Fourier PCA and Robust Tensor Decomposition

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components. The number of component distributions $m$ can be arbitrarily higher than the dimension $n$ and the columns of $A$ only need to satisfy a natural and efficiently verifiable nondegeneracy condition. As a second application, we give an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected; exposition improve

Long Wavelength VCSELs and VCSEL-Based Processing of Microwave Signals

We address the challenge of decreasing the size, cost and power consumption for practical applications of next generation microwave photonics systems by using long-wavelength vertical cavity surface emitting lasers. Several demonstrations of new concepts of microwave photonics devices are presented and discussed

Fluid transport properties under confined conditions

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The problem of adequate description of transport processes of fluids in confined conditions is solved using methods of nonequilibrium statistical mechanics. The «fluid–channel wall» system is regarded as a two-phase medium, in which each phase has a particular velocity and temperature. The obtained results show that the transfer equations describing transport processes in confined spaces should contain not only the stress tensor and the heat flux vector, but also the interfacial forces responsible for the transfer of momentum and heat due to the interaction with the wall surfaces. The stress tensor and the heat flux vector fluid can be expressed in terms of the effective viscosity and thermal conductivity. However, the constitutive relations contain additive terms that correspond to the fluid–surface interactions. Thus, not only do the fluid transport coefficients in nanochannels differ from the bulk transport coefficients, but also they are not determined only by the parameters of the fluid

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

Oxidative Stress Detection With Escherichia Coli Harboring A katG\u27::lux Fusion

A plasmid containing a transcriptional fusion of the Escherichia coli katG promoter to a truncated Vibrio fischeri lux operon (luxCDABE) was constructed. An E. coli strain bearing this plasmid (strain DPD2511) exhibited low basal levels of luminescence, which increased up to 1,000-fold in the presence of hydrogen peroxide, organic peroxides, redox-cycling agents (methyl viologen and menadione), a hydrogen peroxide-producing enzyme system (xanthine and xanthine oxidase), and cigarette smoke. An oxyR deletion abolished hydrogen peroxide-dependent induction, confirming that oxyR controlled katG\u27::lux luminescence. Light emission was also induced by ethanol by an unexplained mechanism. A marked synergistic response was observed when cells were exposed to both ethanol and hydrogen peroxide; the level of luminescence measured in the presence of both inducers was much higher than the sum of the level of luminescence observed with ethanol and the level of luminescence observed with hydrogen peroxide. It is suggested that this construction or similar constructions may be used as a tool for assaying oxidant and antioxidant properties of chemicals, as a biosensor for environmental monitoring and as a tool for studying cellular responses to oxidative hazards

Detection Of DNA Damage By Use Of Escherichia Coli Carrying recA\u27::lux, uvrA\u27::lux, And alkA\u27::lux Reporter Plasmids

Plasmids were constructed in which DNA damage-inducible promoters recA, uvrA, and alkA from Escherichia coli were fused to the Vibrio fischeri luxCDABE operon. Introduction of these plasmids into E. coli allowed the detection of a dose-dependent response to DNA-damaging agents, such as mitomycin and UV irradiation. Bioluminescence was measured in real time over extended periods. The fusion of the recA promoter to luxCDABE showed the most dramatic and sensitive responses. lexA dependence of the bioluminescent SOS response was demonstrated, confirming that this biosensor\u27s reports were transmitted by the expected regulatory circuitry. Comparisons were made between luxCDABE and lacZ fusions to each promoter. It is suggested that the lux biosensors may have use in monitoring chemical, physical, and genotoxic agents as well as in further characterizing the mechanisms of DNA repair

Nonparametric Regression on a Graph

The 'Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L2 norm, and roughness is penalized on every edge in the L1 norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples. The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online. © 2011 American Statistical Association

Transverse instabilities of multiple vortex chains in superconductor-ferromagnet bilayers

Using scanning tunneling microscopy and Ginzburg-Landau simulations we explore vortex configurations in magnetically coupled NbSe$_2$-Permalloy superconductor-ferromagnet bilayer. The Permalloy film with stripe domain structure induces periodic local magnetic induction in the superconductor creating a series of pinning-antipinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-1D arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the system becomes non-linear due to a change in both the number of vortices and the confining potential. The longitudinal instabilities of the resulting vortex structures lead to vortices `levitating' in the anti-pinning channels.Comment: accepted in PRB-Rapid