This book constitutes the refereed proceedings of the First International Conference on Quantum AI and NLP, QNIP 2025, held in Bloomington, Indianna, USA, during August 6–9, 2025.The 17 full papers, one short paper and one abstract included in this volume were carefully reviewed and selected from 45 submissions. They were organized in following topical sections: Artificial Intelligence for Quantum Computing; Quantum Computing for Artificial Intelligence; Quantum Natural Language Pr...

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with infe...

The emerging interdisciplinary field of cognitive choice models integrates theory and recent research findings from both decision process and choice behavior.Cognitive decision processes provide the interface between the environment and brain, enabling choice behavior, and the basic cognitive mechanisms underlying decision processes are fundamental to all fields of human activity. Yet cognitive processes and choice processes are often studied separately, whether by...

A radical new explanation of how life and consciousness emerge from physics and chemistry.As physicists work toward completing a theory of the universe and biologists unravel the molecular complexity of life, a glaring incompleteness in this scientific vision becomes apparent. The "Theory of Everything" that appears to be emerging includes everything but us: the feelings, meanings, consciousness, and purposes that make us (and many of our animal cousins) what we are. These most imm...

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors p...

This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part ...

Ask a traditional mathematician the likely outcome of a coin-toss, and he will reply that no evidence exists on which to base such a prediction. Ask a Bayesian, and he will examine the coin, conclude that it was probably not tampered with, and predict five hundred heads in a thousand tosses; a subsequent experiment would then be used to refine this prediction. The Bayesian approach, in other words, permits the use of prior knowledge when testing a hypothesis.Long the province of ma...

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included.For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, ...

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas ar...

This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formali...

This book declines to take for granted the widespread assumption that existing psychometric procedures provide scientific measurement. The currently fashionable concepts of measurement within psychology -- operationalism and representationalism -- are critically examined, and the classical view, that measurement is the assessment of quantity, is defended. Within this framework, it is shown how conjoint measurement can be used to test the hypothesis that variables are quantitative. This the...

This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Quantum Interaction, QI 2016, held in San Francisco, CA, USA, in July 2016.The 21 papers presented in this book were carefully reviewed and selected from 39 submissions. The papers address topics such as: Fundamentals; Quantum Cognition; Language and Applications; Contextuality and Foundations of Probability; and Quantum-Like Measurements.