Mathematical Modelling of Human Cognitive and Neurophysiological Systems for Biomedical Applications

Abstract

Viktoria Kondratenko and Leonid Slovianov

The complexity of the human psyche remains a central topic in neuroscience, psychology, and biomedical science. This paper introduces a novel approach to understanding the human psyche by integrating cognitive and neurophysiological systems into a unified mathematical framework. The study proposes a formalized model based on logical predicates to explore the interplay between physiological and cognitive processes, shedding light on the mechanisms behind human thoughts, behaviours, and interactions.

The human psyche operates through two primary systems: the first signalling system, rooted in physiological responses, and the second signalling system, which enables cognitive functions like language, reasoning, and abstract thinking. Despite their interconnectedness, a lack of robust feedback mechanisms between these systems often leads to errors in perception, reasoning, and decision-making. This paper examines these gaps and their implications for mental health and behaviour.

The research builds on 14 foundational concepts, ranging from the physical basis of matter to the architecture of the nervous system, to establish a comprehensive theoretical foundation. Key highlights include

• The description of neural networks as the biological substrate for the psyche, emphasizing their adaptability and complexity.

• The identification of "harmful functions" in the psyche, such as selfishness, deceit, and aggression, which arise from evolutionary and genetic constraints.

• The development of a logical model that allows for the prediction and analysis of the psyche’s normative functioning.

The mathematical framework formalizes the relationships between various elements of the psyche and its interactions with the environment. By applying logic and predicate theory, the study demonstrates how these relationships can be expressed in a structured and testable manner. This approach offers a method to evaluate mental processes, identify potential dysfunctions, and propose corrective strategies.

The findings have significant implications for biomedical science. The model provides a foundation for understanding the root causes of mental health disorders, bridging the gap between theoretical research and clinical practice. It also opens avenues for the development of diagnostic tools and therapies aimed at enhancing the feedback mechanisms between physiological and cognitive systems.

In conclusion, this paper presents a ground-breaking step toward the formalization of the human psyche’s functioning. By integrating concepts from neuroscience, psychology, and logic, it offers a new perspective on the challenges and opportunities in understanding mental processes. The proposed model is not only a theoretical construct but also a practical tool for advancing research and improving clinical interventions in mental health.

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