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The challenge of optimal Routing and Spectrum Assignment (RSA) is significant in Elastic Optical Networks. Integrating adaptive modulation formats into the RSA problem - Routing, Modulation Level, and Spectrum Assignment - broadens allocation options and increases complexity. The conventional RSA approach entails predetermining fixed paths and then allocating spectrum within them separately. However, expanding the path set for optimality may not be advisable due to the substantial increase in paths with network size expansion. This paper delves into a novel approach called RMLSA, which proposes a comprehensive solution addressing both route determination and spectrum assignment simultaneously. An objective function named ABACUS, Adaptive Balance of Average Clustering and Utilization of Spectrum, is chosen for its capability to adjust and assign significance to average clustering and spectrum utilization. Our approach involves formulating an Integer Linear Programming model with a straightforward relationship between path and spectrum constraints. The model also integrates Physical Layer Impairments to ensure end-to-end Quality of Transmission for requested connections while maintaining existing ones. We demonstrate that ILP can offer an optimal solution for a dynamic traffic scenario within a reasonable time complexity. To achieve this goal, we adopt a structured formulation approach where essential information is determined beforehand, thus minimizing the need for online computations.

We report the results of first ever spectro-polarimetric analyses of the Galactic ultra-luminous X-ray pulsar Swift J0243.6$+6124$ during the 2023 outburst using quasi-simultaneous {\it IXPE}, {\it NICER} and {\it NuSTAR} observations. A pulsation of period $\sim 9.79$ s is detected in {\it IXPE} and {\it NuSTAR} observations with pulse fractions (PFs) $\sim 18\%$ ($2-8$ keV) and $\sim 28\%$ ($3-78$ keV), respectively. Energy dependent study of the pulse profiles with {\it NuSTAR} indicates an increase in PF from $\sim 27\%$ ($3-10$ keV) to $\sim 50\%$ ($40-78$ keV). Further, epoch-dependent polarimetric measurements during the decay phase of the outburst confirm the detection of significant polarization, with the polarization degree (PD) and polarization angle (PA) ranging between $\sim 2 -3.1\%$ and $\sim8.6^{\circ}-10.8^{\circ}$, respectively, in the $2-8$ keV energy range. We also observe that the PD increases up to $\sim 4.8\%$ at higher energies ($\gtrsim 5$ keV) with dominating \texttt{bbodyrad} flux contribution ($1.5 \lesssim F_{\rm BB}/F_{\rm PL} \lesssim 3.4$) in the {\it IXPE} spectra. The phase-resolved polarimetric study yields PD as $\sim 1.7-3.1\%$ suggesting a marginal correlation with the pulse profiles. Moreover, the broad-band ($0.6-70$ keV) energy spectrum of combined {\it NICER} and {\it NuSTAR} observations is well described by the combination of \texttt{bbodyrad} and \texttt{cutoffpl} components with seed photon temperature ($kT_{\rm bb}$) $\sim 0.86 \pm 0.03$ keV and photon index ($\Gamma$) $\sim 0.98 \pm 0.01$. With the above findings, we infer that the observed `low' PD in Swift J0243.6$+6124$ is attributed possibly due to `vacuum resonance' effect between the overheated and relatively cooler regions of the neutron star boundary layer., Comment: 11 pages + Appendix, 6 figures, 3 tables, accepted for publication in The Astrophysical Journal Letters

We present a comprehensive spectro-polarimetric study of persistent Black hole X-ray binary 4U $1957\!+\!115$ with {\it IXPE} and {\it NICER} observations. The source is observed in disk dominated thermal state with disk temperature, kT$_{in}\approx1.4$ keV. The emission during thermal state from the source is found to be moderately polarized and \textit{IXPE} measures a degree of polarization (PD) $= 1.95\pm0.37\%$ ($>4.79\sigma$) along with a polarization angle (PA) $= -42.78^{\circ}\pm5.41^{\circ}$ in the energy range of $2-8$ keV. PD is found to be an increasing function of energy, whereas PA indicates switching within the energy range which could be due to high inclination and the returning radiation within the system. Simultaneous energy spectra ($0.6-10$ keV) from {\it NICER} are modelled to study the spectral properties. Furthermore, the spin parameter of the black hole is estimated with spectro-polarimetric data as a$_{\ast}=0.988\pm0.001\,(1\sigma)$, which is corroborated by {\it NICER} observations. Finally, we discuss the implications of our findings., Comment: 5 pages, 4 figures, 3 tables, Submitted to MNRAS Letters on 30 September 2023. arXiv admin note: text overlap with arXiv:2303.05462

We present a detailed spectro-polarimetric study of Black hole X-ray binary 4U $1630-47$ during its $2022$ outburst with IXPE and NICER observations. The source is observed in disk dominated thermal state (kT$_{in}\approx1.4$ keV) with clear detection of absorption features at $6.69\pm0.01$ keV and $6.97\pm0.01$ keV from both NICER as well as IXPE spectra, likely indicating a coupling of disk-wind. A significant degree of polarization(PD) $= 8.33\pm0.17\%$ and polarization angle(PA) $=17.78^{\circ}\pm0.60^{\circ}$ in the energy range of $2-8$ keV are measured with IXPE. PD is found to be an increasing function of energy whereas PA remains roughly same within the energy range. Simultaneous energy spectra from NICER in the range of $0.5-12$ keV are modelled to study the spectral properties. Furthermore, the spin parameter of the black hole is estimated with spectro-polarimetric data as a$_{\ast}=0.927\pm0.001\,(1\sigma)$ which is corroborated by NICER observations. Finally, we discuss the implications of our findings., Comment: 6 pages, 4 figures, 4 tables, Accepted for publication in MNRAS Letters

In this paper, we performed a spectro-polarimetric analysis of the transient NS-LMXB XTE J1701-462 using IXPE, NICER, and NuSTAR data during its 2022 outburst. We report the significant detection of energy-dependent polarization in the X-ray signal from the source on 2022 September 29 in the $2-4$ keV, $4-8$ keV and $2-8$ keV energy bands with a polarization degree of $3.9 \pm 0.3$% (10.7$\sigma$), $5.5 \pm 0.6$% (9.1$\sigma$) and $4.5 \pm 0.4$% (12.6$\sigma$), respectively. The polarization angle in the overall $2-8$ keV band was found to be $\sim 143^{\circ}\pm 2^{\circ}$. The spectra were modelled using a combination of thermal emission from an accretion disc, Comptonized emission from a hot electron plasma (or corona) and a Gaussian line. From spectro-polarimetric analysis, the polarization degree due to the disc emission was found to have an upper limit of $\sim 11.5$%, and that of the Comptonized emission was constrained at $7.7 \pm 2.5$% (at the 3$\sigma$ level). The results suggest that the Comptonized component probably originates from a spreading-layer/boundary-layer above the neutron star surface. IXPE observation of the same source on 2022 October 8 does not show significant polarization which can be attributed to a weakening of the coronal Comptonized emission. The implication of these results are discussed., Comment: 6 pages, 3 figures, 4 tables; Accepted for publication in MNRAS

We have carried out the first spectro-polarimetric study of the bright NS-LMXB GX 9+9 using IXPE and AstroSat observations. We report a significant detection of polarization of $1.7\pm 0.4\%$ over the $2-8$ keV energy band, with a polarization angle of $63^{\circ}\pm 7^{\circ}$. The polarization is found to be energy-dependent, with a $3\sigma$ polarization degree consistent with null polarization in $2-4$ keV, and $3.2\%$ in $4-8$ keV. Typical of the spectra seen in NS-LMXBs, we find that a combination of soft thermal emission from the accretion disc and Comptonized component from the optically thick corona produces a good fit to the spectra. We also attempt to infer the individual polarization of these components, and obtain a $3\sigma$ upper limit of $\sim 11\%$ on the polarization degree of the thermal component, and constrain that of the Comptonized component to $\sim 3\%$. We comment on the possible corona geometry of the system based on our results., Comment: 5 pages, 6 figures, Accepted for publication in MNRAS Letters

In this paper, we demonstrate a low-cost method to measure the speed of light. It uses instruments which are readily available in any undergraduate laboratory in a developing country and some components which are inexpensive. The method is direct as it measures the time of flight of the LASER beam and easy to implement. It will allow students to verify the finite value of the speed of light first hand. It can be part of the undergraduate syllabus as a regular experiment or a demonstration experiment., Comment: 4 pages, 5 figures