A Shape Theorem for Riemannian First-Passage Percolation

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one

VIDEO ANALYSIS OF SHOT DISTRIBUTION AND GOALKEEPER MOVEMENT DURING ROLLER HOCKEY MATCH PLAY

The aim of this investigation was to analyse the position of shots and movement of goalkeepers during roller hockey matches. A video camera recorded the movement of 6 goalkeepers during 6 national roller hockey matches. The position of the goalkeeper and the shots were noted manually from the video recordings. The results showed that, of the 331 shots delivered, the greatest percentage was directed at the bottom corners of the goal. Shots were delivered at a mean interval of 67 s (± 79 s) and of the 34 goals scored the greatest percentage were delivered to the top right corner (38%). Goalkeepers displayed a reasonably high number of movements across the goal; however, the greatest duration was spent covering the central area of the goal (69%). Understanding the match play activity of roller hockey goalkeepers enabled greater task specific training

Axion Like Particle Search at Higgs Factories

We study the potential of the future Higgs factories, including the ILC, CEPC, and FCC-ee with $\sqrt{s}$ = 240-250 GeV on discovering axion-like particles (ALPs) through various production channels in the leptonic final states, $e^+e^- \to f\bar{f} a$, where $f=e,\mu,\nu$. We show that the $e^+e^- \to e^+e^- a$ with $a \to \gamma\gamma$ provides the best bounds for the $g_{a\gamma\gamma}$ and $g_{aZZ}$ couplings, while $e^+e^- \to \nu\bar{\nu}a$, with $a \to \gamma\gamma$ offers the best bounds for the $g_{aZZ}$ and $g_{aZ\gamma}$ couplings. The $e^+e^- \to \mu^+\mu^- a$ with $a \to \gamma\gamma$ provides intermediate sensitivity to the $g_{aZZ}$ coupling. Our estimates of the bounds for the $g_{a\gamma\gamma}$, $g_{aZ\gamma}$, and $g_{aZZ}$ couplings as a function of ALP mass ($M_a$) ranging from 0.1 GeV to 100 GeV provide valuable insights for future experiments aiming to detect ALPs. We find that $g_{a\gamma\gamma}$ around $1.5\times10^{-4}~\rm GeV^{-1}$ for $M_a = 0.1-6$ GeV is currently not ruled out by any other experiments.Comment: 20 pages, 8 figure

Beauty Quark Fragmentation Into Strange B Mesons

Using the recent measurement of the total production rate for $B_s$ and $B_s^*$ mesons in electron-positron annihilation to determine the strange quark mass parameter in the $\bar b\to B_s,\, B_s^*$ fragmentation functions we calculate the momentum distributions of the $B_s$ and $B_s^*$ mesons.Comment: 8 pages, 2 figures (not included but available upon request), standard LaTeX file, Report # NUHEP-TH-94-1

Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime

In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_t:t\ge 0\}$ be a L\'evy processes such that $X_1^{(a)}\stackrel{d}{=} Y_1^{(a)}$, $\mathbb E X_1^{(a)}<0$ and $\mathbb E X_1^{(a)}\uparrow0$ as $a\downarrow0$. Let $S^{(a)}_n=\sum_{k=1}^n Y^{(a)}_k$. Then, under some mild assumptions, $\Delta(a)\max_{n\ge 0} S_n^{(a)}\stackrel{d}{\to} R\iff\Delta(a)\sup_{t\ge 0} X^{(a)}_t\stackrel{d}{\to} R$, for some random variable $R$ and some function $\Delta(\cdot)$. We utilize this result to present a number of limit theorems for suprema of L\'evy processes in the heavy-traffic regime

MAXIMUM VELOCITY OF THE STRIKING LEG DURING THE MARTIAL ARTS FRONT, SIDE AND TURNING KICKS AND THE RELATIONSHIP TO TECHNIQUE DURATION

Eight male martial artists performed five repetitions of the front, side and turning kicks at a target. 3-D movement was recorded and automatically digitised at 200 Hz using Peak Motus. The mean maximum velocity (± SE) of the striking leg was 11.77 ± 0.18 m•s-1 for the front kick, 10.44 ± 0.16 m•s-1 for the side kick and 13.06 ± 0.33 m•s-1 for the turning kick. Differences between the front and the side kick, and the front and turning kick were significant (p = 0.001), with the greatest difference between the turning and the side kick (p < 0.0001). The mean duration of the front, side and turning kicks was 0.23 s, 0.25 s and 0.24 s. The side kick was significantly longer than the front kick (p = 0.03). For the front kick, the faster the maximum velocity then the shorter the duration (r = &#8722; 0.751, p < 0.0001)

Parameter estimation in pair hidden Markov models

This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some restrictions with respect to the full parameter space naturally occur. Existence of two different Information divergence rates is established and divergence property (namely positivity at values different from the true one) is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.Comment: corrected typo

Calibrated Tree Priors for Relaxed Phylogenetics and Divergence Time Estimation

The use of fossil evidence to calibrate divergence time estimation has a long history. More recently Bayesian MCMC has become the dominant method of divergence time estimation and fossil evidence has been re-interpreted as the specification of prior distributions on the divergence times of calibration nodes. These so-called "soft calibrations" have become widely used but the statistical properties of calibrated tree priors in a Bayesian setting has not been carefully investigated. Here we clarify that calibration densities, such as those defined in BEAST 1.5, do not represent the marginal prior distribution of the calibration node. We illustrate this with a number of analytical results on small trees. We also describe an alternative construction for a calibrated Yule prior on trees that allows direct specification of the marginal prior distribution of the calibrated divergence time, with or without the restriction of monophyly. This method requires the computation of the Yule prior conditional on the height of the divergence being calibrated. Unfortunately, a practical solution for multiple calibrations remains elusive. Our results suggest that direct estimation of the prior induced by specifying multiple calibration densities should be a prerequisite of any divergence time dating analysis