Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data spaces. This paper provides an introductory overview of the mathematical underpinnings of Topological Data Analysis, the workflow to convert samples of data to topological summary statistics, and some of the statistical methods developed for performing inference on these topological summary statistics. The intention of this non-technical overview is to motivate statisticians who are interested in learning more about the subject.Comment: 15 pages, 7 Figures, 27th Annual Conference on Applied Statistics in Agricultur

Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data spaces. This paper provides an introductory overview of the mathematical underpinnings of Topological Data Analysis, the workflow to convert samples of data to topological summary statistics, and some of the statistical methods developed for performing inference on these topological summary statistics. The intention of this non-technical overview is to motivate statisticians who are interested in learning more about the subject

TOPOLOGICAL METHODS FOR THE QUANTIFICATION AND ANALYSIS OF COMPLEX PHENOTYPES

Quantitative Trait Locus (QTL) mapping of complex traits, such as leaf venation or root structures, require the phenotyping and genotyping of large populations. Sufficient genotyping is accomplished with cost effective high-throughput assays, however labor costs often makes sufficient phenotyping prohibitively limited. In order to develop efficient high-throughput phenotyping platforms for complex traits algorithms and methods for quantifying these traits are needed. It is often desirable to study the spatial organization of these phenotypes from the images generated by high-throughput platforms. With the goal of quantifying the traits, many approaches try to identify several core traits useful in describing the phenotypic morphology. This simplification may lose important information about the phenotype. Rather than reducing the structural information, we introduce a novel method, the Persistence Intensity Array, for studying complex traits using tools from the emergent field of Topological Data Analysis. This approach uses the complete geometry of the phenotype and represents it as a simpler summary of the key topological shape features contained in the data. We demonstrate this method\u27s efficacy by through a simulated QTL analysis

Misinterpretation of the determinants of elevated forward wave amplitude inflates the role of the proximal aorta

Background: The hemodynamic basis for increased pulse pressure (PP) with aging remains controversial. The classic paradigm attributes a predominant role to increased pulse wave velocity (PWV) and premature wave reflections (WRs). A controversial new paradigm proposes increased forward pressure wave amplitude (FWA), attributed to proximal aortic characteristic impedance (Z(c)), as the predominant factor, with minor contributions from WRs. Based on theoretical considerations, we hypothesized that (rectified) WRs drive the increase in FWA, and that the forward pressure wave does not depend solely on the interaction between flow and Z(c) (QZc product). Methods and Results: We performed 3 substudies: (1) open-chest anesthetized dog experiments (n=5); (2) asymmetric T-tube model-based study; and (3) human study in a diverse clinical population (n=193). Animal experiments demonstrated that FWA corresponds to peak QZc only when WRs are minimal. As WRs increased, FWA was systematically greater than QZc and peaked well after peak flow, analogous to late-systolic peaking of pressure attributable to WRs. T-tube modeling confirmed that increased/ premature WRs resulted in increased FWA. Magnitude and timing of WRs explained 80.8% and 74.3% of the variability in the difference between FWA and peak QZc in dog and human substudies, respectively. Conclusions: Only in cases of minimal reflections does FWA primarily reveal the interaction between peak aortic flow and proximal aortic diameter/stiffness. FWA is strongly dependent on rectified reflections. If interpreted out of context with the hemodynamic principles of its derivation, the FWA paradigm inappropriately amplifies the role of the proximal aorta in elevation of FWA and PP

Arterial properties as determinants of left ventricular mass and fibrosis in severe aortic Stenosis : findings from ACRIN PA 4008

Background-The role of arterial load in severe aortic stenosis is increasingly recognized. However, patterns of pulsatile load and their implications in this population are unknown. We aimed to assess the relationship between the arterial properties and both (1) left ventricular remodeling and fibrosis and (2) the clinical course of patients with severe aortic stenosis undergoing aortic valve replacement (AVR). Methods and Results-We enrolled 38 participants with symptomatic severe aortic stenosis scheduled to undergo surgical AVR. Aortic root characteristic impedance, wave reflections parameters (reflection magnitude, reflected wave transit time), and myocardial extracellular mass were measured with cardiac magnetic resonance imaging and arterial tonometry Cardiac magnetic resonance imaging was repeated at 6 months in 30 participants. A reduction in cellular mass (133.6 versus 113.9 g; P=0.002) but not extracellular mass (42.3 versus 40.6 g; P=0.67) was seen after AVR. Participants with higher extracellular mass exhibited greater reflection magnitude (0.68 versus 0.54; P=0.006) and lower aortic root characteristic impedance (56.3 versus 96.9 dynes/s per cm(5); P=0.006). Reflection magnitude was a significant predictor of smaller improvement in the quality of life (Kansas City Cardiomyopathy Questionnaire score) after AVR (R=-0.51; P=0.0026). The 6-minute walk distance at 6 months after AVR was positively correlated with the reflected wave transit time (R=0.52; P=0.01). Conclusions-Consistent with animal studies, arterial wave reflections are associated with interstitial volume expansion in severe aortic stenosis and predict a smaller improvement in quality of life following AVR. Future trials should assess whether wave reflections represent a potential therapeutic target to mitigate myocardial interstitial remodeling and to improve the clinical status of this patient population

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO