Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling

The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a heteroclinic loop connecting a pair of clustered states of the population. We argue that the same behavior can arise in a wider class of oscillator models with the amplitude degree of freedom. We also argue how such heteroclinic loops arise inevitably and persist robustly in a homogeneous population of globally coupled oscillators. Although the heteroclinic loop might seem to arise only exceptionally, we find that it appears rather easily by introducing the time-delay in the population which would otherwise exhibit perfect phase synchrony. We argue that the appearance of the heteroclinic loop induced by the delayed coupling is then characterized by transcritical and saddle-node bifurcations. Slow switching arises when the system with a heteroclinic loop is weakly perturbed. This will be demonstrated with a vector model by applying weak noises. Other types of weak symmetry-breaking perturbations can also cause slow switching.Comment: 10 pages, 14 figures, RevTex, twocolumn, to appear in Phys. Rev.

Dissecting Oct3/4-Regulated Gene Networks in Embryonic Stem Cells by Expression Profiling

POU transcription factor Pou5f1 (Oct3/4) is required to maintain ES cells in an undifferentiated state. Here we show that global expression profiling of Oct3/4-manipulated ES cells delineates the downstream target genes of Oct3/4. Combined with data from genome-wide chromatin-immunoprecipitation (ChIP) assays, this analysis identifies not only primary downstream targets of Oct3/4, but also secondary or tertiary targets. Furthermore, the analysis also reveals that downstream target genes are regulated either positively or negatively by Oct3/4. Identification of a group of genes that show both activation and repression depending on Oct3/4 expression levels provides a possible mechanism for the requirement of appropriate Oct3/4 expression to maintain undifferentiated ES cells. As a proof-of-principle study, one of the downstream genes, Tcl1, has been analyzed in detail. We show that Oct3/4 binds to the promoter region of Tcl1 and activates its transcription. We also show that Tcl1 is involved in the regulation of proliferation, but not differentiation, in ES cells. These findings suggest that the global expression profiling of gene-manipulated ES cells can help to delineate the structure and dynamics of gene regulatory networks

Brisure de bulles dans un écoulement oscillant sur Terre et en gravité réduite

The stability of centimeter scale air bubbles is studied in quiescent suspending liquid under an imposed oscillatory acceleration field. Experiments were performed in reduced- and normal-gravity environments. A strong acceleration resulted in an instability leading to the breakups of the bubbles in both gravity environments. The breakup onset was investigated and found to be characterized by a critical acceleration acr . The influence of the liquid viscosity and the gravitational environment was studied. Empirical correlations for the onset are presented and discussed with the intention to reveal splitting mechanism. The inertial mechanism often deemed to cause the breakup of drops sub jected to a rapid gas stream is shown to give explanations consistent with the experiments. A breakup criterion for both gravitational environments is proposed through discussions from an energetic point of view