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A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the…
Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that updating all weights is…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We study dynamics of a reverberating neural net by means of computer simulation. The net, which is composed of 9 leaky integrate-and-fire (LIF) neurons arranged in a square lattice, is fully connected with interneuronal communication delay…
We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
We investigate the Brusselator system with diffusion and Dirichlet boundary conditions on one dimensional space interval. Our proof demonstrates that, for certain parameter values, a periodic orbit exists. This proof is computer-assisted…
Recurrent neural networks (RNNs) are machine learning models widely used for learning temporal relationships. Current state-of-the-art RNNs use integrating or spiking neurons -- two classes of computing units whose outputs depend directly…
We investigate the dynamics of spinning binaries of compact objects at the next-to-leading order in the quadratic-in-spin effects, which corresponds to the third post-Newtonian order (3PN). Using a Dixon-type multipolar formalism for…
In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir…
Recent studies have shown that functional brain brainwork is dynamic even during rest. A common approach to modeling the brain network in whole brain resting-state fMRI is to compute the correlation between anatomical regions via sliding…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
In this work, an analysis of the performance of different Variational Quantum Circuits is presented, investigating how it changes with respect to entanglement topology, adopted gates, and Quantum Machine Learning tasks to be performed. The…
The effect of exchange interactions within spin pairs on spin-dependent transport and recombination rates through localized states in semiconductors during coherent electron spin resonant excitation is studied theoretically. It is shown…
Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…
Conventional machine learning algorithms have traditionally been designed under the assumption that input data follows a vector-based format, with an emphasis on vector-centric paradigms. However, as the demand for tasks involving set-based…
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns…