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.

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.

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.

Slow wave effect of 2-D photonic crystal coupled cavity array

We designed a two-dimensional coupled photonic crystal resonator array with hexagonal lattice. The calculation by plane-wave-expansion method shows that the dispersion curve of coupled cavity modes in the bandgap are much flattened in all directions in the reciprocal space. We simulated the transmission spectra of transverse electric (TE) wave along the Gamma K direction. Compared with the PC single cavity structure, the transmission ratio of the coupled cavity array increases more than three orders of magnitude, while the group velocity decreases to below 1/10, reaching 0.007c. The slow wave effect has potential application in the field of miniaturized tunable optical delay components and low-threshold photonic crystal lasers.

Defects around self-organized InAs quantum dots measured by slow positron beam

Self-organized InAs quantum dots (QDs) have been fabricated by molecular beam epitaxy. The authors try to use a slow positron beam to detect defects in and around self-organized QDs, and point defects are observed in GaAs cap layer above QDs. For the self-organized InAs QDs without strain-reducing layer, it is free of defects. However, by introducing a strain-reducing layer, the density of point defects around larger sized InAs QDs increased. The above results suggest that low energy positron beam measurements may be a good approach to detect depth profiles of defects in QD materials. (c) 2007 American Institute of Physics.

Slow light at terahertz frequencies in surface plasmon polariton assisted grating waveguide

National Natural Science Foundation of China 60677045 60876049

Experimental study of a pulsed ytterbium-doped fibre laser with fast and slow saturable absorbers in a linear cavity

We present a linear-cavity stretched-pulse fibre laser with mode locking by a nonlinear polarization rotation and by semiconductor saturable-absorber mirrors. A Q-switched mode-locking cw train and a mode-locking pulse train are obtained in the experiment. We investigate the effects of the equivalent fast saturable absorber and the slow saturable absorbers in experiment. It is found that neither the nonlinear polarization evolution effect nor a semiconductor saturable absorber mirror is enough to produce the stable cw mode-locking pulses in this experiment. A nonlinear polarization evolution effect controls the cavity loss to literally carve the pulses; semiconductor saturable absorber mirrors provide the self-restarting and maintain the stability of the mode-locking operation.

Experimental investigation of slow light phenomenon in photonic crystal waveguide line defect laser

The guide mode whose frequency locates in the band edge in photonic crystal single line defect waveguide has very low group velocity. So the confinement and gain of electromagnetic field in the band edge are strongly enhanced. Photonic crystal waveguide laser is fabricated and the slow light phenomenon is investigated. The laser is pumped by pulsed pumping light at 980nm whose duty ratio is 0.05%. The active layer in photonic crystal slab is InGaAsP multiple quantum well. Light is transimited by a photonic crystal chirp waveguide in one facet of the laser. Then the output light is coupled to a fiber and the character of laser is analysis by an optical spectrometer. It is found that single mode and multimode happens with different power of pumping light. Meanwhile the plane wave expansion and finite-difference time-domain methods are used to simulate the phenomenon of slow light. And the result of the experiment is compared with the theory which proves the slow light results in lasing oscillation.

Slow Light Effect and Multimode Lasing in a Photonic Crystal Waveguide Microlaser

The slow light effect in a photonic crystal waveguide is investigated theoretically and experimentally. Theoretical calculation indicates that there is a slow light region for the even mode, from which the resonance and lasing in a microcavity would benefit. A photonic crystal waveguide microlaser is fabricated, which is related to the group velocity of c/120.6.

Transient and nonlinear analysis of slow-light pulse propagation in an optical fiber via stimulated Brillouin scattering

We investigate slow-light pulse propagation in an optical fiber via transient stimulated Brillouin scattering. Space-time evolution of a generating slow-light pulse is numerically calculated by solving three-wave coupled-mode equations between a pump beam, an acoustic wave, and a counterpropagating signal pulse. Our mathematical treatments are applicable to both narrowband and broadband pump cases. We show that the time delay of 85% pulse width can be obtained for a signal pulse of the order of subnanosecond pulse width by using a broadband pump, while the signal pulse is broadened only by 40% of the input signal pulse. The physical origin of the pulse broadening and distortion is explained in terms of the temporal decay of the induced acoustic field. (C) 2009 Optical Society of America