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Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Symbolic perturbations offer a novel approach for influencing neural representations without requiring direct modification of model parameters. The recursive regeneration of symbolic structures introduces structured variations in latent…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to…
The Adler equation with time-periodic frequency modulation is studied. A series of resonances between the period of the frequency modulation and the time scale for the generation of a phase slip is identified. The resulting parameter space…
Neural oscillations are universal phenomena and can be observed at different levels of neural systems, from single neuron to macroscopic brain. The frequency of those oscillations are related to the brain functions. However, little is know…
Stochastic resetting has shown promise in enhancing the stability of dynamical systems. Here, we apply this concept to theta neuron networks with partial resetting, where only a fraction of neurons is intermittently reset. We examine both…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…
We study the large deviations of additive quantities, such as energy or current, in stochastic processes with intermittent reset. Via a mapping from a discrete-time reset process to the Poland-Scheraga model for DNA denaturation, we derive…
We address the exploitation of an optical parametric oscillator (OPO) in the task of mitigating, at least partially, phase noise produced by phase diffusion. In particular, we analyze two scenarios where phase diffusion is typically…
A tipping point can be defined as an abrupt shift in the properties or behaviour of a system. Tipping points in complex systems from a wide variety of scientific disciplines have been compared to phase transitions in physics, but consistent…
Paced finger tapping is one of the simplest tasks to study sensorimotor synchronization. The subject is instructed to tap in synchrony with a periodic sequence of brief tones, and the time difference (called asynchrony) between each…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
We explore quantum phase transitions using two probes of quantum chaos: out-of-time-order correlators (OTOCs) and the $r$-parameter obtained from the level spacing statistics. In particular, we address $p$-spin models associated with…
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are…
Artificial Recurrent Neural Networks are a powerful information processing abstraction, and Reservoir Computing provides an efficient strategy to build robust implementations by projecting external inputs into high dimensional dynamical…
In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…