An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Solid state NMR as a new approach for the structural characterization of rare-earth doped lead lanthanum zirconate titanate laser ceramics

To facilitate the design of laser host materials with optimized emission properties, detailed structural information at the atomic level is essential, regarding the local bonding environment of the active ions (distribution over distinct lattice sites) and their extent of local clustering as well as their population distribution over separate micro- or nanophases. The present study explores the potential of solid state NMR spectroscopy to provide such understanding for rare-earth doped lead lanthanum zirconate titanate (PLZT) ceramics. As the NMR signals of the paramagnetic dopant species cannot be observed directly, two complementary approaches are utilized: (1) direct observation of diamagnetic mimics using Sc-45 NMR and (2) study of the paramagnetic interaction of the constituent host lattice nuclei with the rare-earth dopant, using Pb-207 NMR lineshape analysis. Sc-45 MAS NMR spectra of scandium-doped PLZT samples unambiguously reveal scandium to be six-coordinated, suggesting that this rare-earth ion substitutes in the B site. Static Pb-207 spin echo NMR spectra of a series of Tm-doped PLZT samples reveal a clear influence of paramagnetic rare-earth dopant concentration on the NMR lineshape. In the latter case high-fidelity spectra can be obtained by spin echo mapping under systematic incrementation of the excitation frequency, benefiting from the signal-to-noise enhancement afforded by spin echo train Fourier transforms. Consistent with XRD data, the Pb-207 NMR lineshape analysis suggests that statistical incorporation into the PLZT lattice occurs at dopant levels of up to 1 wt.% Tm3+, while at higher levels the solubility limit is reached. (C) 2008 Elsevier Masson SAS. All rights reserved.

Recording from Two Neurons: Second-Order Stimulus Reconstruction from Spike Trains and Population Coding

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5% of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100% improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Improved voice activity detection algorithm using wavelet and support vector machine

This paper proposes an improved voice activity detection (VAD) algorithm using wavelet and support vector machine (SVM) for European Telecommunication Standards Institution (ETS1) adaptive multi-rate (AMR) narrow-band (NB) and wide-band (WB) speech codecs. First, based on the wavelet transform, the original IIR filter bank and pitch/tone detector are implemented, respectively, via the wavelet filter bank and the wavelet-based pitch/tone detection algorithm. The wavelet filter bank can divide input speech signal into several frequency bands so that the signal power level at each sub-band can be calculated. In addition, the background noise level can be estimated in each sub-band by using the wavelet de-noising method. The wavelet filter bank is also derived to detect correlated complex signals like music. Then the proposed algorithm can apply SVM to train an optimized non-linear VAD decision rule involving the sub-band power, noise level, pitch period, tone flag, and complex signals warning flag of input speech signals. By the use of the trained SVM, the proposed VAD algorithm can produce more accurate detection results. Various experimental results carried out from the Aurora speech database with different noise conditions show that the proposed algorithm gives considerable VAD performances superior to the AMR-NB VAD Options 1 and 2, and AMR-WB VAD. (C) 2009 Elsevier Ltd. All rights reserved.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Dynamic Changes in the Mental Rotation Network Revealed by Pattern Recognition Analysis of fMRI Data

We investigated the temporal dynamics and changes in connectivity in the mental rotation network through the application of spatio-temporal support vector machines (SVMs). The spatio-temporal SVM [Mourao-Miranda, J., Friston, K. J., et al. (2007). Dynamic discrimination analysis: A spatial-temporal SVM. Neuroimage, 36, 88-99] is a pattern recognition approach that is suitable for investigating dynamic changes in the brain network during a complex mental task. It does not require a model describing each component of the task and the precise shape of the BOLD impulse response. By defining a time window including a cognitive event, one can use spatio-temporal fMRI observations from two cognitive states to train the SVM. During the training, the SVM finds the discriminating pattern between the two states and produces a discriminating weight vector encompassing both voxels and time (i.e., spatio-temporal maps). We showed that by applying spatio-temporal SVM to an event-related mental rotation experiment, it is possible to discriminate between different degrees of angular disparity (0 degrees vs. 20 degrees, 0 degrees vs. 60 degrees, and 0 degrees vs. 100 degrees), and the discrimination accuracy is correlated with the difference in angular disparity between the conditions. For the comparison with highest accuracy (08 vs. 1008), we evaluated how the most discriminating areas (visual regions, parietal regions, supplementary, and premotor areas) change their behavior over time. The frontal premotor regions became highly discriminating earlier than the superior parietal cortex. There seems to be a parcellation of the parietal regions with an earlier discrimination of the inferior parietal lobe in the mental rotation in relation to the superior parietal. The SVM also identified a network of regions that had a decrease in BOLD responses during the 100 degrees condition in relation to the 0 degrees condition (posterior cingulate, frontal, and superior temporal gyrus). This network was also highly discriminating between the two conditions. In addition, we investigated changes in functional connectivity between the most discriminating areas identified by the spatio-temporal SVM. We observed an increase in functional connectivity between almost all areas activated during the 100 degrees condition (bilateral inferior and superior parietal lobe, bilateral premotor area, and SMA) but not between the areas that showed a decrease in BOLD response during the 100 degrees condition.

A neural networks study of quinone compounds with trypanocidal activity

This work investigates neural network models for predicting the trypanocidal activity of 28 quinone compounds. Artificial neural networks (ANN), such as multilayer perceptrons (MLP) and Kohonen models, were employed with the aim of modeling the nonlinear relationship between quantum and molecular descriptors and trypanocidal activity. The calculated descriptors and the principal components were used as input to train neural network models to verify the behavior of the nets. The best model for both network models (MLP and Kohonen) was obtained with four descriptors as input. The descriptors were T(5) (torsion angle), QTS1 (sum of absolute values of the atomic charges), VOLS2 (volume of the substituent at region B) and HOMO-1 (energy of the molecular orbital below HOMO). These descriptors provide information on the kind of interaction that occurs between the compounds and the biological receptor. Both neural network models used here can predict the trypanocidal activity of the quinone compounds with good agreement, with low errors in the testing set and a high correctness rate. Thanks to the nonlinear model obtained from the neural network models, we can conclude that electronic and structural properties are important factors in the interaction between quinone compounds that exhibit trypanocidal activity and their biological receptors. The final ANN models should be useful in the design of novel trypanocidal quinones having improved potency.