Non-Parametric Approximations for Anisotropy Estimation in Two-dimensional Differentiable Gaussian Random Fields

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a reference axis and the aspect ratio of the principal correlation lengths. Since these parameters are unknown a priori, sample estimates are needed to define suitable spatial models for the interpolation of incomplete data. The distribution of the anisotropy statistics is determined by a non-Gaussian sampling joint probability density. By means of analytical calculations, we derive an explicit expression for the joint probability density function of the anisotropy statistics for Gaussian, stationary and differentiable random fields. Based on this expression, we obtain an approximate joint density which we use to formulate a statistical test for isotropy. The approximate joint density is independent of the autocovariance function and provides conservative probability and confidence regions for the anisotropy parameters. We validate the theoretical analysis by means of simulations using synthetic data, and we illustrate the detection of anisotropy changes with a case study involving background radiation exposure data. The approximate joint density provides (i) a stand-alone approximate estimate of the anisotropy statistics distribution (ii) informed initial values for maximum likelihood estimation, and (iii) a useful prior for Bayesian anisotropy inference.Comment: 39 pages; 8 figure

Effects of microperfusion in hepatic diffusion weighted imaging

Clinical hepatic diffusion weighted imaging (DWI) generally relies on mono-exponential diffusion. The aim was to demonstrate that mono-exponential diffusion in the liver is contaminated by microperfusion and that the bi-exponential model is required. Nineteen fasting healthy volunteers were examined with DWI (seven b-values) using fat suppression and respiratory triggering (1.5 T). Five different regions in the liver were analysed regarding the mono-exponentially fitted apparent diffusion coefficient (ADC), and the bi-exponential model: molecular diffusion (D (slow) ) microperfusion (D (fast) ) and the respective fractions (f (slow/fast)). Data were compared using ANOVA and Kruskal-Wallis tests. Simulations were performed by repeating our data analyses, using just the DWI series acquired with b-values approximating those of previous studies. Median mono-exponentially fitted ADCs varied significantly (P <0.001) between 1.107 and 1.423 x 10(-3) mm(2)/s for the five regions. Bi-exponential fitted D-slow varied between 0.923 and 1.062 x 10(-3) mm(2)/s without significant differences (P = 0.140). D (fast) varied significantly, between 17.8 and 46.8 x 10(-3) mm(2)/s (P <0.001). F-tests showed that the diffusion data fitted the bi-exponential model significantly better than the mono-exponential model (F > 21.4, P <0.010). These results were confirmed by the simulations. ADCs of normal liver tissue are significantly dependent on the measurement location because of substantial microperfusion contamination; therefore the bi-exponential model should be used. Diffusion weighted MR imaging helps clinicians to differentiate tumours by diffusion properties Fast moving water molecules experience microperfusion, slow molecules diffusion Hepatic diffusion should be measured by bi-exponential models to avoid microperfusion contamination Mono-exponential models are contaminated with microperfusion, resulting in apparent regional diffusion differences Bi-exponential models are necessary to measure diffusion and microperfusion in the liver

Functional Diffusion Tensor Imaging: Measuring Task-Related Fractional Anisotropy Changes in the Human Brain along White Matter Tracts

Functional neural networks in the human brain can be studied from correlations between activated gray matter regions measured with fMRI. However, while providing important information on gray matter activation, no information is gathered on the co-activity along white matter tracts in neural networks.We report on a functional diffusion tensor imaging (fDTI) method that measures task-related changes in fractional anisotropy (FA) along white matter tracts. We hypothesize that these fractional anisotropy changes relate to morphological changes of glial cells induced by axonal activity although the exact physiological underpinnings of the measured FA changes remain to be elucidated. As expected, these changes are very small as compared to the physiological noise and a reliable detection of the signal change would require a large number of measurements. However, a substantial increase in signal-to-noise ratio was achieved by pooling the signal over the complete fiber tract. Adopting such a tract-based statistics enabled us to measure the signal within a practically feasible time period. Activation in the sensory thalamocortical tract and optic radiation in eight healthy human subjects was found during tactile and visual stimulation, respectively.The results of our experiments indicate that these FA changes may serve as a functional contrast mechanism for white matter. This noninvasive fDTI method may provide a new approach to study functional neural networks in the human brain

Analyses of the Microbial Diversity across the Human Microbiome

Analysis of human body microbial diversity is fundamental to understanding community structure, biology and ecology. The National Institutes of Health Human Microbiome Project (HMP) has provided an unprecedented opportunity to examine microbial diversity within and across body habitats and individuals through pyrosequencing-based profiling of 16 S rRNA gene sequences (16 S) from habits of the oral, skin, distal gut, and vaginal body regions from over 200 healthy individuals enabling the application of statistical techniques. In this study, two approaches were applied to elucidate the nature and extent of human microbiome diversity. First, bootstrap and parametric curve fitting techniques were evaluated to estimate the maximum number of unique taxa, Smax, and taxa discovery rate for habitats across individuals. Next, our results demonstrated that the variation of diversity within low abundant taxa across habitats and individuals was not sufficiently quantified with standard ecological diversity indices. This impact from low abundant taxa motivated us to introduce a novel rank-based diversity measure, the Tail statistic, (“τ”), based on the standard deviation of the rank abundance curve if made symmetric by reflection around the most abundant taxon. Due to τ’s greater sensitivity to low abundant taxa, its application to diversity estimation of taxonomic units using taxonomic dependent and independent methods revealed a greater range of values recovered between individuals versus body habitats, and different patterns of diversity within habitats. The greatest range of τ values within and across individuals was found in stool, which also exhibited the most undiscovered taxa. Oral and skin habitats revealed variable diversity patterns, while vaginal habitats were consistently the least diverse. Collectively, these results demonstrate the importance, and motivate the introduction, of several visualization and analysis methods tuned specifically for next-generation sequence data, further revealing that low abundant taxa serve as an important reservoir of genetic diversity in the human microbiome

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Azimuthal anisotropy of charged particles at high transverse momenta in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

The azimuthal anisotropy of charged particles in PbPb collisions at nucleon-nucleon center-of-mass energy of 2.76 TeV is measured with the CMS detector at the LHC over an extended transverse momentum (pt) range up to approximately 60 GeV. The data cover both the low-pt region associated with hydrodynamic flow phenomena and the high-pt region where the anisotropies may reflect the path-length dependence of parton energy loss in the created medium. The anisotropy parameter (v2) of the particles is extracted by correlating charged tracks with respect to the event-plane reconstructed by using the energy deposited in forward-angle calorimeters. For the six bins of collision centrality studied, spanning the range of 0-60% most-central events, the observed v2 values are found to first increase with pt, reaching a maximum around pt = 3 GeV, and then to gradually decrease to almost zero, with the decline persisting up to at least pt = 40 GeV over the full centrality range measured.Comment: Replaced with published version. Added journal reference and DO

X-ray emission from the Sombrero galaxy: discrete sources

We present a study of discrete X-ray sources in and around the bulge-dominated, massive Sa galaxy, Sombrero (M104), based on new and archival Chandra observations with a total exposure of ~200 ks. With a detection limit of L_X = 1E37 erg/s and a field of view covering a galactocentric radius of ~30 kpc (11.5 arcminute), 383 sources are detected. Cross-correlation with Spitler et al.'s catalogue of Sombrero globular clusters (GCs) identified from HST/ACS observations reveals 41 X-rays sources in GCs, presumably low-mass X-ray binaries (LMXBs). We quantify the differential luminosity functions (LFs) for both the detected GC and field LMXBs, whose power-low indices (~1.1 for the GC-LF and ~1.6 for field-LF) are consistent with previous studies for elliptical galaxies. With precise sky positions of the GCs without a detected X-ray source, we further quantify, through a fluctuation analysis, the GC LF at fainter luminosities down to 1E35 erg/s. The derived index rules out a faint-end slope flatter than 1.1 at a 2 sigma significance, contrary to recent findings in several elliptical galaxies and the bulge of M31. On the other hand, the 2-6 keV unresolved emission places a tight constraint on the field LF, implying a flattened index of ~1.0 below 1E37 erg/s. We also detect 101 sources in the halo of Sombrero. The presence of these sources cannot be interpreted as galactic LMXBs whose spatial distribution empirically follows the starlight. Their number is also higher than the expected number of cosmic AGNs (52+/-11 [1 sigma]) whose surface density is constrained by deep X-ray surveys. We suggest that either the cosmic X-ray background is unusually high in the direction of Sombrero, or a distinct population of X-ray sources is present in the halo of Sombrero.Comment: 11 figures, 5 tables, ApJ in pres

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one

Magnetic Resonance Thermometry at 7T for Real-Time Monitoring and Correction of Ultrasound Induced Mild Hyperthermia

While Magnetic Resonance Thermometry (MRT) has been extensively utilized for non-invasive temperature measurement, there is limited data on the use of high field (≥7T) scanners for this purpose. MR-guided Focused Ultrasound (MRgFUS) is a promising non-invasive method for localized hyperthermia and drug delivery. MRT based on the temperature sensitivity of the proton resonance frequency (PRF) has been implemented in both a tissue phantom and in vivo in a mouse Met-1 tumor model, using partial parallel imaging (PPI) to speed acquisition. An MRgFUS system capable of delivering a controlled 3D acoustic dose during real time MRT with proportional, integral, and derivative (PID) feedback control was developed and validated. Real-time MRT was validated in a tofu phantom with fluoroptic temperature measurements, and acoustic heating simulations were in good agreement with MR temperature maps. In an in vivo Met-1 mouse tumor, the real-time PID feedback control is capable of maintaining the desired temperature with high accuracy. We found that real time MR control of hyperthermia is feasible at high field, and k-space based PPI techniques may be implemented for increasing temporal resolution while maintaining temperature accuracy on the order of 1°C