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We present the Australian Square Kilometre Array Pathfinder (ASKAP) localization and follow-up observations of the host galaxy of the repeating fast radio burst (FRB) source, FRB20201124A, the fifth such extragalactic repeating FRB with an identified host. From spectroscopic observations using the 6.5-m MMT Observatory, we derive a redshift of $z=0.0979 \pm 0.0001$, a star formation rate inferred from H$\alpha$ emission of SFR(H$\alpha$) $\approx 2.1 M_{\odot}$ yr$^{-1}$, and a gas-phase metallicity of 12+log(O/H)$\approx 9.0$. By jointly modeling the 12-filter optical-mid-infrared (MIR) photometry and spectroscopy of the host, we infer a median stellar mass of $\approx 2 \times 10^{10} M_{\odot}$, internal dust extinction of $A_V\approx 1-1.5$ mag, and a mass-weighted stellar population age of $\approx 5-6$ Gyr. Connecting these data to the radio and X-ray observations, we cannot reconcile the broad-band behavior with strong AGN activity and instead attribute the dominant source of persistent radio emission to star formation, likely originating from the circumnuclear region of the host. The modeling also indicates a hot dust component contributing to the MIR luminosity at a level of $\approx 10-30\%$. We model the host galaxy's star formation and mass assembly histories, finding that the host assembled $>90\%$ of its mass by 1 Gyr ago and exhibited a fairly constant SFR for most of its existence, with no clear evidence of past star-burst activity., Comment: 18 pages, 5 figures, 5 tables. Added tables and updated to current literature. Accepted to ApJ Letters

We study some factorization properties of the idealization $R \mathop{(\! + \! )} M$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $R \mathop{(\! + \! )} M$ is ACCP if and only if $R$ is ACCP and $M$ satisfies ACC on its cyclic submodules. We give an example to show that the BF property is not necessarily preserved in idealization, and give some conditions under which $R \mathop{(\! + \! )} M$ is a BFR. We also characterize the idealization rings which are UFRs., Comment: Some issues with Example 4 were fixed

We study population protocols, a model of distributed computing appropriate for modeling well-mixed chemical reaction networks and other physical systems where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied *majority* problem is that of determining in an initial population of $n$ agents, each with one of two opinions $A$ or $B$, whether there are more $A$, more $B$, or a tie. A *stable* protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of $\mathsf{A}$, $\mathsf{B}$, or $\mathsf{T}$, from which the consensus cannot change. We describe a protocol that solves this problem using $O(\log n)$ states ($\log \log n + O(1)$ bits of memory) and optimal expected time $O(\log n)$. The number of states $O(\log n)$ is known to be optimal for the class of polylogarithmic time stable protocols that are "output dominant" and "monotone". These are two natural constraints satisfied by our protocol, making it simultaneously time- and state-optimal for that class. We introduce a key technique called a "fixed resolution clock" to achieve partial synchronization. Our protocol is *nonuniform*: the transition function has the value $\left \lceil {\log n} \right \rceil$ encoded in it. We show that the protocol can be modified to be uniform, while increasing the state complexity to $\Theta(\log n \log \log n)$., Comment: Applied FOCS reviewers' comments

In the present article, performance of a glazed photovoltaic thermal system integrated with phase change materials (GPVT/PCM) is numerically examined based on both energy and exergy viewpoints. The effect of PCM volumetric fraction and environmental temperature on thermal and electrical characteristics of the system is evaluated. A three-dimensional model of the system is simulated transiently in the ANSYS Fluent 18.2 using pressure-based finite volume method and SIMPLE algorithm selected for coupling pressure and velocity components. Validity of the numerical results is confirmed based on available data. The results indicate that PCM melting is more likely far from the riser tube and absorption of thermal energy be the PCM is mostly effective for filling the PCM container by around 2/3 of the volume. Increase of the PCM volumetric fraction reduces the module temperature and enhances the electrical performance of the system in terms of both energy and exergy efficiencies, while it decreases the thermal efficiency. An opposite trend is experienced by increase of the environmental temperature in which the thermal efficiency enhances and the electrical efficiency declines., Comment: 23 pages, 10 figures

We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose objective function can be optimized over the binary variables analytically, while preserving convexity in the continuous variables. Exploiting this property, we propose two scalable optimization algorithms, coined as the "best response" and the "dual program", that can efficiently screen the potential indices of the nonzero elements of the original program. We show that the proposed methods are competitive with the existing screening methods in the current sparse regression literature, and it is particularly fast on instances with high number of measurements in experiments with both synthetic and real datasets.

The population protocol model describes a network of $n$ anonymous agents who cannot control with whom they interact. The agents collectively solve some computational problem through random pairwise interactions, each agent updating its own state in response to seeing the state of the other agent. They are equivalent to the model of chemical reaction networks, describing abstract chemical reactions such as $A+B \rightarrow C+D$, when the latter is subject to the restriction that all reactions have two reactants and two products, and all rate constants are 1. The counting problem is that of designing a protocol so that $n$ agents, all starting in the same state, eventually converge to states where each agent encodes in its state an exact or approximate description of population size $n$. In this survey paper, we describe recent algorithmic advances on the counting problem.

For the first $\sim3$ years after the binary neutron star merger event GW 170817 the radio and X-ray radiation has been dominated by emission from a structured relativistic off-axis jet propagating into a low-density medium with n $< 0.01\,\rm{cm^{-3}}$. We report on observational evidence for an excess of X-ray emission at $\delta t>900$ days after the merger. With $L_x\approx5\times 10^{38}\,\rm{erg\,s^{-1}}$ at 1234 days, the recently detected X-ray emission represents a $\ge 3.2\,\sigma$ (Gaussian equivalent) deviation from the universal post jet-break model that best fits the multi-wavelength afterglow at earlier times. In the context of JetFit afterglow models, current data represent a departure with statistical significance $\ge 3.1\,\sigma$, depending on the fireball collimation, with the most realistic models showing excesses at the level of $\ge 3.7\,\sigma$. A lack of detectable 3 GHz radio emission suggests a harder broad-band spectrum than the jet afterglow. These properties are consistent with the emergence of a new emission component such as synchrotron radiation from a mildly relativistic shock generated by the expanding merger ejecta, i.e. a kilonova afterglow. In this context, we present a set of ab-initio numerical-relativity BNS merger simulations that show that an X-ray excess supports the presence of a high-velocity tail in the merger ejecta, and argues against the prompt collapse of the merger remnant into a black hole. Radiation from accretion processes on the compact-object remnant represents a viable alternative. Neither a kilonova afterglow nor accretion-powered emission have been observed before, as detections of BNS mergers at this phase of evolution are unprecedented., Comment: 30 pages, 13 figures, Accepted for publication in ApJL

Stellar population studies provide unique clues to constrain galaxy formation models. So far, detailed studies based on absorption line strengths have mainly focused on the optical spectral range although many diagnostic features are present in other spectral windows. In particular, the near-infrared (NIR) can provide a wealth of information about stars, such as evolved giants, that have less evident optical signatures. Due to significant advances in NIR instrumentation and extension of spectral libraries and stellar population synthesis (SPS) models to this domain, it is now possible to perform in-depth studies of spectral features in the NIR to a high level of precision. In the present work, taking advantage of state-of-the-art SPS models covering the NIR spectral range, we introduce a new set of NIR indices constructed to be maximally sensitive to the main stellar population parameters, namely age, metallicity and initial mass function (IMF). We fully characterize the new indices against these parameters as well as their sensitivity to individual elemental abundance variations, velocity dispersion broadening, wavelength shifts, signal-to-noise ratio and flux calibration. We also present, for the first time, a method to ensure that the analysis of spectral indices is not affected by sky contamination, which is a major challenge when dealing with NIR spectroscopy. Moreover, we discuss two main applications: (i) the ability of some NIR spectral indices to constrain the shape of the low-mass IMF and (ii) current issues in the analysis of NIR spectral indices for future developments of SPS modelling., Comment: 38 pages, 23 figures, published in MNRAS

We develop an algorithm to train individually fair learning-to-rank (LTR) models. The proposed approach ensures items from minority groups appear alongside similar items from majority groups. This notion of fair ranking is based on the definition of individual fairness from supervised learning and is more nuanced than prior fair LTR approaches that simply ensure the ranking model provides underrepresented items with a basic level of exposure. The crux of our method is an optimal transport-based regularizer that enforces individual fairness and an efficient algorithm for optimizing the regularizer. We show that our approach leads to certifiably individually fair LTR models and demonstrate the efficacy of our method on ranking tasks subject to demographic biases., Comment: ICLR Camera-Ready Version

We present detailed radio observations of the tidal disruption event (TDE) AT2019dsg, obtained with the Very Large Array (VLA) and the Atacama Large Millimeter/submillimeter Array (ALMA), and spanning $55-560$ days post-disruption. We find that the peak brightness of the radio emission increases until ~200 days and subsequently begins to decrease steadily. Using the standard equipartition analysis, including the effects of synchrotron cooling as determined by the joint VLA-ALMA spectral energy distributions, we find that the outflow powering the radio emission is in roughly free expansion with a velocity of $\approx 0.07c$, while its kinetic energy increases by a factor of about 5 from 55 to 200 days and plateaus at $\approx 5\times 10^{48}$ erg thereafter. The ambient density traced by the outflow declines as $\approx R^{-1.6}$ on a scale of $\approx (1-4)\times 10^{16}$ cm ($\approx 6300-25000$ $R_s$), followed by a steeper decline to $\approx 6\times 10^{16}$ cm ($\approx 37500$ $R_s$). Allowing for a collimated geometry, we find that to reach even mildly relativistic velocities ($\Gamma=2$) the outflow requires an opening angle of $\theta_j\approx 2^\circ$, which is narrow even by the standards of GRB jets; a truly relativistic outflow requires an unphysically narrow jet. The outflow velocity and kinetic energy in AT2019dsg are typical of previous non-relativistic TDEs, and comparable to those from Type Ib/c supernovae, raising doubts about the claimed association with a high-energy neutrino event., Comment: Accepted to the Astrophysical Journal

We introduce a new method to estimate the probability that an extragalactic transient source is associated with a candidate host galaxy. This approach relies solely on simple observables: sky coordinates and their uncertainties, galaxy fluxes and angular sizes. The formalism invokes Bayes' rule to calculate the posterior probability P(O_i|x) from the galaxy prior P(O), observables x, and an assumed model for the true distribution of transients in/around their host galaxies. Using simulated transients placed in the well-studied COSMOS field, we consider several agnostic and physically motivated priors and offset distributions to explore the method sensitivity. We then apply the methodology to the set of 13~fast radio bursts (FRBs) localized with an uncertainty of several arcseconds. Our methodology finds nine of these are securely associated to a single host galaxy, P(O_i|x)>0.95. We examine the observed and intrinsic properties of these secure FRB hosts, recovering similar distributions as previous works. Furthermore, we find a strong correlation between the apparent magnitude of the securely identified host galaxies and the estimated cosmic dispersion measures of the corresponding FRBs, which results from the Macquart relation. Future work with FRBs will leverage this relation and other measures from the secure hosts as priors for future associations. The methodology is generic to transient type, localization error, and image quality. We encourage its application to other transients where host galaxy associations are critical to the science, e.g. gravitational wave events, gamma-ray bursts, and supernovae. We have encoded the technique in Python on GitHub: https://github.com/FRBs/astropath., Comment: In press, ApJ; comments still welcome; Visit https://github.com/FRBs/astropath to use and build PATH

GW190814 was a compact object binary coalescence detected in gravitational waves by Advanced LIGO and Advanced Virgo that garnered exceptional community interest due to its excellent localization and the uncertain nature of the binary's lighter-mass component (either the heaviest known neutron star, or the lightest known black hole). Despite extensive follow up observations, no electromagnetic counterpart has been identified. Here we present new radio observations of 75 galaxies within the localization volume at $\Delta t\approx 35-266$ days post-merger. Our observations cover $\sim32$% of the total stellar luminosity in the final localization volume and extend to later timescales than previously-reported searches, allowing us to place the deepest constraints to date on the existence of a radio afterglow from a highly off-axis relativistic jet launched during the merger (assuming that the merger occurred within the observed area). For a viewing angle of $\sim46^{\circ}$ (the best-fit binary inclination derived from the gravitational wave signal) and assumed electron and magnetic field energy fractions of $\epsilon_e=0.1$ and $\epsilon_B=0.01$, we can rule out a typical short gamma-ray burst-like Gaussian jet with isotropic-equivalent kinetic energy $2\times10^{51}$ erg propagating into a constant density medium $n\gtrsim0.01$ cm$^{-3}$. These are the first limits resulting from a galaxy-targeted search for a radio counterpart to a gravitational wave event, and we discuss the challenges, and possible advantages, of applying similar search strategies to future events using current and upcoming radio facilities., Comment: Accepted to ApJ; text and figures updated to match accepted version. 20 pages, 6 figures, 1 table

The gauge function, closely related to the atomic norm, measures the complexity of a statistical model, and has found broad applications in machine learning and statistical signal processing. In a high-dimensional learning problem, the gauge function attempts to safeguard against overfitting by promoting a sparse (concise) representation within the learning alphabet. In this work, within the context of linear inverse problems, we pinpoint the source of its success, but also argue that the applicability of the gauge function is inherently limited by its convexity, and showcase several learning problems where the classical gauge function theory fails. We then introduce a new notion of statistical complexity, gauge$_p$ function, which overcomes the limitations of the gauge function. The gauge$_p$ function is a simple generalization of the gauge function that can tightly control the sparsity of a statistical model within the learning alphabet and, perhaps surprisingly, draws further inspiration from the Burer-Monteiro factorization in computational mathematics. We also propose a new learning machine, with the building block of gauge$_p$ function, and arm this machine with a number of statistical guarantees. The potential of the proposed gauge$_p$ function theory is then studied for two stylized applications. Finally, we discuss the computational aspects and, in particular, suggest a tractable numerical algorithm for implementing the new learning machine.