6,939 research outputs found

### An optimal transportation approach for assessing almost stochastic order

When stochastic dominance $F\leq_{st}G$ does not hold, we can improve
agreement to stochastic order by suitably trimming both distributions. In this
work we consider the $L_2-$Wasserstein distance, $\mathcal W_2$, to stochastic
order of these trimmed versions. Our characterization for that distance
naturally leads to consider a $\mathcal W_2$-based index of disagreement with
stochastic order, $\varepsilon_{\mathcal W_2}(F,G)$. We provide asymptotic
results allowing to test $H_0: \varepsilon_{\mathcal W_2}(F,G)\geq
\varepsilon_0$ vs $H_a: \varepsilon_{\mathcal W_2}(F,G)<\varepsilon_0$, that,
under rejection, would give statistical guarantee of almost stochastic
dominance. We include a simulation study showing a good performance of the
index under the normal model

### The two gap transitions in Ge$_{1-x}$Sn$_x$: effect of non-substitutional complex defects

The existence of non-substitutional $\beta$-Sn defects in Ge$_{1-x}$Sn$_{x}$
was confirmed by emission channeling experiments [Decoster et al., Phys. Rev. B
81, 155204 (2010)], which established that although most Sn enters
substitutionally ($\alpha$-Sn) in the Ge lattice, a second significant fraction
corresponds to the Sn-vacancy defect complex in the split-vacancy configuration
( $\beta$-Sn ), in agreement with our previous theoretical study [Ventura et
al., Phys. Rev. B 79, 155202 (2009)]. Here, we present our electronic structure
calculation for Ge$_{1-x}$Sn$_{x}$, including substitutional $\alpha$-Sn as
well as non-substitutional $\beta$-Sn defects. To include the presence of
non-substitutional complex defects in the electronic structure calculation for
this multi-orbital alloy problem, we extended the approach for the purely
substitutional alloy by Jenkins and Dow [Jenkins and Dow, Phys. Rev. B 36, 7994
(1987)]. We employed an effective substitutional two-site cluster equivalent to
the real non-substitutional $\beta$-Sn defect, which was determined by a
Green's functions calculation. We then calculated the electronic structure of
the effective alloy purely in terms of substitutional defects, embedding the
effective substitutional clusters in the lattice. Our results describe the two
transitions of the fundamental gap of Ge$_{1-x}$Sn$_{x}$ as a function of the
total Sn-concentration: namely from an indirect to a direct gap, first, and the
metallization transition at higher $x$. They also highlight the role of
$\beta$-Sn in the reduction of the concentration range which corresponds to the
direct-gap phase of this alloy, of interest for optoelectronics applications.Comment: 11 pages, 9 Figure

### How to generate pentagonal symmetry using Turing systems

We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can be mimicked, such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids

### Regression-based seasonal unit root tests

The contribution of this paper is three-fold. Firstly, a characterisation theorem of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it proposes regressionbased tests for the seasonal unit root hypothesis which allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Thirdly, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large sample null distribution theory for regression t-statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t-statistics for unit roots at the zero and Nyquist frequencies and regression Fstatistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given which is consonant with the predictions from the large sample theory.Seasonal unit root tests; seasonal drifts; characterisation theorem

### MAGIC sensitivity to millisecond-duration optical pulses

The MAGIC telescopes are a system of two Imaging Atmospheric Cherenkov
Telescopes (IACTs) designed to observe very high energy (VHE) gamma rays above
~50 GeV. However, as IACTs are sensitive to Cherenkov light in the UV/blue and
use photo-detectors with a time response well below the ms scale, MAGIC is also
able to perform simultaneous optical observations. Through an alternative
system installed in the central PMT of MAGIC II camera, the so-called central
pixel, MAGIC is sensitive to short (1ms - 1s) optical pulses. Periodic signals
from the Crab pulsar are regularly monitored. Here we report for the first time
the experimental determination of the sensitivity of the central pixel to
isolated 1-10 ms long optical pulses. The result of this study is relevant for
searches of fast transients such as Fast Radio Bursts (FRBs).Comment: Proceedings of the 35th International Cosmic Ray Conference (ICRC
2017), Bexco, Busan, Korea (arXiv:1708.05153

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