Related papers: Neural Field Models: A mathematical overview and u…
The analyses presented herein demonstrate that neuronal electrical activity can be consistently interpreted as a manifestation of murburn redox-mediated electronic dynamics rather than as a process fundamentally driven by transmembrane…
It is essential to understand the complex structure of the human brain to develop new treatment approaches for neurodegenerative disorders (NDDs). This review paper comprehensively discusses the challenges associated with modelling the…
We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…
Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…
This paper considers neural representation through the lens of active inference, a normative framework for understanding brain function. It delves into how living organisms employ generative models to minimize the discrepancy between…
This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…
Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…
Phenomics is concerned with detailed description of all aspects of organisms, from their physical foundations at genetic, molecular and cellular level, to behavioural and psychological traits. Neuropsychiatric phenomics, endorsed by NIMH,…
Although lagging behind classical computational neuroscience, theoretical and computational approaches are beginning to emerge to characterize different aspects of neuron-glial interactions. This chapter aims to provide essential knowledge…
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…
Human learning is a complex phenomenon that requires adaptive processes across a range of temporal and spacial scales. While our understanding of those processes at single scales has increased exponentially over the last few years, a…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
Functional MRI (fMRI) is crucial for studying brain function and diagnosing neurological disorders. However, existing analysis methods suffer from reproducibility and transferability challenges due to complex preprocessing pipelines and…
Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear…
Foundation models (FMs) have emerged as a transformative paradigm in medical image analysis, offering the potential to provide generalizable, task-agnostic solutions across a wide range of clinical tasks and imaging modalities. Their…
There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models…
Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…
Finding general principles underlying brain function has been appealing to scientists. Indeed, in some branches of science like physics and chemistry (and to some degree biology) a general theory often can capture the essence of a wide…