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A large number of eukaryotic cells are able to directly detect external chemical gradients with great accuracy and the ultimate limit to their sensitivity has been a topic of debate for many years. Previous work has been done to understand…
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 analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly…
Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high frequency regime. In addition to the usual excitation threshold there is a smooth crossover…
Extracting stimulus features from neuronal ensembles is of great interest to the development of neuroprosthetics that project sensory information directly to the brain via electrical stimulation. Machine learning strategies that optimize…
This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
Neuronal excitability is known to be affected by transcranial electrical stimulation. However, due to the existence of both excitatory and inhibitory neurons in the cortex, the mechanism of neuronal excitability shift is still not clear.…
Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing…
We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing…
How do humans and animals perform trial-and-error learning when the space of possibilities is infinite? In a previous study, we used an interval timing production task and discovered an updating strategy in which the agent adjusted the…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
The brain can be understood as a collection of interacting neuronal oscillators, but the extent to which its sustained activity is due to coupling among brain areas is still unclear. Here we study the joint dynamics of two cortical columns…
The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
A spin-$s$ variable-range interacting Ising model may display qualitatively different behaviors depending on the fall-off rate of the interactions, as already seen in equilibrium studies of spin-1/2 systems. We propose a dynamical method…
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously…
Statistical properties of environments experienced by biological signaling systems in the real world change, which necessitate adaptive responses to achieve high fidelity information transmission. One form of such adaptive response is gain…