*Morgan André*

We consider a countably infinite system of spiking neurons. In this model each neuron has a membrane potential which takes value in the non-negative integers. Each neuron is also associated with two point processes. The first one is a Poisson process of some parameter γ, representing the \textit{leak times}, that is the times at which the membrane potential of the neuron is spontaneously reset to 0. The second point process, which represents the \textit{spiking times}, has a non-constant rate which depends on the membrane potential of the neuron at time t. This model was previously proven to present a phase transition with respect to the parameter γ. It was also proven that the renormalized time of extinction of a finite version of the system converges in law toward an exponential random variable when the number of neurons goes to infinity, which indicates a metastable behavior. Here we prove a result which is in some sense the symmetrical of this last result: we prove that when γ>1 (super-critical) the renormalized time of extinction converges in probability to 1.

*Morgan André*

In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter γ, corresponding to the rate of the leaking times of the neurons and, as the title says, it was proven there to present a phase transition phenomenon with respect to this γ. Here we prove that this model also exhibit a metastable behavior. By this we mean that if γ is small enough, then the re-normalized time of extinction converges toward an exponential random variable of mean 1 as the number of neurons goes to infinity.

*Saeideh Arsalani, Soudabeh Arsalani, Yaser Hadadian, Diego Ronaldo Thomaz Sampaio, Oswaldo Baffa, Theo Zeferino Pavan and Antonio Adilton Oliveira Carneiro*

The shear wave dispersion magneto-motive ultrasound (SDMMUS) method was recently developed to analyze the mechanical properties of a viscoelastic medium. This technique is based on the interaction of magnetic nanoparticles (MNPs) with an external magnetic field to generate a shear wave within the medium labeled with MNPs. The propagation of this wave provides information about viscoelastic properties of the medium. In the previous work Arsalani et al. magnetite NPs were synthesized by co-precipitation method coated with natural rubber latex (NRL). In order to investigate the effect of NRL on the size and magnetization of MNPs, different amount of NRL, 0 μL, 100 μL, and 800 μL of a stock solution of NRL, were used during the synthesis process. The results showed that MNPs prepared with 800 μL of NRL, named as MNPs-800NRL, had the smallest size and highest magnetization. In the present paper, the main goal is to investigate if the MNPs-800NRL having the highest magnetization is also the best option for SDMMUS experiments among the others. All experiments were performed using gelatin tissue mimicking phantoms labeled with the aforementioned MNPs. Two factors including core size and magnetization were considered and based on the observed results the effect of magnetization was more prominent than the core size on the induced displacements. MNPs coated with a thicker NRL shell having the highest magnetization value enhanced the sensitivity and signal to noise ratio in SDMMUS. Different concentrations of this optimized MNPs were also examined to investigate the lowest possible concentration for observing shear waves in the SDMMUS technique.

Bia Lima Ramalho, Maria Luíza Rangel, Ana Carolina Schmaedeke, Fátima Smith Erthal and Claudia D. Vargas

Unilateral brachial plexus injury (BPI) impairs sensory and motor functions of the upper limb. This study aimed to map in detail brachial plexus sensory impairment both in the injured and the uninjured upper limb. Touch sensation was measured through Semmes-Weinstein monofilaments at the autonomous regions of the brachial plexus nerves, hereafter called points of exclusive innervation (PEIs). Seventeen BPI patients (31.35 years±6.9 SD) and 14 age-matched healthy controls (27.57 years±5.8 SD) were tested bilaterally at six selected PEIs (axillary, musculocutaneous, median, radial, ulnar, and medial antebrachial cutaneous [MABC]). As expected, the comparison between the control group and the brachial plexus patients' injured limb showed a robust difference for all PEIs (*p* ≤ 0.001).

J. Chevallier, A. Duarte, E. Löcherbach and G. Ost

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.

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