Parameter mismatches,variable delay times and synchronization in time-delayed systems

We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only retarded synchronization with the coupling delay time is obtained. We show that with parameter mismatch or without it neither complete nor anticipating synchronization occurs. We derive existence and stability conditions for the retarded synchronization manifold. We demonstrate our approach using examples of the Ikeda and Mackey-Glass models. Also for the first time we investigate chaos synchronization in time-delayed systems with variable delay time and find both existence and sufficient stability conditions for the retarded synchronization manifold with the coupling delay lag time. Also for the first time we consider synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and derive existence and stability conditions for the different anticipating, lag, and complete synchronization regimes.Comment: 12 page

Lichenometric dating (lichenometry) and the biology of the lichen genus rhizocarpon:challenges and future directions

Lichenometric dating (lichenometry) involves the use of lichen measurements to estimate the age of exposure of various substrata. Because of low radial growth rates and considerable longevity, species of the crustose lichen genus Rhizocarpon have been the most useful in lichenometry. The primary assumption of lichenometry is that colonization, growth and mortality of Rhizocarpon are similar on surfaces of known and unknown age so that the largest thalli present on the respective faces are of comparable age. This review describes the current state of knowledge regarding the biology of Rhizocarpon and considers two main questions: (1) to what extent does existing knowledge support this assumption; and (2) what further biological observations would be useful both to test its validity and to improve the accuracy of lichenometric dates? A review of the Rhizocarpon literature identified gaps in knowledge regarding early development, the growth rate/size curve, mortality, regeneration, competitive effects, colonization, and succession on rock surfaces. The data suggest that these processes may not be comparable on different rock surfaces, especially in regions where growth rates and thallus turnover are high. In addition, several variables could differ between rock surfaces and influence maximum thallus size, including rate and timing of colonization, radial growth rates, environmental differences, thallus fusion, allelopathy, thallus mortality, colonization and competition. Comparative measurements of these variables on surfaces of known and unknown age may help to determine whether the basic assumptions of lichenometry are valid. Ultimately, it may be possible to take these differences into account when interpreting estimated dates

'Growth rings' in crustose lichens:comparison with directly measured growth rates and implications for lichenometry

Some species of crustose lichens, such as Ochrolechia parella (L.) Massal., exhibit concentric marginal rings, which may represent an alternative technique of measuring growth rates and potentially, a new lichenometric dating method. To examine this hypothesis, the agreement and correlation between ring widths and directly measured annual radial growth rates (RaGR, mm a-1) were studied in 24 thalli of O. parella in north Wales, UK, using digital photography and image analysis. Variation in ring width was observed at different locations around a thallus, between thalli, and from year to year. The best agreement and correlation between ring width and lichen growth rates was between mean width of the outer two rings (measured in 2011) and mean RaGR (in 2009/10). The O. parella data suggest that mean width of the youngest two growth rings, averaged over a sample of thalli, is a predictor of recent growth rates and therefore could be used in lichenometry. Potential applications include as a convenient method of comparing lichen growth rates on surfaces in different environmental settings; and as an alternative method of constructing lichen growth-rate curves, without having to revisit the same lichen thalli over many years. However, care is needed when using growth rings to estimate growth rates as: growth ring widths may not be stable; ring widths exhibit spatial and temporal variation; rings may not represent 1-year's growth in all thalli; and adjacent rings may not always represent successive year's growth

Control of Rayleigh-Taylor instability by vertical vibration in large aspect ratio containers

We consider a horizontal heavy fluid layer supported by a light, immiscible one in a wide (as compared to depth) container, which is vertically vibrated intending to counterbalance the Rayleigh-Taylor instability of the flat, rigid-body vibrating state. In the simplest case when the density and viscosity of the lighter fluid are small compared to their counterparts in the heavier fluid, we apply a long wave, weakly nonlinear analysis that yields a generalized Cahn-Hilliard equation for the evolution of the fluid interface. This equation shows that the stabilizing effect of vibration is like that of surface tension, and is used to analyze the linear stability of the flat state, the local bifurcation at the instability threshold and some global existence and stability properties concerning the steady states without dry spots. The analysis is extended to two cases of practical interest. Namely, (a) the viscosity of one of the fluids is much smaller than that of the other one, and (b) the densities and viscosities of both fluids are quite close to each other

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types