The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets.

Recent works have demonstrated that neural networks exhibit extreme simplicity bias(SB). That is, they learn only the simplest features to solve a task at hand, even in the presence of other, more robust but more complex features. Due to the lack of a general and rigorous definition of features, these works showcase SB on semi-synthetic datasets such as Color-MNIST, MNIST-CIFAR where defining features is relatively easier. In this work, we rigorously define as well as thoroughly establish SB for one hidden layer neural networks. More concretely, (i) we define SB as the network essentially being a function of a low dimensional projection of the inputs (ii) theoretically, we show that when the data is linearly separable, the network primarily depends on only the linearly separable ($1$-dimensional) subspace even in the presence of an arbitrarily large number of other, more complex features which could have led to a significantly more robust classifier, (iii) empirically, we show that models trained on real datasets such as Imagenette and Waterbirds-Landbirds indeed depend on a low dimensional projection of the inputs, thereby demonstrating SB on these datasets, iv) finally, we present a natural ensemble approach that encourages diversity in models by training successive models on features not used by earlier models, and demonstrate that it yields models that are significantly more robust to Gaussian noise.

Given a finite set of unknown distributions or arms that can be sampled, we consider the problem of identifying the one with the maximum mean using a $\delta$-correct algorithm (an adaptive, sequential algorithm that restricts the probability of error to a specified $\delta$) that has minimum sample complexity. Lower bounds for $\delta$-correct algorithms are well known. $\delta$-correct algorithms that match the lower bound asymptotically as $\delta$ reduces to zero have been previously developed when arm distributions are restricted to a single parameter exponential family. In this paper, we first observe a negative result that some restrictions are essential, as otherwise, under a $\delta$-correct algorithm, distributions with unbounded support would require an infinite number of samples in expectation. We then propose a $\delta$-correct algorithm that matches the lower bound as $\delta$ reduces to zero under the mild restriction that a known bound on the expectation of $(1+\epsilon)^{th}$ moment of the underlying random variables exists, for $\epsilon > 0$. We also propose batch processing and identify near-optimal batch sizes to speed up the proposed algorithm substantially. The best-arm problem has many learning applications, including recommendation systems and product selection. It is also a well-studied classic problem in the simulation community.

Radio relics, arc-like polarized sources with highly aligned magnetic fields, are typically found on the outskirts of merging galaxy clusters. The magneto-ionic media responsible for the significant coherence observed in radio relics remain poorly understood. Low-frequency measurements of radio relics are essential for constraining depolarization models, which provide crucial insights into the magnetic field distribution. However, these measurements are challenging due to the emission properties and interferometer systematics. We have detected polarization signals from the northwest radio relic in Abell 746 at 650 MHz with the upgraded Giant Meterwave Radio Telescope, marking the first-ever detection of polarisation from radio relics below 1 GHz. At this frequency, the average Rotation Measure (RM) corrected magnetic fields align well with shock radio emission, typical of radio relics. The fractional polarization at 650 MHz is $\sim 18\pm4 \%$. Our results indicate that a single internal depolarization model cannot explain the observed depolarization spectra, suggesting a non-uniform magnetic field distribution or complex contribution of different polarized regions in the radio relic. Our detection of polarization signals at 650 MHz reveals critical insights into radio relic magnetic field structures, offering a low-frequency approach to understanding ICM magnetic fields in merging galaxy clusters.

We consider the problem of online regret minimization in linear bandits with access to prior observations (offline data) from the underlying bandit model. There are numerous applications where extensive offline data is often available, such as in recommendation systems, online advertising. Consequently, this problem has been studied intensively in recent literature. Our algorithm, Offline-Online Phased Elimination (OOPE), effectively incorporates the offline data to substantially reduce the online regret compared to prior work. To leverage offline information prudently, OOPE uses an extended D-optimal design within each exploration phase. OOPE achieves an online regret is $\tilde{O}(\sqrt{\deff T \log \left(|\mathcal{A}|T\right)}+d^2)$. $\deff \leq d)$ is the effective problem dimension which measures the number of poorly explored directions in offline data and depends on the eigen-spectrum $(\lambda_k)_{k \in [d]}$ of the Gram matrix of the offline data. The eigen-spectrum $(\lambda_k)_{k \in [d]}$ is a quantitative measure of the \emph{quality} of offline data. If the offline data is poorly explored ($\deff \approx d$), we recover the established regret bounds for purely online setting while, when offline data is abundant ($\Toff >> T$) and well-explored ($\deff = o(1)$), the online regret reduces substantially. Additionally, we provide the first known minimax regret lower bounds in this setting that depend explicitly on the quality of the offline data. These lower bounds establish the optimality of our algorithm in regimes where offline data is either well-explored or poorly explored. Finally, by using a Frank-Wolfe approximation to the extended optimal design we further improve the $O(d^{2})$ term to $O\left(\frac{d^{2}}{\deff} \min \{ \deff,1\} \right)$, which can be substantial in high dimensions with moderate quality of offline data $\deff = \Omega(1)$.

This paper reports the discovery and follow-up of four candidate redback spider pulsars: GPM J1723-33, GPM J1734-28, GPM J1752-30 and GPM J1815-14, discovered with the Murchison Widefield Array (MWA) from an imaging survey of the Galactic Plane. These sources are considered to be redback candidates based on their eclipsing variability, steep negative spectral indices, and potential Fermi $\gamma$-ray associations, with GPM J1723-33 and GPM J1815-14 lying within a Fermi 95% error ellipse. Follow-up pulsation searches with MeerKAT confirmed pulsations from GPM J1723-33, while the non-detections of the other three are likely due to scattering by material ablated from their companion stars. We identify possible orbital periods by applying folding algorithms to the light curves and determine that all sources have short orbital periods (<24 hours), consistent with redback spider systems. Following up on the sources at multiple radio frequencies revealed that the sources exhibit frequency-dependent eclipses, with longer eclipses observed at lower frequencies. We place broad constraints on the eclipse medium, ruling out induced Compton scattering and cyclotron absorption. Three sources are spatially consistent with optical sources in the Dark Energy Camera Plane Survey imaging, which may contain the optical counterparts. Each field is affected by strong dust extinction, and follow-up with large telescopes is needed to identify the true counterparts. Identifying potential radio counterparts to four previously unassociated Fermi sources brings us closer to understanding the origin of the unexplained $\gamma$-ray excess in the Galactic Centre.

A seminal result of Nisan and Szegedy (STOC, 1992) shows that for any total Boolean function, the degree of the real polynomial that computes the function, and the minimal degree of a real polynomial that point-wise approximates the function, are at most polynomially separated. Extending this result from degree to other complexity measures like sparsity of the polynomial representation, or total weight of the coefficients, remains poorly understood. In this work, we consider this problem in the De Morgan basis, and prove an analogous result for the sparsity of the polynomials at a logarithmic scale. Our result further implies that the exact $\ell_1$ norm and its approximate variant are also similarly related to each other at a log scale. This is in contrast to the Fourier basis, where the analog of our results are known to be false. Our proof is based on a novel random restriction method. Unlike most existing random restriction methods used in complexity theory, our random restriction process is adaptive and is based on how various complexity measures simplify during the restriction process.

Fast radio bursts (FRBs) represent an exciting frontier in the study of gravitational lensing, due to their brightness, extragalactic nature, and the compact, coherent characteristics of their emission. In a companion work [Kader, Leung+2022], we use a novel interferometric method to search for gravitationally lensed FRBs in the time domain using bursts detected by CHIME/FRB. There, we dechannelize and autocorrelate electric field data at a time resolution of 1.25 ns. This enables a search for FRBs whose emission is coherently deflected by gravitational lensing around a foreground compact object such as a primordial black hole (PBH). Here, we use our non-detection of lensed FRBs to place novel constraints on the PBH abundance outside the Local Group. We use a novel two-screen model to take into account decoherence from scattering screens in our constraints. Our constraints are subject to a single astrophysical model parameter -- the effective distance between an FRB source and the scattering screen, for which we adopt a fiducial distance of 1 parsec. We find that coherent FRB lensing is a sensitive probe of sub-solar mass compact objects. Having observed no lenses in $172$ bursts from $114$ independent sightlines through the cosmic web, we constrain the fraction of dark matter made of compact objects, such as PBHs, to be $f \lesssim 0.8$, if their masses are $\sim 10^{-3} M_{\odot}$.

The multi-messenger science using different observational windows to the Universe such as Gravitational Waves (GWs), Electromagnetic Waves (EMs), Cosmic Rays (CRs), and Neutrinos offer an opportunity to study from the scale of a neutron star to cosmological scales over a large cosmic time. At the smallest scales, we can explore the structure of the neutron star and the different energetics involved in the transition of a pre-merger neutron star to a post-merger neutron star. This will open up a window to study the properties of matter in extreme conditions and a guaranteed discovery space. On the other hand, at the largest cosmological scales, multi-messenger observations allow us to study the long-standing problems in physical cosmology related to the Hubble constant, dark matter, and dark energy by mapping the expansion history of the Universe using GW sources. Moreover, the multi-messenger studies of astrophysical systems such as white dwarfs, neutron stars, and black holes of different masses, all the way up to a high redshift Universe, will bring insightful understanding into the physical processes associated with them that are inaccessible otherwise. This white paper discusses the key cases in the domain of multi-messenger astronomy and the role of observatories in India which can explore uncharted territories and open discovery spaces in different branches of physics ranging from nuclear physics to astrophysics.

We study the 10 fast radio bursts (FRBs) detected in the far side-lobe region of the CHIME telescope from 2018 August 28 to 2021 August 31. We find that the far side-lobe events have on average $\sim$500 times greater fluxes than events detected in CHIME's main lobe. We show that the side-lobe sample is therefore statistically $\sim$20 times closer than the main-lobe sample. The median dispersion measure (DM) excess, after removing the Galactic disk component using the NE2001 for the free electron density distribution of the Milky Way, of the 10 far side-lobe and 471 non-repeating main-lobe FRBs in the first CHIME/FRB catalog is 183.0 and 433.9 pc\;cm$^{-3}$, respectively. By comparing the DM excesses of the two populations under reasonable assumptions, we statistically constrain that the local degenerate contributions (from the Milky Way halo and the host galaxy) and the intergalactic contribution to the excess DM of the 471 non-repeating main-lobe FRBs for the NE2001 model are 131.2$-$158.3 and 302.7$-$275.6 pc cm$^{-3}$, respectively, which corresponds to a median redshift for the main-lobe FRB sample of $\sim$0.3. These constraints are useful for population studies of FRBs, and in particular for constraining the location of the missing baryons.

Constraining the Epoch of Reionization (EoR) with physically motivated simulations is hampered by the high cost of conventional parameter inference. We present an efficient emulator-based framework that dramatically reduces this bottleneck for the photon-conserving semi-numerical code SCRIPT. Our approach combines (i) a reliable coarse-resolution MCMC to locate the high-likelihood region (exploiting the large-scale convergence of SCRIPT) with (ii) an adaptive, targeted sampling strategy to build a compact high-resolution training set for an artificial neural network based emulator of the model likelihood. With only $\approx 10^3$ high-resolution simulations, the trained emulators achieve excellent predictive accuracy ($R^2 \approx 0.97$--$0.99$) and, when embedded within an MCMC framework, reproduce posterior distributions from full high-resolution runs. Compared to conventional MCMC, our pipeline reduces the number of expensive simulations by a factor of $\sim 100$ and lowers total CPU cost by up to a factor of $\sim 70$, while retaining statistical fidelity. This computational speedup makes inference in much higher-dimensional models tractable (e.g., those needed to incorporate JWST and upcoming 21 cm datasets) and provides a general strategy for building efficient emulators for next generation of EoR constraints.

We study a distributed computation problem in the presence of Byzantine workers where a central node wishes to solve a task that is divided into independent sub-tasks, each of which needs to be solved correctly. The distributed computation is achieved by allocating the sub-task computation across workers with replication, as well as solving a small number of sub-tasks locally, which we wish to minimize due to it being expensive. For a general balanced job allocation, we propose a protocol that successfully solves for all sub-tasks using an optimal number of local computations under no communication constraints. Closed-form performance results are presented for cyclic allocations. Furthermore, we propose a modification to this protocol to improve communication efficiency without compromising on the amount of local computation.

The Indian Pulsar Timing Array (InPTA) employs unique features of the upgraded Giant Metrewave Radio Telescope (uGMRT) to monitor dozens of the International Pulsar Timing Array (IPTA) millisecond pulsars (MSPs), simultaneously in the 300-500 MHz and the 1260-1460 MHz bands. This dual-band approach ensures that any frequency-dependent delays are accurately characterized, significantly improving the timing precision for pulsar observations, which is crucial for pulsar timing arrays. We present details of InPTA's second data release that involves 7 yrs of data on 27 IPTA MSPs. This includes sub-banded Times of Arrival (ToAs), Dispersion Measures (DM), and initial timing ephemerides for our MSPs. A part of this dataset, originally released in InPTA's first data release, is being incorporated into IPTA's third data release which is expected to detect and characterize nanohertz gravitational waves in the coming years. The entire dataset is reprocessed in this second data release providing some of the highest precision DM estimates so far and interesting solar wind related DM variations in some pulsars. This is likely to characterize the noise introduced by the dynamic inter-stellar ionised medium much better than the previous release thereby increasing sensitivity to any future gravitational wave search.

The identification of persistent radio sources (PRSs) coincident with two repeating fast radio bursts (FRBs) supports FRB theories requiring a compact central engine. However, deep non-detections in other cases highlight the diversity of repeating FRBs and their local environments. Here, we perform a systematic search for radio sources towards 37 CHIME/FRB repeaters using their arcminute localizations and a combination of archival surveys and targeted observations. Through multi-wavelength analysis of individual radio sources, we identify two (20181030A-S1 and 20190417A-S1) for which we disfavor an origin of either star formation or an active galactic nucleus in their host galaxies and thus consider them candidate PRSs. We do not find any associated PRSs for the majority of the repeating FRBs in our sample. For 8 FRB fields with Very Large Array imaging, we provide deep limits on the presence of PRSs that are 2--4 orders of magnitude fainter than the PRS associated with FRB\,20121102A. Using Very Large Array Sky Survey imaging of all 37 fields, we constrain the rate of luminous ($\gtrsim$10$^{40}$ erg s$^{-1}$) PRSs associated with repeating FRBs to be low. Within the context of FRB-PRS models, we find that 20181030A-S1 and 20190417A-S1 can be reasonably explained within the context of magnetar, hypernebulae, gamma-ray burst afterglow, or supernova ejecta models -- although we note that both sources follow the radio luminosity versus rotation measure relationship predicted in the nebula model framework. Future observations will be required to both further characterize and confirm the association of these PRS candidates with the FRBs.

Context. Fast Radio Burst 20180916B is a repeating FRB whose activity window has a 16.34 day periodicity that also shifts and varies in duration with the observing frequency. Recently, arxiv:2205.09221 reported the FRB has started to show secular Rotation Measure (RM) increasing trend after only showing stochastic variability around a constant value of $-114.6$ rad m$^{-2}$ since its discovery. Aims. We aim to further study the RM variability of FRB 20180916B. The data comes from the ongoing campaigns of FRB 20180916B using the upgraded Giant Metrewave Radio Telescope (uGMRT). The majority of the observations are in Band 4, which is centered at 650 MHz with 200 MHz bandwidth. Methods. We apply a standard single pulse search pipeline to search for bursts. In total, we detect 116 bursts with $\sim$36 hours of on-source time spanning 1200 days, with two bursts detected during simultaneous frequency coverage observations. We develop and apply a polarization calibration strategy suited for our dataset. On the calibrated bursts, we use QU-fitting to measure RM. Lastly, we also measure various other properties such as rate, linear polarization fraction and fluence distribution. Results. Of the 116 detected bursts, we could calibrate 79 of them. From which, we observed in our early observations the RM continued to follow linear trend as modeled by arxiv:2205.09221. However, our later observations suggest the source switch from the linear trend to stochastic variations around a constant value of $-58.75$ rad m$^{-2}$. We also study cumulative rate against fluence and note that rate at higher fluences (> 1.2 Jy ms) scales as $\gamma = -1.09(7)$ whereas that at lower fluences (between 0.2 and 1.2 Jy ms) only scales as $\gamma = -0.51(1)$, meaning rate at higher fluence regime is steeper than at lower fluence regime.

We present multi-frequency and high-resolution studies of a sample of 24 radio transients sources discovered by comparing the NRAO VLA Sky Survey (NVSS) and Very Large Array Sky Survey (VLASS) surveys. All of them are characterized by a significant increase in radio flux density over the last two this http URL convex spectra, small sizes and high brightness temperatures are typical for young gigahertz-peaked spectrum (GPS) radio sources and indicative of an AGN buried in the host galaxy. On the other hand, they are much weaker than the archetypical GPS objects and their parsec-scale radio structures, although indicating the presence of young radio jets, are similar to radio-quiet AGNs like Seyfert and low-ionization nuclear emission-line region (LINER) galaxies. Based on the distribution of these objects in power$-$size ($P - D$) and peak frequency$-$size ($\nu_p - D$) diagrams, we suggest that after stabilizing their radio activity, some of the GHz-peaked radio transients (galaxies and quasars) will develop into radio-intermediate and radio-quiet (RI/RQ) quasars and low-frequency peaked-spectrum (PS) objects. We discuss several possible origins for the transient radio emission in our sources and conclude that changes in the accretion rate combined with low-power radio ejecta are the most probable cause. This is the scenario we also propose for one of our sources, 101841$-$13, which was independently identified as a candidate tidal disruption event (TDE) based on its infrared variability. However, we cannot exclude that 101841$-$13 or other sources in our sample are TDEs.

Given an ODE and its perturbation, the Alekseev formula expresses the solutions of the latter in terms related to the former. By exploiting this formula and a new concentration inequality for martingale-differences, we develop a novel approach for analyzing nonlinear Stochastic Approximation (SA). This approach is useful for studying a SA's behaviour close to a Locally Asymptotically Stable Equilibrium (LASE) of its limiting ODE; this LASE need not be the limiting ODE's only attractor. As an application, we obtain a new concentration bound for nonlinear SA. That is, given $\epsilon >0$ and that the current iterate is in a neighbourhood of a LASE, we provide an estimate for i.) the time required to hit the $\epsilon-$ball of this LASE, and ii.) the probability that after this time the iterates are indeed within this $\epsilon-$ball and stay there thereafter. The latter estimate can also be viewed as the `lock-in' probability. Compared to related results, our concentration bound is tighter and holds under significantly weaker assumptions. In particular, our bound applies even when the stepsizes are not square-summable. Despite the weaker hypothesis, we show that the celebrated Kushner-Clark lemma continues to hold. %

We present the results of a nation-wide baseline survey, conducted by us, for the status of Astronomy education among secondary school students in India. The survey was administered in 10 different languages to over 2000 students from diverse backgrounds, and it explored multiple facets of their perspectives on astronomy. The topics included students' views on the incorporation of astronomy in curricula, their grasp of fundamental astronomical concepts, access to educational resources, cultural connections to astronomy, and their levels of interest and aspirations in the subject. We find notable deficiencies in students' knowledge of basic astronomical principles, with only a minority demonstrating proficiency in key areas such as celestial sizes, distances, and lunar phases. Furthermore, access to resources such as telescopes and planetariums remain limited across the country. Despite these challenges, a significant majority of students expressed a keen interest in astronomy. We further analyze the data along socioeconomic and gender lines. Particularly striking were the socioeconomic disparities, with students from resource-poor backgrounds often having lower levels of access and proficiency. Some differences were observed between genders, although not very pronounced. The insights gleaned from this study hold valuable implications for the development of a more robust astronomy curriculum and the design of effective teacher training programs in the future.

Low-frequency, wide field-of-view (FoV) radio telescopes such as the Murchison Widefield Array (MWA) enable the ionosphere to be sampled at high spatial completeness. We present the results of the first power spectrum analysis of ionospheric fluctuations in MWA data, where we examined the position offsets of radio sources appearing in two datasets. The refractive shifts in the positions of celestial sources are proportional to spatial gradients in the electron column density transverse to the line of sight. These can be used to probe plasma structures and waves in the ionosphere. The regional (10-100 km) scales probed by the MWA, determined by the size of its FoV and the spatial density of radio sources (typically thousands in a single FoV), complement the global (100-1000 km) scales of GPS studies and local (0.01-1 km) scales of radar scattering measurements. Our data exhibit a range of complex structures and waves. Some fluctuations have the characteristics of travelling ionospheric disturbances (TIDs), while others take the form of narrow, slowly-drifting bands aligned along the Earth's magnetic field.