On the stability of periodic orbits in delay equations with large delay

We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay.Comment: postprint versio

Optimization of double pulse pumping for Ni-like Sm x-ray lasers

We report a systematic study of double pulse pumping of the Ni-like Sm x-ray laser at 73 Angstrom, currently the shortest wavelength saturated x-ray laser. It is found that the Sm x-ray laser output can change by orders of magnitude when the intensity ratio of the pumping pulses and their relative delay are varied. Optimum pumping conditions are found and interpreted in terms of a simple model. (C) 1999 American Institute of Physics. [S0021-8979(99)07102-9]

Phase sensitive excitability of a limit cycle

The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e the excitability happens to be phase sensitive. As a paradigmatic example of this concept we employ the classical FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase sensitive nonlinear threshold-like response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase sensitive excitability of the relaxation oscillations by noise we find a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitation and the degradation of the nonlinear response

The leber congenital amaurosis protein AIPL1 and EB proteins co-localize at the photoreceptor cilium

Purpose: The aim of this study was to investigate the interaction and co-localization of novel interacting proteins with the Leber congenital amaurosis (LCA) associated protein aryl hydrocarbon receptor interacting protein-like 1 (AIPL1). Methods: The CytoTrapXR yeast two-hybrid system was used to screen a bovine retinal cDNA library. A novel interaction between AIPL1 and members of the family of EB proteins was confirmed by directed yeast two-hybrid analysis and co-immunoprecipitation assays. The localization of AIPL1 and the EB proteins in cultured cells and in retinal cryosections was examined by immunofluorescence microscopy and cryo-immunogold electron microscopy. Results: Yeast two-hybrid (Y2H) analysis identified the interaction between AIPL1 and the EB proteins, EB1 and EB3. EB1 and EB3 were specifically co-immunoprecipitated with AIPL1 from SK-N-SH neuroblastoma cells. In directed 1:1 Y2H analysis, the interaction of EB1 with AIPL1 harbouring the LCA-causing mutations A197P, C239R and W278X was severely compromised. Immunofluorescent confocal microscopy revealed that AIPL1 did not co-localize with endogenous EB1 at the tips of microtubules, endogenous EB1 at the microtu-bule organising centre following disruption of the microtubule network, or with endogenous β-tubulin. Moreover, AIPL1 did not localize to primary cilia in ARPE-19 cells, whereas EB1 co-localized with the centrosomal marker pericentrin at the base of primary cilia. However, both AIPL1 and the EB proteins, EB1 and EB3, co-localized with centrin-3 in the connecting cilium of photoreceptor cells. Cryo-immunogold electron microscopy confirmed the co-localization of AIPL1 and EB1 in the connecting cilia in human retinal photoreceptors. Conclusions: AIPL1 and the EB proteins, EB1 and EB3, localize at the connecting cilia of retinal photore-ceptor cells, but do not co-localize in the cellular microtubule network or in primary cilia in non-retinal cells. These findings suggest that AIPL1 function in these cells is not related to the role of EB proteins in microtubule dynamics or primary ciliogenesis, but that their association may be related to a specific role in the specialized cilia apparatus of retinal photoreceptors