Related papers: A Mathematical Approach to the Sleep-Waking Cycle
Understanding the time evolution of physical systems is crucial to revealing fundamental characteristics that are hidden in frequency domain. In optical science, high-quality resonance cavities and enhanced interactions with matters are at…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
Cellular phones are now offering an ubiquitous means for scientists to observe life: how people act, move and respond to external influences. They can be utilized as measurement devices of individual persons and for groups of people of the…
Sleep is essential for learning and cognition, but the mechanisms by which it stabilizes learning, supports creativity, and manages the energy consumption of networks engaged in post-sleep task have not been yet modelled. During sleep, the…
Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of…
Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must…
Human sleep is cyclical with a period of approximately 90 minutes, implying long temporal dependency in the sleep data. Yet, exploring this long-term dependency when developing sleep staging models has remained untouched. In this work, we…
This paper proposes a practical approach for automatic sleep stage classification based on a multi-level feature learning framework and Recurrent Neural Network (RNN) classifier using heart rate and wrist actigraphy derived from a wearable…
This work presents a comprehensive theory of consciousness grounded in mathematical formalism and supported by clinical data analysis. The framework developed herein demonstrates that consciousness exists as a continuous, non-monotonic…
I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states,…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
Artificial neural networks (ANNs) show limited performance with scarce or imbalanced training data and face challenges with continuous learning, such as forgetting previously learned data after new tasks training. In contrast, the human…
Sleep is a complex physiological process evaluated through various modalities recording electrical brain, cardiac, and respiratory activities. We curate a large polysomnography dataset from over 14,000 participants comprising over 100,000…
Phase resetting is a common experimental approach to investigating the behaviour of oscillating neurons. Assuming repeated spiking or bursting, a phase reset amounts to a brief perturbation that causes a shift in the phase of this periodic…
Owing to the absence of the phase space attractors in the Hamiltonian dynamical systems, the concept of the identical synchronization between the dissipative systems is inapplicable to the Hamiltonian systems for which, thus, one defines a…
For switched systems that switch between distinct globally stable equilibria, we offer closed-form formulas that lock oscillations in the required neighborhood of the equilibria. Motivated by non-spiking neuron models, the main focus of the…
Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
Learning in the brain requires complementary mechanisms: potentiation and activity-dependent homeostatic scaling. We introduce synaptic scaling to a biologically-realistic spiking model of neocortex which can learn changes in oscillatory…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…