arXiv subjects

A. Rao

Publications and source records attributed to A. Rao.

14 recordsLinked to original sources

arXiv2025

Generating fractal functions associated with Suzuki iterated function systems

This article constructs a fractal interpolation function, also referred to as $\alpha$-fractal function, using Suzuki-type generalized $\varphi$-contraction mappings (STGPC). The STGPC is a generalization of $\varphi$-contraction mappings. The process of constructing $\alpha$-fractal functions using the STGPC is detailed, and examples of STGPC are given. The FIF has broad applications in data analysis, finance and price prediction. We have included a case study analyzing the price volatility of spinach in the Azadpur vegetable market in New Delhi. The fractal analysis gives a unique perspective on understanding price fluctuations over a period. Finally, the box-dimensional analysis is presented to comprehend the complexity of price fluctuations.

math.FA↗

arXiv2022

The First High-Contrast Images of X-Ray Binaries: Detection of Candidate Companions in the $γ$ Cas Analog RX J1744.7$-$2713

X-ray binaries provide exceptional laboratories for understanding the physics of matter under the most extreme conditions. Until recently, there were few, if any, observational constraints on the circumbinary environments of X-ray binaries at $\sim$ 100-5000 AU scales; it remains unclear how the accretion onto the compact objects or the explosions giving rise to the compact objects interact with their immediate surroundings. Here, we present the first high-contrast adaptive optics images of X-ray binaries. These observations target all X-ray binaries within $\sim$ 3 kpc accessible with the Keck/NIRC2 vortex coronagraph. This paper focuses on one of the first key results from this campaign: our images reveal the presence of 21 sources potentially associated with the $γ$ Cassiopeiae analog high-mass X-ray binary RX J1744.7$-$2713. By conducting different analyses - a preliminary proper motion analysis, a color-magnitude diagram and a probability of chance alignment calculation - we found that three of these 21 sources have a high probability of being bound to the system. If confirmed, they would be in wide orbits ($\sim$ 450 AU to 2500 AU). While follow-up astrometric observations will be needed in $\sim$ 5-10 years to confirm further the bound nature of these detections, these discoveries emphasize that such observations may provide a major breakthrough in the field. In fact, they would be useful not only for our understanding of stellar multiplicity but also for our understanding of how planets, brown dwarfs and stars can form even in the most extreme environments.

astro-ph.EP↗

arXiv2020

Astrometric excess noise in Gaia DR2 and the search for X-ray emitting binaries

Astrometric noise in excess of parallax and proper motion could be a signature of orbital wobble of individual components in binary star systems. The combination of X-ray selection with astrometric noise can then be a powerful tool for identifying accreting binaries. Here, we mine the Gaia DR2 catalogue for Galactic sources with significant values of astrometric noise over the parameter space expected for known and candidate X-ray binaries (XRBs). Cross-matching our sample with the Chandra Source Catalogue CSC2.0 returns a primary sample of ~1,500 X-ray sources with significant excess noise, constituting ~0.04% of the initial Gaia sample. By contrast, the fraction of matched X-ray sources in a control sample with smaller excess noise is a factor of about 7 lower. The primary sample branches off the main sequence much more than control objects in colour-mag space, shows a distinct spatial distribution in terms of Galactic latitudes, comprises more objects with an Halpha excess and larger X-ray-to-optical flux ratios, and includes a higher fraction of known binaries, variables and young stellar object class types. However, for individual XRBs with known system parameters, excess noise can exceed expectations, especially for small wobble. It is likely that other factors (possibly attitude and modelling uncertainties, as well as source variability) currently dominate the observed noise in such systems. Confirmation must therefore await future Gaia releases. The full Chandra/Gaia matched catalogue is released here to enable legacy follow-up.

astro-ph.HE↗

arXiv2020

Estimation of the black hole spin in LMC X-1 using AstroSat

LMC X-1, a persistent, rapidly rotating, extra-galactic, black hole X-ray binary (BHXB) discovered in 1969, has always been observed in its high soft state. Unlike many other BHXBs, the black hole mass, source distance and binary orbital inclination are well established. In this work, we report the results of simultaneous broadband spectral studies of LMC X-1 carried out using the data from Soft X-ray Telescope and Large Area X-ray Proportional Counter aboard AstroSat as observed on 2016 November 26$^{th}$ and 2017 August 28$^{th}$. The combined spectrum was modelled with a multicolour blackbody emission (diskbb), a Gaussian along with a Comptonization component (simpl) in the energy range 0.7$-$30.0 keV. The spectral analysis revealed that the source was in its high soft state ($Γ$=2.67$^{+0.24}_{-0.24}$ and $Γ$=2.12$^{+0.19}_{-0.20}$) with a hot disc (kT$_{in}$=0.86$^{+0.01}_{-0.01}$ and kT$_{in}$=0.87$^{+0.02}_{-0.02}$). Thermal disc emission was fit with a relativistic model (kerrbb) and spin of the black hole was estimated to be 0.93$^{+0.01}_{-0.01}$ and 0.93$^{+0.04}_{-0.03}$ (statistical errors) for the two Epochs through X-ray continuum-fitting, which agrees with the previous results.

astro-ph.HE↗

arXiv2020

Orbital period dependent spatial scatter of Galactic Black Hole Transients

There remain significant uncertainties in the origin and evolution of black holes in binary systems, in particular regarding their birth sites and the influence of natal kicks. These are long-standing issues, but their debate has been reinvigorated in the era of gravitational wave detections and the improving precision of astrometric measurements. Using recent and archival characterisation of Galactic black hole X-ray binaries (BHXBs), we report here an apparent anticorrelation between P{orb} (system orbital periods) and scatter in z (elevation above the Galactic plane). The absence of long period sources at high z is not an obvious observational bias, and two possible explanatory scenarios are qualitatively explored: (1) a disc origin for BHXBs followed by natal kicks producing the scatter in z, with only the tightest binaries preferentially surviving strong kicks; (2) a halo origin, with P{orb} shortening through dynamical interactions in globular clusters (GCs). For the latter case, we show a correspondence in z-scatter between BHXBs and the GCs with most compact core radii of <0.1pc. However, the known absence of outbursting BHXB transients within Galactic GCs remains puzzling in this case, in contrast to the multitude of known GC neutron star XRBs. These results provide an interesting observational constraint for any black hole binary evolutionary model to satisfy.

astro-ph.HE↗

arXiv2019

Origins Space Telescope Mission Concept Study Report

The Origins Space Telescope (Origins) traces our cosmic history, from the formation of the first galaxies and the rise of metals to the development of habitable worlds and present-day life. Origins does this through exquisite sensitivity to infrared radiation from ions, atoms, molecules, dust, water vapor and ice, and observations of extra-solar planetary atmospheres, protoplanetary disks, and large-area extragalactic fields. Origins operates in the wavelength range 2.8 to 588 microns and is 1000 times more sensitive than its predecessors due to its large, cold (4.5 K) telescope and advanced instruments. Origins was one of four large missions studied by the community with support from NASA and industry in preparation for the 2020 Decadal Survey in Astrophysics. This is the final study report.

astro-ph.IM↗

arXiv2019

A stochastic propagation model to the energy dependent rapid temporal behaviour of Cygnus X-1 as observed by AstroSat in the hard state

We report the results from analysis of six observations of Cygnus X-1 by Large Area X-ray Proportional Counters (LAXPC) and Soft X-ray Telescope (SXT) on-board AstroSat, when the source was in the hard spectral state as revealed by the broad band spectra. The spectra obtained from all the observations can be described by a single temperature Comptonizing region with disk and reflection components. The event mode data from LAXPC provides unprecedented energy dependent fractional root mean square (rms) and time-lag at different frequencies which we fit with empirical functions. We invoke a fluctuation propagation model for a simple geometry of a truncated disk with a hot inner region. Unlike other propagation models, the hard X-ray emission (> 4 keV) is assumed to be from the hot inner disk by a single temperature thermal Comptonization process. The fluctuations first cause a variation in the temperature of the truncated disk and then the temperature of the inner disk after a frequency dependent time delay. We find that the model can explain the energy dependent rms and time-lag at different frequencies.

astro-ph.HE↗

arXiv2017

High Rate LDPC Codes from Difference Covering Arrays

This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from difference covering arrays. While the original construction by Gallagher was by randomly allocating bits in a sparse parity-check matrix, over the past 20 years researchers have used a variety of more structured approaches to construct these codes, with the more recent constructions of well-structured LDPC coming from balanced incomplete block designs (BIBDs) and from Latin squares over finite fields. However these constructions have suffered from the limited orders for which these designs exist. Here we present a construction of LDPC codes of length $4n^2 - 2n$ for all $n$ using the cyclic group of order $2n$. These codes achieve high information rate (greater than 0.8) for $n \geq 8$, have girth at least 6 and have minimum distance 6 for $n$ odd.

math.CO↗

arXiv2015

Predicting Item Popularity: Analysing Local Clustering Behaviour of Users

Predicting the popularity of items in rating networks is an interesting but challenging problem. This is especially so when an item has first appeared and has received very few ratings. In this paper, we propose a novel approach to predicting the future popularity of new items in rating networks, defining a new bipartite clustering coefficient to predict the popularity of movies and stories in the MovieLens and Digg networks respectively. We show that the clustering behaviour of the first user who rates a new item gives insight into the future popularity of that item. Our method predicts, with a success rate of over 65% for the MovieLens network and over 50% for the Digg network, the future popularity of an item. This is a major improvement on current results.

cs.SI↗

arXiv2015

Identifying Influential Nodes in Bipartite Networks Using the Clustering Coefficient

The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities.

cs.SI↗

arXiv2015

Equivalences of ${\mathbb Z} _t \times {\mathbb Z}_2^2$-cocyclic Hadamard matrices

One of the most promising structural approaches to resolving the Hadamard Conjecture uses the family of cocyclic matrices over ${\mathbb Z} _t \times {\mathbb Z}_2^2$. Two types of equivalence relations for classifying cocyclic matrices over ${\mathbb Z} _t \times {\mathbb Z}_2^2$ have been found. Any cocyclic matrix equivalent by either of these relations to a Hadamard matrix will also be Hadamard. One type, based on algebraic relations between cocycles over any finite group, has been known for some time. Recently, and independently, a second type, based on four geometric relations between diagrammatic visualisations of cocyclic matrices over ${\mathbb Z} _t \times {\mathbb Z}_2^2$, has been found. Here we translate the algebraic equivalences to diagrammatic equivalences and show one of the diagrammatic equivalences cannot be obtained this way. This additional equivalence is shown to be the geometric translation of matrix transposition.

math.CO↗

arXiv2013

AM-DisCNT: Angular Multi-hop DIStance based Circular Network Transmission Protocol for WSNs

The nodes in wireless sensor networks (WSNs) contain limited energy resources, which are needed to transmit data to base station (BS). Routing protocols are designed to reduce the energy consumption. Clustering algorithms are best in this aspect. Such clustering algorithms increase the stability and lifetime of the network. However, every routing protocol is not suitable for heterogeneous environments. AM-DisCNT is proposed and evaluated as a new energy efficient protocol for wireless sensor networks. AM-DisCNT uses circular deployment for even consumption of energy in entire wireless sensor network. Cluster-head selection is on the basis of energy. Highest energy node becomes CH for that round. Energy is again compared in the next round to check the highest energy node of that round. The simulation results show that AM-DisCNT performs better than the existing heterogeneous protocols on the basis of network lifetime, throughput and stability of the system.

cs.NI↗

arXiv2013

Distance Aware Relaying Energy-efficient: DARE to Monitor Patients in Multi-hop Body Area Sensor Networks

In recent years, interests in the applications of Wireless Body Area Sensor Network (WBASN) is noticeably developed. WBASN is playing a significant role to get the real time and precise data with reduced level of energy consumption. It comprises of tiny, lightweight and energy restricted sensors, placed in/on the human body, to monitor any ambiguity in body organs and measure various biomedical parameters. In this study, a protocol named Distance Aware Relaying Energy-efficient (DARE) to monitor patients in multi-hop Body Area Sensor Networks (BASNs) is proposed. The protocol operates by investigating the ward of a hospital comprising of eight patients, under different topologies by positioning the sink at different locations or making it static or mobile. Seven sensors are attached to each patient, measuring different parameters of Electrocardiogram (ECG), pulse rate, heart rate, temperature level, glucose level, toxins level and motion. To reduce the energy consumption, these sensors communicate with the sink via an on-body relay, affixed on the chest of each patient. The body relay possesses higher energy resources as compared to the body sensors as, they perform aggregation and relaying of data to the sink node. A comparison is also conducted conducted with another protocol of BAN named, Mobility-supporting Adaptive Threshold-based Thermal-aware Energy-efficient Multi-hop ProTocol (M-ATTEMPT). The simulation results show that, the proposed protocol achieves increased network lifetime and efficiently reduces the energy consumption, in relative to M-ATTEMPT protocol.

cs.NI↗

arXiv2013

THE-FAME: THreshold based Energy-efficient FAtigue MEasurment for Wireless Body Area Sensor Networks using Multiple Sinks

Wireless Body Area Sensor Network (WBASN) is a technology employed mainly for patient health monitoring. New research is being done to take the technology to the next level i.e. player's fatigue monitoring in sports. Muscle fatigue is the main cause of player's performance degradation. This type of fatigue can be measured by sensing the accumulation of lactic acid in muscles. Excess of lactic acid makes muscles feel lethargic. Keeping this in mind we propose a protocol \underline{TH}reshold based \underline{E}nergy-efficient \underline{FA}tigue \underline{ME}asurement (THE-FAME) for soccer players using WBASN. In THE-FAME protocol, a composite parameter has been used that consists of a threshold parameter for lactic acid accumulation and a parameter for measuring distance covered by a particular player. When any parameters's value in this composite parameter shows an increase beyond threshold, the players is declared to be in a fatigue state. The size of battery and sensor should be very small for the sake of players' best performance. These sensor nodes, implanted inside player's body, are made energy efficient by using multiple sinks instead of a single sink. Matlab simulation results show the effectiveness of THE-FAME.

cs.NI↗