Mathematical Models of Perception and Cognition


Book Description

In this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend¿s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.




Mathematical Models of Perception and Cognition Volume II


Book Description

In this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend’s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.




Mathematical Models of Perception and Cognition Volume I


Book Description

In this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend’s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.




Multidimensional Models of Perception and Cognition


Book Description

The mental representations of perceptual and cognitive stimuli vary on many dimensions. In addition, because of quantal fluctuations in the stimulus, spontaneous neural activity, and fluctuations in arousal and attentiveness, mental events are characterized by an inherent variability. During the last several years, a number of models and theories have been developed that explicitly assume the appropriate mental representation is both multidimensional and probabilistic. This new approach has the potential to revolutionize the study of perception and cognition in the same way that signal detection theory revolutionized the study of psychophysics. This unique volume is the first to critically survey this important new area of research.




Cognition and Perception


Book Description

An argument that there are perceptual mechanisms that retrieve information in cognitively and conceptually unmediated ways and that this sheds light on various philosophical issues. In Cognition and Perception, Athanassios Raftopoulos discusses the cognitive penetrability of perception and claims that there is a part of visual processes (which he calls “perception”) that results in representational states with nonconceptual content; that is, a part that retrieves information from visual scenes in conceptually unmediated, “bottom-up,” theory-neutral ways. Raftopoulos applies this insight to problems in philosophy of science, philosophy of mind, and epistemology, and examines how we access the external world through our perception as well as what we can know of that world. To show that there is a theory-neutral part of existence, Raftopoulos turns to cognitive science and argues that there is substantial scientific evidence. He then claims that perception induces representational states with nonconceptual content and examines the nature of the nonconceptual content. The nonconceptual information retrieved, he argues, does not allow the identification or recognition of an object but only its individuation as a discrete persistent object with certain spatiotemporal properties and other features. Object individuation, however, suffices to determine the referents of perceptual demonstratives. Raftopoulos defends his account in the context of current discussions on the issue of the theory-ladenness of perception (namely the Fodor-Churchland debate), and then discusses the repercussions of his thesis for problems in the philosophy of science. Finally, Raftopoulos claims that there is a minimal form of realism that is defensible. This minimal realism holds that objects, their spatiotemporal properties, and such features as shape, orientation, and motion are real, mind-independent properties in the world.




Cognitive Modeling


Book Description

Responding to an explosion of new mathematical and computational models used in the fields of cognitive science, this book provides simple tutorials concerning the development and testing of such models. The authors focus on a few key models, with a primary goal of equipping readers with the fundamental principles, methods, and tools necessary for evaluating and testing any type of model encountered in the field of cognitive science.




Mathematical Psychology and Psychophysiology


Book Description

Mathematical Psychology and Psychophysiology promotes an understanding of the mind and its neural substrates by applying interdisciplinary approaches to issues concerning behavior and the brain. The contributions present model from many disciplines that share common, conceptual, functional, or mechanistic substrates and summarize recent models and data from neural networks, mathematical genetics, psychoacoustics, olfactory coding, visual perception, measurement, psychophysics, cognitive development, and other areas. The contributors to Mathematical Psychology and Psychophysiology show the conceptual and mathematical interconnectedness of several approaches to the fundamental scientific problem of understanding mind and brain. The book's interdisciplinary approach permits a deeper understanding of theoretical advances as it formally structures a broad overview of the data.




Introduction to Modeling Cognitive Processes


Book Description

An introduction to computational modeling for cognitive neuroscientists, covering both foundational work and recent developments. Cognitive neuroscientists need sophisticated conceptual tools to make sense of their field’s proliferation of novel theories, methods, and data. Computational modeling is such a tool, enabling researchers to turn theories into precise formulations. This book offers a mathematically gentle and theoretically unified introduction to modeling cognitive processes. Theoretical exercises of varying degrees of difficulty throughout help readers develop their modeling skills. After a general introduction to cognitive modeling and optimization, the book covers models of decision making; supervised learning algorithms, including Hebbian learning, delta rule, and backpropagation; the statistical model analysis methods of model parameter estimation and model evaluation; the three recent cognitive modeling approaches of reinforcement learning, unsupervised learning, and Bayesian models; and models of social interaction. All mathematical concepts are introduced gradually, with no background in advanced topics required. Hints and solutions for exercises and a glossary follow the main text. All code in the book is Python, with the Spyder editor in the Anaconda environment. A GitHub repository with Python files enables readers to access the computer code used and start programming themselves. The book is suitable as an introduction to modeling cognitive processes for students across a range of disciplines and as a reference for researchers interested in a broad overview.




Trends and Challenges in Cognitive Modeling


Book Description

This book presents interdisciplinary research in the science of Human Cognition through mathematical and computational modeling and simulation. Featuring new approaches developed by leading experts in the field of cognitive science, it highlights the relevance and depth of this important area of social sciences and its expanding reach into the biological, physical, computational and mathematical sciences. This contributed volume compiles the most recent advancements and cutting-edge applications of cognitive modeling, employing a genuinely multidisciplinary approach to simulate thinking, memory, and decision-making. The topics covered encompass a wide range of subjects, such as Agent-based Modeling in psychological research, the Nyayasutra proof pattern, the utilization of the Pheromone Trail Algorithm for modeling Analog Memory, the theory and practical applications of Social Laser Theory, addressing the challenges of probabilistic learning in brain and behavior models, adopting a Physicalistic perspective to understand the emergence of cognition and computation, an in-depth analysis of the conjunction fallacy as a factual occurrence, exploring quantum modeling and causality in physics and its extensions, examining compositional vector semantics within spiking neural networks, delving into the realms of Optimality, Prototypes, and Bilingualism, and finally, investigating the intricate dimensionality of color perception. Given its scope and approach, the book will benefit researchers and students of computational social sciences, mathematics and its applications, quantum physics.




An Interdisciplinary Approach to Cognitive Modelling


Book Description

An Interdisciplinary Approach to Cognitive Modelling presents a new approach to cognition that challenges long-held views. It systematically develops a broad-based framework to model cognition, which is mathematically equivalent to the emerging ‘quantum-like modelling’ of the human mind. The book argues that a satisfactory physical and philosophical basis of such an approach is missing, a particular issue being the application of quantization to the mind for which there is no empirical evidence as yet. In response to this issue, the book adopts a COM (classical optical modelling) approach, broad-based but mathematically equivalent to quantum-like modelling while avoiding its problematic features. It presents a philosophically informed and empirically motivated mathematical model of cognition, mainly concerning decision-making processes. It also deals with applications to different areas of the social sciences. It will be of interest to scholars and research students interested in the mathematical modelling of cognition and decision-making, and also interdisciplinary researchers interested in broader issues of cognition.