Q-linear convergence of AGN represents a substantial enhancement over the convergence of the existing methods for the overparameterized non-convex LRMS.

Q-linear convergence of AGN represents a substantial enhancement over the convergence of the existing methods for the overparameterized non-convex LRMS.

A \emph{bidding} game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the higher bidder moves the token, and pays the bid to the lower bidder. We focus on \emph{discrete}-bidding, which are motivated by practical applications and restrict the granularity of the players' bids, e.g, bids must be given in cents. We study, for the first time, discrete-bidding games with {\em mean-payoff} and {\em energy} objectives. In contrast, mean-payoff {\em continuous}-bidding games (i.e., no granularity restrictions) are understood and exhibit a rich mathematical structure. The {\em threshold} budget is a necessary and sufficient initial budget for winning an energy game or guaranteeing a target payoff in a mean-payoff game. We first establish existence of threshold budgets; a non-trivial property due to the concurrent moves of the players. Moreover, we identify the structure of the thresholds, which is key in obtaining compact strategies, and in turn, showing that finding threshold is in \NP~and \coNP even in succinctly-represented games.

Active Galactic Nuclei (AGNs) are among the most luminous objects in the universe, making them valuable probes for studying galaxy evolution. However, understanding how AGN properties evolve over cosmic time remains a fundamental challenge. This study investigates whether AGNs at low redshift (nearby) can serve as proxies for their high-redshift (distant) counterparts by identifying spectral 'doppelgängers', AGNs with remarkably similar emission line properties despite being separated by vast cosmic distances. We analyze key spectral features of bona fide AGNs using the Sloan Digital Sky Survey's Data Release 16, including continuum and emission lines: Nitrogen (N V), Carbon (C IV), Magnesium (Mg II), Hydrogen-beta (H$β$), and Iron (Fe II - optical and UV) emission lines. We incorporated properties such as equivalent width, velocity dispersion in the form of full width at half maximum (FWHM), and continuum luminosities (135nm, 300nm, and 510nm) closest to these prominent lines. Our initial findings suggest the existence of multiple AGNs with highly similar spectra, hinting at the possibility that local AGNs may indeed share intrinsic properties with high-redshift ones. We showcase here one of the better candidate pairs of AGNs resulting from our analyses.

Galaxies are often modelled as composites of separable components with distinct spectral signatures, implying that different wavelength ranges are only weakly correlated. They are not. We present a data-driven model which exploits subtle correlations between physical processes to accurately predict infrared (IR) WISE photometry from a neural summary of optical SDSS spectra. The model achieves accuracies of $\chi^2_N \approx 1$ for all photometric bands in WISE, as well as good colors. We are also able to tightly constrain typically IR-derived properties, e.g. the bolometric luminosities of AGN and dust parameters such as $\mathrm{q_{PAH}}$. We find that current SED-fitting methods are incapable of making comparable predictions, and that model misspecification often leads to correlated biases in star-formation rates and AGN luminosities. To help improve SED models, we determine what features of the optical spectrum are responsible for our improved predictions, and identify several lines (CaII, SrII, FeI, [OII] and H$\alpha$), which point to the complex chronology of star formation and chemical enrichment being incorrectly modelled.

In the case of Type-2 AGNs, estimating the mass of the black hole is challenging. Understanding how galaxies form and evolve requires considerable insight into the mass of black holes. This work compared different classical and quantum machine learning (QML) algorithms for black hole mass estimation, wherein the classical algorithms are Linear Regression, XGBoost Regression, Random Forest Regressor, Support Vector Regressor (SVR), Lasso Regression, Ridge Regression, Elastic Net Regression, Bayesian Regression, Decision Tree Regressor, Gradient Booster Regressor, Classical Neural Networks, Gated Recurrent Unit (GRU), LSTM, Deep Residual Networks (ResNets) and Transformer-Based Regression. On the other hand, quantum algorithms including Hybrid Quantum Neural Networks (QNN), Quantum Long Short-Term Memory (Q-LSTM), Sampler-QNN, Estimator-QNN, Variational Quantum Regressor (VQR), Quantum Linear Regression(Q-LR), QML with JAX optimization were also tested. The results revealed that classical algorithms gave better R^2, MAE, MSE, and RMSE results than the quantum models. Among the classical models, LSTM has the best result with an accuracy of 99.77%. Estimator-QNN has the highest accuracy for quantum algorithms with an MSE of 0.0124 and an accuracy of 99.75%. This study ascertains both the strengths and weaknesses of the classical and the quantum approaches. As far as our knowledge goes, this work could pave the way for the future application of quantum algorithms in astrophysical data analysis.

Computing photo-z for AGN is challenging, primarily due to the interplay of relative emissions associated with the SMBH and its host galaxy. SED fitting methods, effective in pencil-beam surveys, face limitations in all-sky surveys with fewer bands available, lacking the ability to capture the AGN contribution to the SED accurately. This limitation affects the many 10s of millions of AGN clearly singled out and identified by SRG/eROSITA. Our goal is to significantly enhance photometric redshift performance for AGN in all-sky surveys while avoiding the need to merge multiple data sets. Instead, we employ readily available data products from the 10th Data Release of the Imaging Legacy Survey for DESI, covering > 20,000 deg$^{2}$ with deep images and catalog-based photometry in the grizW1-W4 bands. We introduce PICZL, a machine-learning algorithm leveraging an ensemble of CNNs. Utilizing a cross-channel approach, the algorithm integrates distinct SED features from images with those obtained from catalog-level data. Full probability distributions are achieved via the integration of Gaussian mixture models. On a validation sample of 8098 AGN, PICZL achieves a variance $\sigma_{\textrm{NMAD}}$ of 4.5% with an outlier fraction $\eta$ of 5.6%, outperforming previous attempts to compute accurate photo-z for AGN using ML. We highlight that the model's performance depends on many variables, predominantly the depth of the data. A thorough evaluation of these dependencies is presented in the paper. Our streamlined methodology maintains consistent performance across the entire survey area when accounting for differing data quality. The same approach can be adopted for future deep photometric surveys such as LSST and Euclid, showcasing its potential for wide-scale realisation. With this paper, we release updated photo-z (including errors) for the XMM-SERVS W-CDF-S, ELAIS-S1 and LSS fields.

Large language models (LLMs) generate diverse, situated, persuasive texts from a plurality of potential perspectives, influenced heavily by their prompts and training data. As part of LLM adoption, we seek to characterize - and ideally, manage - the socio-cultural values that they express, for reasons of safety, accuracy, inclusion, and cultural fidelity. We present a validated approach to automatically (1) extracting heterogeneous latent value propositions from texts, (2) assessing resonance and conflict of values with texts, and (3) combining these operations to characterize the pluralistic value alignment of human-sourced and LLM-sourced textual data.

The automatic classification of X-ray detections is a necessary step in extracting astrophysical information from compiled catalogs of astrophysical sources. Classification is useful for the study of individual objects, statistics for population studies, as well as for anomaly detection, i.e., the identification of new unexplored phenomena, including transients and spectrally extreme sources. Despite the importance of this task, classification remains challenging in X-ray astronomy due to the lack of optical counterparts and representative training sets. We develop an alternative methodology that employs an unsupervised machine learning approach to provide probabilistic classes to Chandra Source Catalog sources with a limited number of labeled sources, and without ancillary information from optical and infrared catalogs. We provide a catalog of probabilistic classes for 8,756 sources, comprising a total of 14,507 detections, and demonstrate the success of the method at identifying emission from young stellar objects, as well as distinguishing between small-scale and large-scale compact accretors with a significant level of confidence. We investigate the consistency between the distribution of features among classified objects and well-established astrophysical hypotheses such as the unified AGN model. This provides interpretability to the probabilistic classifier. Code and tables are available publicly through GitHub. We provide a web playground for readers to explore our final classification at https://umlcaxs-playground.streamlit.app.