Relation between stress heterogeneity and aftershock rate in the rate-and-state model

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994].We show that an exponential stress distribution Pt(au) ~exp(-tautau_0) gives an Omori law decay of aftershocks with time ~1/t^p, with an exponent p=1-A sigma_n/tau_0, where A is a parameter of the rate-and-state friction law, and \sigma_n the normal stress. Omori exponent p thus decreases if the stress "heterogeneity" tau_0 decreases. We also invert the stress distribution P(tau) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant "k^2" slip model [Herrero and Bernard, 1994]. We generate synthetic aftershock catalogs from this stress change.The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault.This stochastic slip model gives a Gaussian stress distribution, but nevertheless produces an aftershock rate which is very close to Omori's law, with an effective p<=1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs, when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of A\sigma_n can also modify the parameters p and c of Omori's law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.Comment: In press in JG

Bioreactor and methods for producing synchronous cells

Apparatus and methods are directed to a perfusion culture system in which a rotating bioreactor is used to grow cells in a liquid culture medium, while these cells are attached to an adhesive-treated porous surface. As a result of this arrangement and its rotation, the attached cells divide, with one cell remaining attached to the substrate, while the other cell, a newborn cell is released. These newborn cells are of approximately the same age, that are collected upon leaving the bioreactor. The populations of newborn cells collected are of synchronous and are minimally, if at all, disturbed metabolically

Response Functions to Critical Shocks in Social Sciences: An Empirical and Numerical Study

We show that, provided one focuses on properly selected episodes, one can apply to the social sciences the same observational strategy that has proved successful in natural sciences such as astrophysics or geodynamics. For instance, in order to probe the cohesion of a policy, one can, in different countries, study the reactions to some huge and sudden exogenous shocks, which we call Dirac shocks. This approach naturally leads to the notion of structural (as opposed or complementary to temporal) forecast. Although structural predictions are by far the most common way to test theories in the natural sciences, they have been much less used in the social sciences. The Dirac shock approach opens the way to testing structural predictions in the social sciences. The examples reported here suggest that critical events are able to reveal pre-existing ``cracks'' because they probe the social cohesion which is an indicator and predictor of future evolution of the system, and in some cases foreshadows a bifurcation. We complement our empirical work with numerical simulations of the response function (``damage spreading'') to Dirac shocks in the Sznajd model of consensus build-up. We quantify the slow relaxation of the difference between perturbed and unperturbed systems, the conditions under which the consensus is modified by the shock and the large variability from one realization to another

Listening to the Divine Lyre: Greek Epigrams and Theories of Lyric

I ask whether or not the Lyric can be defined solely in structural terms as a self-referential linguistic artifact, and if so, in what sense we should construe the poem’s relationship to the world and to knowledge. Using close readings of ancient and classical Greek epigrams, I first turn to Michael Riffaterre’s semiotics of poetry, in which it is proposed that the sign/signifier relationships generated in the text of poems can be exhausted in principle in an intertextual system of signs that makes no reference to the world. I then turn to Paul de Man, who suspects that Riffaterre may be conflating semiotics with interpretation in a rationalistic attempt to account fully for the nature of literary language. This critique serves as a bridge to a brief look at Thomist philosopher Jacques Maritain’s contention that the lyric poem displays both a rational correspondence to a linguistic system and a pre-rational connection to the body and soul. His comments are compared to those of Julia Kristeva, who asserts that the body itself is the matrix of signification and that this phenomenon is foregrounded in poetic language. This primal relationship of experience to language leads to an examination of Martin Heidegger’s advice to philosophers to “listen to the poets.” His contention that language is a gift of Being that comes to us through the poet is analyzed in the light of de Man’s criticism that Heidegger, in his eagerness to attain transcendence via language, oversteps the boundaries of legitimate philosophical inquiry. Then it is taken up in the context of Paul Ricoeur’s more generous appraisal that poetic language, understood as a form of linguistically innovative metaphor, can transcend semiosis to achieve a revelation of some new aspect of the world

The mechanisms of spatial and temporal earthquake clustering

The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent spatial and temporal clustering features of earthquakes are not reproduced by this kind of modeling. We show that when a spring-block model is complemented with a mechanism allowing for structural relaxation, realistic earthquake patterns are obtained. The proposed model does not need to include a phenomenological velocity weakening friction law, as traditional spring-block models do, since this behavior is effectively induced by the relaxational mechanism as well. In this way, the model provides also a simple microscopic basis for the widely used phenomenological rate-and-state equations of rock friction.Comment: 7 pages, 10 figures, comments welcom

Prediction of extreme events in the OFC model on a small world network

We investigate the predictability of extreme events in a dissipative Olami-Feder-Christensen model on a small world topology. Due to the mechanism of self-organized criticality, it is impossible to predict the magnitude of the next event knowing previous ones, if the system has an infinite size. However, by exploiting the finite size effects, we show that probabilistic predictions of the occurrence of extreme events in the next time step are possible in a finite system. In particular, the finiteness of the system unavoidably leads to repulsive temporal correlations of extreme events. The predictability of those is higher for larger magnitudes and for larger complex network sizes. Finally, we show that our prediction analysis is also robust by remarkably reducing the accessible number of events used to construct the optimal predictor.Comment: 5 pages, 4 figure

Rate Maintenance of Cell Division in Escherichia coli B/r: Analysis of a Simple Nutritional Shift-Down

A competitive (nonmetabolizable) inhibitor of glucose uptake, α- methylglucoside, was used to limit the growth of Escherichia coli. Cell division during such a nutritional shift-down was studied in batch cultures and with the \u27baby-machine\u27 technique. Following a brief delay, the rate of division was maintained for 60 to 70 min in batch cultures and for an extended period in the baby machine. Decreases in cell size were due, in part, to a possible reduction in the mass per chromosome origin at the time of replication initiation and a shorter time interval between initiation and the subsequent division. These unusual findings suggest that this method for abrupt change in growth rate without modifying repression patterns is useful for studying the control of various aspects of the bacterial cell

Relationship between ftsZ Gene Expression and Chromosome Replication in Escherichia coli

Transcriptional levels within the ftsQAZ region of the Escherichia coli chromosome were correlated with chromosome replication and the division cycle. The transcripts were measured either in synchronous cultures generated by the baby machine technique or in dnaC2(Ts) mutants that had been aligned for initiation of chromosome replication by temperature shifts. Transcription within the ftsZ reading frame was found to fluctuate during the cell cycle, with maximal levels about midcycle and a minimum level at division, in cells growing with a doubling time of 24 min at 37°C. Examination of transcription in dnaC(Ts) mutants aligned for chromosome replication indicated that the periodicity was due to a reduction in transcripts coincident with replication of the ftsQAZ region. Transcription originating upstream of the ftsA gene exhibited the periodicity and accounted for a significant proportion of the transcripts entering ftsZ. The most obvious interpretation of the data is that replication of the region transiently inhibits transcription, but alternative explanations have not been ruled out. However, no other relationship between transcription and either replication or division was detected

mioC Transcription, Initiation of Replication, and the Eclipse in Escherichia coli

The potential role of mioC transcription as a negative regulator of initiation of chromosome replication in Escherichia coli was evaluated. When initiation was aligned by a shift of dnaC2(Ts) mutants to nonpermissive temperature (40°C), mioC transcript levels measured at the 5\u27 end or reading through oriC disappeared within one mass doubling. Upon return to permissive temperature (30°C), the transcripts reappeared coordinately about 15 min after the first synchronized initiation and then declined sharply again 10 min later, just before the second initiation. Although these observations were consistent with the idea that mioC transcription might have to be terminated prior to initiation, it was found that the interval between initiations at permissive temperature, i.e., the eclipse period, was not influenced by the time required to shut down mioC transcription, since the eclipse was the same for chromosomes and minichromosomes which lacked mioC transcription. This finding did not, in itself, rule out the possibility that mioC transcription must he terminated prior to initiation of replication, since it might normally he shut off before initiation, and never be limiting, even during the eclipse. Therefore, experiments were performed to determine whether the continued presence of mioC transcription during the process of initiation altered the timing of initiation. It was found that minichromosomes possessing a deletion in the DnaA box upstream of the promoter transcribed mioC continuously and replicated with the same timing as those that either shut down expression prior to initiation or lacked expression entirely. It was further shown that mioC transcription was present throughout the induction of initiation by addition of chloramphenicol to a dnaA5(Ts) mutant growing at a semipermissive temperature. Thus, transcription through oriC emanating from the mioC gene promoter is normally inhibited prior to initiation of replication by the binding of DnaA protein, but replication can initiate with the proper timing even when transcription is not shut down; i.e., mioC does not serve as a negative regulator of initiation. It is proposed, however, that the reappearance and subsequent disappearance of mioC transcription during a 10-min interval at the end of the eclipse serves as an index of the minimum time required for the establishment of active protein-DNA complexes at the DnaA boxes in the fully methylated origin region of the chromosome. On this basis, the eclipse constitutes the time for methylation of the newly formed DNA strands (15 to 20 min at 30°C) followed by the time for DnaA protein to bind and activate oriC for replication (10 min)