Time-Dependent Random Walks and the Theory of Complex Adaptive Systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.Comment: 5 pages, 2 figure

Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We show that the particle survives with probability Q(t) \sim t^{-\theta} with \theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-}, however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-}, and we determine this dependence.Comment: 4 page

The problem of analytical calculation of barrier crossing characteristics for Levy flights

By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Levy noise. After shortly review recent results obtained with different approaches on the time characteristics of the barrier crossing, we derive a general differential equation useful to calculate the nonlinear relaxation time. We obtain analytically the nonlinear relaxation time for free Levy flights and a closed expression in quadrature of the same characteristics for cubic potential.Comment: 12 pages, 2 figures, presented at 5th International Conference on Unsolved Problems on Noise, Lyon, France, 2008, to appear in J. Stat. Mech.: Theory and Experimen

Generalized persistence exponents: an exactly soluble model

It was recently realized that the persistence exponent appearing in the dynamics of nonequilibrium systems is a special member of a continuously varying family of exponents, describing generalized persistence properties. We propose and solve a simplified model of coarsening, where time intervals between spin flips are independent, and distributed according to a L\'evy law. Both the limit distribution of the mean magnetization and the generalized persistence exponents are obtained exactly.Comment: 4 pages, 3 figures Submitted to PR

Discovery of the broad-lined Type Ic SN 2013cq associated with the very energetic GRB 130427A

Long-duration gamma-ray bursts (GRBs) at z < 1 are in most cases found to be accompanied by bright, broad-lined Type Ic supernovae (SNe Ic-BL). The highest-energy GRBs are mostly located at higher redshifts, where the associated SNe are hard to detect observationally. Here we present early and late observations of the optical counterpart of the very energetic GRB 130427A. Despite its moderate redshift z = 0.3399+/-0.0002, GRB 130427A is at the high end of the GRB energy distribution, with an isotropic-equivalent energy release of Eiso ~ 9.6x10^53 erg, more than an order of magnitude more energetic than other GRBs with spectroscopically confirmed SNe. In our dense photometric monitoring, we detect excess flux in the host-subtracted r-band light curve, consistent with what expected from an emerging SN, ~0.2 mag fainter than the prototypical SN 1998bw. A spectrum obtained around the time of the SN peak (16.7 days after the GRB) reveals broad undulations typical of SNe Ic-BL, confirming the presence of a SN, designated SN 2013cq. The spectral shape and early peak time are similar to those of the high expansion velocity SN 2010bh associated with GRB 100316D. Our findings demonstrate that high-energy long-duration GRBs, commonly detected at high redshift, can also be associated with SNe Ic-BL, pointing to a common progenitor mechanism.Comment: 12 pages, 4 figures, 1 table, accepted for publication in Ap

VLT/X-shooter spectroscopy of the afterglow of the Swift GRB 130606A: Chemical abundances and reionisation at z∼6z\sim6

The reionisation of the Universe is thought to have ended around z~6, as inferred from spectroscopy of distant bright background sources, such as quasars (QSO) and gamma-ray burst (GRB) afterglows. Furthermore, spectroscopy of a GRB afterglow provides insight in its host galaxy, which is often too dim and distant to study otherwise. We present the high S/N VLT/X-shooter spectrum of GRB130606A at z=5.913. We aim to measure the degree of ionisation of the IGM between 5.02<z<5.84 and to study the chemical abundance pattern and dust content of its host galaxy. We measured the flux decrement due to absorption at Ly$\alpha$, $\beta$ and $\gamma$ wavelength regions. The hydrogen and metal absorption lines formed in the host galaxy were fitted with Voigt profiles to obtain column densities. Our measurements of the Ly$\alpha$-forest optical depth are consistent with previous measurements of QSOs, but have a much smaller uncertainty. The analysis of the red damping wing yields a neutral fraction $x_{HI}<0.05$ (3$\sigma$). We obtain column density measurements of several elements. The ionisation corrections due to the GRB is estimated to be negligible (<0.03 dex), but larger corrections may apply due to the pre-existing radiation field (up to 0.4 dex based on sub-DLA studies). Our measurements confirm that the Universe is already predominantly ionised over the redshift range probed in this work, but was slightly more neutral at z>5.6. GRBs are useful probes of the ionisation state of the IGM in the early Universe, but because of internal scatter we need a larger statistical sample to draw robust conclusions. The high [Si/Fe] in the host can be due to dust depletion, alpha-element enhancement, or a combination of both. The very high value of [Al/Fe]=2.40+/-0.78 might connected to the stellar population history. We estimate the host metallicity to be -1.7<[M/H]<-0.9 (2%-13% of solar). (trunc.)Comment: 15 pages, 12 figure

Using Corticomuscular and Intermuscular Coherence to Assess Cortical Contribution to Ankle Plantar Flexor Activity During Gait

The present study used coherence and directionality analyses to explore whether the motor cortex contributes to plantar flexor muscle activity during the stance phase and push-off phase during gait. Subjects walked on a treadmill, while EEG over the leg motorcortex area and EMG from the medial gastrocnemius and soleus muscles was recorded. Corticomuscular and intermuscular coherence were calculated from pair-wise recordings. Significant EEG-EMG and EMG-EMG coherence in the beta and gamma frequency bands was found throughout the stance phase with the largest coherence towards push-off. Analysis of directionality revealed that EEG activity preceded EMG activity throughout the stance phase until the time of push-off. These findings suggest that the motor cortex contributes to ankle plantar flexor muscle activity and forward propulsion during gait

The mysterious optical afterglow spectrum of GRB140506A at z=0.889

Context. Gamma-ray burst (GRBs) afterglows probe sightlines to star-forming regions in distant star-forming galaxies. Here we present a study of the peculiar afterglow spectrum of the z = 0.889 Swift GRB 140506A. Aims. Our aim is to understand the origin of the very unusual properties of the absorption along the line-of-sight. Methods. We analyse spectroscopic observations obtained with the X-shooter spectrograph mounted on the ESO/VLT at two epochs 8.8 h and 33 h after the burst as well as imaging from the GROND instrument. We also present imaging and spectroscopy of the host galaxy obtained with the Magellan telescope. Results. The underlying afterglow appears to be a typical afterglow of a long-duration GRB. However, the material along the line-of- sight has imprinted very unusual features on the spectrum. Firstly, there is a very broad and strong flux drop below 8000 AA (4000 AA in the rest frame), which seems to be variable between the two spectroscopic epochs. We can reproduce the flux-drops both as a giant 2175 AA extinction bump and as an effect of multiple scattering on dust grains in a dense environment. Secondly, we detect absorption lines from excited H i and He i. We also detect molecular absorption from CH+ . Conclusions. We interpret the unusual properties of these spectra as reflecting the presence of three distinct regions along the line-of-sight: the excited He i absorption originates from an H ii-region, whereas the Balmer absorption must originate from an associated photodissociation region. The strong metal line and molecular absorption and the dust extinction must originate from a third, cooler region along the line-of-sight. The presence of (at least) three separate regions is reflected in the fact that the different absorption components have different velocities relative to the systemic redshift of the host galaxy.Comment: 8 pages, 4 figures. Accepted for publications in A&