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In this work, we investigate the impact of the possibility of a small, subsolar mass compact star, such as the recently reported central compact object of HESS J1731-347, on the equation of state (EOS) of neutron stars. We have used a hybrid approach to the nuclear EOS developed recently where the matter around nuclear saturation density is described by a parametric expansion in terms of nuclear empirical parameters and represented in an agnostic way at higher density using piecewise polytropes. We have incorporated the inputs provided by the latest neutron skin measurement experiments from PREX-II and CREX, simultaneous mass-radius measurements of pulsars PSR J0030+0451 and PSR J0740+6620, and the gravitational wave events GW170817 and GW190425. The main results of the study show the effect of HESS J1731-347 on the nuclear parameters and neutron star observables. Our analysis yields the slope of symmetry energy $L=45.71^{+38.18}_{-22.11}$ MeV, the radius of a $1.4 M_\odot$ star, $R_{1.4}=12.18^{+0.71}_{-0.88}$ km, and the maximum mass of a static star, $M_{\rm max}= 2.14^{+0.26}_{-0.17} M_\odot$ within $90\%$ confidence interval, respectively.

With ongoing advancements in nuclear theory and experimentation, together with a growing body of neutron star (NS) observations, a wealth of information on the equation of state (EOS) for matter at extreme densities has become accessible. Here, we utilize a hybrid EOS formulation that combines an empirical parameterization centered around the nuclear saturation density with a generic three-segment piecewise polytrope model at higher densities. We incorporate data derived from chiral effective field theory ($\chi$EFT), perturbative quantum chromodynamics (pQCD), and from experiments such as PREX-II and CREX. Furthermore, we examine the influence of a total of 129 NS mass measurements up to April 2023, as well as simultaneous mass and radius measurements derived from the X-ray emission from surface hot spots on NSs. Additionally, we consider constraints on tidal properties inferred from the gravitational waves emitted by coalescing NS binaries. To integrate this extensive and varied array of constraints, we utilize a hierarchical Bayesian statistical framework to simultaneously deduce the EOS and the distribution of NS masses. We find that incorporating data from $\chi$EFT significantly tightens the constraints on the EOS of NSs near or below the nuclear saturation density. However, constraints derived from pQCD computations and nuclear experiments such as PREX-II and CREX have minimal impact., Comment: 19 pages, 8 figures

This work presents the design and development of IIT Bombay Racing's Formula Student style autonomous racecar algorithm capable of running at the racing events of Formula Student-AI, held in the UK. The car employs a cutting-edge sensor suite of the compute unit NVIDIA Jetson Orin AGX, 2 ZED2i stereo cameras, 1 Velodyne Puck VLP16 LiDAR and SBG Systems Ellipse N GNSS/INS IMU. It features deep learning algorithms and control systems to navigate complex tracks and execute maneuvers without any human intervention. The design process involved extensive simulations and testing to optimize the vehicle's performance and ensure its safety. The algorithms have been tested on a small scale, in-house manufactured 4-wheeled robot and on simulation software. The results obtained for testing various algorithms in perception, simultaneous localization and mapping, path planning and controls have been detailed., Comment: 8 pages, 19 figures

Gravitational waves (GWs) from binary neutron stars (BNSs) are expected to be accompanied by electromagnetic (EM) emissions, which help to identify the host galaxy. Since GW events directly measure their luminosity distances, joint GW-EM observations from BNSs help to study cosmology, particularly the Hubble constant, unaffected by cosmic distance ladder systematics. However, detecting EM counterparts from BNS mergers is not always possible. Additionally, the tidal deformations of BNS components offer insights into the neutron star (NS) equation of state (EoS). In such cases, the tidal parameters of NSs, combined with the knowledge of the NS EoS, can break the degeneracy between mass parameters and redshift, allowing for the inference of the Hubble constant. Several efforts have aimed to infer the Hubble constant using the tidal parameters of BNSs, without EM counterparts, termed dark BNSs. Moreover, some studies have focused on the joint estimation of population and NS EoS for unbiased NS EoS estimation. However, none of the works consistently combined the uncertainties of population, cosmology, and NS EoS within a Bayesian framework. In this study, we propose a novel Bayesian analysis to jointly constrain the NS EoS, population, and cosmological parameters using a population of dark BNSs detected through GW observations. This method can well constrain the Hubble constant with as few as $5$ BNS observations using current-generation detectors. This level of precision is unattainable without incorporating the NS EoS, especially when observing BNS mergers without EM counterpart information., Comment: 26 pages, 14 figures, 4 tables

Despite its elegance, the theory of General Relativity is subject to experimental, observational, and theoretical scrutiny to arrive at tighter constraints or an alternative, more preferred theory. In alternative gravity theories, the macroscopic properties of neutron stars, such as mass, radius, tidal deformability, etc. are modified. This creates a degeneracy between the uncertainties in the equation of state (EoS) and gravity since assuming a different EoS can be mimicked by changing to a different theory of gravity. We formulate a hierarchical Bayesian framework to simultaneously infer the EoS and gravity parameters by combining multiple astrophysical observations. We test this framework for a particular 4D Horndeski scalar-tensor theory originating from higher-dimensional Einstein-Gauss-Bonnet gravity and a set of 20 realistic EoS and place improved constraints on the coupling constant of the theory with current observations. Assuming a large number of observations with upgraded or third-generation detectors, we find that the $A+$ upgrade could place interesting bounds on the coupling constant of the theory, whereas with the LIGO Voyager upgrade or the third-generation detectors (Einstein Telescope and Cosmic Explorer), the degeneracy between EoS and gravity could be resolved with high confidence, even for small deviations from GR., Comment: Comments are welcome!

We construct an efficient parameterization of the pure neutron-matter equation of state (EoS) that incorporates the uncertainties from both chiral effective field theory ($\chi$EFT) and phenomenological potential calculations. This parameterization yields a family of EoSs including and extending the forms based purely on these two calculations. In combination with an agnostic inner core EoS, this parameterization is used in a Bayesian inference pipeline to obtain constraints on the e os parameters using multi-messenger observations of neutron stars. We specifically considered observations of the massive pulsar J0740+6620, the binary neutron star coalescence GW170817, and the NICER pulsar J0030+0451. Constraints on neutron star mass-radius relations are obtained and compared. The Bayes factors for the different EoS models are also computed. While current constraints do not reveal any significant preference among these models, the framework developed here may enable future observations with more sensitive detectors to discriminate them.

Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial dynamical systems. Employment of a positive definite function called shape function within the Sum-of-Squares procedure helps to find a richer representation of the Lyapunov function and a larger corresponding Region of Attraction estimation. However, existing Sum-of-Squares optimization techniques demonstrate very conservative results. The main novelty of this paper is the Union theorem which enables the use of multiple shape functions to create a polynomial Lyapunov function encompassing all the areas generated by the shape functions. The main contribution of this paper is a novel computationally-efficient numerical method for Region of Attraction estimation, which remarkably improves estimation performance and overcomes limitations of existing methods, while maintaining the resultant Lyapunov function polynomial, thus facilitating control system design and construction of control Lyapunov function with enhanced Region of Attraction using conventional Sum-of-Squares tools. A mathematical proof of the Union theorem along with its application to the numerical algorithm of Region of Attraction estimation is provided. The method yields significantly enlarged Region of Attraction estimations even for systems with non-symmetric or unbounded Region of Attraction, which is demonstrated via simulations of several benchmark examples.

Neutron stars are the densest objects known in our visible universe. Properties of matter inside a neutron star are encoded in its equation of state, which has wide-ranging uncertainty from a theoretical perspective. With the current understanding of quantum chromodynamics, it is hard to determine the interactions of neutron star matter at such high densities. Also performing many body calculations is computationally intractable. Besides the constitution of the neutron star core is highly speculative -- it is not ruled out that it contains exotic matter like strange baryons, meson condensates, quark matter, etc. Although the matter inside the neutron star is extremely dense, but the temperature of this object is very cold in most of its life span. We cannot produce such dense but rather cold material in our laboratory. Since probing the physics of neutron star matter is inaccessible by our earth based experiments, we look for astrophysical observations of neutron stars. This thesis deals with the theoretical and computational techniques required to translate neutron star observables from astrophysical observations to its equation of state., Comment: PhD thesis

We develop a method for implementing a proposal on utilizing knowledge of neutron star (NS) equation of state (EoS) for inferring the Hubble constant from a population of binary neutron star (BNS) mergers. This method is useful in exploiting BNSs as standard sirens when their redshifts are not available. Gravitational wave (GW) signals from compact object binaries provide a direct measurement of their luminosity distances, but not their redshifts. Unlike in the past, here we employ a realistic EoS parametrization in a Bayesian framework to simultaneously measure the Hubble constant and refine the constraints on the EoS parameters. The uncertainty in the redshift depends on the uncertainties in the EoS and the mass parameters estimated from GW data. Combining the inferred BNS redshifts with the corresponding luminosity distances, one constructs a redshift-distance relation and deduces the Hubble constant from it. Here, we show that in the Cosmic Explorer era, one can measure the Hubble constant to a precision of $\lesssim 5\%$ (with a $90\%$ credible interval) with a realistic distribution of a thousand BNSs, while allowing for uncertainties in their EoS parameters. Such a measurement can potentially resolve the current tension in the measurements of the Hubble constant from the early- and late-time universe. The methodology implemented in this work demonstrates a comprehensive prescription for inferring the NS EoS and the Hubble constant by simultaneously combining GW observations from merging NSs, while employing a simple population model for NS masses and keeping the merger rate of NSs constant in redshift. This method can be immediately extended to incorporate merger rate, population properties, and additional cosmological parameters., Comment: Published in PRD

Instead of parameterizing the pressure-density relation of a neutron star (NS), one can parameterize its macroscopic properties such as mass ($M$), radius ($R$), and dimensionless tidal deformability ($\Lambda$) to infer the equation of state (EoS) combining electromagnetic and gravitational wave (GW) observations. We present a new method to parameterize $R(M)$ and $\Lambda(M)$ relations, which approximate the candidate EoSs with accuracy better than 5\% for all masses and span a broad region of $M-R-\Lambda$ plane. Using this method we combine the $M-\Lambda$ measurement from GW170817 and GW190425, and simultaneous $M-R$ measurement of PSR J0030+0451 and PSR J0740+6620 to place joint constraints on NS properties. At 90 \% confidence, we infer $R_{1.4}=12.05_{-0.87}^{+0.98}$ km and $\Lambda_{1.4}=372_{-150}^{+220}$ for a $1.4 M_{\odot}$ NS, and $R_{2.08}=12.65_{-1.46}^{+1.36}$ km for a $2.08 M_{\odot}$ NS. Furthermore, we use the inferred values of the maximum mass of a nonrotating NS $M_{\rm max}=2.52_{-0.29}^{+0.33} M_{\odot}$ to investigate the nature of the secondary objects in three potential neutron star-black hole merger (NSBH) system., Comment: Published in PRD

Measurement of macroscopic properties of neutron stars, whether in binary or in an isolated system, provides us a key opportunity to place a stringent constraint on its equation of state. In this paper, we perform Bayesian model-selection on a wide variety of neutron star equation of state using multi-messenger observations. In particular, (i) we use the mass and tidal deformability measurement from two binary neutron star merger event, GW170817 and GW190425; (ii) simultaneous mass-radius measurement of PSR J0030+0451 and PSR J0740+6620 by NICER collaboration, while the latter has been analyzed by joint NICER/radio/XMM-Newton collaboration. Among the 31 equations of state considered in this analysis, we are able to rule out different variants of MS1 family, SKI5, H4, and WFF1 EoSs decisively, which are either extremely stiff or soft equations of state. The most preferred equation of state model turns out to be AP3 (or MPA1), which predicts the radius and dimensionless tidal deformability of a $1.4 M_{\odot}$ neutron star to be 12.10 (12.50) km and 393 (513) respectively.

In this paper, we discuss the impact of the following laboratory experiments and astrophysical observation of neutron stars (NSs) on its equation of state (EoS): (a) The new measurement of neutron skin thickness of $\rm ^{208} \! Pb$, $R_{\rm skin}^{208} = 0.29 \pm 0.07$ fm by the PREX-II experiment. (b) The mass measurement of PSR J0740+6620 has been slightly revised down by including additional $\sim 1.5$ years of pulsar timing data. As well as the radius measurement of PSR J0740+6620 by joint NICER/XMM-Newton collaboration which has a similar size to PSR J0030+0451. We combine these information using Bayesian statistics along with the previous LIGO/Virgo and NICER observations of NS using a hybrid nuclear+piecewise polytrope (PP) EoS parameterization. Our findings are as follows: (a). Adding PREX-II result yields the value of empirical parameter $L = 69^{+21}_{-19}$ MeV, $R_{\rm skin}^{208} = 0.20_{-0.05}^{+0.05}$ fm, and radius of a $1.4 M_{\odot}$ ($R_{1.4}) = 12.75_{-0.54}^{+ 0.42}$ km at $1 \sigma$ confidence interval (CI). We find these inferred values are mostly dominated by the combined astrophysical observations as the measurement uncertainty in $R_{\rm skin}^{208}$ by PREX-II is much broader. Also, a better measurement of $R_{\rm skin}^{208}$ might have a little effect on the radius of low mass NSs, but for the high masses there will be almost no effect. (b) After adding The revised mass and radius measurement of PSR J0740+6620, we find the inferred radius of NSs is slightly pushed towards the larger values and the uncertainty on the radius of a $2.08 M_{\odot}$ NS is moderately improved.

We show that the odds of the mass-gap (secondary) object in GW190814 being a neutron star (NS) improve if one allows for a stiff high-density equation of state (EoS) or a large spin. Since its mass is $\in (2.50,2.67) M_{\odot}$, establishing its true nature will make it either the heaviest NS or the lightest black hole (BH), and can have far-reaching implications on NS EoS and compact object formation channels. When limiting oneself to the NS hypothesis, we deduce the secondary's properties by using a Bayesian framework with a hybrid EoS formulation that employs a parabolic expansion-based nuclear empirical parameterization around the nuclear saturation density augmented by a generic 3-segment piecewise polytrope (PP) model at higher densities and combining a variety of astrophysical observations. For the slow-rotation scenario, GW190814 implies a very stiff EoS and a stringent constraint on the EoS specially in the high-density region. On the other hand assuming the secondary object is a rapidly rotating NS, we constrain its rotational frequency to be $f=1170^{+389}_{-495}$ Hz, within a $90\%$ confidence interval. In this scenario, the secondary object in GW190814 would qualify as the fastest rotating NS ever observed. However, for this scenario to be viable, rotational instabilities would have to be suppressed both during formation and the subsequent evolution until merger, otherwise the secondary of GW190814 is more likely to be a BH., Comment: Matches with the MNRAS published version

Observations of neutron stars (NSs) by the LIGO-Virgo and NICER collaborations have provided reasonably precise measurements of their various macroscopic properties. In this paper, we employ a Bayesian framework to combine them and place improved joint constraints on the properties of NS equation of state (EoS). We use a hybrid EoS formulation that employs a parabolic expansion-based nuclear empirical parameterization around the nuclear saturation density augmented by a generic 3-segment piecewise polytrope model at higher densities. Within the $90 \%$ credible level this parameterization predicts $R_{1.4} = 12.57_{-0.92}^{+0.73}$ km and $\Lambda_{1.4} = 550_{-225}^{+223}$ for the radius and dimensionless tidal deformability, respectively, of a $1.4 M_{\odot}$ NS. Finally, we show how the construction of the full NS EoS based solely on the nuclear empirical parameters at saturation density leads to certain tension with the astrophysical data, and how the hybrid approach provides a resolution to it.

Early classification of time series has been extensively studied for minimizing class prediction delay in time-sensitive applications such as healthcare and finance. A primary task of an early classification approach is to classify an incomplete time series as soon as possible with some desired level of accuracy. Recent years have witnessed several approaches for early classification of time series. As most of the approaches have solved the early classification problem with different aspects, it becomes very important to make a thorough review of the existing solutions to know the current status of the area. These solutions have demonstrated reasonable performance in a wide range of applications including human activity recognition, gene expression based health diagnostic, industrial monitoring, and so on. In this paper, we present a systematic review of current literature on early classification approaches for both univariate and multivariate time series. We divide various existing approaches into four exclusive categories based on their proposed solution strategies. The four categories include prefix based, shapelet based, model based, and miscellaneous approaches. The authors also discuss the applications of early classification in many areas including industrial monitoring, intelligent transportation, and medical. Finally, we provide a quick summary of the current literature with future research directions., Comment: 15 pages, 6 figures, 6 tables

In the late inspiral phase, gravitational waves from binary neutron star mergers carry the imprint of the equation of state due to the tidally deformed structure of the components. If the stars contain solid crusts, then their shear modulus can affect the deformability of the star and, thereby, modify the emitted signal. Here, we investigate the effect of realistic equations of state (EOSs) of the crustal matter, with a realistic model for the shear modulus of the stellar crust in a fully general relativistic framework. This allows us to systematically study the deviations that are expected from fluid models. In particular, we use unified EOSs, both relativistic and non-relativistic, in our calculations. We find that realistic EOSs of crusts cause a small correction, of $\sim 1\%$, in the second Love number. This correction will likely be subdominant to the statistical error expected in LIGO-Virgo observations at their respective advanced design sensitivities, but rival that error in third generation detectors. For completeness, we also study the effect of crustal shear on the magnetic-type Love number and find it to be much smaller., Comment: 26 pages, 10 figures

We use gravitational wave (GW) and electromagnetic (EM) observations of GW170817 to constrain the extent of pressure anisotropy in it. While it is quite likely that the pressure inside a neutron star is mostly isotropic, certain physical processes or characteristics, such as phase transitions in nuclear matter or the presence of strong magnetic fields, can introduce pressure anisotropy. In this work, we show that anisotropic pressure in neutron stars can reduce their tidal deformability substantially. For the anisotropy-pressure model of Bowers and Liang and a couple of relativistic EOSs -- DDH$\delta$ and GM1 -- we demonstrate that this reduction in spherical neutron stars with masses in the range of 1 to 2 $M_\odot$ can be 23% to 46%. This suggests that certain EOSs that are ruled out by GW170817 observations, under assumptions of pressure isotropy, can become viable if the stars had a significant enough anisotropic pressure component, but do not violate causality. We also show how the inference of the star radius can be used to rule out certain EOSs (such as GM1), even for high anisotropic pressure, because their radii are larger than what the observations find., Comment: 11 pages, 25 figures