This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers o…
This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on ℓ́ℓsimpleℓ́ℓ situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutoria…
This books is a general introduction to Marine Ecology, accompanying a lecture and excursion. It targets students without prior knowledge of the subject. The content is taken largely from Wikipedia, but curated and augmented by the authors.
This interdisciplinary thesis introduces a systems biology approach to study the cell fate decision mediated by autophagy. A mathematical model of interaction between Autophagy and Apoptosis in mammalian cells is proposed. In this dynamic model autophagy acts as a gradual response to stress (Rheostat) that delays the initiation of bistable switch of apoptosis to give the cells an opportunity to…
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Du…
The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday o…
This book presents the latest advances in ultrafast science, including both ultrafast optical technology and the study of ultrafast phenomena. It covers picosecond, femtosecond, and attosecond processes relevant to applications in physics, chemistry, biology, and engineering. Ultrafast technology has a profound impact in a wide range of applications, amongst them biomedical imaging, chemical dy…
This publication showcases the work of UK mathematicians and statisticians by describing industrial problems that have been successfully solved, together with a summary of the financial and/or societal impact that arose from the work. The articles are grouped by sector, and include contributions to climate modelling, engineering and health. The articles are based on Impact Case Studies that wer…
This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and …
This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of computability theory as well as on generalised Turing computability. By looking at the roots and at the philosophical and technical infl…