AVVISO di SEMINARIO

Dipartimento di Matematica e Applicazioni “R. Caccioppoli”

Università degli Studi di Napoli Federico II

Il giorno 13 maggio 2025, alle ore 11:30, in SP2L, aula S. Rionero, del Dipartimento di Matematica e Applicazioni R. Caccioppoli, il Prof. Kei Kobayashi, Department of Mathematics, Fordham University, terrà il seguente seminario:

“Numerical approximation of stochastic differential equations modeling subdiffusion”

Abstract: Standard Brownian motion composed with a random time change given by an inverse subordinator has been used to model subdiffusions, where particles spread more slowly than the classical Brownian particles. The time-changed Brownian motion is neither Markovian nor Gaussian, and standard procedures known for normal diffusions do not generally work. This talk gives an overview of the framework of numerical approximation schemes for the time-changed Brownian motion and its associated stochastic differential equations, along with the rates of convergence. This is based on joint work with Sixian Jin and Ernest Jum.

Avviso di Seminario
Nell’ambito delle attività del progetto EBRAINS-Italy, il giorno lunedì 19 maggio dalle ore 15:00 alle ore 16:00, nell’aula Professori II livello, la dott.ssa Simona Olmi dell’Istituto dei Sistemi Complessi – Consiglio Nazionale delle Ricerche, terrà il seminario:
Relaxation oscillations in next-generation neural masses
with spike-frequency adaptation
Abstract: Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean-field reduction, which gives rise to next-generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favors the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry, namely, chimera-like solutions in the inhibitory case and antiphase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling among the fast synaptic timescale and the slow adaptation one, ranging from antiphase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. In a PING configuration, where SFA affects the excitatory population only, it is possible to observe the emergence of relaxation oscillations due to the interplay between the nonlinear dynamics of the firing rate and the self-inhibition modulated by SFA. A characterization of Up and Down states, together with that of the spike adding process, is provided in the PING configuration for different parameters.

Seminario_Olmi

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Roberta Marziani (Siena)

Mercoledì, 28 maggio⋅15:00 – 16:00

Sala Professori I livello

Titolo: Gamma-convergence for plane to wrinkles transition region Abstract: Motivated by physical experiments, we consider a variational problem modelling wrinkling effect of a thin annular sheet radially stretched. We start with a brief introduction on elasticity theory for thin films. We then settle a model for an annular domain radially stretched and describe an energy scaling result for low energy wrinkle patterns [Bella-Kohn 2014]. Afterwards, to better characterize the wrinkle pattern, in particular to describe the transition  between flat and wrinkled regions we set up a toy problem and perform an asymptotic analysis, via Gamma-concergence, as the sheet thickness goes to 0.  The limiting problem is scalar and convex, but constrained and posed for measures. The latter are in some sense related to Fourier coefficients of the vertical displacement of the elastic deformation.  Eventually for the limiting problem we show existence of a minimizer and equipartition of the energy for each frequency. This is based on a joint work with Peter Bella (TU Dortmund).

Avviso di Seminario