arXiv subjects

Benjamin Ambrosio

Publications and source records attributed to Benjamin Ambrosio.

4 recordsLinked to original sources

arXiv2025

Quantifying Mental States in Work Environment: Mathematical Perspectives

We introduce a novel framework for quantifying mental and emotional states over time by combining virtual reality (VR) exposure with EEG recordings. Participants experienced a stress-inducing work scenario in VR, originally designed as a training tool for bank employees, providing a controlled proxy for high-stakes situations. This setup enables integration of subjective emotional self-assessments with objective neural data, from which an algorithm was efficiently used to infer emotional states. Building on these measurements, we propose possible mathematical models to capture the temporal dynamics of mental states, offering a quantitative approach to studying emotional processing and informing adaptive training in complex environments.

q-bio.NC↗

arXiv2023

Qualitative Analysis of certain Reaction-Diffusion Systems of the FitzHugh-Nagumo type

This article aims to provide insights into the qualitative analysis of some nonlinear Reaction-Diffusion (RD) systems arising in Neuroscience. We first introduce a non-homogeneous FitzHugh-Nagumo (nhFHN) featuring excitability and oscillatory properties. Then, we discuss the qualitative analysis of a toy model related to nhFHN. In particular, we focus on the convergence of solutions of the toy model toward different solutions (fixed point, periodic) and show the existence of a cascade of Hopf bifurcations. Finally, we connect this analysis to the nhFHN system.

math.DS↗

arXiv2020

On a coupled time-dependent SIR models fitting with New York and New-Jersey states COVID-19 data

This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. The death rate is also secondarily adjusted. Our fitting is made under the assumption that due to limiting number of tests, a large part of the infected population has not been tested positive. In the last part, we extend the model to take into account the daily fluxes between New Jersey (NJ) and NY states and fit the data for both states. Our simple model fits the available data, and illustrates typical dynamics of the disease: exponential increase, apex and decrease. The model highlights a decrease in the transmission rate over the period which gives a quantitative illustration about how lockdown policies reduce the spread of the pandemic. The coupled model with NY and NJ states shows a wave in NJ following the NY wave, illustrating the mechanism of spread from one attractive hot spot to its neighbor. }

q-bio.PE↗

arXiv2020

Simulating brain rhythms using an ODE with stochastically varying coefficients

The brain produces rhythms in a variety of frequency bands. Some are likely by-products of neuronal processes; others are thought to be top-down. Produced entirely naturally, these rhythms have clearly recognizable beats, but they are very far from periodic in the sense of mathematics. They produce signals that are broad-band, episodic, wandering in magnitude, in frequency and in phase; the rhythm comes and goes, degrading and regenerating. Rhythms with these characteristics do not match standard dynamical systems paradigms of periodicity, quasi-periodicity, or periodic motion in the presence of a Brownian noise. Thus far they have been satisfactorily reproduced only using networks of hundreds of integrate-and-fire neurons. In this paper, we tackle the mathematical question of whether signals with these properties can be generated from simpler dynamical systems. Using an ODE with two variables inspired by the FitzHugh-Nagumo model, and varying randomly three parameters that control the magnitude, frequency and degree of degradation, we were able to replicate the qualitative characteristics of these natural brain rhythms. Viewing the two variables as Excitatory and Inhibitory conductances of a typical neuron in a local population, our model produces results that closely resemble gamma-band activity in real cortex, including the moment-to-moment balancing of E and I-currents seen in experiments.

math.DS↗