Nonlinear Bloch-wave interaction and Bragg scattering in optically-induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically-induced photonic lattices and reveal the key physical mechanisms which govern nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.Comment: 4 pages, 6 figure

Hubble Space Telescope Near-IR Transmission Spectroscopy of the Super-Earth HD 97658b

Recent results from the Kepler mission indicate that super-Earths (planets with masses between 1-10 times that of the Earth) are the most common kind of planet around nearby Sun-like stars. These planets have no direct solar system analogue, and are currently one of the least well-understood classes of extrasolar planets. Many super-Earths have average densities that are consistent with a broad range of bulk compositions, including both water-dominated worlds and rocky planets covered by a thick hydrogen and helium atmosphere. Measurements of the transmission spectra of these planets offer the opportunity to resolve this degeneracy by directly constraining the scale heights and corresponding mean molecular weights of their atmospheres. We present Hubble Space Telescope near-infrared spectroscopy of two transits of the newly discovered transiting super-Earth HD 97658b. We use the Wide Field Camera 3's scanning mode to measure the wavelength-dependent transit depth in thirty individual bandpasses. Our averaged differential transmission spectrum has a median 1 sigma uncertainty of 23 ppm in individual bins, making this the most precise observation of an exoplanetary transmission spectrum obtained with WFC3 to date. Our data are inconsistent with a cloud-free solar metallicity atmosphere at the 10 sigma level. They are consistent at the 0.4 sigma level with a flat line model, as well as effectively flat models corresponding to a metal-rich atmosphere or a solar metallicity atmosphere with a cloud or haze layer located at pressures of 10 mbar or higher.Comment: ApJ in press; revised version includes an updated orbital ephemeris for the plane

Estimating Annual CO2 Flux for Lutjewad Station Using Three Different Gap-Filling Techniques

Long-term measurements of CO2 flux can be obtained using the eddy covariance technique, but these datasets are affected by gaps which hinder the estimation of robust long-term means and annual ecosystem exchanges. We compare results obtained using three gap-fill techniques: multiple regression (MR), multiple imputation (MI), and artificial neural networks (ANNs), applied to a one-year dataset of hourly CO2 flux measurements collected in Lutjewad, over a flat agriculture area near the Wadden Sea dike in the north of the Netherlands. The dataset was separated in two subsets: a learning and a validation set. The performances of gap-filling techniques were analysed by calculating statistical criteria: coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), maximum absolute error (MaxAE), and mean square bias (MSB). The gap-fill accuracy is seasonally dependent, with better results in cold seasons. The highest accuracy is obtained using ANN technique which is also less sensitive to environmental/seasonal conditions. We argue that filling gaps directly on measured CO2 fluxes is more advantageous than the common method of filling gaps on calculated net ecosystem change, because ANN is an empirical method and smaller scatter is expected when gap filling is applied directly to measurements

Nonlinear Aharonov-Bohm scattering by optical vortices

We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wavepacket) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wavefront splitting of the scattered wave develops into transverse modulational instability, ``unzipping'' the stripe into trains of vortices with opposite charges.Comment: 4 pages, 4 figure

Controlled generation and steering of spatial gap solitons

We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and reveal the key features of gap solitons which distinguish them from conventional counterparts, including a dynamical transformation of gap solitons due to nonlinear inter-band coupling. We also predict theoretically and confirm experimentally the effect of anomalous steering of gap solitons in optically-induced photonic lattices.Comment: 4 pages, 5 figure

On transversally elliptic operators and the quantization of manifolds with ff-structure

An $f$-structure on a manifold $M$ is an endomorphism field \phi\in\Gamma(M,\End(TM)) such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure E_{1,0}\subset T_\C M given by the $+i$-eigenbundle of $\phi$. Using a compatible metric $g$ and connection $\nabla$ on $M$, we construct an odd first-order differential operator $D$, acting on sections of $\S=\Lambda E_{0,1}^*$, whose principal symbol is of the type considered in arXiv:0810.0338. In the special case of a CR-integrable almost $\S$-structure, we show that when $\nabla$ is the generalized Tanaka-Webster connection of Lotta and Pastore, the operator $D$ is given by D = \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann operator. We then describe two "quantizations" of manifolds with $f$-structure that reduce to familiar methods in symplectic geometry in the case that $\phi$ is a compatible almost complex structure, and to the contact quantization defined in \cite{F4} when $\phi$ comes from a contact metric structure. The first is an index-theoretic approach involving the operator $D$; for certain group actions $D$ will be transversally elliptic, and using the results in arXiv:0810.0338, we can give a Riemann-Roch type formula for its index. The second approach uses an analogue of the polarized sections of a prequantum line bundle, with a CR structure playing the role of a complex polarization.Comment: 31 page

Reduced-symmetry two-dimensional solitons in photonic lattices

We demonstrate theoretically and experimentally a novel type of localized beams supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.Comment: 5 pages, 4 figure

Small non-coding RNA profiling in plasma extracellular vesicles of bladder cancer patients by next-generation sequencing: Expression levels of miR-126-3p and piR-5936 increase with higher histologic grades

Bladder cancer (BC) is the tenth most frequent cancer worldwide. Due to the need for recurrent cystoscopies and the lack of non-invasive biomarkers, BC is associated with a high management burden. In this respect, small non-coding RNAs (sncRNAs) have been investigated in urine as possible biomarkers for BC, but in plasma their potential has not yet been defined. The expression levels of sncRNAs contained in plasma extracellular vesicles (EVs) from 47 men with BC and 46 healthy controls were assessed by next-generation sequencing. The sncRNA profiles were compared with urinary profiles from the same subjects. miR-4508 resulted downregulated in plasma EVs of muscle-invasive BC patients, compared to controls (adj-p = 0.04). In World Health Organization (WHO) grade 3 (G3) BC, miR-126-3p was upregulated both in plasma EVs and urine, when compared to controls (for both, adj-p < 0.05). Interestingly, two sncRNAs were associated with the risk class: miR-4508 with a downward trend going from controls to high risk BC, and piR-hsa-5936 with an upward trend (adj-p = 0.04 and adj-p = 0.05, respectively). Additionally, BC cases with low expression of miR-185-5p and miR-106a-5p or high expression of miR-10b-5p showed shorter survival (adj-p = 0.0013, adj-p = 0.039 and adj-p = 0.047, respectively). SncRNAs from plasma EVs could be diagnostic biomarkers for BC, especially in advanced grade

Novel results on Hermite-Hadamard kind inequalities for η\eta-convex functions by means of (k,r)(k,r)-fractional integral operators

We establish new integral inequalities of Hermite-Hadamard type for the recent class of $\eta$-convex functions. This is done via generalized $(k,r)$-Riemann-Liouville fractional integral operators. Our results generalize some known theorems in the literature. By choosing different values for the parameters $k$ and $r$, one obtains interesting new results.Comment: This is a preprint of a paper whose final and definite form is a Springer chapter in the Book 'Advances in Mathematical Inequalities and Applications', published under the Birkhauser series 'Trends in Mathematics', ISSN: 2297-0215 [see http://www.springer.com/series/4961]. Submitted 02-Jan-2018; Revised 10-Jan-2018; Accepted 13-Feb-201