A first order binomial mixed poisson integer-valued autoregressive model with serially dependent innovations

Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system

Localizing Brain Activity from Multiple Distinct Sources via EEG

An important question arousing in the framework of electroencephalography (EEG) is the possibility to recognize, by means of a recorded surface potential, the number of activated areas in the brain. In the present paper, employing a homogeneous spherical conductor serving as an approximation of the brain, we provide a criterion which determines whether the measured surface potential is evoked by a single or multiple localized neuronal excitations. We show that the uniqueness of the inverse problem for a single dipole is closely connected with attaining certain relations connecting the measured data. Further, we present the necessary and sufficient conditions which decide whether the collected data originates from a single dipole or from numerous dipoles. In the case where the EEG data arouses from multiple parallel dipoles, an isolation of the source is, in general, not possible

Autonomous inspection and repair of aircraft composite structures

This paper deals with the development of an innovative approach for inspection and repair of damage in aeronautical composites that took place in the first two years of the H2020 CompInnova project which. The aim is a newly designed robotic platform for autonomous inspection using combined infrared thermography (IRT) and phased array (PA) non-destructive investigation for damage detection and characterization, while integrated with laser repair capabilities. This will affect the increasing societal need for safer aircraft in the lowest possible cost, while new and effective techniques of inspection are needed because of the rapidly expanding use of composites in the aerospace industry

CONVERGENT LOW-FREQUENCY EXPANSIONS FOR PENETRABLE SCATTERERS.

CONVERGENT LOW-FREQUENCY EXPANSIONS FOR PENETRABLE SCATTERERS

On the non-uniqueness of the inverse problem associated with electroencephalography

We present here a quantitative characterization of the non-uniqueness for the inverse problem of electroencephalography (EEG). First, we identify the singular support of the electric potential generated by a dipolar current which is fired inside the spherical model of the brain. Next, we extend this result to a continuously distributed neuronal current and we derive the equivalent Green's integral representation. Then, using the Hansen representation of the current, we show that among the three scalar representation functions, only two are needed to represent the observed electric potential on the surface or outside the head. The scalar function that is missed by the EEG recordings is exactly the one that is recorded by magnetoencephalography (MEG). Finally, the solution of the inverse EEG problem is reduced to a specific moment problem, which is exactly solved under the minimum-current assumption

The 3D Happel model for complete isotropic Stokes flow

The creeping flow through a swarm of spherical particles that move with constant velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity in a quiescent Newtonian fluid is analyzed with a 3D sphere-in-cell model. The mathematical treatment is based on the two-concentric-spheres model. The inner sphere comprises one of the particles in the swarm and the outer sphere consists of a fluid envelope. The appropriate boundary conditions of this non-axisymmetric formulation are similar to those of the 2D sphere-in-cell Happel model, namely, nonslip flow condition on the surface of the solid sphere and nil normal velocity component and shear stress on the external spherical surface. The boundary value problem is solved with the aim of the complete Papkovich-Neuber differential representation of the solutions for Stokes flow, which is valid in non-axisymmetric geometries and provides us with the velocity and total pressure fields in terms of harmonic spherical eigenfunctions. The solution of this 3D model, which is self-sufficient in mechanical energy, is obtained in closed form and analytical expressions for the velocity, the total pressure, the angular velocity, and the stress tensor fields are provided

Sensitivity Analysis of the Forward Electroencephalographic Problem Depending on Head Shape Variations

A crucial aspect in clinical practice is the knowledge of whether Electroencephalographic (EEG) measurements can be assigned to the functioning of the brain or to geometrical deviations of the human cranium. The present work is focused on continuing to advance understanding on how sensitive the solution of the forward EEG problem is in regard to the geometry of the head. This has been achieved by developing a novel analytic algorithm by performing a perturbation analysis in the linear regime using a homogenous spherical model. Notably, the suggested procedure provides a criterion which recognizes whether surface deformations will have an impact on EEG recordings. The presented deformations represent two major cases: (1) acquired alterations of the surface inflicted by external forces and (2) deformations of the upper part of the human head where EEG signals are recorded. Our results illustrate that neglecting geometric variations present on the heads surface leads to errors in the recorded EEG measurements less than 2%. However, for severe instances of deformations combined with cortical brain activity in the vicinity of the distortion site, the errors rise to almost 25%. Therefore, the accurate description of the head shape plays an important role in understanding the forward EEG problem only in these cases