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A Tour Through Graph Theory (Textbooks in Mathematics)
by Karin R Saoub<p>A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts. <p>This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course.</p>
Tourism Analytics Before and After COVID-19: Case Studies from Asia and Europe
by Yok Yen NguwiThis book is compilation of different analytics and machine learning techniques focusing on the tourism industry, particularly in measuring the impact of COVID-19 as well as forging a path ahead toward recovery. It includes case studies on COVID-19's effects on tourism in Europe, Hong Kong, China, and Singapore with the objective of looking at the issues through a data analytical lens and uncovering potential solutions. It adopts descriptive analytics, predictive analytics, machine learning predictive models, and some simulation models to provide holistic understanding.There are three ways in which readers will benefit from reading this work. Firstly, readers gain an insightful understanding of how tourism is impacted by different factors, its intermingled relationship with macro and business data, and how different analytics approaches can be used to visualize the issues, scenarios, and resolutions. Secondly, readers learn to pick up data analytics skills from the illustrated examples. Thirdly, readers learn the basics of Python programming to work with the different kinds of datasets that may be applicable to the tourism industry.
Tournament Design: How Operations Research Can Improve Sports Rules (Palgrave Pivots in Sports Economics)
by László CsatóThis Palgrave Pivot presents tournament design mainly within the axioms of incentive compatibility and fairness. It illustrates the advantages of an axiomatic approach through various examples, including several FIFA and UEFA tournaments, and uses theoretical tools and simulation methodology in its analysis. Chapter 1 discusses scoring systems of championships with multiple competitions, ranking in Swiss-system tournaments, and tie-breaking rules in round-robin leagues. It is followed by a thorough critical analysis of the current and previous FIFA World Rankings. The broad focus is substantially narrowed in Chapter 2, which turns to the topic of incentive (in)compatibility in multiple qualifiers. It is revealed that UEFA has faced at least three times recently this problem in the qualification to the UEFA Europa League, qualification to the UEFA Champions League, and the draw of the UEFA Champions League groups. Analogously, Chapter 3 discusses incentive (in)compatibility when there is only one group-based tournament but the complex progression rules to the subsequent stage can be designed poorly. Our examples include the qualifying tournaments of recent FIFA World Cups and UEFA European Championships. Chapter 4 moves to the problem of penalty shootout rules in soccer, where the fairness and complexity of some alternative mechanisms from the literature are evaluated. Fairness remains the central issue in Chapter 5, which presents the challenges of designing a tournament with 24 teams if the number of teams per group cannot exceed four. As expected, there is no perfect solution, and both FIFA and UEFA have introduced a reform in this format recently. Chapter 6 deals with the qualification for the 2020 UEFA European Football Championship. Its tournament design is perhaps the most complicated one that has ever been implemented in the real-world and suffers from serious shortcomings.
Toward a Health Statistics System for the 21st Century: SUMMARY OF A WORKSHOP
by Committee on National StatisticsA summary Toward a Health Statistics System for the 21st Century
Toward a New Council of Florence: On the Peace of Faith and other Works by Nicolaus of Cusa
by Marianna Wertz William WertzThis is a book of English translations of the writings of one of the most important geniuses in history--Cardinal Nicolaus of Cusa (1401-1464). He created ideas which had never been conceived before and which changed history for the better--up through our time and far, far into the future. His thinking processes are sometimes summed up in his concept of the “coincidence of opposites.” Instead of starting his thought process from accumulated sense perceptions and deducing law from observed appearances, Cusa starts with the hypothesis that there must be an original potential from which all multiplicity derives. By starting from the top, or “the Origin,” Cusa was able to solve previously insoluble problems. For example, his idea that the “right to govern comes from the consent of the governed” was not only the basis for solving clashes within the Catholic Church, and even the attempt to reunify all of the various Christian churches at the Council of Florence, but also lay at the heart of the experiments in government set up in the New England colonies of North America and the later creation of the United States Constitution. Besides the title work “On the Peace of Faith” which resolves the conflicts among the religions, 17 other papers are translated into English--14 for the first time. The ongoing renaissance in the study of Cusa worldwide is the basis for resolving the conflicts which still plague the world.
Toward a Small Family Ethic
by Travis N. N. RiederThis thought-provoking treatise argues that current human fertility rates are fueling a public health crisis that is at once local and global. Its analysis and data summarize the ecological costs of having children, presenting ethical dilemmas for prospective parents in an era of competition for scarce resources, huge disparities of wealth and poverty, and unsustainable practices putting irreparable stress on the planet. Questions of individual responsibility and integrity as well as personal moral and procreative issues are examined carefully against larger and more long-range concerns. The author's assertion that even modest efforts toward reducing global fertility rates would help curb carbon emissions, slow rising global temperatures, and forestall large-scale climate disaster is well reasoned and more than plausible. Among the topics covered: · The multiplier effect: food, water, energy, and climate. · The role of population in mitigating climate change. · The carbon legacy of procreation. · Obligations to our possible children. · Rights, what is right, and the right to do wrong. · The moral burden to have small families. Toward a Small Family Ethic sounds a clarion call for bioethics students and working bioethicists. This brief, thought-rich volume steers readers toward challenges that need to be met, and consequences that will need to be addressed if they are not.
Toward a Visually-Oriented School Mathematics Curriculum
by Ferdinand RiveraWhat does it mean to have a visual representation of a mathematical object, concept, or process? What visualization strategies support growth in mathematical thinking, reasoning, generalization, and knowledge? Is mathematical seeing culture-free? How can information drawn from studies in blind subjects help us understand the significance of a multimodal approach to learning mathematics? Toward a Visually-Oriented School Mathematics Curriculum explores a unified theory of visualization in school mathematical learning via the notion of progressive modeling. Based on the author's longitudinal research investigations in elementary and middle school classrooms, the book provides a compelling empirical account of ways in which instruction can effectively orchestrate the transition from personally-constructed visuals, both externally-drawn and internally-derived, into more structured visual representations within the context of a socioculturally grounded mathematical activity. Both for teachers and researchers, a discussion of this topic is relevant in the history of the present. The ubiquity of technological tools and virtual spaces for learning and doing mathematics has aroused interest among concerned stakeholders about the role of mathematics in these contexts. The book begins with a prolegomenon on the author's reflections on past and present visual studies in mathematics education. In the remaining seven chapters, visualization is pursued in terms of its role in bringing about progressions in mathematical symbolization, abduction, pattern generalization, and diagrammatization. Toward a Visually-Oriented School Mathematics Curriculum views issues surrounding visualization through the eyes of a classroom teacher-researcher; it draws on findings within and outside of mathematics education that help practitioners and scholars gain a better understanding of what it means to pleasurably experience the symmetric visual/symbolic reversal phenomenon - that is, seeing the visual in the symbolic and the symbolic in the visual."
Toward Connected, Cooperative and Intelligent IoV: Frontier Technologies and Applications
by Kai Liu Penglin Dai Victor C.S. Lee Joseph Kee-Yin Ng Sang Hyuk SonThis book offers a comprehensive introduction to technological advances in Internet of Vehicles (IoV), including vehicular communications, vehicular system architectures, data dissemination algorithms, resource allocation schemes, and AI-enabled applications. It focuses on the state-of-the-art IoV with regard to three major directions, namely networking, cooperation, and intelligence, including advanced wireless communication technologies, algorithm theory, optimization mechanisms, and AI technologies. In addition, the book includes a number of case studies with system prototype implementation and hands-on experiments in IoV, making it suitable both as a technical reference work for professionals and as a textbook for graduate students.
Toward Equity and Social Justice in Mathematics Education (Research In Mathematics Education Ser.)
by Tonya Gau BartellThis critical volume responds to the enduring challenge in mathematics education of addressing the needs of marginalized students in school mathematics, and stems from the 2015 Annual Meeting of the North American Group of the Psychology of Mathematics Education (PME-NA). This timely analysis brings greater clarity and support to such challenges by narrowing in on four foci: theoretical and political perspectives toward equity and justice in mathematics education, identifying and connecting to family and community funds of knowledge, student learning and engagement in preK-12 mathematics classrooms, and supporting teachers in addressing the needs of marginalized learners. Each of these areas examines how race, class, culture, power, justice and mathematics teaching and learning intersect in mathematics education to sustain or disrupt inequities, and include contributions from scholars writing about mathematics education in diverse contexts. Included in the coverage: Disrupting policies and reforms to address the needs of marginalized learnersA socio-spatial framework for urban mathematics educationLinking literature on allywork to the work of mathematics teacher educatorsTransnational families’ mathematical funds of knowledgeMultilingual and technological contexts for supporting learners’ mathematical discoursePreservice teachers’ strategies for teaching mathematics with English learners Toward Equity and Social Justice in Mathematics Education is of significant interest to mathematics teacher educators and mathematics education researchers currently addressing the needs of marginalized students in school mathematics. It is also relevant to teachers of related disciplines, administrators, and instructional designers interested in pushing our thinking and work toward equity and justice in mathematics education.
Toward Human-Level Artificial Intelligence: Representation and Computation of Meaning in Natural Language (Dover Books on Mathematics)
by Philip C. JacksonHow can human-level artificial intelligence be achieved? What are the potential consequences? This book describes a research approach toward achieving human-level AI, combining a doctoral thesis and research papers by the author.The research approach, called TalaMind, involves developing an AI system that uses a 'natural language of thought' based on the unconstrained syntax of a language such as English; designing the system as a collection of concepts that can create and modify concepts to behave intelligently in an environment; and using methods from cognitive linguistics for multiple levels of mental representation. Proposing a design-inspection alternative to the Turing Test, these pages discuss 'higher-level mentalities' of human intelligence, which include natural language understanding, higher-level forms of learning and reasoning, imagination, and consciousness. Dr. Jackson gives a comprehensive review of other research, addresses theoretical objections to the proposed approach and to achieving human-level AI in principle, and describes a prototype system that illustrates the potential of the approach.This book discusses economic risks and benefits of AI, considers how to ensure that human-level AI and superintelligence will be beneficial for humanity, and gives reasons why human-level AI may be necessary for humanity's survival and prosperity.
Toward Mathematics for All: Reinterpreting History of Mathematics in North America 1607-1865 (History of Mathematics Education)
by Nerida Ellerton M. A. ClementsThis book presents a history of mathematic between 1607 and 1865 in that part of mainland North America which is north of Mexico but excludes the present-day Canada and Alaska. Unlike most other histories of mathematics now available, the emphasis is on the gradual emergence of "mathematics for all" programs and associated changes in thinking which drove this emergence. The book takes account of changing ideas about intended, implemented and attained mathematics curricula for learners of all ages. It also pays attention to the mathematics itself, and to how it was taught and learned.
Toward Predicate Approaches to Modality
by Johannes SternIn this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conceived as predicates. The idea is to characterize the modal predicate by appeal to its interaction with the truth predicate. This strategy is put to use by developing the modal theories Modal Friedman-Sheard and Modal Kripke-Feferman.
Toward Robots That Reason: Logic, Probability & Causal Laws (Synthesis Lectures on Artificial Intelligence and Machine Learning)
by Vaishak BelleThis book discusses the two fundamental elements that underline the science and design of artificial intelligence (AI) systems: the learning and acquisition of knowledge from observational data, and the reasoning of that knowledge together with whatever information is available about the application at hand. It then presents a mathematical treatment of the core issues that arise when unifying first-order logic and probability, especially in the presence of dynamics, including physical actions, sensing actions and their effects. A model for expressing causal laws describing dynamics is also considered, along with computational ideas for reasoning with such laws over probabilistic logical knowledge.
Toward Social Reporting: Next Steps (Social Science Frontiers)
by Otis Dudley DuncanA volume of Social Science Frontiers, a series of publications reviewing new fields for social development, aimed at foundation executives, administrators of research grant programs, directors of research organizations, and others concerned with making contemporary social science more useful for the function of social reporting.
Toward the Rule of Law in Russia: Political and Legal Reform in the Transition Period
by Donald D. BarryThe contributors to this volume - all specialists on Soviet law and politics - offer a comprehensive examination of the effort to create a "law-based" state in the Gorbachev-era U.S.S.R., thus effecting a fundamental change in the relationship between the state and private groups and individuals. Gianmaria Ajani, Donald Barry, Harold Berman, Frances Foster-Simons, George Ginsburgs, John Hazard, Kathryn Hendley, Eugene Huskey, Dietrich Loeber, Peter Maggs, Hiroshi Oda, Nicolai Petro, Robert Sharlet, Louise Shelley, Will Simons and Peter Solomon, with commentary by Soviet scholars, discuss conceptual, historical, social, cultural, and institutional aspects of Soviet legal development, and supply detailed analysis of recent developments in the areas of civil, criminal, and labour law and the rights of individuals, economic organizations, and political and social groups.
Towards a General Theory of Classifications
by Daniel Parrochia Pierre NeuvilleThis book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, the authors essentially put forward a number of key questions. Their aim is rather to reveal the "state of art" of this dynamic field and the philosophy one may eventually adopt to go further. To this end they present some advances made in the course of the last century, discuss a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionals interested in the epistemology and philosophy of science, library science, logic and set theory, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in this field.
Towards a Peaceful Development of Cyberspace: De-Escalation of State-Led Cyber Conflicts and Arms Control of Cyber Weapons (Technology, Peace and Security I Technologie, Frieden und Sicherheit)
by Thomas ReinholdThe cyberspace and its global infrastructures are essential for our civilizations, the economy and administration. However, cyberspace is also increasingly developing into an intelligence and military operational area, visible in the creation of military cyber departments and the integration of cyberspace into states' security and defense strategies. Unfortunately, many of the established toolset of transparency, de-escalation and arms control measures do not work for cyberspace due to its specific technical characteristics. But how de-escalation of state-led conflicts in cyberspace can be achieved and how arms control of cyber weapons can be developed? Based on a technical perspective with regard to the underlying political challenges, the book follows an approach of adopting already existing technical measures from other fields of the computer science. It presents a classification system for cyberweapons, an approach for the mutual reduction of vulnerability stockpiles and provides an approach to prove the non-involvement in a cyber conflict. Beyond this, it aims to provide some impulses regarding the responsibility and creative options of the computer science with a view to the peaceful development and use of cyberspace.
Towards a Post-Bertalanffy Systemics
by Gianfranco Minati Mario R. Abram Eliano PessaThis book contains the proceedings of the Sixth National Conference of the Italian Systems Society. The title, Towards a post-Bertalanffy Systemics, aims to underline the need for Systemics and Systems Science to generalize theoretically concepts related to complexity (the great enemy of Bertalanffy Systemics). Hopefully this goal should be achieved by working in an inter-disciplinary and trans-disciplinary fashion, using systemic concepts arising from various disciplines and from the original, or Bertalanffy Systemics, as well. The interdisciplinary nature of the original Systemics and its power of generalization were given, overall, by the fact that the problems and solutions of one discipline become problems and solutions for another. Today, the modeling and interpretation of multidisciplinary approaches and representations makes easier to recognize these interconnections. The context, however, has changed dramatically. Of course, the challenge is still to find theoretical generalizations and applications, even where we have a lot of specificities, but we know very little on how to combine them. We cannot, however, simply replace the old with the new, but we must introduce strategies to recognize, represent, model and act on new levels, combining multiple representations, functions and emergence. In many disciplines this has been already done, and inevitably well, since targets and projects are well specified and oriented. The challenge is to do it for Systemics, with the vocations of cultural and theoretical generalization. Examples of new issues introduced by such theoretical disciplinary improvements, dealt with by many disciplines, include the study of mesoscopic or middle-way level, of multiple and dynamic coherence, of equivalence/non-equivalence, of fractality, of networks, of non-causality, of non-invasiveness, of non-prescribability, of non-separability, of quasi properties, of symmetry properties, of topological dynamics, as well as of quantum theories and concepts. The conference was devoted to identifying, discussing and understanding possible interrelationships of theoretical disciplinary improvements, recognized as having prospective fundamental roles for a new post-Bertalanffy Systemics. The latter should be able to deal with problems related to complexity in a generalized way. In this context the inter-disciplinarity should consists, for instance, in a disciplinary reformulation of problems, as from algebraic to geometrical, from military to political, from biological to chemical, while the trans-disciplinarity should be related to the study of such reformulations and their properties. The Italian Systems Society (AIRS) was founded in the 1996. The AIRS is a network of academicians, scientists, researchers and professionals involved in Systemics. A partial list of disciplines represented is: Architecture Biology Economics Education Engineering Mathematics Neurosciences Medicine Music Philosophy Psychology Physics. Previous conferences had as open lecturers professors Arecchi, Haken, Klir, and Kauffman. The proceedings have been published as: 1. Minati, G. , (ed. ), (1998), Proceedings of the first Italian Conference on Systemics, Apogeo Scientifica, Milan, Italy. 2. Minati, G. , and Pessa, E. , (eds. ) (2002), Emergence in Complex Cognitive, Social and Biological Systems. Kluwer, New York. 3. Minati, G. , Pessa, E. , and Abram, M. , (eds. ), (2006), Systemics of Emergence: Research and Applications. Springer, New York. 4. Minati, G. , Abram, M. and Pessa, E. , (eds. ), (2009), Processes of emergence of systems and systemic properties. Towards a general theory of emergence. World Scientific, Singapore. 5. Minati, G. , Abram, M. and Pessa, E. , (eds. ), (2012), Methods, Models, simulations and approaches - towards a general theory of change. World Scientific, Singapore.
Towards an Arithmetical Logic
by Yvon GauthierThis book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic and combines Fermat's method of infinite descent with Kronecker's general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author's critical approach to the foundations of logic and mathematics.
Towards an Information Theory of Complex Networks: Statistical Methods and Applications
by Alexander Mehler Matthias Dehmer Frank Emmert-StreibFor over a decade, complex networks have steadily grown as an important tool across a broad array of academic disciplines, with applications ranging from physics to social media. A tightly organized collection of carefully-selected papers on the subject, Towards an Information Theory of Complex Networks: Statistical Methods and Applications presents theoretical and practical results about information-theoretic and statistical models of complex networks in the natural sciences and humanities. The book's major goal is to advocate and promote a combination of graph-theoretic, information-theoretic, and statistical methods as a way to better understand and characterize real-world networks. This volume is the first to present a self-contained, comprehensive overview of information-theoretic models of complex networks with an emphasis on applications. As such, it marks a first step toward establishing advanced statistical information theory as a unified theoretical basis of complex networks for all scientific disciplines and can serve as a valuable resource for a diverse audience of advanced students and professional scientists. While it is primarily intended as a reference for research, the book could also be a useful supplemental graduate text in courses related to information science, graph theory, machine learning, and computational biology, among others.
Towards Bayesian Model-Based Demography: Agency, Complexity and Uncertainty in Migration Studies (Methodos Series #17)
by Jakub BijakThis open access book presents a ground-breaking approach to developing micro-foundations for demography and migration studies. It offers a unique and novel methodology for creating empirically grounded agent-based models of international migration – one of the most uncertain population processes and a top-priority policy area. The book discusses in detail the process of building a simulation model of migration, based on a population of intelligent, cognitive agents, their networks and institutions, all interacting with one another. The proposed model-based approach integrates behavioural and social theory with formal modelling, by embedding the interdisciplinary modelling process within a wider inductive framework based on the Bayesian statistical reasoning. Principles of uncertainty quantification are used to devise innovative computer-based simulations, and to learn about modelling the simulated individuals and the way they make decisions. The identified knowledge gaps are subsequently filled with information from dedicated laboratory experiments on cognitive aspects of human decision-making under uncertainty. In this way, the models are built iteratively, from the bottom up, filling an important epistemological gap in migration studies, and social sciences more broadly.
Towards Equity in Mathematics Education
by Helen Forgasz Ferdinand RiveraThis volume gathers together twenty major chapters that tackle a variety of issues associated with equity in mathematics education along the dimensions of gender, culture, curriculum diversity, and matters of a biological nature. The pursuit of equity in mathematics education is an important concern in the history of the present. Since there is no doubt about the significant role of mathematics in almost every aspect of life, it means that all individuals regardless of sex, in any age range, and in whatever context need to be provided with an opportunity to become mathematically able. The publication of this Springer volume on equity in mathematics education is situated at a time when there is strong and sustained research evidence indicating the persistence of an equity gap in mathematics, which has now enabled the mathematics education community to engage in a discourse of access for all. The research studies that are reported and discussed in the volume have been drawn from an international group of distinguished scholars whose impressive, forward-looking, and thought-provoking perspectives on relevant issues incite, broaden, and expand complicated conversations on how we might effectively achieve equity in mathematics education at the local, institutional, and systemic levels. Further, the up-to-date research knowledge in the field that is reflected in this volume provides conceptual and practical outlines for mechanisms of change, including models, examples, and usable theories that can inform the development of powerful equitable practices and the mobilization of meaningful equity interventions in different contexts of mathematics education.
Towards Ethical and Socially Responsible Explainable AI: Challenges and Opportunities (Studies in Systems, Decision and Control #551)
by Mohammad Amir Akhtar Mohit Kumar Anand Nayyar"Dive deep into the evolving landscape of AI with 'Towards Ethical and Socially Responsible Explainable AI'. This transformative book explores the profound impact of AI on society, emphasizing transparency, accountability, and fairness in decision-making processes. It offers invaluable insights into creating AI systems that not only perform effectively but also uphold ethical standards and foster trust. Essential reading for technologists, policymakers, and all stakeholders invested in shaping a responsible AI future."
Towards Higher Mathematics: A Companion
by Richard EarlContaining a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.
Towards Infrared Finite S-matrix in Quantum Field Theory (Springer Theses)
by Hayato HiraiThis book presents the better understanding of infrared structures of particle scattering processes in quantum electrodynamics (QED) in four-dimensional spacetime. An S-matrix is the fundamental quantity in scattering theory. However, if a theory involves massless particles, such as QED and gravity, the conventional S-matrix has not been well defined due to the infrared divergence, and infrared dynamics thus needs to be understood in-depth to figure out the S-matrix. The book begins with introducing fundamental nature of the charge conservation law associated with asymptotic symmetry, and explaining its relations to soft theorems and memory effect. Subsequently it looks into an appropriate asymptotic state of the S-matrix without infrared divergences. The Faddeev-Kulish dressed state is known as a candidate of such a state, and its gauge invariant condition and its relation to the asymptotic symmetry are discussed. It offers an important building blocks for constructing the S-matrix without infrared divergences.