Mathematical Modeling of Software Bug Complexity

During testing of software, most of the bugs lying dormant in the software gets uncovered once the test cases are executed. Different bugs may take different amounts of effort and expertise for their removal. To understand the complexity of bugs from a developer‟s perspective, researchers have developed different mathematical models. Software consists of two types of bugs, dependent and independent. Dependent bugs are those whose removal depends upon the removal of some other bugs on which it is dependent. Dependency of bugs also makes the bug complex and bugs will take more time during fixing. Different debugging time lags functions have been taken to model different complexity of bugs. The aim of this paper is to study the bugs of different complexity. The complexity of bugs has been also modeled using dependency concept. Testing effort dependent bug complexity model using fault dependency has been also discussed. We also feel that that more complex bug will take more time and less complex bug will take less time during fixing. During removal of bugs, the removal team gets more familiar with the code during the fixing. The learning effect during testing has been incorporated using logistic removal rate. The models are validated based on different comparison criteria namely MSE, R2 , Bias, Variation and Root mean squared error.Keywords/Index Terms: Non-homogeneous Poisson process, bug complexity, bugs types

The population of merging compact binaries inferred using gravitational waves through GWTC-3

We report on the population properties of 76 compact binary mergers detected with gravitational waves below a false alarm rate of 1 per year through GWTC-3. The catalog contains three classes of binary mergers: BBH, BNS, and NSBH mergers. We infer the BNS merger rate to be between 10 $\rm{Gpc^{-3} yr^{-1}}$ and 1700 $\rm{Gpc^{-3} yr^{-1}}$ and the NSBH merger rate to be between 7.8 $\rm{Gpc^{-3}\, yr^{-1}}$ and 140 $\rm{Gpc^{-3} yr^{-1}}$ , assuming a constant rate density versus comoving volume and taking the union of 90% credible intervals for methods used in this work. Accounting for the BBH merger rate to evolve with redshift, we find the BBH merger rate to be between 17.9 $\rm{Gpc^{-3}\, yr^{-1}}$ and 44 $\rm{Gpc^{-3}\, yr^{-1}}$ at a fiducial redshift (z=0.2). We obtain a broad neutron star mass distribution extending from $1.2^{+0.1}_{-0.2} M_\odot$ to $2.0^{+0.3}_{-0.3} M_\odot$. We can confidently identify a rapid decrease in merger rate versus component mass between neutron star-like masses and black-hole-like masses, but there is no evidence that the merger rate increases again before 10 $M_\odot$. We also find the BBH mass distribution has localized over- and under-densities relative to a power law distribution. While we continue to find 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 $\sim 60 M_\odot$. The rate of BBH mergers is observed to increase with redshift at a rate proportional to $(1+z)^{\kappa}$ with $\kappa = 2.9^{+1.7}_{-1.8}$ for $z\lesssim 1$. Observed black hole spins are small, with half of spin magnitudes below $\chi_i \simeq 0.25$. We observe evidence of negative aligned spins in the population, and an increase in spin magnitude for systems with more unequal mass ratio

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M>70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0<e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level

Ultralight vector dark matter search using data from the KAGRA O3GK run

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U(1)B−L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U(1)B−L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM

Mathematical Modeling of Software Bug Complexity

During testing of software, most of the bugs lying dormant in the software gets uncovered once the test cases are executed. Different bugs may take different amounts of effort and expertise for their removal. To understand the complexity of bugs from a developer‟s perspective, researchers have developed different mathematical models. Software consists of two types of bugs, dependent and independent. Dependent bugs are those whose removal depends upon the removal of some other bugs on which it is dependent. Dependency of bugs also makes the bug complex and bugs will take more time during fixing. Different debugging time lags functions have been taken to model different complexity of bugs. The aim of this paper is to study the bugs of different complexity. The complexity of bugs has been also modeled using dependency concept. Testing effort dependent bug complexity model using fault dependency has been also discussed. We also feel that that more complex bug will take more time and less complex bug will take less time during fixing. During removal of bugs, the removal team gets more familiar with the code during the fixing. The learning effect during testing has been incorporated using logistic removal rate. The models are validated based on different comparison criteria namely MSE, R2 , Bias, Variation and Root mean squared error.Keywords/Index Terms: Non-homogeneous Poisson process, bug complexity, bugs types

Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo

Advanced LIGO and Advanced Virgo are monitoring the sky and collecting gravitational-wave strain data with sufficient sensitivity to detect signals routinely. In this paper we describe the data recorded by these instruments during their first and second observing runs. The main data products are gravitational-wave strain time series sampled at 16384 Hz. The datasets that include this strain measurement can be freely accessed through the Gravitational Wave Open Science Center at http://gw-openscience.org, together with data-quality information essential for the analysis of LIGO and Virgo data, documentation, tutorials, and supporting software

Gravitational-wave Constraints on the Equatorial Ellipticity of Millisecond Pulsars

We present a search for continuous gravitational waves from five radio pulsars, comprising three recycled pulsars (PSR J0437-4715, PSR J0711-6830, and PSR J0737-3039A) and two young pulsars: the Crab pulsar (J0534+2200) and the Vela pulsar (J0835-4510). We use data from the third observing run of Advanced LIGO and Virgo combined with data from their first and second observing runs. For the first time, we are able to match (for PSR J0437-4715) or surpass (for PSR J0711-6830) the indirect limits on gravitational-wave emission from recycled pulsars inferred from their observed spin-downs, and constrain their equatorial ellipticities to be less than 10(-8). For each of the five pulsars, we perform targeted searches that assume a tight coupling between the gravitational-wave and electromagnetic signal phase evolution. We also present constraints on PSR J0711-6830, the Crab pulsar, and the Vela pulsar from a search that relaxes this assumption, allowing the gravitational-wave signal to vary from the electromagnetic expectation within a narrow band of frequencies and frequency derivatives

Search for intermediate-mass black hole binaries in the third observing run of Advanced LIGO and Advanced Virgo

International audienceIntermediate-mass black holes (IMBHs) span the approximate mass range 100−105 M⊙, between black holes (BHs) that formed by stellar collapse and the supermassive BHs at the centers of galaxies. Mergers of IMBH binaries are the most energetic gravitational-wave sources accessible by the terrestrial detector network. Searches of the first two observing runs of Advanced LIGO and Advanced Virgo did not yield any significant IMBH binary signals. In the third observing run (O3), the increased network sensitivity enabled the detection of GW190521, a signal consistent with a binary merger of mass ∼150 M⊙ providing direct evidence of IMBH formation. Here, we report on a dedicated search of O3 data for further IMBH binary mergers, combining both modeled (matched filter) and model-independent search methods. We find some marginal candidates, but none are sufficiently significant to indicate detection of further IMBH mergers. We quantify the sensitivity of the individual search methods and of the combined search using a suite of IMBH binary signals obtained via numerical relativity, including the effects of spins misaligned with the binary orbital axis, and present the resulting upper limits on astrophysical merger rates. Our most stringent limit is for equal mass and aligned spin BH binary of total mass 200 M⊙ and effective aligned spin 0.8 at 0.056 Gpc−3 yr−1 (90% confidence), a factor of 3.5 more constraining than previous LIGO-Virgo limits. We also update the estimated rate of mergers similar to GW190521 to 0.08 Gpc−3 yr−1.Key words: gravitational waves / stars: black holes / black hole physicsCorresponding author: W. Del Pozzo, e-mail: [email protected]† Deceased, August 2020