The influence of hubs in the structure of a neuronal network during an epileptic seizure

In this work, we propose changes in the structure of a neuronal network with the intention to provoke strong synchronization to simulate episodes of epileptic seizure. Starting with a network of Izhikevich neurons we slowly increase the number of connections in selected nodes in a controlled way, to produce (or not) hubs. We study how these structures alter the synchronization on the spike firings interval, on individual neurons as well as on mean values, as a function of the concentration of connections for random and non-random (hubs) distribution. We also analyze how the post-ictal signal varies for the different distributions. We conclude that a network with hubs is more appropriate to represent an epileptic state.     

Antennal morphology, structure and sensilla distribution in Microplitis pallidipes (Hymenoptera: Braconidae)

Microplitis pallidipes (Hymenoptera: Braconidae) is an important larval parasitoid of noctuid larval pests. In this study, we describe the morphology, ultrastructure and distribution of sensilla on the antennae of both male and female adults using scanning electron microscopy; complemented with transmission electron microscopy. Observations determined that the antennae of M. pallidipes were threadlike and the flagella were composed of 16 sub-segments. Totally, there were six types of sensilla found on the antennae. They were identified as Sensilla trichodea, Sensilla chaetica, Sensilla basiconica type I, S. basiconica type II, Sensilla coeloconicum, and elongated Sensilla placodea, respectively. The S. trichodea were the most abundant sensilla and distributed over the entire antennae, while S. basiconica I and II, S. coeloconicum, and elongated S. placodea were limited to the flagellum. S. chaetica were found on the scape and pedicle in very low numbers. The S. basiconica II and elongated S. placodea walls were full of pores as evident in transmission electron micrographs. Though the shape and structure of antennae between male and female adults were not basically different, the length and width of the antennae on male wasps were significantly greater than that of females. Also, the number, size and density of S. placodea of the male were significantly greater than those of females. The morphology and structure of these sensilla were compared with that found in other braconid wasps. Their possible functions are discussed in light of previously published literature.     

On a hierarchical error estimator combined with a stabilized method for the Navier–Stokes equations

This work combines two complementary strategies for solving the steady incompressible Navier–Stokes model with a zeroth‐order term, namely, a stabilized finite element method and a mesh–refinement approach based on an error estimator. First, equal order interpolation spaces are adopted to approximate both the velocity and the pressure while stability is recovered within the stabilization approach. Also designed to handle advection dominated flows under zeroth‐order term influence, the stabilized method incorporates a new parameter with a threefold asymptotic behavior. Mesh adaptivity driven by a new hierarchical error estimator and built on the stabilized method is the second ingredient. The estimator construction process circumvents the saturation assumption by using an enhancing space strategy which is shown to be equivalent to the error. Several numerical tests validate the methodology. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

An Analysis of Stapp’s “A Bell-Type Theorem without Hidden Variables”

H.P. Stapp has proposed a number of demonstrations of a Bell-type theorem which dispensed with an assumption of hidden variables, but relied only upon locality together with an assumption that experimenters can choose freely which of several incompatible observables to measure. In recent papers his strategy has centered upon counterfactual conditionals. Stapp’s paper in American Journal of Physics, 2004, replies to objections raised against earlier expositions of this strategy and proposes a simplified demonstration. The new demonstration is criticized, several subtleties in the logic of counterfactuals are pointed out, and the proofs of J.S. Bell and his followers are advocated.Dedicated to the memory of my dear friend Asher Peres.     

Synchronization structure of evolving epileptic networks using cross-entropy

In this paper we present connectivity patterns of evolving large scale epileptic networks. We employed a cross-entropy measure in the frequency domain on EEG signals to infer the networks, before and during episodes of epileptic seizures. This measure allowed us to make a richer portrait about the node interactions on the graph and to identify emergent structures associated with the synchronization of brain activity. Our results points to a more complex scenario of network organization than the synchronized/unsynchronized dichotomy, with two main results: first, showing regions with unsynchronized (or independent) behavior, even during absence seizures, contradicting the concept of hypersynchrony. Furthermore, we explore the cross-entropy fluctuations along the seizure: a group of nodes became more similar over time while another group became more different, showing a complementary behaviour and different local brain activities. These results bring new questions about the spreading and the sustenance of the epileptic seizures and others synchronization phenomena in living systems.     

Tensor FEM for Spectral Fractional Diffusion

Foundations of Computational Mathematics - We design and analyze several finite element methods (FEMs) applied to the Caffarelli–Silvestre extension that localizes the fractional powers of...     

A note on the Stokes operator and its powers

The so-called Stokes operator is an important tool in the analysis of the solutions of the Navier-Stokes equations and their numerical approximation. The aim of this note is to clarify certain properties of the fractional powers of this operator which are sometimes misused.