Volume and heat kernel fluctuations for the three-dimensional uniform spanning tree

Let $\mathcal{U}$ be the uniform spanning tree on $\mathbb{Z}^{3}$. We show the occurrence of log-logarithmic fluctuations around the leading order for the volume of intrinsic balls in $\mathcal{U}$. As an application, we obtain similar fluctuations for the quenched heat kernel of the simple random walk on $\mathcal{U}$.Comment: 39 pages, 20 figure

Annealed transition density of simple random walk on a high-dimensional loop-erased random walk

We derive sub-Gaussian bounds for the annealed transition density of the simple random walk on a high-dimensional loop-erased random walk. The walk dimension that appears in these is the exponent governing the space-time scaling of the process with respect to the extrinsic Euclidean distance, which contrasts with the exponent given by the intrinsic graph distance that appears in the corresponding quenched bounds. We prove our main result using novel pointwise Gaussian estimates on the distribution of the high-dimensional loop-erased random walk.Comment: 36 pages, 7 figure

Preserving the C7 spinous process in laminectomy combined with lateral mass screw to prevent axial symptom

AbstractBackgroundPreserving the C7 spinous process during cervical laminoplasty has been reported to prevent axial symptom. Some patients underwent laminectomy and fixation developed the symptom. The objective of this article was to investigate whether axial symptom can be reduced by preserving the C7 spinous process during cervical laminectomy and fixation with lateral mass screw.MethodsBetween 2005 and 2008, data of 53 patients who underwent laminectomy and lateral mass-screw fixation for multilevel cervical myelopathy were reviewed. Analysis consisted of the incidence of axial symptom, Japan Orthopaedic Association (JOA) scores, recovery rate, cervical lordotic angle, and atrophy rate of cervical posterior muscle. Axial symptom severity was quantified by a visual analog scale (VAS). Twenty-five patients were decompressed from C3 to C7 (group A) and 28 from C3 to C6 with dome-shape removal of the C7 superior lamina (group B).ResultsAnalysis of final follow-up data showed improvement in clinical outcome for both groups. No difference in recovery rate, cervical lordotic angle and atrophy rate was observed between groups. Postoperative axial-neck pain was significantly rarer in group B than in group A. Axial symptom severity was correlated with cervical posterior muscle atrophy rate; correlation coefficient was 0.665.ConclusionThe C7 spinous process might play an important role in preventing axial symptom, but there is a need for randomized, control studies with long-term follow-up to clarify the results

Radiation induction of delayed recombination in Schizosaccharomyces pombe.

Ionizing radiation is known to induce delayed chromosome and gene mutations in the descendants of the irradiated tissue culture cells. Molecular mechanisms of such delayed mutations are yet to be elucidated, since high genomic complexity of mammalian cells makes it difficult to analyze. We now tested radiation induction of delayed recombination in the fission yeast Schizosaccharomyces pombe by monitoring the frequency of homologous recombination after X-irradiation. A reporter with 200 bp tandem repeats went through spontaneous recombination at a frequency of 1.0 x 10(-4), and the frequency increased dose-dependently to around 10 x 10(-4) at 500 Gy of X-irradiation. Although the repair of initial DNA damage was thought to be completed before the restart of cell division cycle, the elevation of the recombination frequency persisted for 8-10 cell generations after irradiation (delayed recombination). The delayed recombination suggests that descendants of the irradiated cells keep a memory of the initial DNA damage which upregulates recombination machinery for 8-10 generations even in the absence of DNA double-strand breaks (DSBs). Since radical scavengers were ineffective in inhibiting the delayed recombination, a memory by continuous production of DNA damaging agents such as reactive oxygen species (ROS) was excluded. Recombination was induced in trans in a reporter on chromosome III by a DNA DSB at a site on chromosome I, suggesting the untargeted nature of delayed recombination. Interestingly, Rad22 foci persisted in the X-irradiated population in parallel with the elevation of the recombination frequency. These results suggest that the epigenetic damage memory induced by DNA DSB upregulates untargeted and delayed recombination in S. pombe

Wavefront-sensor-based electron density measurements for laser-plasma accelerators

Characterization of the electron density in laser produced plasmas is presented using direct wavefront analysis of a probe laser beam. The performance of a laser-driven plasma-wakefield accelerator depends on the plasma wavelength, hence on the electron density. Density measurements using a conventional folded-wave interferometer and using a commercial wavefront sensor are compared for different regimes of the laser-plasma accelerator. It is shown that direct wavefront measurements agree with interferometric measurements and, because of the robustness of the compact commercial device, have greater phase sensitivity, straightforward analysis, improving shot-to-shot plasma-density diagnostics