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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 inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

An accessible introduction to the principles of computational and mathematical modeling in psychology and cognitive scienceThis practical and readable work provides students and researchers, who are new to cognitive modeling, with the background and core knowledge they need to interpret published reports, and develop and apply models of their own. The book is structured to help readers understand the logic of individual component techniques and their relationships to each other.

This book is a practical guide to building computational models of high-level cognitive processes and systems. High-level processes are those central cognitive processes involved in thinking, reasoning, planning, and so on. These processes appear to share representational and processing requirements, and it is for this reason that they are considered together in this text. The book is divided into three parts. Part I considers foundational and background issues. Part II provides a series of case studies spanning a range of cognitive domains. Part III reflects upon issues raised by the case studies. Teachers of cognitive modeling may use material from Part I to structure lectures and practical sessions, with chapters in Part II forming the basis of in-depth student projects. All models discussed in this book are developed within the COGENT environments. COGENT provides a graphical interface in which models may be sketched as \"box and arrow\" diagrams and is both a useful teaching tool and a productive research tool. As such, this book is designed to be of use to both students of cognitive modeling and active researchers. For students, the book provides essential background material plus an extensive set of example models, exercises and project material. Researchers of both symbolic and connectionist persuasions will find the book of interest for its approach to cognitive modeling, which emphasizes methodological issues. They will also find that the COGENT environment itself has much to offer.

Currently there is growing interest in the application of dynamical methods to the study of cognition.Computation, Dynamics, and Cognition investigates this convergence from a theoretical and philosophical perspective, generating a provocative new view of the aims and methods of cognitive science.

This book offers a systemic perspective on cognition and the development of mathematics. First the yoyo model is discussed: a recent development of systems research which has yielded revolutionary applications. After revealing the systemic structure of thought, mathematics is analyzed by using the age-old concepts of actual and potential infinities. A new look is cast at some important paradoxes, each of which played a crucial role in the development of mathematics. Attention then turns to constructing the logical foundation of two different systems of mathematics, one assuming that actual infinity is different than potential infinity, and the other that these infinities are the same.

The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in chemistry or physics. Hence, it is essential to incorporate such knowledge-based processes into animal movement models. Here, we summarize popular deterministic mathematical models derived from first principles that begin to incorporate such influences on movement behaviour mechanisms. Most generally, these models take the form of nonlocal reaction-diffusion-advection equations, where the nonlocality may appear in the spatial domain, the temporal domain, or both. Mathematical rules of thumb are provided to judge the model rationality, to aid in model development or interpretation, and to streamline an understanding of the range of difficulty in possible model conceptions. To emphasize the importance of biological conclusions drawn from these models, we briefly present available mathematical techniques and introduce some existing “measures of success” to compare and contrast the possible predictions and outcomes. Throughout the review, we propose a large number of open problems relevant to this relatively new area, ranging from precise technical mathematical challenges, to more broad conceptual challenges at the cross-section between mathematics and ecology. This review paper is expected to act as a synthesis of existing efforts while also pushing the boundaries of current modelling perspectives to better understand the influence of cognitive movement mechanisms on movement behaviours and space use outcomes.

Recent work has begun to relate individual differences in brain functional organization to human behaviors and cognition, but the best brain state to reveal such relationships remains an open question. In two large, independent data sets, we here show that cognitive tasks amplify trait-relevant individual differences in patterns of functional connectivity, such that predictive models built from task fMRI data outperform models built from resting-state fMRI data. Further, certain tasks consistently yield better predictions of fluid intelligence than others, and the task that generates the best-performing models varies by sex. By considering task-induced brain state and sex, the best-performing model explains over 20% of the variance in fluid intelligence scores, as compared to <6% of variance explained by rest-based models. This suggests that identifying and inducing the right brain state in a given group can better reveal brain-behavior relationships, motivating a paradigm shift from rest- to task-based functional connectivity analyses. Decoding or predicting cognitive traits from brain activity is an exciting prospect. Here, the authors show that task-based functional connectivity better predicts intelligence-related measures than rest-based connectivity, suggesting that cognitive tasks amplify individual differences in trait-relevant circuitry.

To learn how cognition is implemented in the brain, we must build computational models that can perform cognitive tasks, and test such models with brain and behavioral experiments. Cognitive science has developed computational models that decompose cognition into functional components. Computational neuroscience has modeled how interacting neurons can implement elementary components of cognition. It is time to assemble the pieces of the puzzle of brain computation and to better integrate these separate disciplines. Modern technologies enable us to measure and manipulate brain activity in unprecedentedly rich ways in animals and humans. However, experiments will yield theoretical insight only when employed to test brain-computational models. Here we review recent work in the intersection of cognitive science, computational neuroscience and artificial intelligence. Computational models that mimic brain information processing during perceptual, cognitive and control tasks are beginning to be developed and tested with brain and behavioral data.