Discriminability and uncertainty in principal component analysis (PCA) of temporal check-all-that-apply (TCATA) data

Temporal check-all-that-apply (TCATA) data can be summarized and explored using principal component analysis (PCA). Here we analyze TCATA data on Syrah wines obtained from a trained sensory panel. We evaluate new and existing methods to explore the uncertainty in the PCA scores. To do so, we use the bootstrap procedure to obtain many virtual panels from the real panel’s data. Virtual-panel PCA scores are obtained using two methods. The first method, called the partial bootstrap (PB), obtains virtual-panel scores from regression. The second method, called the truncated total bootstrap (TTB), applies PCA to the virtual-panel results to obtain scores, which are truncated and superimposed on the real-panel scores by Procrustes rotation. We use the virtual scores from each method to investigate uncertainty in the real-panel PCA scores visually and numerically. To understand the uncertainty of the scores, we obtain confidence ellipses (CEs) and their areas, as well as confidence intervals (CIs) and their widths. Next, to determine whether PCA scores for different samples are well separated, we propose a procedure for approximating the standard errors of sample differences and correcting for multiple comparisons. We propose a discriminability index, and show that it can enhance the interpretability of PCA results. We incorporate graphical features into our PCA biplots to visualize discriminability. We did not find a large difference between the PB and TTB methods for understanding the uncertainty and discriminability in PCA scores. Although the TCATA data that we analyzed have a special structure, the methodological approaches presented here can be readily adapted to other applications of PCA.submittedVersio

X-Ray Polarization of Solar Flares Measured with Rhessi

The degree of linear polarization in solar flares has not yet been precisely determined despite multiple attempts to measure it with different missions. The high energy range in particular has very rarely been explored, due to its greater instrumental difficulties. We approached the subject using the Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) satellite to study 6 X-class and 1 M-class flares in the energy range between 100 keV and 350 keV. Using RHESSI as a polarimeter requires the application of strict cuts to the event list in order to extract those photons that are Compton scattered between two detectors. Our measurements show polarization values between 2% and 54%, with errors ranging from 10% to 26% in 1 sigma level. In view of the large uncertainties in both the magnitude and direction of the polarization vector, the results can only reject source models with extreme properties.Comment: 26 pages, 11 figures, accepted for publication by Solar Physic

All-particle cosmic ray energy spectrum measured with 26 IceTop stations

We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array, the surface component of the IceCube Neutrino Observatory at the South Pole. The data used in this analysis were taken between June and October, 2007, with 26 surface stations operational at that time, corresponding to about one third of the final array. The fiducial area used in this analysis was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV measured for three different zenith angle ranges between 0{\deg} and 46{\deg}. Because of the isotropy of cosmic rays in this energy range the spectra from all zenith angle intervals have to agree. The cosmic-ray energy spectrum was determined under different assumptions on the primary mass composition. Good agreement of spectra in the three zenith angle ranges was found for the assumption of pure proton and a simple two-component model. For zenith angles {\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on composition assumption. Spectral indices above the knee range from -3.08 to -3.11 depending on primary mass composition assumption. Moreover, an indication of a flattening of the spectrum above 22 PeV were observed.Comment: 38 pages, 17 figure

Theory of magnetically powered jets

The magnetic theory for the production of jets by accreting objects is reviewed with emphasis on outstanding problem areas. An effort is made to show the connections behind the occasionally diverging nomenclature in the literature, to contrast the different points of view about basic mechanisms, and to highlight concepts for interpreting the results of numerical simulations. The role of dissipation of magnetic energy in accelerating the flow is discussed, and its importance for explaining high Lorentz factors. The collimation of jets to the observed narrow angles is discussed, including a critical discussion of the role of `hoop stress'. The transition between disk and outflow is one of the least understood parts of the magnetic theory; its role in setting the mass flux in the wind, in possible modulations of the mass flux, and the uncertainties in treating it realistically are discussed. Current views on most of these problems are still strongly influenced by the restriction to 2 dimensions (axisymmetry) in previous analytical and numerical work; 3-D effects likely to be important are suggested. An interesting problem area is the nature and origin of the strong, preferably highly ordered magnetic fields known to work best for jet production. The observational evidence for such fields and their behavior in numerical simulations is discussed. I argue that the presence or absence of such fields may well be the `second parameter' governing not only the presence of jets but also the X-ray spectra and timing behavior of X-ray binaries.Comment: 29 pages. Publication delays offered the opportunity for further corrections, an expansion of sect 4.2, and one more Fig. To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009

Discriminability and uncertainty in principal component analysis (PCA) of temporal check-all-that-apply (TCATA) data

Temporal check-all-that-apply (TCATA) data can be summarized and explored using principal component analysis (PCA). Here we analyze TCATA data on Syrah wines obtained from a trained sensory panel. We evaluate new and existing methods to explore the uncertainty in the PCA scores. To do so, we use the bootstrap procedure to obtain many virtual panels from the real panel’s data. Virtual-panel PCA scores are obtained using two methods. The first method, called the partial bootstrap (PB), obtains virtual-panel scores from regression. The second method, called the truncated total bootstrap (TTB), applies PCA to the virtual-panel results to obtain scores, which are truncated and superimposed on the real-panel scores by Procrustes rotation. We use the virtual scores from each method to investigate uncertainty in the real-panel PCA scores visually and numerically. To understand the uncertainty of the scores, we obtain confidence ellipses (CEs) and their areas, as well as confidence intervals (CIs) and their widths. Next, to determine whether PCA scores for different samples are well separated, we propose a procedure for approximating the standard errors of sample differences and correcting for multiple comparisons. We propose a discriminability index, and show that it can enhance the interpretability of PCA results. We incorporate graphical features into our PCA biplots to visualize discriminability. We did not find a large difference between the PB and TTB methods for understanding the uncertainty and discriminability in PCA scores. Although the TCATA data that we analyzed have a special structure, the methodological approaches presented here can be readily adapted to other applications of PCA

Abstract # 3195 HIV disease duration and endothelial progenitor cell function predict subcortical cerebral blood flow in post-menopausal women

Chronic infection with HIV is associated with impaired endothelial function and altered cerebral blood flow (CBF). Using fMRI Arterial Spin Labeling, we sought to determine 1) whether CBF in HIV+ postmenopausal women (n = 8, mean age = 55.13, SD = 5.38) differs from that of HIV- controls (n = 13, mean age = 53.77, SD = 6.41), and 2) whether a marker of angiogenic potential, i.e. endothelial progenitor cell (EPC) cluster formation, and time since HIV infection covary with CBF in HIV+ women (n = 8). After controlling for age, HIV+ individuals showed increased ventral perfusion extending from the inferior frontal lobes through the basal ganglia and cerebellar regions, k = 105271, p = .001, FWE-corrected (cluster). However, longer disease duration was associated with reduced perfusion to the right parahippocampal gyrus, k = 4,916, p = .001, uncorrected. Paradoxically, higher EPC clusters predicted greater CBF to the right parahippocampal gyrus, k = 10791, p  .05. While longer disease duration places postmenopausal HIV+ women at risk of lower CBF to the parahippocampal gyrus, this effect may be mitigated by the angiogenic potential of peripheral blood mononuclear cell derived EPCs