Finding Periodic Discrete Events in Noisy Streams

Periodic phenomena are ubiquitous, but detecting and predicting periodic events can be difficult in noisy environments. We describe a model of periodic events that covers both idealized and realistic scenarios characterized by multiple kinds of noise. Thee model incorporates false-positive events and the possibility that the underlying period and phase of the events change over time. We then describe a particle €filter that can efficiently and accurately estimate the parameters of the process generating periodic events intermingled with independent noise events. Thee system has a small memory footprint, and, unlike alternative methods, its computational complexity is constant in the number of events that have been observed. As a result, it can be applied in low-resource settings that require real-time performance over long periods of time. In experiments on real and simulated data we €find that it outperforms existing methods in accuracy and can track changes in periodicity and other characteristics in dynamic event streams

Testing the no-hair nature of binary black holes using the consistency of multipolar gravitational radiation

Gravitational-wave (GW) observations of binary black holes offer the best probes of the relativistic, strong-field regime of gravity. Gravitational radiation in the leading order is quadrupolar. However, nonquadrupole (higher order) modes make appreciable contribution to the radiation from binary black holes with large mass ratios and misaligned spins. The multipolar structure of the radiation is fully determined by the intrinsic parameters (masses and spin angular momenta of the companion black holes) of a binary in quasicircular orbit. Following our previous work [S. Dhanpal, A. Ghosh, A. K. Mehta, P. Ajith, and B. S. Sathyaprakash, Phys. Rev. D 99, 104056 (2019).], we develop multiple ways of testing the consistency of the observed GW signal with the expected multipolar structure of radiation from binary black holes in general relativity. We call this a no-hair test of binary black holes as this is similar to testing the no-hair theorem for isolated black holes through mutual consistency of the quasinormal mode spectrum. We use Bayesian inference on simulated GW signals that are consistent/inconsistent with binary black holes in general relativity to demonstrate the power of the proposed tests. We also make estimate systematic errors arising as a result of neglecting companion spins

Testing general relativity using golden black-hole binaries

The coalescences of stellar-mass black-hole binaries through their inspiral, merger, and ringdown are among the most promising sources for ground-based gravitational-wave (GW) detectors. If a GW signal is observed with sufficient signal-to-noise ratio, the masses and spins of the black holes can be estimated from just the inspiral part of the signal. Using these estimates of the initial parameters of the binary, the mass and spin of the final black hole can be uniquely predicted making use of general-relativistic numerical simulations. In addition, the mass and spin of the final black hole can be independently estimated from the merger--ringdown part of the signal. If the binary black hole dynamics is correctly described by general relativity (GR), these independent estimates have to be consistent with each other. We present a Bayesian implementation of such a test of general relativity, which allows us to combine the constraints from multiple observations. Using kludge modified GR waveforms, we demonstrate that this test can detect sufficiently large deviations from GR, and outline the expected constraints from upcoming GW observations using the second-generation of ground-based GW detectors.Comment: 5 pages, 2 fig

Machine learning and privacy preserving algorithms for spatial and temporal sensing

Sensing physical and social environments are ubiquitous in modern mobile phones, IoT devices, and infrastructure-based settings. Information engraved in such data, especially the time and location attributes have unprecedented potential to characterize individual and crowd behaviour, natural and technological processes. However, it is challenging to extract abstract knowledge from the data due to its massive size, sequential structure, asynchronous operation, noisy characteristics, privacy concerns, and real time analysis requirements. Therefore, the primary goal of this thesis is to propose theoretically grounded and practically useful algorithms to learn from location and time stamps in sensor data. The proposed methods are inspired by tools from geometry, topology, and statistics. They leverage structures in the temporal and spatial data by probabilistically modeling noise, exploring topological structures embedded, and utilizing statistical structure to protect personal information and simultaneously learn aggregate information. Proposed algorithms are geared towards streaming and distributed operation for efficiency. The usefulness of the methods is argued using mathematical analysis and empirical experiments on real and artificial datasets

Constraints on quasi-normal-mode frequencies with LIGO-Virgo binary-black-hole observations

The no-hair conjecture in General Relativity (GR) states that a Kerr black hole (BH) is completely described by its mass and spin. As a consequence, the complex quasi-normal-mode (QNM) frequencies of a binary-black-hole (BBH) ringdown can be uniquely determined by the mass and spin of the remnant object. Conversely, measurement of the QNM frequencies could be an independent test of the no-hair conjecture. This paper extends to spinning BHs earlier work that proposed to test the no-hair conjecture by measuring the complex QNM frequencies of a BBH ringdown using parameterized inspiral-merger-ringdown waveforms in the effective-one-body formalism, thereby taking full advantage of the entire signal power and removing dependency on the predicted or estimated start time of the ringdown. Our method was used to analyze the properties of the merger remnants for BBHs observed by LIGO-Virgo in the first half of their third observing (O3a) run. After testing our method with GR and non-GR synthetic-signal injections in Gaussian noise, we analyze, for the first time, two BBHs from the first (O1) and second (O2) LIGO-Virgo observing runs, and two additional BBHs from the O3a run. We then provide joint constraints with published results from the O3a run. In the most agnostic and conservative scenario where we combine the information from different events using a hierarchical approach, we obtain, at $90\%$ credibility, that the fractional deviations in the frequency (damping time) of the dominant QNM are $\delta f_{220}=0.03^{+0.10}_{-0.09}$ ($\delta \tau_{220}=0.10^{+0.44}_{-0.39}$), respectively, an improvement of a factor of $\sim 4$ ($\sim 2$) over the results obtained with our model in the LIGO-Virgo publication. The single-event most-stringent constraint to date continues to be GW150914 for which we obtain $\delta f_{220}=0.05^{+0.11}_{-0.07}$ and $\delta \tau_{220}=0.07^{+0.26}_{-0.23}$.Comment: 15 pages, 8 figure

Constraining extra dimensions using observations of black hole quasi-normal modes

The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass $M$ and the angular momentum $J$, known as the `tidal charge' parameter, $\beta$. In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through -- (a) negative values of $\beta$, and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of $\beta$ correspond to a diminishing imaginary part of the quasi-normal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted values (for a given $\beta$) of the frequency and damping time of the least-damped $\ell=2,m=2$ quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, $\beta \lesssim -0.05$, providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.Comment: 11 pages, 2 figures, 1 table, Revised version accepted in EPJ

Publishing Asynchronous Event Times with Pufferfish Privacy

Publishing data from IoT devices raises concerns of leaking sensitive information. In this paper we consider the scenario of publishing data on events with timestamps. We formulate three privacy issues, namely, whether one can tell if an event happened or not; whether one can nail down the timestamp of an event within a given time interval; and whether one can infer the relative order of any two nearby events. We show that perturbation of event timestamps or adding fake events following carefully chosen distributions can address these privacy concerns. We present a rigorous study of privately publishing discrete event timestamps with privacy guarantees under the Pufferfish privacy framework. We also conduct extensive experiments to evaluate utility of the modified time series with real world location check-in and app usage data. Our mechanisms preserve the statistical utility of event data which are suitable for aggregate queries