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We investigate the temporal dynamics of the PT-Symmetric nonlinear oscillators in the presence of Duffing nonlinearity for two forms of oscillator configuration. In the former, we consider two oscillator coupled to each other. One oscillator is amplified and the other is attenuated. From the bifurcation analysis, we find that the temporal evolution of oscillators exhibit the transition from quasiperiodic to chaotic dynamics. This has been corroborated by the maximal Lyapunov exponent of the system. Furthermore, on investigating the correlation of the time-series using the Pearson's correlation coefficient, it is found that the chaotic system is anti-phase synchronized, whereas the quasiperiodic is not synchronized in any form. The parametric regime where this transition has been observed is from the Unbroken PT regime to the Broken PT regime. Similarly, in the latter configuration with two amplified oscillators coupled to two attenuated oscillators, a similar transition has been observed. But in the neighbourhood of the Exceptional Point (EP) of the system, the system is shown to exhibit in-phase synchronized dynamics as is evident from the correlation analysis., Comment: 14 pages, 11 figures

In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG (DDAG). In particular, we consider a DDAG where the nodal dynamics are driven by unobserved exogenous noise sources that are wide-sense stationary (WSS) in time but are mutually uncorrelated, and have the same {power spectral density (PSD)}. Inspired by the static DAG setting, a metric and an algorithm based on the PSD matrix of the observed time series are proposed to reconstruct the DDAG. It is shown that the optimal sample complexity (or length of state trajectory) needed to learn the DDAG is $n=\Theta(q\log(p/q))$, where $p$ is the number of nodes and $q$ is the maximum number of parents per node. To prove the sample complexity upper bound, a concentration bound for the PSD estimation is derived, under two different sampling strategies. A matching min-max lower bound using generalized Fano's inequality also is provided, thus showing the order optimality of the proposed algorithm., Comment: 21 pages. Accepted for publication in AISTATS 2024

The MeerKAT Absorption Line Survey (MALS) has observed 391 telescope pointings at L-band (900 - 1670 MHz) at $\delta\lesssim$ $+20\deg$. We present radio continuum images and a catalog of 495,325 (240,321) radio sources detected at a signal-to-noise ratio (SNR) $>$5 over an area of 2289 deg$^2$ (1132 deg$^2$) at 1006 MHz (1381 MHz). Every MALS pointing contains a central bright radio source ($S_{1\,\mathrm{GHz}} \gtrsim 0.2$ Jy). The median spatial resolution is $12^{\prime\prime}$ ($8^{\prime\prime}$). The median rms noise away from the pointing center is 25 $\mu$Jy beam$^{-1}$ (22 $\mu$Jy beam$^{-1}$) and is within $\sim$ 15% of the achievable theoretical sensitivity. The flux density scale ratio and astrometric accuracy deduced from multiply observed sources in MALS are less than 1% (8% scatter) and $1^{\prime\prime}$, respectively. Through comparisons with NVSS and FIRST at 1.4 GHz, we establish the catalog's accuracy in the flux density scale and astrometry to be better than 6% (15% scatter) and $0.8^{\prime\prime}$, respectively. The median flux density offset is higher (9%) for an alternate beam model based on holographic measurements. The MALS radio source counts at 1.4 GHz are in agreement with literature. We estimate spectral indices ($\alpha$) of a subset of 125,621 sources (SNR$>$8), confirm the flattening of spectral indices with decreasing flux density and identify 140 ultra steep-spectrum ($\alpha<-1.3$) sources as prospective high-$z$ radio galaxies ($z>2$). We have identified 1308 variable and 122 transient radio sources comprising primarily of AGN that demonstrate long-term (26 years) variability in their observed flux densities. The MALS catalogs and images are publicly available at https://mals.iucaa.in., Comment: 64 pages, 25 figures, accepted for publication in the ApJS (full version of the paper with complete tables is available at DR1 release notes)

Intelligent reflecting surface (IRS) has recently emerged as a promising technology for beyond fifth-generation (B5G) and 6G networks conceived from metamaterials that smartly tunes the signal reflections via a large number of low-cost passive reflecting elements. However, the IRS-assisted communication model and the optimization of available resources needs to be improved further for more efficient communications. This paper investigates the enhancement of received power at the user end in an IRS assisted wireless communication by jointly optimizing the phase shifts at the IRS elements and its location. Employing the conventional Friss transmission model, the relationship between the transmitted power and reflected power is established. The expression of received power incorporates the free space loss, reflection loss factor, physical dimension of the IRS panel, and radiation pattern of the transmit signal. Also, the expression of reflection coefficient of IRS panel is obtained by exploiting the existing data of radar communications. Initially exploring a single IRS element within a two-ray reflection model, we extend it to a more complex multi-ray reflection model with multiple IRS elements in 3D Cartesian space. The received power expression is derived in a more tractable form, then, it is maximized by jointly optimizing the underlying underlying variables, the IRS location and the phase shifts. To realize the joint optimization of underlying variables, first, the phase shifts of the IRS elements are optimized to achieve constructive interference of received signal components at the user. Subsequently, the location of the IRS is optimized at the obtained optimal phase shifts. Numerical insights and performance comparison reveal that joint optimization leads to a substantial 37% enhancement in received power compared to the closest competitive benchmark scheme.

This paper presents a graph-structured Gaussian process (GP) model for data-driven risk assessment of critical voltage constraints. The proposed GP is based on a novel kernel, named the vertex-degree kernel (VDK), that decomposes the voltage-load relationship based on the network graph. To estimate the GP efficiently, we propose a novel active learning scheme that leverages the additive structure of VDK. Further, we prove a probabilistic bound on the error in risk estimation using VDK-GP model that demonstrates that it is statistically comparable to using standard AC power flow (AC-PF), but does not require computing a large number of ACPF solutions. Simulations demonstrate that the proposed VDK-GP achieves more than two fold sample complexity reduction, compared to a generic GP on medium scale 500-Bus and large scale 1354-Bus power systems. Moreover, active learning achieves an impressive reduction of over 15 times in comparison to the time complexity of Monte-Carlo simulations (MCS), and have risk estimation error of order 1E-4 for both 500-Bus and 1354-Bus system, demonstrating its superior efficiency in risk estimation., Comment: 9 pages

In this work, we investigate how multinucleon enhancement and RPA (Random Phase Approximation) suppression can affect the measurement of three unknown neutrino oscillation parameters - the CP-violating phase $\delta_{CP}$, the octant of the atmospheric mixing angle $\theta_{23}$, and the determination of the mass hierarchy, in the appearance channel of the NO$\nu$A experiment. We include the presence of the detector effect as well in the analysis, which is crucial for capturing realistic experimental scenarios. We also conducted a comparison between the nuclear model Effective Spectral Function (calculated within the RFG model) with and without Transverse Enhancement in terms of sensitivity analysis. It is found that the analysis using our comprehensive model QE(+RPA)+2p2h along with Effective Spectral Function+Transverse Enhancement exhibits significantly enhanced sensitivity compared to the pure QE interaction process, in all the cases.Also, the higher octant of $\theta_{23}$, the lower half plane of $\delta_{CP}$, and the normal mass hierarchy (HO-LHP-NH) exhibit improved sensitivity, enabling a more precise determination of the corresponding parameters. Furthermore, it is also noted that improving the performance of the detector also improves the results. Thus, including multinucleon effects and improving detector efficiency have the potential to enhance the capabilities of the NO$\nu$A (and other long baseline) experiment in conducting precise parameter studies., Comment: 25 pages, 8 figures, 3 tables

While ostensibly coined in 1989 by Xiao-Gang Wen, the term "topological order" has been in use since 1972 to describe the behavior of the classical xy model. It has been noted that the xy model does not have Wen's topological order since it is also subject a non-topological U(1) gauge action. We show in a sense this is the only obstruction. That is, if gauge invariance is enforced energetically then the $xy$ model becomes purely topologically ordered. In fact, we show that the quantum $xy$ topological order is an infinite lattice limit of Kitaev's quantum double model applied to the group G=Z., Comment: 4 pages, 3 figures

Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of the cosmic ray transport equation. To conduct numerical simulations of time-dependent cosmic ray transport, implicit integrators (namely, Crank-Nicolson (CN)) have been traditionally favoured over the CFL-bound explicit integrators in order to be able to take large step sizes. We propose exponential methods to treat the linear anisotropc diffusion equation in the presence of advection and time-independent and time-dependent sources. These methods allow us to take even larger step sizes that can substantially speed-up the simulations whilst generating highly accurate solutions. In or subsequent work, we will use these exponential solvers in the Picard code to study anisotropic cosmic ray diffusion and we will consider additional physical processes such as continuous momentum losses and reacceleration., Comment: The 38th International Cosmic Ray Conference (ICRC2023)

The paper is about the computation of the principal spectrum of the Koopman operator (i.e., eigenvalues and eigenfunctions). The principal eigenfunctions of the Koopman operator are the ones with the corresponding eigenvalues equal to the eigenvalues of the linearization of the nonlinear system at an equilibrium point. The main contribution of this paper is to provide a novel approach for computing the principal eigenfunctions using a path-integral formula. Furthermore, we provide conditions based on the stability property of the dynamical system and the eigenvalues of the linearization towards computing the principal eigenfunction using the path-integral formula. Further, we provide a Deep Neural Network framework that utilizes our proposed path-integral approach for eigenfunction computation in high-dimension systems. Finally, we present simulation results for the computation of principal eigenfunction and demonstrate their application for determining the stable and unstable manifolds and constructing the Lyapunov function.

A methodical inquiry of the outcome of oxygen plasma exposure in low bandwidth compounds belonging to the perovskite family Pr1-xSrxMnO3 manganites where x = 0.5, has been presented in this communication by comparing the structural and transport properties of the untreated and plasma treated samples. It is witnessed that the high-temperature transmission is carried out by small polarons while the low-temperature transmission is attributed to variable range polarons. The changes in the transport properties may be attributed to the structural modification due to plasma exposure as revealed by the Rietveld analysis of the X-ray diffraction pattern. Further, oxygen plasma exposure boosts the conductivity due to the integration of oxygen ions in the plasma-exposed samples, thereby rendering them oxygen-rich., Comment: 21 pages, 9 Figures, 3 Tables

The effects of metallicity on the evolution of protoplanetary disks may be studied in the outer Galaxy where the metallicity is lower than in the solar neighbourhood. We present the VLT/KMOS integral field spectroscopy in the near-infrared of $\sim$120 candidate young stellar objects (YSOs) in the CMa-$\ell$224 star-forming region located at a Galactocentric distance of 9.1 kpc. We characterise the YSO accretion luminosities and accretion rates using the hydrogen Br$\gamma$ emission and find the median accretion luminosity of $\log{(L_{\rm acc})} = -0.82^{+0.80}_{-0.82} L_\odot$. Based on the measured accretion luminosities, we investigate the hypothesis of star formation history in the CMa-$\ell$224. Their median values suggest that Cluster C, where most of YSO candidates have been identified, might be the most evolved part of the region. The accretion luminosities are similar to those observed toward low-mass YSOs in the Perseus and Orion molecular clouds, and do not reveal the impact of lower metallicity. Similar studies in other outer Galaxy clouds covering a wide range of metallicities are critical to gain a complete picture of star formation in the Galaxy., Comment: Accepted for publication in APJS, 51 pages, 37 figures, 6 tables

Large-scale multi-input multi-output (MIMO) code domain non-orthogonal multiple access (CD-NOMA) techniques are one of the potential candidates to address the next-generation wireless needs such as massive connectivity, and high reliability. This work focuses on two primary CD-NOMA techniques: sparse-code multiple access (SCMA) and dense-code multiple access (DCMA). One of the primary challenges in implementing MIMO-CD-NOMA systems is designing the optimal detector with affordable computation cost and complexity. This paper proposes an iterative linear detector based on the alternating direction method of multipliers (ADMM). First, the maximum likelihood (ML) detection problem is converted into a sharing optimization problem. The set constraint in the ML detection problem is relaxed into the box constraint sharing problem. An alternative variable is introduced via the penalty term, which compensates for the loss incurred by the constraint relaxation. The system models, i.e., the relation between the input signal and the received signal, are reformulated so that the proposed sharing optimization problem can be readily applied. The ADMM is a robust algorithm to solve the sharing problem in a distributed manner. The proposed detector leverages the distributive nature to reduce per-iteration cost and time. An ADMM-based linear detector is designed for three MIMO-CD-NOMA systems: single input multi output CD-NOMA (SIMO-CD-NOMA), spatial multiplexing CD-NOMA (SMX-CD-NOMA), and spatial modulated CD-NOMA (SM-CD-NOMA). The impact of various system parameters and ADMM parameters on computational complexity and symbol error rate (SER) has been thoroughly examined through extensive Monte Carlo simulations.

Next-generation wide-field optical polarimeters like the Wide-Area Linear Optical Polarimeters (WALOPs) have a field of view (FoV) of tens of arcminutes. For efficient and accurate calibration of these instruments, wide-field polarimetric flat sources will be essential. Currently, no established wide-field polarimetric standard or flat sources exist. This paper tests the feasibility of using the polarized sky patches of the size of around ten-by-ten arcminutes, at a distance of up to 20 degrees from the Moon, on bright-Moon nights as a wide-field linear polarimetric flat source. We observed 19 patches of the sky adjacent to the bright-Moon with the RoboPol instrument in the SDSS-r broadband filter. These were observed on five nights within two days of the full-Moon across two RoboPol observing seasons. We find that for 18 of the 19 patches, the uniformity in the measured normalized Stokes parameters $q$ and $u$ is within 0.2 %, with 12 patches exhibiting uniformity within 0.07 % or better for both $q$ and $u$ simultaneously, making them reliable and stable wide-field linear polarization flats. We demonstrate that the sky on bright-Moon nights is an excellent wide-field linear polarization flat source. Various combinations of the normalized Stokes parameters $q$ and $u$ can be obtained by choosing suitable locations of the sky patch with respect to the Moon, Comment: 8 pages including appendix, 6 figures and 3 tables. Submitted to Astronomy and Astrophysics for review. Comments are welcome

We present an analysis of the theoretical and observed light curve parameters of the fundamental mode (FU) classical Cepheids in the Magellanic Clouds in $V$- and $I$- photometric bands. The state-of-the-art 1D non-linear radial stellar pulsation (RSP) code in MESA (\textsc{mesa-rsp}) has been utilized to generate the theoretical light curves using four sets of convection parameters. Theoretical light curves with two chemical compositions: $Z=0.008$ and $Z=0.004$ appropriate for the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), respectively, covered a wide range of periods ($3

1$) and all periods. The multiphase relations obtained from theoretical and observed light curves in the PL/PC/AC plane are found to be dynamic in nature, with the effect more pronounced at $\Phi \sim 0.75-0.85$. Furthermore, a contrasting behaviour of the theoretical/observed multiphase PL and PC relations between the short and long periods has been found for both LMC and SMC. The analysis shows that multiphase PL relations are more stringent to test the models with observations over the FPs. Distances to the LMC/SMC determined using long period Cepheids are found to be in good agreement with the literature values when the term $R_{21}$ is added to the PL relation., Comment: 17 pages, 11 Figures and 9 Tables. Accepted for publication by MNRAS

Wildfires pose a significant threat to the safe and reliable operations of the electric grid. To mitigate wildfire risk, system operators resort to public safety power shutoffs, or PSPS, that shed load for a subset of customers. As wildfire risk forecasts are stochastic, such decision-making may often be sub-optimal. This paper proposes a two-stage topology control problem that jointly minimizes generation and load-shedding costs in the face of uncertain fire risk. Compared to existing work, we include preand post-event topology control actions and consider scenarios where the wildfire risk is known with low and high confidence. The effectiveness of the proposed approach is demonstrated using a benchmark test system, artificially geo-located in Southern California, and using stochastic wildfire risk data that exists in the literature. Our work provides a crucial study of the comparative benefits of pre-event versus post-event control and the effects of wildfire risk accuracy on each control strategy., Comment: 6 pages, 6 figures