On S-asymptotically omega-periodic functions and applications

Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. In this paper, we establish conditions under which an S-asymptotically omega-periodic function is asymptotically omega-periodic and we discuss the existence of S-asymptotically omega-periodic and asymptotically omega-periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered. (C) 2011 Elsevier Ltd. All rights reserved.

Semilinear functional difference equations with infinite delay

We obtain boundedness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications to Volterra difference equations with infinite delay are shown. (C) 2011 Elsevier Ltd. All rights reserved.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Disruption of vitellogenin gene function in adult honeybees by intra-abdominal injection of double-stranded RNA

Abstract Background The ability to manipulate the genetic networks underlying the physiological and behavioural repertoires of the adult honeybee worker (Apis mellifera) is likely to deepen our understanding of issues such as learning and memory generation, ageing, and the regulatory anatomy of social systems in proximate as well as evolutionary terms. Here we assess two methods for probing gene function by RNA interference (RNAi) in adult honeybees. Results The vitellogenin gene was chosen as target because its expression is unlikely to have a phenotypic effect until the adult stage in bees. This allowed us to introduce dsRNA in preblastoderm eggs without affecting gene function during development. Of workers reared from eggs injected with dsRNA derived from a 504 bp stretch of the vitellogenin coding sequence, 15% had strongly reduced levels of vitellogenin mRNA. When dsRNA was introduced by intra-abdominal injection in newly emerged bees, almost all individuals (96 %) showed the mutant phenotype. An RNA-fragment with an apparent size similar to the template dsRNA was still present in this group after 15 days. Conclusion Injection of dsRNA in eggs at the preblastoderm stage seems to allow disruption of gene function in all developmental stages. To dissect gene function in the adult stage, the intra-abdominal injection technique seems superior to egg injection as it gives a much higher penetrance, it is much simpler, and it makes it possible to address genes that are also expressed in the embryonic, larval or pupal stages.