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The 1994 discovery of Shor's quantum algorithm for integer factorization—an important practical problem in the area of cryptography—demonstrated quantum computing's potential for real-world impact. Since then, researchers have worked intensively to expand the list of practical problems that quantum algorithms can solve effectively. This book surveys the fruits of this effort, covering proposed quantum algorithms for concrete problems in many application areas, including quantum chemistry, optimization, finance, and machine learning. For each quantum algorithm considered, the book clearly states the problem being solved and the full computational complexity of the procedure, making sure to account for the contribution from all the underlying primitive ingredients. Separately, the book provides a detailed, independent summary of the most common algorithmic primitives. It has a modular, encyclopedic format to facilitate navigation of the material and to provide a quick reference for designers of quantum algorithms and quantum computing researchers.
In this original and modern book, the complexities of quantum phenomena and quantum resource theories are meticulously unravelled, from foundational entanglement and thermodynamics to the nuanced realms of asymmetry and beyond. Ideal for those aspiring to grasp the full scope of quantum resources, the text integrates advanced mathematical methods and physical principles within a comprehensive, accessible framework. Including over 760 exercises throughout, to develop and expand key concepts, readers will gain an unrivalled understanding of the topic. With its unique blend of pedagogical depth and cutting-edge research, it not only paves the way for a deep understanding of quantum resource theories but also illuminates the path toward innovative research directions. Providing the latest developments in the field as well as established knowledge within a unified framework, this book will be indispensable to students, educators, and researchers interested in quantum science's profound mysteries and applications.
In a technologically advanced and competitive landscape dominated by major tech companies and burgeoning start-ups, the key asset lies in boosting monthly active users. Traditionally, product design has relied on fragmented insights from personal experience, common sense, or isolated experiments. This work endeavours to establish a theoretical framework for predicting and influencing the digital behaviour of technology users. Drawing on over a century of scientific research in behaviour, cognition, and physiology, this presents a comprehensive approach to customizing digital stimuli. The objective is to enhance user interactions with digital and virtual environments. Through real and cost-effective examples, diagrams, and formulas, the text offers theoretical knowledge and a practical methodology to elevate digital product designs, setting them apart from the competition. With the potential to reshape the digital design landscape, this book emerges as a game-changer, promising to revolutionize how digital products and services are conceived and delivered.
Methods comprise a significant part of the knowledge engineers are taught and that they use in professional practice. However, methods have been largely neglected in discussions of the nature of engineering knowledge. In particular, methods prove to be hard to track down in the best-known and most influential typology of engineering knowledge, put forward by Walter G. Vincenti in his book What Engineers Know and How They Know It. This article discusses contemporary views of what engineering methods are and what they contain, how methods (fail to) fit into Vincenti’s analysis, and some characteristics of method knowledge. It argues that methods should be seen as a distinct type of engineering knowledge. While characterizing the knowledge that methods include can be done in different ways for different purposes, the core of method knowledge that does not fit into other categories is explicit ‘how-to’ knowledge of procedures, that draw on other types of knowledge.
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
This chapter dissects the modeling of time series and the estimation of scaling laws. It introduced methodologies to estimate the generalized Hurst exponent and discusses stationarity tests. Tools for modeling temporal patterns such as rolling windows, empirical mode decomposition, and temporal clustering are introduced.
This chapter introduces the concept of entropy and its significance in modeling. The focus extends to joint entropy, Kullback–Leibler divergence, and conditional entropy. Readers are equipped with tools to quantify information and uncertainty, pivotal in probabilistic modeling. The chapter focuses on Shannon entropy but also introduces to other entropy formulations.
Centered on multivariate probabilities, this chapter unravels the intricacies of joint probabilities, covariance matrices, and multivariate normal distributions. The discussion on conditional probability and Bayes’ theorem provides a robust foundation for modeling complex relationships between several variables.
Diving into stochastic processes, this chapter explores stationarity, scaling laws, and fractal dimensions. It delves into diverse processes, from random walks to more general self-affine processes, unraveling their implications in modeling complex phenomena. In line with the rest of the book, it discusses the modeling of stochastic processes as an instance of multivariate sets of random variables.
This chapter navigates the construction of networks from data. Various network-building tools from thresholding to information filtering are introduced and discussed. The reader is guided through the use of network representations for the construction of effective multivariate probabilistic models.