Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a reduced set of multi-way compressive measurements by exploiting its low multilinear-rank structure. Moreover, we show that, an interesting property of multi-way measurements allows us to build the reconstruction based on compressive linear measurements taken only in two selected modes, independently of the tensor order $N$. In addition, it is proved that, in the matrix case and in a particular case with $3$rd-order tensors where the same 2D sensor operator is applied to all mode-3 slices, the proposed reconstruction $\underline{\mathbf{X}}_\tau$ is stable in the sense that the approximation error is comparable to the one provided by the best low-multilinear-rank approximation, where $\tau$ is a threshold parameter that controls the approximation error. Through the analysis of the upper bound of the approximation error we show that, in the 2D case, an optimal value for the threshold parameter $\tau=\tau_0 > 0$ exists, which is confirmed by our simulation results. On the other hand, our experiments on 3D datasets show that very good reconstructions are obtained using $\tau=0$, which means that this parameter does not need to be tuned. Our extensive simulation results demonstrate the stability and robustness of the method when it is applied to real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity based CS methods specialized for multidimensional signals is also included. A very attractive characteristic of the proposed method is that it provides a direct computation, i.e. it is non-iterative in contrast to all existing sparsity based CS algorithms, thus providing super fast computations, even for large datasets.Comment: Submitted to IEEE Transactions on Signal Processin

Comparison between the Torquato-Rintoul theory of the interface effect in composite media and elementary results

We show that the interface effect on the properties of composite media recently proposed by Torquato and Rintoul (TR) [Phys. Rev. Lett. 75, 4067 (1995)] is in fact elementary, and follows directly from taking the limit in the dipolar polarizability of a coated sphere: the TR ``critical values'' are simply those that make the dipolar polarizability vanish. Furthermore, the new bounds developed by TR either coincide with the Clausius-Mossotti (CM) relation or provide poor estimates. Finally, we show that the new bounds of TR do not agree particularly well with the original experimental data that they quote.Comment: 13 pages, Revtex, 8 Postscript figure

Brain-Computer Interfaces: Towards Practical Implementations and Potential Applications

[No abstract available

Plasma propulsion simulation using particles

This perspective paper deals with an overview of particle-in-cell / Monte Carlo collision models applied to different plasma-propulsion configurations and scenarios, from electrostatic (E x B and pulsed arc) devices to electromagnetic (RF inductive, helicon, electron cyclotron resonance) thrusters, with an emphasis on plasma plumes and their interaction with the satellite. The most important elements related to the modeling of plasma-wall interaction are also presented. Finally, the paper reports new progress in the particle-in-cell computational methodology, in particular regarding accelerating computational techniques for multi-dimensional simulations and plasma chemistry Monte Carlo modules for molecular and alternative propellan

Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. For a soft potential it is shown that, to leading order steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werff et al, if the usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient $D_s(\phi)$ for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur

Surface Periodic Poling in Lithium Niobate and Lithium Tantalate

Periodic Poling of Lithium Niobate crystals (PPLN) by means of electric field has revealed the best technique for finely tailoring PPLN structures and parameters, which play a central role in many current researches in the field of nonlinear integrated optics. Besides the most studied technique of bulk poling, recently a novel technique where domain inversion occurs just in a surface layer using photoresist or silica masks has been devised and studied. This surface periodic poling (SPP) approach is best suited when light is confined in a thin surface guiding layer or stripe, as in the case of optical waveguide devices. Also, we found that SPP respect to bulk poling offers two orders of magnitude reduction on the scale of periodicity, so that even nanostructures can be obtained provided an high resolution holographic mask writing technique is adopted. We were able to demonstrate 200 nm domain size, and also good compatibility with alpha-phase proton exchange channel waveguide fabrication. Our first experiments on Lithium Tantalate have also shown that the SPP technology appears to be applicable to this crystal (SPPLT), whose properties can allow to overcome limitations such as optical damage or UV absorption still present in PPLN devices. Finally, the issue of SPP compatibility with proton exchange waveguide fabrication will be addresse

Hybrid networks: Improving deep learning networks via integrating two views of images

© 2018, Springer Nature Switzerland AG. The principal component analysis network (PCANet) is an unsupervised parsimonious deep network, utilizing principal components as filters in the layers. It creates an amalgamated view of the data by transforming it into column vectors which destroys its spatial structure while obtaining the principal components. In this research, we first propose a tensor-factorization based method referred as the Tensor Factorization Networks (TFNet). The TFNet retains the spatial structure of the data by preserving its individual modes. This presentation provides a minutiae view of the data while extracting matrix factors. However, the above methods are restricted to extract a single representation and thus incurs information loss. To alleviate this information loss with the above methods we propose Hybrid Network (HybridNet) to simultaneously learn filters from both the views of the data. Comprehensive results on multiple benchmark datasets validate the superiority of integrating both the views of the data in our proposed HybridNet