arXiv subjects

Maham Siddiqi

Publications and source records attributed to Maham Siddiqi.

3 recordsLinked to original sources

arXiv2020

Tempered and Hadamard-type fractional calculus with respect to functions

Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type fractional calculus and tempered fractional calculus. This paper establishes a connection between these two definitions, writing one in terms of the other by making use of the theory of fractional calculus with respect to functions. By extending this connection in a natural way, a generalisation is developed which unifies several existing fractional operators: Riemann--Liouville, Caputo, classical Hadamard, Hadamard-type, tempered, and all of these taken with respect to functions. The fundamental calculus of these generalised operators is established, including semigroup and reciprocal properties as well as application to some example functions. Function spaces are constructed in which the new operators are defined and bounded. Finally, some formulae are derived for fractional integration by parts with these operators.

math.CA↗

arXiv2015

Search for continuous gravitational waves: Improving robustness versus instrumental artifacts

The standard multidetector F-statistic for continuous gravitational waves is susceptible to false alarms from instrumental artifacts, for example monochromatic sinusoidal disturbances ('lines'). This vulnerability to line artifacts arises because the F-statistic compares the signal hypothesis to a Gaussian-noise hypothesis, and hence is triggered by anything that resembles the signal hypothesis more than Gaussian noise. Various ad-hoc veto methods to deal with such line artifacts have been proposed and used in the past. Here we develop a Bayesian framework that includes an explicit alternative hypothesis to model disturbed data. We introduce a simple line model that defines lines as signal candidates appearing only in one detector. This allows us to explicitly compute the odds between the signal hypothesis and an extended noise hypothesis, resulting in a new detection statistic that is more robust to instrumental artifacts. We present and discuss results from Monte-Carlo tests on both simulated data and on detector data from the fifth LIGO science run. We find that the line-robust statistic retains the detection power of the standard F-statistic in Gaussian noise. In the presence of line artifacts it is more sensitive, even compared to the popular F-statistic consistency veto, over which it improves by as much as a factor of two in detectable signal strength.

gr-qc↗

arXiv2012

An F-statistic based multi-detector veto for detector artifacts in continuous-wave gravitational wave data

Continuous gravitational waves (CW) are expected from spinning neutron stars with non-axisymmetric deformations. A network of interferometric detectors (LIGO, Virgo and GEO600) is looking for these signals. They are predicted to be very weak and retrievable only by integration over long observation times. One of the standard methods of CW data analysis is the multi-detector F-statistic. In a typical search, the F-statistic is computed over a range in frequency, spin-down and sky position, and the candidates with highest F values are kept for further analysis. However, this detection statistic is susceptible to a class of noise artifacts, strong monochromatic lines in a single detector. By assuming an extended noise model - standard Gaussian noise plus single-detector lines - we can use a Bayesian odds ratio to derive a generalized detection statistic, the line veto (LV-) statistic. In the absence of lines, it behaves similarly to the F-statistic, but it is more robust against line artifacts. In the past, ad-hoc post-processing vetoes have been implemented in searches to remove these artifacts. Here we provide a systematic framework to develop and benchmark this class of vetoes. We present our results from testing this LV-statistic on simulated data.

gr-qc↗