A rule of thumb for riffle shuffling

We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, e.g. suits disregarded or only the colors of interest. For these features, the number of shuffles drops from 3/2 log_2(n) to log_2(n). We derive closed formulae and an asymptotic `rule of thumb' formula which is remarkably accurate.Comment: 27 pages, 5 table

High Curie temperature Mn 5 Ge 3 thin films produced by non-diffusive reaction

Polycrystalline Mn 5 Ge 3 thin films were produced on SiO 2 using magnetron sputtering and reactive diffusion (RD) or non-diffusive reaction (NDR). In situ X-ray diffraction and atomic force microscopy were used to determine the layer structures, and magnetic force microscopy, superconducting quantum interference device and ferromagnetic resonance were used to determine their magnetic properties. RD-mediated layers exhibit similar magnetic properties as MBE-grown monocrystalline Mn 5 Ge 3 thin films, while NDR-mediated layers show magnetic properties similar to monocrystalline C-doped Mn 5 Ge 3 C x thin films with $0.1 \leq x \leq 0.2.$ NDR appears as a CMOS-compatible efficient method to produce good magnetic quality high-curie temperature Mn 5 Ge 3 thin films

The 43GHz SiO maser in the circumstellar envelope of the AGB star R Cassiopeiae

We present multi-epoch, total intensity, high-resolution images of 43GHz, v=1, J=1-0 SiO maser emission toward the Mira variable R Cas. In total we have 23 epochs of data for R Cas at approximate monthly intervals over an optical pulsation phase range from 0.158 to 1.78. These maps show a ring-like distribution of the maser features in a shell, which is assumed to be centred on the star at a radius of 1.6 to 2.3 times the stellar radii. It is clear from these images that the maser emission is significantly extended around the star. At some epochs a faint outer arc can be seen at 2.2 stellar radii. The intensity of the emission waxes and wanes during the stellar phase. Some maser features are seen infalling as well as outflowing. We have made initial comparisons of our data with models by Gray et. al. (2009).Comment: 12 pages, 14 figure

Polarization morphology of SiO masers in the circumstellar envelope of the AGB star R Cassiopeiae

Silicon monoxide maser emission has been detected in the circumstellar envelopes of many evolved stars in various vibrationally-excited rotational transitions. It is considered a good tracer of the wind dynamics close to the photosphere of the star. We have investigated the polarization morphology in the circumstellar envelope of an AGB star, R Cas. We mapped the linear and circular polarization of SiO masers in the v=1, J=1-0 transition. The linear polarization is typically a few tens of percent while the circular polarization is a few percent. The fractional polarization tends to be higher for emission of lower total intensity. We found that, in some isolated features the fractional linear polarization appears to exceed 100%. We found the Faraday rotation is not negligible but is ~15 deg., which could produce small scale structure in polarized emission whilst total intensity is smoother and partly resolved out. The polarization angles vary considerably from feature to feature but there is a tendency to favour the directions parallel or perpendicular to the radial direction with respect to the star. In some features, the polarization angle abruptly flips 90 deg. We found that our data are in the regime where the model of Goldreich et al (1973) can be applied and the polarization angle flip is caused when the magnetic field is at close to 55 deg. to the line of sight. The polarization angle configuration is consistent with a radial magnetic field although other configurations are not excluded.Comment: 14 pages, 15 figures. Accepted for publication in MNRA

Jitter-Camera: High Resolution Video from a Low Resolution Detector

Video cameras must produce images at a reasonable frame-rate and with a reasonable depth of field. These requirements impose fundamental physical limits on the spatial resolution of the image detector. As a result, current cameras produce videos with a very low resolution. The resolution of videos can be computationally enhanced by moving the camera and applying super-resolution reconstruction algorithms. However, a moving camera introduces motion blur, which limits super-resolution quality. We analyze this effect and derive a theoretical result showing that motion blur has a substantial degrading effect on the performance of super resolution. The conclusion is, that in order to achieve the highest resolution, motion blur should be avoided. Motion blur can be minimized by sampling the space-time volume of the video in a specific manner. We have developed a novel camera, called the jitter camera, that achieves this sampling. By applying an adaptive super-resolution algorithm to the video produced by the jitter camera, we show that resolution can be notably enhanced for stationary or slowly moving objects, while it is improved slightly or left unchanged for objects with fast and complex motions. The end result is a video that has a significantly higher resolution than the captured one

A Population Dynamics Model for Clonal Diversity in a Germinal Center

Germinal centers (GCs) are micro-domains where B cells mature to develop high affinity antibodies. Inside a GC, B cells compete for antigen and T cell help, and the successful ones continue to evolve. New experimental results suggest that, under identical conditions, a wide spectrum of clonal diversity is observed in different GCs, and high affinity B cells are not always the ones selected. We use a birth, death and mutation model to study clonal competition in a GC over time. We find that, like all evolutionary processes, diversity loss is inherently stochastic. We study two selection mechanisms, birth-limited and death limited selection. While death limited selection maintains diversity and allows for slow clonal homogenization as affinity increases, birth limited selection results in more rapid takeover of successful clones. Finally, we qualitatively compare our model to experimental observations of clonal selection in mice

T1 relaxometry of crossing fibres in the human brain

A comprehensive tract-based characterisation of white matter should include the ability to quantify myelin and axonal attributes irrespective of the complexity of fibre organisation within the voxel. Recently, a new experimental framework that combines inversion recovery and diffusion MRI, called inversion recovery diffusion tensor imaging (IR-DTI), was introduced and applied in an animal study. IR-DTI provides the ability to assign to each unique fibre population within a voxel a specific value of the longitudinal relaxation time, T1, which is a proxy for myelin content. Here, we apply the IR-DTI approach to the human brain in vivo on 7 healthy subjects for the first time. We demonstrate that the approach is able to measure differential tract properties in crossing fibre areas, reflecting the different myelination of tracts. We also show that tract-specific T1 has less inter-subject variability compared to conventional T1 in areas of crossing fibres, suggesting increased specificity to distinct fibre populations. Finally we show in simulations that changes in myelination selectively affecting one fibre bundle in crossing fibre areas can potentially be detected earlier using IR-DTI