PDE models for network flows are used in a number of different applications, including modeling of water channel networks. While the theory and first-order numerics are well developed, there is a lack of high-order schemes. We propose a Runge-Kutta discontinu- ous Galerkin method as an efficient, effective and compact numerical approach for numerical simulations of water flow in open canals. Our numerical tests show the advantages of RKDG over first-order schemes.

Electrocorticography (ECoG) is a neurophysiological modality that measures the distribution of electrical potentials, associated with either spontaneous or evoked neural activity, by means of electrodes grids implanted close to the cortical surface. A full interpretation of ECoG data, however, requires solving the ill-posed inverse problem of reconstructing the spatio-temporal distribution of neural currents responsible for the recorded signals.

Magnetoencephalopgraphy (MEG) is a non-invasive functional imaging modality for mapping cerebral electromagnetic activity from measurements of the weak magnetic field that it generates. It is well known that the MEG inverse problem, i.e. the problem of identifying electric currents from the induced magnetic fields, is a severely underdetermined problem and, without complementary prior information, no unique solution can be found.

Source modeling of EEG data is an important tool for both neuroscience and clinical applications, such as epilepsy. Despite their simplicity, multiple dipole models remain highly desirable to explain neural sources. However, estimating dipole models from EEG time-series remains a difficult task, mainly due to the ill-posedness of the inverse problem and to the fact that the number of dipoles is usually not known a priori.

The formation of methane-hydrate precursors at large planar water-methane interfaces has been studied using massively parallel molecular dynamics in systems of varying size from around 10 000 to almost 7 x 10(6) molecules. This process took two distinct steps. First, the concentration of solvated methane clusters increases just inside the aqueous domain via slow diffusion from the methane-water interface, forming "clusters" of solvated methane molecules.

The brain is a connected network, requiring complex-system measures to describe its organization principles. The normalized compression distance (NCD) [1] is a parameter -free, quasi universal similarity measure that estimates the information shared by two signals comparing the compression length of one signal given the other. Here, we aim at testing whether this new measure is a suitable quantifier of the functional connectivity between cortical regions.

The paper concerns a continuous model governed by a ODE system originated by a discrete duopoly model with bounded rationality, based on constant conjectural variation. The aim of the paper is to show (i) the existence of an absorbing set in the phase space; (ii) linear stability analysis of the critical points of the system; (iii) nonlinear, global asymptotic stability of equilibrium of constant conjectural variation.

A {0, 1}-matrix A is balanced if it does not contain a submatrix of odd order having exactly two 1's per row and per column. A graph is balanced if its clique-matrix is balanced. No characterization of minimally unbalanced graphs is known, and even no conjecture on the structure of such graphs has been posed, contrary to what happened for perfect graphs. In this paper, we provide such a characterization for the class of diamond-free graphs and establish a connection between minimally unbalanced diamond-free graphs and Dyck-paths.

In this study, we compare different diffuse and sharp interface schemes of direct-forcing immersed boundary - thermal lattice Boltzmann method (IB-TLBM) for non-Newtonian flow over a heated circular cylinder. Both effects of the discrete lattice and the body force on the momentum and energy equations are considered, by applying the split-forcing Lattice Boltzmann equations. A new technique based on predetermined parameters of direct forcing IB-TLBM is presented for computing the Nusselt number.