and Borel transformations, combined with analytic mappings; (2) using modern variational perturbation theory, where the results follow from a simple strong-coupling formula. As a crucial test of the accuracy of the methods, the critical exponent α governing the divergence of the specific heat of superfluid helium is shown to agree very well with the extremely precise experimental number found in the space shuttle orbiting the earth (whose data are displayed on the cover of the book).The phi4-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of phi4-theories are sketched, such as variational perturbation expansions in three rather than 4-ε dimensions, and improved ratio tests in high-temperature expansions of lattice models.
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