EXTENSION OF THE FUZZY C MEANS CLUSTERING ALGORITHM TO FIT WITH THE COMPOSITE GRAPH MODEL FOR WEB DOCUMENT REPRESENTATION

Clustering techniques are mostly unsupervised methods that can be used to organize data into groups based on similarities among the individual data items. Fuzzy c-means (FCM) clustering is one of well known unsupervised clustering techniques, which can also be used for unsupervised web document clustering. In this chapter we will introduce a modified method of clustering where the data to be clustered will be represented by graphs instead of vectors or other models. Specifically, we will extend the classical FCM clustering algorithm to work with graphs that represent web documents (Phukon, K. K. (2012), Zadeh, L. A. (1965). Dunn, J. C.(1974)). We wish to use graphs because they can allow us to retain information which is often discarded in simpler models

Towards establishing the presence or absence of horizons in coalescing binaries of compact objects by using their gravitational wave signals

The quest for distinguishing black holes (BH) from horizonless compactobjects using gravitational wave (GW) signals from coalescing compact binariescan be helped by utilizing the phenomenon of tidal heating (TH), which leavesits imprint on binary waveforms through the horizon parameters. We investigatethe effects of TH on GWs to probe the observability of the horizon parameters,mainly using Fisher matrix analysis to determine the errors and covariancesbetween them. The horizon parameters are defined as $H_1$ and $H_2$ for the twobinary components, with $H_{1,2} \in [0,1]$, and combined with the componentmasses and spins to form two new parameters, $H_{\rm eff5}$ and $H_{\rm eff8}$,to minimize their covariances in parameter estimation studies. In this work, weadd the phase contribution due to TH in terms of $H_{\rm eff5}$ and H_{\rmeff8} to a post-Newtonian waveform and examine the variation of theirmeasurement errors with the binary's total mass, mass ratio, luminositydistance, and component spins. Since the Fisher matrix approach works well forhigh signal-to-noise ratio, we focus mainly on third-generation (3G) GWdetectors Einstein Telescope and Cosmic Explorer and use LIGO and Virgo forcomparison. We find that the region in the total binary mass where measurementsof $H_{\rm eff5}$ and $H_{\rm eff8}$ are most precise are $\sim 20 - 30M_\odot$for LIGO-Virgo and $\sim 50 - 80M_\odot$ for 3G detectors. Higher componentspins allow more precise measurements of $H_{\rm eff5}$ and $H_{\rm eff8}$. Fora binary situated at 200 Mpc with component masses $12M_\odot$ and $18M_\odot$,equal spins $\chi_1=\chi_2=0.8$, and $H_{\rm eff5}=0.6$, $H_{\rm eff8}=12$, the1-$\sigma$ errors in these two parameters are $\sim 0.01$ and $\sim 0.04$,respectively, in 3G detectors. We substantiate our results from Fisher studieswith a set of Bayesian simulations.<br

Distinguishing binary black hole precessional morphologies with gravitational wave observations

The precessional motion of binary black holes can be classified into one of three morphologies, based on the evolution of the angle between the components of the spins in the orbital plane: Circulating, librating around 0, and librating around $\pi$. These different morphologies can be related to the binary's formation channel and are imprinted in the binary's gravitational wave signal. In this paper, we develop a Bayesian model selection method to determine the preferred spin morphology of a detected binary black hole. The method involves a fast calculation of the morphology which allows us to restrict to a specific morphology in the Bayesian stochastic sampling. We investigate the prospects for distinguishing between the different morphologies using gravitational waves in the Advanced LIGO/Advanced Virgo network with their plus-era sensitivities. For this, we consider fiducial high- and low-mass binaries having different spin magnitudes and signal-to-noise ratios (SNRs). We find that in the cases with high spin and high SNR, the true morphology is strongly favored with $\log_{10}$ Bayes factors $\gtrsim 4$ compared to both alternative morphologies when the binary's parameters are not close to the boundary between morphologies. However, when the binary parameters are close to the boundary between morphologies, only one alternative morphology is strongly disfavored. In the low-spin, high-SNR cases, the true morphology is still favored with a $\log_{10}$ Bayes factor $\sim 2$ compared to one alternative morphology. We also consider the gravitational wave signal from GW200129_065458 that has some evidence for precession (modulo data quality issues) and find that there is no preference for a specific morphology. Our method for restricting the prior to a given morphology is publicly available through an easy-to-use Python package called bbh_spin_morphology_prior. (Abridged)Comment: 14 pages, 5 figures, version accepted by PR

Distinguishing binary black hole precessional morphologies with gravitational wave observations

The precessional motion of binary black holes can be classified into one of three morphologies, based on the evolution of the angle between the components of the spins in the orbital plane: Circulating, librating around 0, and librating around π. These different morphologies can be related to the binary’s formation channel and are imprinted in the binary’s gravitational wave signal. In this paper, we develop a Bayesian model selection method to determine the preferred spin morphology of a detected binary black hole. The method involves a fast calculation of the morphology which allows us to restrict to a specific morphology in the Bayesian stochastic sampling. We investigate the prospects for distinguishing between the different morphologies using gravitational waves in the Advanced LIGO/Advanced Virgo network with their plus-era sensitivities. For this, we consider fiducial high- and low-mass binaries having different spin magnitudes and signal-to-noise ratios (SNRs). We find that in the cases with high spin and high SNR, the true morphology is strongly favored with log10 Bayes factors ≳ 4 compared to both alternative morphologies when the binary’s parameters are not close to the boundary between morphologies. However, when the binary parameters are close to the boundary between morphologies, only one alternative morphology is strongly disfavored. In the low-spin, high-SNR cases, the true morphology is still favored with a log10 Bayes factor ∼ 2 compared to one alternative morphology, while in the low-SNR cases the log10 Bayes factors are at most ∼1 for many binaries. We also consider the gravitational wave signal from GW200129_065458 that has some evidence for precession (modulo data quality issues) and find that there is no preference for a specific morphology. Our method for restricting the prior to a given morphology is publicly available through an easy-to-use python package called bbh_spin_morphology_prior

Inferring spin tilts of binary black holes at formation with plus-era gravitational wave detectors

The spin orientations of spinning binary black hole (BBH) mergers detected by ground-based gravitational wave detectors such as LIGO and Virgo can provide important clues about the formation of such binaries. However, these spin tilts, i.e., the angles between the spin vector of each black hole and the binary’s orbital angular momentum vector, can change due to precessional effects as the black holes evolve from a large separation to their merger. The tilts inferred at a frequency in the sensitive band of the detectors by comparing the signal with theoretical waveforms can thus be significantly different from the tilts when the binary originally formed. These tilts at the binary’s formation are well approximated in many scenarios by evolving the BBH backward in time to a formally infinite separation. Using the tilts at infinite separation also places all binaries on an equal footing in analyzing their population properties. In this paper, we perform parameter estimation for simulated BBHs and investigate the differences between the tilts one infers directly close to merger and those obtained by evolving back to infinite separation. We select simulated observations such that their configurations show particularly large differences in their orientations close to merger and at infinity. While these differences may be buried in the statistical noise for current detections, we show that in future plus-era (Aþ and Virgoþ) detectors, they can be easily distinguished in some cases. We also consider the tilts at infinity for BBHs in various spin morphologies and at the endpoint of the up-down instability. In particular, we find that we are able to easily identify the up-down instability cases as such from the tilts at infinity

SSR marker-based DNA fingerprinting of Sub1 introgressed lines in the background of traditional rice varieties of Assam India

350-356Rice varieties are usually characterized by agro-morphological descriptors used for seed certification and seed characterization by following distinctiveness, uniformity, and stability (DUS) test. But in fact, these primary distinguishing morphological descriptors among rice varieties are very limited and hence face problems to distinguish germplasm accessions. Germplasm certification in NBPGR requires a DNA fingerprinting profile to explain germplasm uniqueness compared to existing varieties. Varietal identification has gained a key role worldwide, particularly in plant variety protection. Sixty-two morphological descriptors studies have shown the Sub1 introgressed advanced lines E-6, C-210, C-196, 1189-1 and 1160-1 are distinct from the other varieties for more than 15morphological traits, based on these variations the lines were selected for DNA fingerprinting. About68 SSRs markers were used for DNA fingerprinting in seven genotypes, two of which were parents (Ranjit, Bahadur) and three Sub1 introgressed advanced lines (E6, C210, C196) in Ranjit background, and two Sub1 introgressed advanced lines (1189-1, 1160-1) in Bahadur background. DNA fingerprinting was done on these genotypes of rice using SSR markers. Among the 68 SSR markers, total 65 markers were amplified and three were found not amplified. Out of 65 markersfour of them viz. RM 152, RM 172, RM 251, and RM 346 showed better polymorphism with amplicon size ranges from 155-163 bp, 150-159 bp, 137-147 bp, and 166-175 bp, respectively, and remaining 61 showed monomorphic amplification. Therefore, SSR (Simple-sequence repeats) based DNA fingerprinting helped to differentiate Ranjit, Bahadur, E-6, C-210, C-196, 1189-1, and 1160-1. Hence, the research reveals that newly developed high-yielding Sub1 introgressed advanced lines in the background of traditional Assam rice varieties (Ranjit and Bahadur) are unique in their identity

Bayesian inference for compact binary coalescences with BILBY:Validation and application to the first LIGO-Virgo gravitational-wave transient catalogue

Gravitational waves provide a unique tool for observational astronomy. While the first LIGO–Virgo catalogue of gravitational-wave transients (GWTC-1) contains eleven signals from black hole and neutron star binaries, the number of observations is increasing rapidly as detector sensitivity improves. To extract information from the observed signals, it is imperative to have fast, flexible, and scalable inference techniques. In a previous paper, we introduced BILBY: a modular and user-friendly Bayesian inference library adapted to address the needs of gravitational-wave inference. In this work, we demonstrate that BILBY produces reliable results for simulated gravitational-wave signals from compact binary mergers, and verify that it accurately reproduces results reported for the eleven GWTC-1 signals. Additionally, we provide configuration and output files for all analyses to allow for easy reproduction, modification, and future use. This work establishes that BILBY is primed and ready to analyse the rapidly growing population of compact binary coalescence gravitational-wave signals

Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3

We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star-black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc-3 yr-1 and the neutron star-black hole merger rate to be between 7.8 and 140 Gpc-3 yr-1, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc-3 yr-1 at a fiducial redshift (z=0.2). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to (1+z)κ with κ=2.9-1.8+1.7 for z≲1. Using both binary neutron star and neutron star-black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from 1.2-0.2+0.1 to 2.0-0.3+0.3M⊙. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of 8.3-0.5+0.3 and 27.9-1.8+1.9M⊙. While we continue to find that the mass distribution of a binary's more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately 60M⊙, which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below χi≈0.25. While the majority of spins are preferentially aligned with the orbital angular momentum, we infer evidence of antialigned spins among the binary population. We observe an increase in spin magnitude for systems with more unequal-mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum

All-sky search for long-duration gravitational-wave bursts in the third Advanced LIGO and Advanced Virgo run

After the detection of gravitational waves from compact binary coalescences, the search for transient gravitational-wave signals with less well-defined waveforms for which matched filtering is not well suited is one of the frontiers for gravitational-wave astronomy. Broadly classified into “short” ≲1  s and “long” ≳1  s duration signals, these signals are expected from a variety of astrophysical processes, including non-axisymmetric deformations in magnetars or eccentric binary black hole coalescences. In this work, we present a search for long-duration gravitational-wave transients from Advanced LIGO and Advanced Virgo’s third observing run from April 2019 to March 2020. For this search, we use minimal assumptions for the sky location, event time, waveform morphology, and duration of the source. The search covers the range of 2–500 s in duration and a frequency band of 24–2048 Hz. We find no significant triggers within this parameter space; we report sensitivity limits on the signal strength of gravitational waves characterized by the root-sum-square amplitude hrss as a function of waveform morphology. These hrss limits improve upon the results from the second observing run by an average factor of 1.8