Coping with dating errors in causality estimation

We consider the problem of estimating causal influences between observed processes from time series possibly corrupted by errors in the time variable (dating errors) which are typical in palaeoclimatology, planetary science and astrophysics. "Causality ratio" based on the Wiener-Granger causality is proposed and studied for a paradigmatic class of model systems to reveal conditions under which it correctly indicates directionality of unidirectional coupling. It is argued that in the case of a priori known directionality, the causality ratio allows a characterization of dating errors and observational noise. Finally, we apply the developed approach to palaeoclimatic data and quantify the influence of solar activity on tropical Atlantic climate dynamics over the last two millennia. A stronger solar influence in the first millennium A.D. is inferred. The results also suggest a dating error of about 20 years in the solar proxy time series over the same period

Bidirectional cooperative motion of myosin-II motors on actin tracks with randomly alternating polarities

The cooperative action of many molecular motors is essential for dynamic processes such as cell motility and mitosis. This action can be studied by using motility assays in which the motion of cytoskeletal filaments over a surface coated with motor proteins is tracked. In previous studies of actin-myosin II systems, fast directional motion was observed, reflecting the tendency of myosin II motors to propagate unidirectionally along actin filaments. Here, we present a motility assay with actin bundles consisting of short filamentous segments with randomly alternating polarities. These actin tracks exhibit bidirectional motion with macroscopically large time intervals (of the order of several seconds) between direction reversals. Analysis of this bidirectional motion reveals that the characteristic reversal time, $\tau_{rev}$, does not depend on the size of the moving bundle or on the number of motors, $N$. This observation contradicts previous theoretical calculations based on a two-state ratchet model [Badoual et al., Proc. Natl. Acad. Sci. USA, vol. 99, p. 6696 (2002)], predicting an exponential increase of $\tau_{rev}$ with $N$. We present a modified version of this model that takes into account the elastic energy due to the stretching of the actin track by the myosin II motors. The new model yields a very good quantitative agreement with the experimental results.Comment: A slightly revised version. Figures 2 and 7 were modified. Accepted for publication in "Soft Matter

Finding the direction of disturbance propagation in a chemical process using transfer entropy

Published versio

All-optical spatio-temporal control of electron emission from SiO2 nanospheres with femtosecond two-color laser fields

Field localization by nanostructures illuminated with laser pulses of well-defined waveform enables spatio-temporal tailoring of the near-fields for sub-cycle control of electron dynamics at the nanoscale. Here, we apply intense linearly-polarized two-color laser pulses for all-optical control of the highest energy electron emission from SiO2 nanoparticles. For the size regime where light propagation effects become important, we demonstrate the possibility to control the preferential emission angle of a considerable fraction of the fastest electrons by varying the relative phase of the two-color field. Trajectory based semi-classical simulations show that for the investigated nanoparticle size range the directional steering can be attributed to the two-color effect on the electron trajectories, while the accompanied modification of the spatial distribution of the ionization rate on the nanoparticle surface has only a minor effect

Directional emission from asymmetric resonant cavities

Asymmetric resonant cavities (ARCs) with highly non-circular but convex cross-sections are predicted theoretically to have high-Q whispering gallery modes with very anisotropic emission. We develop a ray dynamics model for the emission pattern and present numerical and experimental confirmation of the theory.Comment: 7 pages LaTeX, 3 postscript figure

Transport in a Levy ratchet: Group velocity and distribution spread

We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric L\'evy noise, being a minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the L\'evy noise, the particle exhibits a motion with a preferred direction even in the absence of whatever additional time-dependent forces. The examination of the L\'evy ratchet has to be based on the characteristics of directionality which are different from typically used measures like mean current and the dispersion of particles' positions, since these get inappropriate when the moments of the noise diverge. To overcome this problem, we discuss robust measures of directionality of transport like the position of the median of the particles displacements' distribution characterizing the group velocity, and the interquantile distance giving the measure of the distributions' width. Moreover, we analyze the behavior of splitting probabilities for leaving an interval of a given length unveiling qualitative differences between the noises with L\'evy indices below and above unity. Finally, we inspect the problem of the first escape from an interval of given length revealing independence of exit times on the structure of the potential.Comment: 9 pages, 12 figure

Cooperative molecular motors moving back and forth

We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., {\em Proc. Natl. Acad. Sci. USA} {\bf 99}, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that develops in the cytoskeletal track due to the joint action of the walking motors. We show, both computationally and analytically, that this additional cooperativity effect leads to a dramatic reduction in the characteristic reversal time of the bidirectional motion, especially in systems with a large number of motors. We also find that bidirectional motion takes place only on (almost) a-polar tracks, while on even slightly polar tracks the motion is unidirectional. We argue that the origin of these observations is the sensitive dependence of the cooperative dynamics on the difference between the number of motors typically working in and against the instantaneous direction of motion.Comment: Accepted for publication in Phys. Rev.