Human and machine discovery are gradual problem-solving processes of searching large problem spaces for incompletely defined goal objects. Research on problem solving has usually focused on searching an `instance space' (empirical exploration) and a `hypothesis space' (generation of theories). In scientific discovery, searching must often extend to other spaces as well: spaces of possible problems, of new or improved scientific instruments, of new problem representations, of new concepts, ...

From a leading computer scientist, a unifying theory that will revolutionize our understanding of how life evolves and learns.How does life prosper in a complex and erratic world? While we know that nature follows patterns -- such as the law of gravity -- our everyday lives are beyond what known science can predict. We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?In Probably Approximately Correct, c...

This book provides a historic overview of what is defined as "soft computing" with its techniques: neural networks, fuzzy logic, genetic algorithms and cellular automata.

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written...

The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. ...

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 basics of computer algebra and the language of Mathematica are described in this textbook, leading towards an understanding of Mathematica that allows the reader to solve problems in physics, mathematics, and chemistry.Mathematica is the most widely used system for doing mathematical calculations by computer, including symbolic and numeric calculations and graphics. It is used in physics and other branches of science, in mathematics, education and many other areas.

Perceptual organization is the neuro-cognitive process that enables us to perceive scenes as structured wholes consisting of objects arranged in space. Simplicity in Vision explores the intriguing idea that these perceived wholes are given by the simplest organizations of the scenes. Peter A. van der Helm presents a truly multidisciplinary approach to answer fundamental questions such as: Are simplest organizations sufficiently reliable to guide our actions? What is the nature of the regul...

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, ...

Aristotle's convincing philosophy is likely to have shaped (even indirectly) many of our current beliefs, prejudices and attitudes to life. This includes the way in which our mind (that is, our capacity to have private thoughts) appears to elude a scientific description. This book is about a scientific ingredient that was not available to Aristotle: the science of information. Would the course of the philosophy of the mind have been different had Aristotle pronounced that the matter of min...

This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significa...

This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Quantum Interaction, QI 2015, held in Filzbach, Switzerland, in July 2015.The 20 papers together with 2 invited keynotes presented in this book were carefully selected from 27 submissions. Quantum Interaction has developed into an emerging interdisciplinary area of science combining research topics in mathematics, physics, psychology, economics, cognitive science, and co...