Despite numerous important contributions, the investigation of brain connectivity with magnetoencephalography (MEG) still faces multiple challenges. One critical aspect of source-level connectivity, largely overlooked in the literature, is the putative effect of the choice of the inverse method on the subsequent cortico-cortical coupling analysis. We set out to investigate the impact of three inverse methods on source coherence detection using simulated MEG data. To this end, thousands of randomly located pairs of sources were created.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions under oscillatory shear flow are investigated by Brownian multi-particle collision dynamics. Two different scenarios will be considered: Filaments with both fixed ends [1] and wall-anchored chains [2].The results of the numerical studies will be presented and discussed. 1] A. Lamura, R. G. Winkler, 'Tethered semiflexible polymer under large amplitude oscillatory shear', Polymers 11, 737 (2019) [2] A. Lamura, R. G. Winkler, G.

Background: Neutrophils are one of the key players in the human innate immune system (HIIS). In the event of an insult where the body is exposed to inflammation triggering moieties (ITMs), neutrophils are mobilized towards the site of insult and antagonize the inflammation. If the inflammation is cleared, neutrophils go into a programmed death called apoptosis.

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function.

A reaction-diffusion system governing the prey-predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions under oscillatory shear flow are investigated by Brownian multi-particle collision dynamics. Two different scenarios will be considered: Filaments with both fixed ends [1] and wall-anchored chains [2]. The results of the numerical studies will be presented and discussed. References [1] A. Lamura, R. G. Winkler Polymers 2019, 11, 737. DOI:10.3390/polym11040737 [2] A. Lamura, R. G. Winkler, G. Gompper pre-print 2021

We numerically study by lattice Boltzmann simulations the rheological properties of an active emulsion made of a suspension of an active polar gel embedded in an isotropic passive background. We find that the hexatic equilibrium configuration of polar droplets is highly sensitive to both active injection and external forcing and may either lead to asymmetric unidirectional states which break top-bottom symmetry or symmetric ones. In this latter case, for large enough activity, the system develops a shear thickening regime at low shear rates.

A (2+2)-dimensional kinetic equation, directly inspired by the run-and-tumble modeling of chemotaxis dynamics is studied so as to derive a both ''2D well-balanced'' and ''asymptotic-preserving'' numerical approximation. To this end, exact stationary regimes are expressed by means of Laplace transforms of Fourier-Bessel solutions of associated elliptic equations. This yields a scattering S-matrix which permits to formulate a timemarching scheme in the form of a convex combination in kinetic scaling.

Numerical resolution of two-stream kinetic models in a strong aggregative setting is considered. To illustrate our approach, we consider a one-dimensional kinetic model for chemotaxis in hydrodynamic scaling and the high field limit of the Vlasov-Poisson-Fokker-Planck system. A difficulty is that, in this aggregative setting, weak solutions of the limiting model blow up in finite time, and therefore the scheme should be able to handle Dirac measures.

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.