Hierarchical bases for non-hierarchic 3Dtriangular meshes

We describe a novel basis of hierarchical, multiscale functions that are linear combinations of standard Rao-Wilton- Glisson (RWG) functions. When the basis is used for discretizing the electric field integral equation (EFIE) for PEC objects it gives rise to a linear system immune from low-frequency breakdown, and well conditioned for dense meshes. The proposed scheme can be applied to any mesh with triangular facets, and therefore it can be used as if it were an algebraic preconditioner. The properties of the new system are confirmed by numerical results that show fast convergence rates of iterative solvers, significantly better than those for the loop-tree basis. As a byproduct of the basis generation, a generalization of the RWG functions to nonsimplex cells is introduced

An impedance boundary condition EFIE that is low-frequency and refinement stable

A discretization of the impedance boundary condition electric field integral equation (IBC-EFIE) is introduced that: 1) yields the correct solution at arbitrarily small frequencies and 2) requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases. The low frequency stabilization is based on a projector-based discrete Helmholtz splitting, rescaling, and recombination that depends on the low frequency behavior of both the EFIE operator and the surface impedance condition. The dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the IBC term

Brain-Computer Interfaces: Investigating the Transition from Visually Evoked to Purely Imagined Steady-State Potentials

Brain-Computer Interfaces (BCIs) based on Steady State Visually Evoked Potentials (SSVEPs) have proven effective and provide significant accuracy and information-transfer rates. This family of strategies, however, requires external devices that provide the frequency stimuli required by the technique. This limits the scenarios in which they can be applied, especially when compared to other BCI approaches. In this work, we have investigated the possibility of obtaining frequency responses in the EEG output based on the pure visual imagination of SSVEP-eliciting stimuli. Our results show that not only that EEG signals present frequency-specific peaks related to the frequency the user is focusing on, but also that promising classification accuracy can be achieved, paving the way for a robust and reliable visual imagery BCI modality. Clinical relevance-Brain computer interfaces play a fundamental role in enhancing the quality of life of patients with severe motor impairments. Strategies based on purely imagined stimuli, like the one presented here, are particularly impacting, especially in the most severe cases

Serum Albumin Is Inversely Associated With Portal Vein Thrombosis in Cirrhosis

We analyzed whether serum albumin is independently associated with portal vein thrombosis (PVT) in liver cirrhosis (LC) and if a biologic plausibility exists. This study was divided into three parts. In part 1 (retrospective analysis), 753 consecutive patients with LC with ultrasound-detected PVT were retrospectively analyzed. In part 2, 112 patients with LC and 56 matched controls were entered in the cross-sectional study. In part 3, 5 patients with cirrhosis were entered in the in vivo study and 4 healthy subjects (HSs) were entered in the in vitro study to explore if albumin may affect platelet activation by modulating oxidative stress. In the 753 patients with LC, the prevalence of PVT was 16.7%; logistic analysis showed that only age (odds ratio [OR], 1.024; P = 0.012) and serum albumin (OR, -0.422; P = 0.0001) significantly predicted patients with PVT. Analyzing the 112 patients with LC and controls, soluble clusters of differentiation (CD)40-ligand (P = 0.0238), soluble Nox2-derived peptide (sNox2-dp; P < 0.0001), and urinary excretion of isoprostanes (P = 0.0078) were higher in patients with LC. In LC, albumin was correlated with sCD4OL (Spearman's rank correlation coefficient [r(s)], -0.33; P < 0.001), sNox2-dp (r(s), -0.57; P < 0.0001), and urinary excretion of isoprostanes (r(s), -0.48; P < 0.0001) levels. The in vivo study showed a progressive decrease in platelet aggregation, sNox2-dp, and urinary 8-iso prostaglandin F2 alpha-III formation 2 hours and 3 days after albumin infusion. Finally, platelet aggregation, sNox2-dp, and isoprostane formation significantly decreased in platelets from HSs incubated with scalar concentrations of albumin. Conclusion: Low serum albumin in LC is associated with PVT, suggesting that albumin could be a modulator of the hemostatic system through interference with mechanisms regulating platelet activation

Loop-Star and Loop-Tree Decompositions: Analysis and Efficient Algorithms

International audienceA new analysis of the spectral properties of Loop-Star and Loop-Tree decompositions is presented in this work. The analysis will shed light on the behavior of these decompositions when used with regular operators such as the magnetic field and the Calderón preconditioned electric field integral operators. This work will explain the ill-conditioning problems reported in literature and will provide a family of efficient algorithms to solve the ill-conditioning and regularizing several Loop-Star/Tree decomposed equations of interest for applications. The theory will be corroborated by numerical results that will show the practical impact of the theoretical development

Maximally Orthogonal High-Order Basis Functions Have a Well-Conditioned Gram Matrix

Recently, a novel high-order finite-element space for wires, quadrilaterals, and hexahedrons was presented [M. Kostic and B. Kolundzija, "Maximally Orthogonalized Higher Order Bases Over Generalized Wires, Quadrilaterals, and Hexahedra," IEEE Trans. Antennas Propag., vol. 61, no. 6, pp. 3135-3148, 2013]. Numerical results have shown a very favorable behavior of the condition number of the Gram matrix of this finite-element space as a function of the polynomial degree. In this paper, this high-order finite-element space is recognized to be expressible in terms of Jacobi polynomials, which can be easily computed using a three-term recurrence. In addition, the condition number of the Gram matrix of the one-dimensional finite-element space is rigorously analyzed for the general case of a piecewise smooth (possibly curved) geometry. An explicit upper bound for the condition number in terms of the mesh quality is proved. This bound implies that the one-dimensional finite-element space is stable for arbitrarily high polynomial degree. Numerical results corroborate the theoretical results and show that the basis can be used to perform hp-refinement, leading to an accurate handling of both large smooth regions and corners

On a Frequency-Stabilized Single Current Inverse Source Formulation

Several strategies are available for solving the inverse source problem in electromagnetics. Among them, many have been focusing in retrieving Love currents by solving, after regularization, for Love's electric and magnetic currents. In this work we present a dual-element discretization, analysis, and stabilization of an inverse source formulation providing Love data by solving for only one current. This results in substantial savings and allows for an effective quasi-Helmholtz projector stabilization of the resulting operator. Theoretical considerations are complemented by numerical tests showing effectiveness and efficiency of the newly proposed method

A DC Stable and Large-Time Step Well-Balanced TD-EFIE Based on Quasi-Helmholtz Projectors

The marching-on-in-time (MOT) solution of the time-domain electric field integral equation (TD-EFIE) has traditionally suffered from a number of issues, including the emergence of spurious static currents (dc instability) and ill-conditioning at large-time steps (low frequencies). In this contribution, a space-time Galerkin discretization of the TD-EFIE is proposed, which separates the loop and star components of both the equation and the unknown. Judiciously integrating or differentiating these components with respect to time leads to an equation which is free from dc instability. By choosing the correct temporal basis and testing functions for each of the components, a stable MOT system is obtained. Furthermore, the scaling of these basis and testing functions ensure that the system remains well conditioned for large-time steps. The loop-star decomposition is performed using quasi-Helmholtz projectors to avoid the explicit transformation to the unstable bases of loops and stars (or trees), and to avoid the search for global loops, which is a computationally expensive operation