Statistics of seismic cluster durations

Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maximal magnitudes. We find the remarkable result that the magnitude difference between the largest and second largest event in the future temporal cluster is distributed according to the regular Gutenberg-Richer law that controls the unconditional distribution of earthquake magnitudes. For earthquakes obeying the Omori-Utsu law for the distribution of waiting times between triggering and triggered events, we show that the distribution of the durations of temporal clusters of events of magnitudes above some detection threshold \nu has a power law tail that is fatter in the non-critical regime $n<1$ than in the critical case n=1. This paradoxical behavior can be rationalised from the fact that generations of all orders cascade very fast in the critical regime and accelerate the temporal decay of the cluster dynamics.Comment: 45 pages, 15 figure

Short Copy Number Variations Potentially Associated with Tonic Immobility Responses in Newly Hatched Chicks

<div><p>Introduction</p><p>Tonic immobility (TI) is fear-induced freezing that animals may undergo when confronted by a threat. It is principally observed in prey species as defence mechanisms. In our preliminary research, we detected large inter-individual variations in the frequency and duration of freezing behavior among newly hatched domestic chicks (<i>Gallus gallus</i>). In this study we aim to identify the copy number variations (CNVs) in the genome of chicks as genetic candidates that underlie the behavioral plasticity to fearful stimuli.</p><p>Methods</p><p>A total of 110 domestic chicks were used for an association study between TI responses and copy number polymorphisms. Array comparative genomic hybridization (aCGH) was conducted between chicks with high and low TI scores using an Agilent 4×180 custom microarray. We specifically focused on 3 genomic regions (>60 Mb) of chromosome 1 where previous quantitative trait loci (QTL) analysis showed significant F-values for fearful responses.</p><p>Results</p><p>ACGH successfully detected short CNVs within the regions overlapping 3 QTL peaks. Eleven of these identified loci were validated by real-time quantitative polymerase chain reaction (qPCR) as copy number polymorphisms. Although there wkas no significant <i>p</i> value in the correlation analysis between TI scores and the relative copy number within each breed, several CNV loci showed significant differences in the relative copy number between 2 breeds of chicken (White Leghorn and Nagoya) which had different quantitative characteristics of fear-induced responses.</p><p>Conclusion</p><p>Our data shows the potential CNVs that may be responsible for innate fear response in domestic chicks.</p></div

Candidate short Copy Number Variations identified by array Comparative Genomic Hybridization and subsequent qPCR validation.

<p><b>Note</b>: Only loci displaying quantitative difference in qPCR validation are shown here.</p

The induction and duration of TI response in each chicken breed/strain.

<p><b>Note</b>: Standard error of the mean (SEM) are shown with the time until righting (sec).</p

Probe coverage on chicken chromosome 1 for array comparative genomic hybridization.

<p>Probes are designed in 3 regions (>60 Mb) where significant <i>F</i>-values have been identified by previous quantitative trait loci analysis. Genome-wide <i>F</i>-values for tonic immobility duration (thick line) and induction attempts (thin line) are quoted from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080205#pone.0080205-Schtz1" target="_blank">[7]</a>.</p

Comparison of relative copy number between chicken breeds with different sensitivity to fear.

<p>Relative copy number is calculated as log2^ΔCt, where ΔCt = Ct_β-actin – Ct_target. NG and WL indicate Nagoya and White Leghorn, respectively. The number of samples in each group was; <i>n</i> = 13 (NG; TI induction 1), <i>n</i> = 58 (NG; TI induction 2∼7), <i>n</i> = 13 (WL; TI induction 1), and <i>n</i> = 26 (WL; TI induction 2∼7).</p