Inverse sampling and triangular sequential designs to compare a small proportion with a reference value

Inverse sampling and formal sequential designs may prove useful in reducing the sample size in studies where a small population proportion p is compared with a hypothesized reference proportion p0. These methods are applied to the design of a cytogenetic study about chromosomal abnormalities in men with a daughter affected by Turner's syndrome. First it is shown how the calculated sample size for a classical design depends on the parameterization used. Later this sample size is compared with the required sample size in an inverse sampling design and a triangular sequential design using four different parameterizations (absolute differences, log-odds ratio, angular transform and Sprott's transform). The expected savings in sample size, when the alternative hypothesis is true, are 20% of the fixed sample size for the inverse sampling design and 40% for the triangular sequential design

Joint Distribution of Distance and Angles in Finite Wireless Networks

Directional beamforming will play a paramount role in 5G and beyond networks in order to combat the higher path losses incurred at millimeter wave bands. Appropriate modeling and analysis of the angles and distances between transmitters and receivers in these networks are thus essential to understand performance and limiting factors. Most existing literature considers either infinite and uniform networks, where nodes are drawn according to a Poisson point process, or finite networks with the reference receiver placed at the origin of a disk. Under either of these assumptions, the distance and azimuth angle between transmitter and receiver are independent, and the angle follows a uniform distribution between $0$ and $2\pi$. Here, we consider a more realistic case of finite networks where the reference node is placed at any arbitrary location. We obtain the joint distribution between the distance and azimuth angle and demonstrate that these random variables do exhibit certain correlation, which depends on the shape of the region and the location of the reference node. To conduct the analysis, we present a general mathematical framework which is specialized to exemplify the case of a rectangular region. We then also derive the statistics for the 3D case where, considering antenna heights, the joint distribution of distance, azimuth and zenith angles is obtained. Finally, we describe some immediate applications of the present work, including the analysis of directional beamforming, the design of analog codebooks and wireless routing algorithms.Comment: 14 pages, 14 figure

The magnetic precursor of L1448-mm: Excitation differences between ion and neutral fluids

Shock modelling predicts an electron density enhancement within the magnetic precursor of C-shocks. Previous observations of SiO, H13CO+, HN13C and H13CN toward the young L1448-mm outflow showed an over-excitation of the ion fluid that was attributed to an electron density enhancement in the precursor. We re-visit this interpretation and test if it still holds when we consider different source morphologies and kinetic temperatures for the observed molecules, and also give some insight on the spatial extent of the electron density enhancement around L1448-mm. We estimate the opacities of H13CO+ and HN13C by observing the J=3\to2 lines of rarer isotopologues to confirm that the emission is optically thin. To model the excitation of the molecules, we use the large velocity gradient (LVG) approximation with updated collisional coefficients to i) re- analyse the observations toward the positions where the over-excitation of H13CO+ has previously been observed [i.e. toward L1448- mm at offsets (0,0) and (0,-10)], and ii) to investigate if the electron density enhancement is still required for the cases of extended and compact emission, and for kinetic temperatures of up to 400 K. We also report several lines of SiO, HN13C and H13CO+ toward new positions around this outflow, to investigate the spatial extent of the over-excitation of the ions in L1448-mm. From the isotopologue observations, we find that the emission of H13CO+ and HN13C from the precursor is optically thin if this emission is extended. Using the new collisional coefficients, an electron density enhancement is still needed to explain the excitation of H13CO+ for extended emission and for gas temperatures of\le 400 K toward L1448-mm (0,-10), and possibly also toward L1448-mm (0,0). For compact emission the data cannot be fitted. We do not find any evidence for the over-excitation of the ion fluid toward the newly observed positions around L1448-mm. The observed line emission of SiO, H13CO+ and HN13C toward L1448-mm (0,0) and (0,-10) is consistent with an electron density enhancement in the precursor component, if this emission is spatially extended. This is also true for the case of high gas temperatures (\le400 K) toward the (0,-10) offset. The electron density enhancement seems to be restricted to the southern, redshifted lobe of the L1448-mm outflow. Interferometric images of the line emission of these molecules are needed to confirm the spatial extent of the over-excitation of the ions and thus, of the electron density enhancement in the magnetic precursor of L1448-mm.Comment: Accepted for publication in A&A; 9 pages, 3 figure

Revisiting the evolution of nonradiative supernova remnants: A hydrodynamical-informed parameterization of the shock positions

Understanding the evolution of a supernova remnant shell in time is fundamental. Such understanding is critical to build reliable models of the dynamics of the supernova remnant shell interaction with any pulsar wind nebula it might contain. Here, we perform a large study of the parameter space for the one-dimensional spherically symmetric evolution of a supernova remnant, accompanying it by analytical analysis. Assuming, as is usual, an ejecta density profile with a power-law core and an envelope, and a uniform ambient medium, we provide a set of highly-accurate approximations for the evolution of the main structural features of supernova remnants, such as the reverse and forward shocks and the contact discontinuity. We compare our results with previously adopted approximations, showing that existing simplified prescriptions can easily lead to large errors. In particular, in the context of pulsar wind nebulae modelling, an accurate description for the supernova remnant reverse shock is required. We also study in depth the self-similar solutions for the initial phase of evolution, when the reverse shock propagates through the envelope of the ejecta. Since these self-similar solutions are exact, but not fully analytical, we here provide highly-accurate approximations as well

Reflection and transmission of waves in surface-disordered waveguides

The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type disorder on the behavior of the ensemble average and fluctuations of the reflection and transmission coefficients, reflectance, transmittance, and conductance. Our results show anomalous effects stemming from the combination of mode dispersion and rough surface scattering: For a given waveguide length, the larger the mode transverse momentum is, the more strongly is the mode scattered. These effects manifest themselves in the mode selectivity of the transmission coefficients, anomalous backscattering enhancement, and speckle pattern both in reflection and transmission, reflectance and transmittance, and also in the conductance and its universal fluctuations. It is shown that, in contrast to volume impurities, surface scattering in quasi-one-dimensional structures (waveguides) gives rise to the coexistence of the ballistic, diffusive, and localized regimes within the same sample.Comment: LaTeX (REVTeX), 12 pages with 14 EPS figures (epsf macro), minor change

Molecules as tracers of galaxy evolution: an EMIR survey. I. Presentation of the data and first results

We investigate the molecular gas properties of a sample of 23 galaxies in order to find and test chemical signatures of galaxy evolution and to compare them to IR evolutionary tracers. Observation at 3 mm wavelengths were obtained with the EMIR broadband receiver, mounted on the IRAM 30 m telescope on Pico Veleta, Spain. We compare the emission of the main molecular species with existing models of chemical evolution by means of line intensity ratios diagrams and principal component analysis. We detect molecular emission in 19 galaxies in two 8 GHz-wide bands centred at 88 and 112 GHz. The main detected transitions are the J=1-0 lines of CO, 13CO, HCN, HNC, HCO+, CN, and C2H. We also detect HC3N J=10-9 in the galaxies IRAS 17208, IC 860, NGC 4418, NGC 7771, and NGC 1068. The only HC3N detections are in objects with HCO+/HCN<1 and warm IRAS colours. Galaxies with the highest HC3N/HCN ratios have warm IRAS colours (60/100 {\mu}m>0.8). The brightest HC3N emission is found in IC 860, where we also detect the molecule in its vibrationally excited state.We find low HNC/HCN line ratios (<0.5), that cannot be explained by existing PDR or XDR chemical models. Bright HC3N emission in HCO+-faint objects may imply that these are not dominated by X-ray chemistry. Thus the HCN/HCO+ line ratio is not, by itself, a reliable tracer of XDRs. Bright HC3N and faint HCO+ could be signatures of embedded starformation, instead of AGN activity