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Neuronal models based on the Hodgkin-Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modeled deterministically, experimental recordings show stochastic fluctuations,…
Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…
The dynamic mode decomposition (DMD) technique extracts the dominant modes characterizing the innate dynamical behavior of the system within the measurement data. For appropriate identification of dominant modes from the measurement data,…
EEG-based analysis of pain perception, enhanced by machine learning, reveals how the brain encodes pain by identifying neural patterns evoked by noxious stimulation. However, a major challenge that remains is the generalization of machine…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
With respect to biological findings underlying fly's physiology in the past decade, we present a directionally selective neural network, with a feed-forward structure and entirely low-level visual processing, so as to implement direction…
Neural oscillations are electrical activities of the brain measurable at different frequencies. This paper studies the interaction between the fast and slow processes in the brain. We recorded signals intracranially from the simple Wistar…
This work explores four nonlinear classical models of neural oscillators, the Hodgkin-Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Nonlinear contraction theory is used to develop observers…
Background: The treatment of depressive episodes is well established, with clearly demonstrated effectiveness of antidepressants and psychotherapies. However, more than one-third of depressed patients do not respond to treatment.…
Emergent behavior, which arises from local interactions between simple elements, is pervasive in nature. It underlies the energy-efficient computing in our brains. However, realizing such dynamics in artificial materials, particularly under…
The extant versions of many basal ganglia models use a `gating' model of dopamine function which enhances input to D1 receptor units and attenuates input to D2 receptor units. There is evidence that this model is unsatisfactory because (a)…
The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with…
$n$-particle reduced density matrices ($n$-RDMs) play a central role in understanding correlated phases of matter, but their calculation is often computationally inefficient for strongly-correlated states at large system sizes. In this…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
The describing function (DF) and phase response curve (PRC) are classical tools for the analysis of feedback oscillations and rhythmic behaviors, widely used across control engineering, biology, and neuroscience. These tools are known to…
We develop a biophysical model of neuro-sensory integration in the model organism Caenorhabditis elegans. Building on recent experimental findings of the neuron conductances and their resolved connectome, we posit the first full dynamic…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
Chronic pain is a significant global health issue, with many patients experiencing persistent pain despite no identifiable organic cause, classified as nociplastic pain. Increasing evidence highlights the role of danger signal processing in…
The dynamical mechanism underlying the processes of anesthesia-induced loss of consciousness and recovery is key to gaining insights into the working of the nervous system. Previous experiments revealed an asymmetry between neural signals…