Mathematics

Advances in Brain Inspired Cognitive Systems

The two-volume set LNAI 15497 and LNAI 15498 constitutes the refereed proceedings of the 14th International Conference on Brain Inspired Cognitive Systems, BICS 2024, held in Hefei, China, during December 6–8, 2024.

1. Michael Rescorla

Bayesian Models of the Mind

Bayesian decision theory is a mathematical framework that models reasoning and decision-making under uncertain conditions. The Bayesian paradigm originated as a theory of how people should operate, not a theory of how they actually operate. Nevertheless, cognitive scientists increasingly use it to describe the actual workings of the human mind. Over the past few decades, cognitive science has produced impressive Bayesian models of mental activity. The models postulate that certain mental processes conform, or approximately conform, to Bayesian norms. Bayesian models offered within cognitive science have illuminated numerous mental phenomena, such as perception, motor control, and navigation. This Element provides a self-contained introduction to the foundations of Bayesian cognitive science. It then explores what we can learn about the mind from Bayesian models offered by cognitive scientists.

1. Michael Rescorla

Bayesian Models of the Mind

Bayesian decision theory is a mathematical framework that models reasoning and decision-making under uncertain conditions. The Bayesian paradigm originated as a theory of how people should operate, not a theory of how they actually operate. Nevertheless, cognitive scientists increasingly use it to describe the actual workings of the human mind. Over the past few decades, cognitive science has produced impressive Bayesian models of mental activity. The models postulate that certain mental processes conform, or approximately conform, to Bayesian norms. Bayesian models offered within cognitive science have illuminated numerous mental phenomena, such as perception, motor control, and navigation. This Element provides a self-contained introduction to the foundations of Bayesian cognitive science. It then explores what we can learn about the mind from Bayesian models offered by cognitive scientists.

1. Xiao-Jing Wang

Theoretical Neuroscience

This textbook synthesizes neuroscience and cognitive science. Cognition and intelligence arise from neural circuits endowed with many feedback loops, which is difficult to understand by intuition alone. The book covers basic computational neuroscience required for discussions of brain mechanisms and computational principles of cognition.

Trends and Challenges in Cognitive Modeling

Tomas Veloz has a PhD in Interdisciplinary Studies and a Master's degree in Computer Science, with majors in Mathematics and Physics. His research focuses on interdisciplinary mathematical modeling. His main research areas are Chemical Organization theory, where he has proven mathematical results such as the decomposition theorem and the existence of quantum-like organizational structures, and quantum cognition, where he has developed methods to represent collections of concepts in a Hilbert Space, and has shown that various cognitive and language phenomena exhibit quantum structure. Dr. Veloz is the Founder and Director of the Foundation for the Interdisciplinary Development of Science, Technology and Arts (DICTA), Chile, which collaborates with various institutions around the world for the generation and dissemination of integrated knowledge, and the development of projects with social impact.   Andrei Khrennikov holds a PhD in Mathematical Physics from the Moscow State University, Russia. Since 1997 he is a Professor at Linnaueus University, Sweden. In 2002, he became the Director of the International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. His research interests are characterized by multi-disciplinarity, e.g., foundations of quantum physics and quantum information, foundations of probability, cognitive modeling, ultrametric (non-Archimedean) mathematics, dynamical systems, quantum-like models in psychology, economics and finances, social and political sciences. Dr. Khrennikov is the organizer of the worldwide known series of annual conferences in Växjö on foundations of quantum physics, information, and probability, held since 2000.   Bourama Toni is graduate of Université de Montreal, and is presently a full Professor and Chair of the Department of Mathematics at Howard University, Washington DC, USA. He isalso a founder and the Editor-in-Chief of the Springer's STEAM-H series. Dr. Toni's research interests are in differential and nonlinear analysis and related topics, including p-adic analysis, game theory and feedback loops analysis, and applications to naval engineering and biosciences. He has published several books with Springer.Bourama Toni is graduate of Université de Montreal, and is presently a full Professor and Chair of the Department of Mathematics at Howard University, Washington DC, USA. He is also a founder and the Editor-in-Chief of the Springer's STEAM-H series. Dr. Toni's research interests are in differential and nonlinear analysis and related topics, including p-adic analysis, game theory and feedback loops analysis, and applications to naval engineering and biosciences. He has published several books with Springer. Ramón D. Castillo holds a Ph. D. in Psychology and M. A. in Psychology, University of Cincinnati, McMicken College of Arts and Sciences, Ohio, USA; he is an Associate Professor of the Faculty of Psychology at the University of Talca. He researches reasoning and learning processes in humans. Specifically, he seeks to understand how human beings reason with the mental states of others (Intentionality); and how they learn to predict or anticipate the occurrence of events in nature (Physical Causation). He currently directs the Cognitive Sciences Research Center (CICC) and the Cognitive Sciences Associative Research Program funded by the University of Talca. He teaches in the Psychology department at under and postgraduate levels. He is a member of the Psychology Study Panel at CONICYT, and a member of the editorial committee of the International Journal of Psychological Research. He is also a manuscript reviewer for Neuroscience Letters and European Child & Adolescent Psychiatry.

1. Kit Yates

How to Expect the Unexpected