Structural Complexity of Random Binary Trees

Abstract — For each positive integer n, let Tn be a random rooted binary tree having finitely many vertices and exactly n leaves. We can view H(Tn), the entropy of Tn, as a measure of the structural complexity of tree Tn in the sense that approximately H(Tn) bits suffice to construct Tn. We are interested in determining conditions on the sequence (Tn: n = 1, 2, · · ·) under which H(Tn)/n converges to a limit as n → ∞. We exhibit some of our progress on the way to the solution of this problem. I

On a zero speed sensitive cellular automaton

Using an unusual, yet natural invariant measure we show that there exists a sensitive cellular automaton whose perturbations propagate at asymptotically null speed for almost all configurations. More specifically, we prove that Lyapunov Exponents measuring pointwise or average linear speeds of the faster perturbations are equal to zero. We show that this implies the nullity of the measurable entropy. The measure m we consider gives the m-expansiveness property to the automaton. It is constructed with respect to a factor dynamical system based on simple "counter dynamics". As a counterpart, we prove that in the case of positively expansive automata, the perturbations move at positive linear speed over all the configurations

Softening of the insulating phase near Tc for the photo-induced insulator-to-metal phase transition in vanadium dioxide

We use optical-pump terahertz-probe spectroscopy to investigate the near-threshold behavior of the photoinduced insulator-to-metal (IM) transition in vanadium dioxide thin films. Upon approaching Tc a reduction in the fluence required to drive the IM transition is observed, consistent with a softening of the insulating state due to an increasing metallic volume fraction (below the percolation limit). This phase coexistence facilitates the growth of a homogeneous metallic conducting phase following superheating via photoexcitation. A simple dynamic model using Bruggeman effective medium theory describes the observed initial condition sensitivity.Comment: accepted for publication in Physical Review Letter

“Glass is frozen beauty”-a memorial issue in honor of C. Austen Angell (1933–2021)

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The Effect of Caffeine on Motor Task Performance

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Generation of broad XUV continuous high harmonic spectra and isolated attosecond pulses with intense mid-infrared lasers

We present experimental results showing the appearance of a near-continuum in the high-order harmonic generation (HHG) spectra of atomic and molecular species as the driving laser intensity of an infrared pulse increases. Detailed macroscopic simulations reveal that these near-continuum spectra are capable of producing IAPs in the far field if a proper spatial filter is applied. Further, our simulations show that the near-continuum spectra and the IAPs are a product of strong temporal and spatial reshaping (blue shift and defocusing) of the driving field. This offers a possibility of producing IAPs with a broad range of photon energy, including plateau harmonics, by mid-IR laser pulses even without carrier-envelope phase stabilization.Comment: 7 pages, 5 figures, submitted to J.Phys. B (Oct 2011

Effect of experimental laser imperfections on laser wakefield acceleration and betatron source

International audienceLaser pulses in current ultra-short TW systems are far from being ideal Gaussian beams. The influence of the presence of non-Gaussian features of the laser pulse is investigated here from experiments and 3D Particle-in-Cell simulations. Both the experimental intensity distribution and wavefront are used as input in the simulations. It is shown that a quantitative agreement between experimental data and simulations requires to use realistic pulse features. Moreover, some trends found in the experiments, such as the growing of the X-ray signal with the plasma length, can only be retrieved in simulations with realistic pulses. The performances on the electron acceleration and the synchrotron X-ray emission are strongly degraded by these non-Gaussian features, even keeping constant the total laser energy. A drop on the X-ray photon number by one order of magnitude was found. This clearly put forward the limitation of using a Gaussian beam in the simulations

Estrogen dependent expression of the receptor tyrosine kinase axl in normal and malignant human breast

Summary Background: Axl, a member of a family of receptor tyrosine kinases characterized by an extracellular domain resembling cell adhesion molecules and an intracellular conserved tyrosine kinase domain has been reported to induce cell proliferation and transformation. In mice, axl is expressed in the normal mammary gland and over-expressed in aggressive mammary tumors. Patients and methods: We have investigated the expression of axl immunohistochemically in 23 normal human breast samples and in 111 consecutive breast carcinomas. Expression of axl was correlated with tumour characteristics (lymph node involvement, stage, grade) and immunohistochemical expression of ER, PR, Ki-67 and c-erbB-2. Results: In normal tissue, axl localizes to the membrane of breast epithelial cells. Axl protein shows membrane associated staining in high correlation (P = 0.004) with the expression of the estrogen receptor (ER). Axl expression was found in a subset of breast carcinomas and was also correlated with high significance (P < 0.0001) with the presence of ER. Conclusion: Our results suggest that axl may serve as a mediator of estrogen stimulation preventing the completion of the breast epithelial life cycle and that estrogen induced axl expression may give a survival signal to cancerous cells, preventing them from dying through apoptosi