Related papers: A Modified Equation for Neural Conductance and Res…
In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of…
We present an exact solution of a supersymmetric nonlinear sigma model describing the crossover between a quantum dot and a disordered quantum wire with unitary symmetry. The system is coupled ideally to two electron reservoirs via…
Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution…
Despite their elegant formulation and lightweight memory cost, neural ordinary differential equations (NODEs) suffer from known representational limitations. In particular, the single flow learned by NODEs cannot express all homeomorphisms…
Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate,…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
Machine learning with artificial neural networks (ANNs), provides solutions for the growing complexity of modern communication systems. This complexity, however, increases power consumption, making the systems energy-intensive. Spiking…
An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS $s$-wave superconductor and a quantum spin. It is shown that known results…
Spiking neural networks (SNNs) offer a promising pathway to implement deep neural networks (DNNs) in a more energy-efficient manner since their neurons are sparsely activated and inferences are event-driven. However, there have been very…
Simplified neuronal models capture the essence of the electrical activity of a generic neuron, besides being more interesting from the computational point of view when compared to higher dimensional models such as the Hodgkin-Huxley one. In…
The Blackstock-Crighton equations describe the motion of a viscous, heat-conducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into…
The discovery of neural plasticity has proved that throughout the life of a human being, the brain reorganizes itself through forming new neural connections. The formation of new neural connections are achieved through the brain's effort to…
Evolutionary symbolic regression (SR) fits a symbolic equation to data, which gives a concise interpretable model. We explore using SR as a method to propose which data to gather in an active learning setting with physical constraints. SR…
We analyze the nonequilibrium Kondo model at finite voltage and temperature by using a new formulation of the real-time renormalization group method with the Laplace variable as the flow parameter. We evaluate the energy-dependent spin…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
In a previous article (Rahman, Guns, Rousseau, and Engels, 2015) we described several approaches to determine the cognitive distance between two units. One of these approaches was based on what we called barycenters in N dimensions. The…
Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive…
Cross-modal retrieval is generally performed by projecting and aligning the data from two different modalities onto a shared representation space. This shared space often also acts as a bridge for translating the modalities. We address the…
We have studied the classical and quantum expressions of electrical conductivity and their numerical estimation in the presence of a magnetic field for hadron resonance gas (HRG) and massless quark matter. Classical results of transport…