An integro-differential equation model for alignment and orientational aggregation

We study an integro-differential equation modeling angular alignment of interacting bundles of cells or filaments. A bifurcation analysis of the related stationary problem was done by Geigant and Stoll in [E. Geigant, M. Stoll, Bifurcation analysis of an orientational aggregation model, J. Math. Biol. 46 (6) (2003) 537-563]. Here we analyze the time-dependent problem and prove that the type of alignment (one- or multi-directional) depends on the initial distribution, the interaction potential, and the preferred optimal orientation of the bundles of cells or filaments. Our main technical tool is the analysis of the evolution of suitable functionals for the cell density, which allows to also specify the direction(s) where the final alignment takes place.     

Di(1H,1H,2H,2H-perfluorooctyl)-dibenzo-18-crown-6: A “light fluorous” recyclable phase transfer catalyst

A series of dibenzo-18-crown-6 lariat ethers containing two C₇H₁₅ (11), (CH₂)₂C₆F₁₃ (14), (CH₂)₂C₈F₁₇ (15), NHC₇H₁₅ (18) and NHCH₂C₆F₁₃ (19) sidearms were prepared and the single crystal X-ray structure of cis-4,4′-di(1H,1H,2H,2H-perfluorodecyl)-dibenzo-18-crown-6 (15a) is reported. The “light fluorous” dibenzo-18-crown-6 ether (14) has emerged as a stable and robust PTC catalyst, which can be recycled efficiently by fluorous solid-phase extraction, and gives better PTC catalytic activity compared to the parent, non-fluorinated PTC catalyst, dibenzo-18-crown-6, and the alkylated derivative (11) in aliphatic and aromatic nucleophilic substitutions.     

Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation

This Note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in Berestycki et al. (2009) [3] but their asymptotic behavior was still unclear. We use here a new numerical approximation of these traveling waves which shows that some traveling waves connect the two homogeneous steady states 0 and 1, which is a striking fact since 0 is dynamically unstable and 1 is unstable in the sense of Turing.     

Linear and nonlinear optical properties of carbon nanotube-coated single-mode optical fiber gratings

Single-wall carbon nanotube deposition on the cladding of optical fibers has been carried out to fabricate an all-fiber nonlinear device. Two different nanotube deposition techniques were studied. The first consisted of repeatedly immersing the optical fiber into a nanotube supension, increasing the thickness of the coating in each step. The second deposition involved wrapping a thin film of nanotubes around the optical fiber. For both cases, interaction of transmitted light through the fiber core with the external coating was assisted by the cladding mode resonances of a tilted fiber Bragg grating. Ultrafast nonlinear effects of the nanotube-coated fiber were measured by means of a pump-probe pulses experiment.     

Inverse problem approaches for stationary Fourier transform spectrometers

A design of a miniaturized stationary Fourier transform IR spectrometer has been developed that produces a two-dimensional interferogram. The latter is disturbed by effects like parasitic interferences or disparities in the cutoff wavelength of the pixels. Thus, a simple Fourier transform cannot be used to estimate the spectrum of the scene. However, as these defects are deterministic, they can be measured and taken into account by inversion methods. A regularization term can also be added. The first experimental results prove the efficiency of this processing methodology.     

A sliced inverse regression approach for data stream

In this article, we focus on data arriving sequentially by blocks in a stream. A semiparametric regression model involving a common effective dimension reduction (EDR) direction \(\beta \) is assumed in each block. Our goal is to estimate this direction at each arrival of a new block. A simple direct approach consists of pooling all the observed blocks and estimating the EDR direction by the sliced inverse regression (SIR) method. But in practice, some disadvantages appear such as the storage of the blocks and the running time for large sample sizes. To overcome these drawbacks, we propose an adaptive SIR estimator of \(\beta \) based on the optimization of a quality measure. The corresponding approach is faster both in terms of computational complexity and running time, and provides data storage benefits. The consistency of our estimator is established and its asymptotic distribution is given. An extension to multiple indices model is proposed. A graphical tool is also provided in order to detect changes in the underlying model, i.e., drift in the EDR direction or aberrant blocks in the data stream. A simulation study illustrates the numerical behavior of our estimator. Finally, an application to real data concerning the estimation of physical properties of the Mars surface is presented.     

New aspects of the Hunsdiecker-Barton halodecarboxylation—syntheses of phospha-shikimic acid and derivatives

We report an efficient synthetic approach to phospha-isosteres of important intermediates of the shikimic acid pathway by the application of the Hunsdiecker-Barton halodecarboxylation to cyclohexenylcarboxylic acids. As examples, phospha-shikimic acid, its 3-dehydro derivative and the respective monomethyl esters were synthesized. The approach has proven equally useful in the synthesis of isosteres of the antiviral agent oseltamivir.     

ATMOS (ATM optical switching)—system perspective

The expected traffic growth from new broadband services will require network capacities that can be beneficially provided by optical WDM transport networks. Optical packet techniques are essential for large networks to provide flexibility and granularity. A layered network architecture with a transparent optical layer and optical packet layers has been elaborated. Four switching concept options for large optical ATM switch fabrics in the public network and small access nodes are presented. The technology for the related key functions of space and wavelength switching was developed in the RACE ATMOS project and the feasibility of concepts and technologies was verified in four system demonstrators.