A New Approach to Time Domain Classification of Broadband Noise in Gravitational Wave Data

Broadband noise in gravitational wave (GW) detectors, also known as triggers, can often be a deterrant to the efficiency with which astrophysical search pipelines detect sources. It is important to understand their instrumental or environmental origin so that they could be eliminated or accounted for in the data. Since the number of triggers is large, data mining approaches such as clustering and classification are useful tools for this task. Classification of triggers based on a handful of discrete properties has been done in the past. A rich information content is available in the waveform or 'shape' of the triggers that has had a rather restricted exploration so far. This paper presents a new way to classify triggers deriving information from both trigger waveforms as well as their discrete physical properties using a sequential combination of the Longest Common Sub-Sequence (LCSS) and LCSS coupled with Fast Time Series Evaluation (FTSE) for waveform classification and the multidimensional hierarchical classification (MHC) analysis for the grouping based on physical properties. A generalized k-means algorithm is used with the LCSS (and LCSS+FTSE) for clustering the triggers using a validity measure to determine the correct number of clusters in absence of any prior knowledge. The results have been demonstrated by simulations and by application to a segment of real LIGO data from the sixth science run.Comment: 16 pages, 16 figure

Fast parameter inference in a biomechanical model of the left ventricle by using statistical emulation

A central problem in biomechanical studies of personalized human left ventricular modelling is estimating the material properties and biophysical parameters from in vivo clinical measurements in a timeframe that is suitable for use within a clinic. Understanding these properties can provide insight into heart function or dysfunction and help to inform personalized medicine. However, finding a solution to the differential equations which mathematically describe the kinematics and dynamics of the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of emulation to infer the myocardial properties of a healthy volunteer in a viable clinical timeframe by using in vivo magnetic resonance image data. Emulation methods avoid computationally expensive simulations from the left ventricular model by replacing the biomechanical model, which is defined in terms of explicit partial differential equations, with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving computational efficiency at the clinic. We compare and contrast two emulation strategies: emulation of the computational model outputs and emulation of the loss between the observed patient data and the computational model outputs. These strategies are tested with two interpolation methods, as well as two loss functions. The best combination of methods is found by comparing the accuracy of parameter inference on simulated data for each combination. This combination, using the output emulation method, with local Gaussian process interpolation and the Euclidean loss function, provides accurate parameter inference in both simulated and clinical data, with a reduction in the computational cost of about three orders of magnitude compared with numerical integration of the differential equations by using finite element discretization techniques

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

A geometric approach to visualization of variability in functional data

We propose a new method for the construction and visualization of boxplot-type displays for functional data. We use a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose observed variation in functional data into three main components: amplitude, phase, and vertical translation. We then construct separate displays for each component, using the geometry and metric of each representation space, based on a novel definition of the median, the two quartiles, and extreme observations. The outlyingness of functional data is a very complex concept. Thus, we propose to identify outliers based on any of the three main components after decomposition. We provide a variety of visualization tools for the proposed boxplot-type displays including surface plots. We evaluate the proposed method using extensive simulations and then focus our attention on three real data applications including exploratory data analysis of sea surface temperature functions, electrocardiogram functions and growth curves

The Energy Spectrum of TeV Gamma-Rays from the Crab Nebula as measured by the HEGRA system of imaging air Cherenkov telescopes

The Crab Nebula has been observed by the HEGRA (High-Energy Gamma-Ray Astronomy) stereoscopic system of imaging air Cherenkov telescopes (IACTs) for a total of about 200 hrs during two observational campaigns: from September 1997 to March 1998 and from August 1998 to April 1999. The recent detailed studies of system performance give an energy threshold and an energy resolution for gamma-rays of 500 GeV and ~ 18%, respectively. The Crab energy spectrum was measured with the HEGRA IACT system in a very broad energy range up to 20 TeV, using observations at zenith angles up to 65 degrees. The Crab data can be fitted in the energy range from 1 to 20 TeV by a simple power-law, which yields dJg/dE = (2.79+/-0.02 +/- 0.5) 10^{-7} E^{-2.59 +/- 0.03 +/- 0.05}, ph m^{-2} s^{-1} TeV^{-1} The Crab Nebula energy spectrum, as measured with the HEGRA IACT system, agrees within 15% in the absolute scale and within 0.1 units in the power law index with the latest measurements by the Whipple, CANGAROO and CAT groups, consistent within the statistical and systematic errors quoted by the experiments. The pure power-law spectrum of TeV gamma-rays from the Crab Nebula constrains the physics parameters of the nebula environment as well as the models of photon emission.Comment: to appear in ApJ, 29 pages, 6 figure

Effectiveness of TeV Gamma-Ray Observations at Large Zenith Angles with a Stereoscopic System of Imaging Atmospheric Cherenkov Telescopes

The sensitivity of imaging atmospheric Cherenkov telescopes (IACTs) in TeV gamma-ray observations reachs its maximum at small zenith angles (< 30 degree) which provide the minimum attainable energy threshold of an instrument. However, for a specific telescope site a number of gamma-ray sources, or source candidates, can only be observed at much larger zenith angles (< 60 degree). Moreover the observations at large zenith angles allow to extend the observation time window for any object seen at small zenith angles, as well as to enlarge the dynamic energy range of an instrument towards the highest observable energies of gamma-rays. Based on Monte Carlo simulations we present here the results on the sensitivity of a stereoscopic system of 5 IACTs in observations at large zenith angles. We point out some important parameters of the telescope design which could substantially improve the efficiency of such observations with forthcoming IACT arrays like CANGAROO III, HESS and VERITAS.Comment: 14 pages LaTeX, 5 tables, 7 postscript figures; Accepted for publication in Journal of Physics G: Nuclear and Particle Physics 24 June 199