Rank-Ordering Statistics of Extreme Events: Application to the Distribution of Large Earthquakes

Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can be determined with good accuracy by rank-ordering statistics from the observation of only a few tens of the largest events. Using analytical results and synthetic tests, we quantify the systematic and the random errors. We also study the case of a distribution defined by two branches, each having a power law distribution, one defined for the largest events and the other for smaller events, with application to the World-Wide (Harvard) and Southern California earthquake catalogs. In the case of the Harvard moment catalog, we make more precise earlier claims of the existence of a transition of the earthquake magnitude distribution between small and large earthquakes; the $b$-values are $b_2 = 2.3 \pm 0.3$ for large shallow earthquakes and $b_1 = 1.00 \pm 0.02$ for smaller shallow earthquakes. However, the cross-over magnitude between the two distributions is ill-defined. The data available at present do not provide a strong constraint on the cross-over which has a $50\%$ probability of being between magnitudes $7.1$ and $7.6$ for shallow earthquakes; this interval may be too conservatively estimated. Thus, any influence of a universal geometry of rupture on the distribution of earthquakes world-wide is ill-defined at best. We caution that there is no direct evidence to confirm the hypothesis that the large-moment branch is indeed a power law. In fact, a gamma distribution fits the entire suite of earthquake moments from the smallest to the largest satisfactorily. There is no evidence that the earthquakes of the Southern California catalog have a distribution with tw

Modes of random lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, directivity, and polarization. In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. We review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. The past decade has witnessed the emergence of the idea that even the low-Q resonances of such open systems could play a role similar to the cavity modes of a conventional laser and produce sharp lasing peaks. We focus here on the nearthreshold single-mode lasing regime where nonlinear effects associated with gain saturation and mode competition can be neglected.We discuss in particular the link between random laser modes near threshold and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized (strong scattering) regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime, where it was observed that increasing the openness of such systems eventually resulted in measurable and increasing differences between quasi-bound states and lasing modes. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the threshold lasing modes are in fact distinct from QB states of the passive system and are better described in terms of a new class of states, the so-called constant-flux states. The correspondence between QB states and lasing modes is found to improve in the strong scattering limit, confirming the validity of initial work in the strong scattering limit. © 2010 Optical Society of America

Emission of photon echoes in a strongly scattering medium

We observe the two- and three-pulse photon echo emission from a scattering powder, obtained by grinding a Pr$^{3+}$:Y$_2$SiO$_5$ rare earth doped single crystal. We show that the collective emission is coherently constructed over several grains. A well defined atomic coherence can therefore be created between randomly placed particles. Observation of photon echo on powders as opposed to bulk materials opens the way to faster material development. More generally, time-domain resonant four-wave mixing offers an attractive approach to investigate coherent propagation in scattering media

Strong Interactions in Multimode Random Lasers

Unlike conventional lasers, diffusive random lasers (DRLs) have no resonator to trap light and no high-Q resonances to support lasing. Due to this lack of sharp resonances the DRL has presented a challenge to conventional laser theory. We present a theory able to treat the DRL rigorously, and provide results on the lasing spectra, internal fields and output intensities of DRLs. Typically DRLs are highly multimode lasers, emitting light at a number of wavelengths. We show that the modal interactions through the gain medium in such lasers are extremely strong and lead to a uniformly spaced frequency spectrum, in agreement with recent experimental observations.Comment: 13 pages, 4 figures. Supplementary information available at arXiv:0805.449

N-Acyl Homoserine Lactones and Lux Solos Regulate Social Behaviour and Virulence of Pseudomonas syringae pv. actinidiae

The phyllosphere is a complex environment where microbes communicate through signalling molecules in a system, generally known as quorum sensing (QS). One of the most common QS systems in Gram-negative proteobacteria is based on the production of N-acyl homoserine lactones (AHLs) by a LuxI synthase and their perception by a LuxR sensor. Pseudomonas syringae pv. actinidiae (Psa), the aetiological agent of the bacterial canker of kiwifruit, colonises plant phyllosphere before penetrating via wounds and natural openings. Since Psa genome encodes three LuxR solos without a cognate LuxI, this bacterium may perceive diffusible signals, but it cannot produce AHLs, displaying a non-canonical QS system. The elucidation of the mechanisms underlying the perception of environmental cues in the phyllosphere by this pathogen and their influence on the onset of pathogenesis are of crucial importance for a long-lasting and sustainable management of the bacterial canker of kiwifruit. Here, we report the ability of Psa to sense its own population density and the presence of surrounding bacteria. Moreover, we show that Psa can perceive AHLs, indicating that AHL-producing neighbouring bacteria may regulate Psa virulence in the host. Our results suggest that the ecological environment is important in determining Psa fitness and pathogenic potential. This opens new perspectives in the use of more advanced biochemical and microbiological tools for the control of bacterial canker of kiwifruit

Comparative transcriptome analysis of the interaction between Actinidia chinensis var. chinensis and Pseudomonas syringae pv. Actinidiae in absence and presence of acibenzolar-S-methyl

Background: Since 2007, bacterial canker caused by Pseudomonas syringae pv. actinidiae (Psa) has become a pandemic disease leading to important economic losses in every country where kiwifruit is widely cultivated. Options for controlling this disease are very limited and rely primarily on the use of bactericidal compounds, such as copper, and resistance inducers. Among the latter, the most widely studied is acibenzolar-S-methyl. To elucidate the early molecular reaction of kiwifruit plants (Actinidia chinensis var. chinensis) to Psa infection and acibenzolar-S-methyl treatment, a RNA seq analysis was performed at different phases of the infection process, from the epiphytic phase to the endophytic invasion on acibenzolar-S-methyl treated and on non-treated plants. The infection process was monitored in vivo by confocal laser scanning microscopy. Results: De novo assembly of kiwifruit transcriptome revealed a total of 39,607 transcripts, of which 3360 were differentially expressed during the infection process, primarily 3 h post inoculation. The study revealed the coordinated changes of important gene functional categories such as signaling, hormonal balance and transcriptional regulation. Among the transcription factor families, AP2/ERF, MYB, Myc, bHLH, GATA, NAC, WRKY and GRAS were found differentially expressed in response to Psa infection and acibenzolar-S-methyl treatment. Finally, in plants treated with acibenzolar-S-methyl, a number of gene functions related to plant resistance, such as PR proteins, were modulated, suggesting the set-up of a more effective defense response against the pathogen. Weighted-gene coexpression network analysis confirmed these results. Conclusions: Our work provides an in-depth description of the plant molecular reactions to Psa, it highlights the metabolic pathway related to acibenzolar-S-methyl-induced resistance and it contributes to the development of effective control strategies in open field

Arabidopsis hypocotyl adventitious root formation is suppressed by ABA signaling

Roots are composed of different root types and, in the dicotyledonous Arabidopsis, typically consist of a primary root that branches into lateral roots. Adventitious roots emerge from non-root tissue and are formed upon wounding or other types of abiotic stress. Here, we investigated adventitious root (AR) formation in Arabidopsis hypocotyls under conditions of altered abscisic acid (ABA) signaling. Exogenously applied ABA suppressed AR formation at 0.25 µM or higher doses. AR formation was less sensitive to the synthetic ABA analog pyrabactin (PB). However, PB was a more potent inhibitor at concentrations above 1 µM, suggesting that it was more selective in triggering a root inhibition response. Analysis of a series of phosphonamide and phosphonate pyrabactin analogs suggested that adventitious root formation and lateral root branching are differentially regulated by ABA signaling. ABA biosynthesis and signaling mutants affirmed a general inhibitory role of ABA and point to PYL1 and PYL2 as candidate ABA receptors that regulate AR inhibition