The neuronal functional connectivity is a complex and non-stationary phenomenon creating dynamic networks synchronization determining the brain states and needed to produce tasks. Here, as a measure that quantifies the synchronization between the neuronal electrical activity of two brain regions, we used the normalized compression distance (NCD), which is the length of the compressed file constituted by the concatenated two signals, normalized by the length of the two compressed files including each single signal.

We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field.

In the description of the relativistic two-body interaction, together with the effects of energy and angular momentum losses due to the emission of gravitational radiation, one has to take into account also the loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum flux for a nonspinning binary system either along hyperboliclike or ellipticlike orbits.

Blue phases are liquid crystals made up by networks of defects, or disclination lines. While existing phase diagrams show a striking variety of competing metastable topologies for these networks, very little is known as to how to kinetically reach a target structure, or how to switch from one to the other, which is of paramount importance for devices. We theoretically identify two confined blue phase I systems in which by applying an appropriate series of electric field it is possible to select one of two bistable defect patterns.

In this paper, we consider the isoperimetric problem in the space R with a density. Our result states that, if the density f is lower semi-continuous and converges to a limit a> 0 at infinity, with f<= a far from the origin, then isoperimetric sets exist for all volumes. Several known results or counterexamples show that the present result is essentially sharp. The special case of our result for radial and increasing densities positively answers a conjecture of Morgan and Pratelli (Ann Glob Anal Geom 43(4):331-365, 2013.

We consider the Dirichlet eigenvalue problem, (the eigenfunction) and ? > 0 (the eigen value), ? is an arbitrary domain in RN with finite measure, 1 < p < ?, 1 < q < p*, p* = Np/(N - p) if 1 < p < N and p* = ? if p >= N. We study several existence and uniqueness results as well as some properties of the solutions. Moreover, we indicate how to extend to the general case some proofs known in the classical case p = q. © 2010 Texas State University - San Marcos.

Given a bounded open set in [Formula presented], [Formula presented], and a sequence [Formula presented] of compact sets converging to an [Formula presented]-dimensional manifold [Formula presented], we study the asymptotic behaviour of the solutions to some minimum problems for integral functionals on [Formula presented], with Neumann boundary conditions on [Formula presented].

In this paper, we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown to capture the deformation and breakup dynamics of droplets interacting within the constriction, in agreement with experimental evidence. In addition, it permits us to investigate in detail the hydrodynamic phenomena occurring during breakup stages.

Given an open set ?, we consider the problem of providing sharp lower bounds for ? (?), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong-Krahn-Szego inequality, asserting that the disjoint unions of two equal balls minimize ? among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ? are considered as well. © 2012 Springer-Verlag Berlin Heidelberg.