Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

On the relation of slow feature analysis and Laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.

A theory of slow feature analysis for transformation-based input signals with an application to complex cells

We develop a group-theoretical analysis of slow feature analysis for the case where the input data are generated by applying a set of continuous transformations to static templates. As an application of the theory, we analytically derive nonlinear visual receptive fields and show that their optimal stimuli, as well as the orientation and frequency tuning, are in good agreement with previous simulations of complex cells in primary visual cortex (Berkes and Wiskott, 2005). The theory suggests that side and end stopping can be interpreted as a weak breaking of translation invariance. Direction selectivity is also discussed. © 2011 Massachusetts Institute of Technology.

Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Theory of high-power mode-locked lasers with a slow absorber

We develop an analytical theory of high-power passively mode-locked lasers with a slow absorber; the theory is valid at pulse energies well exceeding the saturation energy. We analyze the Haus modelocking master equation in the pulse-energy-domain representation, approximating the intensity profile function by a series in the vicinity of its peak value. We consider the high-power operation regime of subpicosecond blue-violet GaN mode-locked diode lasers, using the approach developed. © 2010 Springer Science+Business Media, Inc.

Cecum lymph node dendritic cells harbor slow-growing bacteria phenotypically tolerant to antibiotic treatment.

In vivo, antibiotics are often much less efficient than ex vivo and relapses can occur. The reasons for poor in vivo activity are still not completely understood. We have studied the fluoroquinolone antibiotic ciprofloxacin in an animal model for complicated Salmonellosis. High-dose ciprofloxacin treatment efficiently reduced pathogen loads in feces and most organs. However, the cecum draining lymph node (cLN), the gut tissue, and the spleen retained surviving bacteria. In cLN, approximately 10%-20% of the bacteria remained viable. These phenotypically tolerant bacteria lodged mostly within CD103⁺CX₃CR1⁻CD11c⁺ dendritic cells, remained genetically susceptible to ciprofloxacin, were sufficient to reinitiate infection after the end of the therapy, and displayed an extremely slow growth rate, as shown by mathematical analysis of infections with mixed inocula and segregative plasmid experiments. The slow growth was sufficient to explain recalcitrance to antibiotics treatment. Therefore, slow-growing antibiotic-tolerant bacteria lodged within dendritic cells can explain poor in vivo antibiotic activity and relapse. Administration of LPS or CpG, known elicitors of innate immune defense, reduced the loads of tolerant bacteria. Thus, manipulating innate immunity may augment the in vivo activity of antibiotics.

On kinematic relaxation and deposition of water droplets in the last stages of low pressure steam turbines

In the first part of the paper steady two-phase flow predictions have been performed for the last stage of a model steam turbine to examine the influence of drag between condensed fog droplets and the continuous vapour phase. In general, droplets due to homogeneous condensation are small and thus kinematic relaxation provides only a minor contribution to the wetness losses. Different droplet size distributions have been investigated to estimate at which size inter-phase friction becomes more important. The second part of the paper deals with the deposition of fog droplets on stator blades. Results from several references are repeated to introduce the two main deposition mechanisms which are inertia and turbulent diffusion. Extensive postprocessing routines have been programmed to calculate droplet deposition due to these effects for a last stage stator blade in three-dimensions. In principle the method to determine droplet deposition by turbulent diffusion equates to that of Yau and Young [1] and the advantages and disadvantages of this relatively simple method are discussed. The investigation includes the influence of different droplet sizes on droplet deposition rates and shows that for small fog droplets turbulent diffusion is the main deposition mechanism. If the droplets size is increased inertial effects become more and more important and for droplets around 1 μm inertial deposition dominates. Assuming realistic droplet sizes the overall deposition equates to about 1% to 3% of the incoming wetness for the investigated guide vane at normal operating conditions. Copyright © 2013 by Solar Turbines Incorporated.

An extension of slow feature analysis for nonlinear blind source separation

We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a high reliability. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources. © 2014 Henning Sprekeler, Tiziano Zito and Laurenz Wiskott.

Temperature dependence of hole spin relaxation in ultrathin InAs monolayers

The temperature dependence of hole spin relaxation time in both neutral and n-doped ultrathin InAs monolayers has been investigated. It has been suggested that D'yakonov-Perel (DP) mechanism dominates the spin relaxation process at both low and high temperature regimes. The appearance of a peak in temperature dependent spin relaxation time reveals the important contribution of Coulomb scatterings between carriers to the spin kinetics at low temperature, though electron-phonon scattering becomes dominant at higher temperatures. Increased electron screening effect in the n-doped sample has been suggested to account for the shortened spin relaxation time compared with the undoped one. The results suggest that hole spins are also promising for building solid-state qubits.

Promoting strain relaxation of Si0.72Ge0.28 film on Si (100) substrate by inserting a low-temperature Ge islands layer in UHVCVD

A flat, fully strain-relaxed Si0.72Ge0.28 thin film was grown on Si (1 0 0) substrate with a combination of thin low-temperature (LT) Ge and LT-Si0.72Ge0.28 buffer layers by ultrahigh vacuum chemical vapor deposition. The strain relaxation ratio in the Si0.72Ge0.28 film was enhanced up to 99% with the assistance of three-dimensional Ge islands and point defects introduced in the layers, which furthermore facilitated an ultra-low threading dislocation density of 5 x 10(4) cm (2) for the top SiGe film. More interestingly, no cross-hatch pattern was observed on the SiGe surface and the surface root-mean-square roughness was less than 2 nm. The temperature for the growth of LT-Ge layer was optimized to be 300 degrees C. (C) 2008 Elsevier B.V. All rights reserved.

High transmission of slow light in the photonic crystal waveguide bends

We present the research on the transmission characteristic of slow-light-mode in the photonic crystal line-defect waveguide bends on SOL After optimizing the structure parameters in the vicinity of the bends, the normalized transmission efficiency of slow-light-mode through the photonic crystal 60 degree and 120 degree waveguide bends are as high as 80% and 60% respectively, which are 10 times higher than that in the undeformed case. To slow down light further, we design novel coupled cavity waveguide bend structures with high quality-factor. High normalized transmission efficiency of 75% and low group velocity of c/170 ( c is the light velocity in vacuum) are realized. These results are beneficial to enhance the slow light effect of photonic crystal structures and improve the miniaturization and integration of photonic crystal slow light devices.

Carrier spin relaxation in (Ga, Mn) As at room temperature

In this paper, the excitation energy density dependence of carrier spin relaxation is studied at room temperature for the as-grown and annealed (Ga, Mn) As samples using femtosecond time-resolved pump-probe Kerr spectroscopy. It is found that spin relaxation lifetime of electrons lengthens with increasing excitation energy density for both samples, and the annealed ( Ga, Mn) As has shorter carrier recombination and electron spin relaxation lifetimes as well as larger Kerr rotation angle than the as-grown ( Ga. Mn) As under the same excitation condition. which shows that DP mechanism is dominant in the spin relaxation process for ( Ga, Mn)As at room temperature. The enhanced ultrafast Kerr effect in the annealed (Ga,Mn)As shows the potential application of the annealed ( Ga, Mn) As in ultrafast all-optical spin switches, and also provides a further evidence for the p-d exchange mechanism of the ferromagnetic origin of (Ga, Mn) As.

Localized and free exciton spin relaxation dynamics in GaInNAs/GaAs quantum well

We have investigated the exciton spin relaxation in a GaInNAs/GaAs quantum well. The recombination from free and localized excitons is resolved on the basis of an analysis of the photoluminescence characteristics. The free exciton spin relaxation time is measured to be 192 ps at 10 K, while the localized exciton spin relaxation time is one order of magnitude longer than that of the free exciton. The dependence of the free exciton spin relaxation time on the temperature above 50 K suggests that both the D'yakonov-Perel' and the Elliot-Yafet effects dominate the spin relaxation process. The temperature independence below 50 K is considered to be due to the spin exchange interaction. The ultralong spin relaxation time of the localized excitons is explained to be due to the influence of nonradiative deep centers. (c) 2008 American Institute of Physics.