Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance

Persistent homology can extract hidden topological signals present in brain networks. Persistent homology summarizes the changes of topological structures over multiple different scales called filtrations. Doing so detect hidden topological signals that persist over multiple scales. However, a key obstacle of applying persistent homology to brain network studies has always been the lack of coherent statistical inference framework. To address this problem, we present a unified topological inference framework based on the Wasserstein distance. Our approach has no explicit models and distributional assumptions. The inference is performed in a completely data driven fashion. The method is applied to the resting-state functional magnetic resonance images (rs-fMRI) of the temporal lobe epilepsy patients collected at two different sites: University of Wisconsin-Madison and the Medical College of Wisconsin. However, the topological method is robust to variations due to sex and acquisition, and thus there is no need to account for sex and site as categorical nuisance covariates. We are able to localize brain regions that contribute the most to topological differences. We made MATLAB package available at https://github.com/laplcebeltrami/dynamicTDA that was used to perform all the analysis in this study

The pulsating hot subdwarf Balloon 090100001: results of the 2005 multisite campaign

We present the results of a multisite photometric campaign on the pulsating sdB star Balloon 090100001. The star is one of the two known hybrid hot subdwarfs with both long- and short-period oscillations. The campaign involved eight telescopes with three obtaining UBVR data, four B-band data, and one Stromgren uvby photometry. The campaign covered 48 nights, providing a temporal resolution of 0.36microHz with a detection threshold of about 0.2mmag in B-filter data. Balloon 090100001 has the richest pulsation spectrum of any known pulsating subdwarf B star and our analysis detected 114 frequencies including 97 independent and 17 combination ones. The strongest mode (f_1) in the 2.8mHz region is most likely radial while the remaining ones in this region form two nearly symmetric multiplets: a triplet and quintuplet, attributed to rotationally split \ell=1 and 2 modes, respectively. We find clear increases of splitting in both multiplets between the 2004 and 2005 observing campaigns, amounting to 15% on average. The observed splittings imply that the rotational rate in Bal09 depends on stellar latitude and is the fastest on the equator. We use a small grid of models to constrain the main mode (f_1), which most likely represents the radial fundamental pulsation. The groups of p-mode frequencies appear to lie in the vicinity of consecutive radial overtones, up to the third one. Despite the large number of g-mode frequencies observed, we failed to identify them, most likely because of the disruption of asymptotic behaviour by mode trapping. The observed frequencies were not, however, fully exploited in terms of seismic analysis which should be done in the future with a larger grid of reliable evolutionary models of hot subdwarfs.Comment: accepted for publication in MNRA

Lunar surface outgassing and alpha particle measurements

The Lunar Prospector Alpha Particle Spectrometer (LP APS) searched for lunar surface gas release events and mapped their distribution by detecting alpha particle?; produced by the decay of gaseous radon-222 (5.5 MeV, 3.8 day half-life), solid polonium-2 18 (6.0 MeV, 3 minute half-life), and solid polonium-210 (5.3 MeV, 138 day half-life, but held up in production by the 21 year half-life of lead-210). These three nuclides are radioactive daughters from the decay of uranium-238

Evidence of water ice near the lunar poles

Lunar Prospector epithermal neutron data were studied to evaluate the probable chemical state of enhanced hydrogen, [H], reported previously to be near both lunar poles [1,2]. Improved versions of thermal and epithermal neutron data were developed for this purpose. Most important is the improved spatial resolution obtained by using shortened integration times. A new data set was created, Epi* = [Epithermal - 0.057 x Thermal], to reduce effects of composition variations other than those due to hydrogen. The Epi* counting rates are generally low near both lunar poles and high over terrane near recent impact events such as Tycho and Jackson. However, other lunar features are also associated with high Epi* rates, which represent a wide range of terrane types that seem to have little in common. If we postulate that one property all bright Epi* features do have in common is low [H], then measured Epi* counting rates appear to be quantitatively self consistent. If we assume that [H]=O above the top 98th percentile of Epi* counting rates at 2{sup o} x 2{sup o} spatial resolution, then [H]{sub ave} = 55 ppm for latitudes equatorward of [75{sup o}]. This value is close to the average found in returned lunar soil samples, [H]{sub ave} {approx} 50 ppm [3]. Using the foregoing physical interpretation of Epi* counting rates, we find that the Epi* counts within most of the large craters poleward of {+-}70{sup o} are higher, and therefore [H] is lower, than that in neighboring inter-crater plains, as shown in Figure 1. Fourteen of these craters that have areas larger than the LP epithermal spatial resolution (55 km diameter at 30 km altitude), were singled out for study. [H] is generally found to increase with decreasing distance from the poles (hence decreasing temperature). However, quantitative estimates of the diffusivity of hydrogen at low temperature show that diffusion can not be an important factor in explaining the difference between the relatively low [H] observed within the large sunlit polar craters and the relatively high [H] in neighboring inter-crater plains. A closer look at the 'inter-crater' plains near the poles, shows that they are covered by many small craters that harbor permanent shade [4]. The temperatures within many of these craters are low enough [5] that they can disable sublimation as a viable loss process of [H{sub 2}O]. It is therefore tempting to postulate that the enhanced hydrogen within most regions of permanent shade is in the form of water molecules. This postulate is certainly viable within the bottoms of several large, permanently shaded craters near the south pole. Predicted temperatures within them [5] fall well below the 100 K temperature that is needed to stabilize water ice for aeons. The picture is different near the north pole. Here, there are relatively few permanently-shaded craters that are large enough to harbor temperatures that are sufficiently low to stabilize water ice indefinitely against sublimation [5]. Instead, the 'inter-crater' polar plains are a jumble of many permanently-shaded craters that have diameters less than 10 km [4]. Although simulations of temperatures within this class of craters show they are only marginally cold enough to indefinitely stabilize water ice [5], this terrane appears to have the highest [H]. Nevertheless, predicted temperatures are close enough to that needed to permanently stabilize [H{sub 2}O] to suggest that sublimation is indeed the process that discriminates between polar terrane that contains enhanced [H] and those that do not (see, e.g., the temperature estimates for doubly-shaded craters [6]). If correct, then an important fraction of the hydrogen near the north pole must be in the form of H{sub 2}O, which then resides within these small craters. Estimates using our improved data set of [H] within craters near the south pole remain unchanged from those derived from our previous analysis [2], [H] = 1700{+-}900 ppm. This translates to [H{sub 2}O]=1.5{+-}0.8%. If all of the enhanced hydrogen in the north is in the form of H{sub 2}O and is confined to the jumble of small permanently-shaded craters identified by radar [4], then we can estimate their water-ice fraction, [H{sub 2}O], using Figure 1a in [2]. We chose two regions near the north pole for this purpose. They each have areas just larger than the surface foot-print of the LP epithermal neutron spectrometer. The first was an inter-crater region nestled between Rozhdestvenskiy and Plaskett, and the second covered the southeast comer of Peary. Using Figure 3 of [4], the first area contains 232 km{sup 2} of measured permanent shade, and the second contains 129 km{sup 2}. Adopting the prescription used in Table 1 of [4] for estimating actual from sampled shaded areas, multiplication of sampled areas by 1.5 yields permanently shaded areas that amount to 350 km{sup 2} in region 1, and 200 km{sup 2} in the southeast comer of Peary

Distribution of iron&titanium on the lunar surface from lunar prospector gamma ray spectra

Gamma ray pulse height spectra acquired by the Lunar Prospector (LP) Gamma-Ray Spectrometer (GRS) contain information on the abundance of major elements in the lunar surface, including O, Si, Ti, Al, Fe, Mg, Ca, K, and Th. With the exception of Th and K, prompt gamma rays produced by cosmic ray interactions with surface materials are used to determine elemental abundance. Most of these gamma rays are produced by inelastic scattering of fast neutrons and by neutron capture. The production of neutron-induced gamma rays reaches a maximum deep below the surface (e.g. {approx}140 g/cm{sup 2} for inelastic scattering and {approx}50 g/cm{sup 2} for capture). Consequently, gamma rays sense the bulk composition of lunar materials, in contrast to optical methods [e.g. Clementine Spectral Reflectance (CSR)], which only sample the top few microns. Because most of the gamma rays are produced deep beneath the surface, few escape unscattered and the continuum of scattered gamma rays dominates the spectrum. In addition, due to the resolution of the spectrometer, there are few well-isolated peaks and peak fitting algorithms must be used to deconvolve the spectrum in order to determine the contribution of individual elements