Modeling galaxy formation in a cosmological context presents one of the greatest challenges in astrophysics today, due to the vast range of scales and numerous physical processes involved. Here we review the current status of models that employ two leading techniques to simulate the physics of galaxy formation: semi-analytic models and numerical hydrodynamic simulations. We focus on a set of observational targets that describe the evolution of the global and structural properties of galaxies from roughly Cosmic High Noon ($z\sim 2-3$) to the present. Although minor discrepancies remain, overall, models show remarkable convergence between different methods and make predictions that are in qualitative agreement with observations. Modelers seem to have converged on a core set of physical processes that are critical for shaping galaxy properties. This core set includes cosmological accretion, strong stellar-driven winds that are more efficient at low masses, black hole feedback that preferentially suppresses star formation at high masses, and structural and morphological evolution through merging and environmental processes. However, all cosmological models currently adopt phenomenological implementations of many of these core processes, which must be tuned to observations. Many details of how these diverse processes interact within a hierarchical structure formation setting remain poorly understood. Emerging multi-scale simulations are helping to bridge the gap between stellar and cosmological scales, placing models on a firmer, more physically grounded footing. Concurrently, upcoming telescope facilities will provide new challenges and constraints for models, particularly by directly constraining inflows and outflows through observations of gas in and around galaxies.

We study Hamiltonicity in the union of an $n$-vertex graph $H$ with high minimum degree and a binomial random graph on the same vertex set. In particular, we consider the case when $H$ has minimum degree close to $n/2$. We determine the perturbed threshold for Hamiltonicity in this setting. To be precise, let $\eta:= n/2-\delta(H)$. For $\eta=\omega(1)$, we show that it suffices to add $\Theta(\eta)$ random edges to $H$ to a.a.s. obtain a Hamiltonian graph; for $\eta=\Theta(1)$, we show that $\omega(1)$ edges suffice. In fact, when $\eta=o(n)$ and $\eta=\omega(1)$, we show that $(8+o(1))\eta$ random edges suffice, which is best possible up to the error term. This determines the sharp perturbed threshold for Hamiltonicity in this range of degrees. We also obtain analogous results for perfect matchings, showing that, in this range of degrees, the sharp perturbed thresholds for Hamiltonicity and for perfect matchings differ by a factor of $2$.

We take a step towards addressing the under-representation of the African continent in NLP research by creating the first large publicly available high-quality dataset for named entity recognition (NER) in ten African languages, bringing together a variety of stakeholders. We detail characteristics of the languages to help researchers understand the challenges that these languages pose for NER. We analyze our datasets and conduct an extensive empirical evaluation of state-of-the-art methods across both supervised and transfer learning settings. We release the data, code, and models in order to inspire future research on African NLP.

Retinal blood vessel segmentation can extract clinically relevant information from fundus images. As manual tracing is cumbersome, algorithms based on Convolution Neural Networks have been developed. Such studies have used small publicly available datasets for training and measuring performance, running the risk of overfitting. Here, we provide a rigorous benchmark for various architectural and training choices commonly used in the literature on the largest dataset published to date. We train and evaluate five published models on the publicly available FIVES fundus image dataset, which exceeds previous ones in size and quality and which contains also images from common ophthalmological conditions (diabetic retinopathy, age-related macular degeneration, glaucoma). We compare the performance of different model architectures across different loss functions, levels of image qualitiy and ophthalmological conditions and assess their ability to perform well in the face of disease-induced domain shifts. Given sufficient training data, basic architectures such as U-Net perform just as well as more advanced ones, and transfer across disease-induced domain shifts typically works well for most architectures. However, we find that image quality is a key factor determining segmentation outcomes. When optimizing for segmentation performance, investing into a well curated dataset to train a standard architecture yields better results than tuning a sophisticated architecture on a smaller dataset or one with lower image quality. We distilled the utility of architectural advances in terms of their clinical relevance therefore providing practical guidance for model choices depending on the circumstances of the clinical setting

Uncertainty estimation is critical for reliable medical image segmentation, particularly in retinal vessel analysis, where accurate predictions are essential for diagnostic applications. Deep Ensembles, where multiple networks are trained individually, are widely used to improve medical image segmentation performance. However, training and testing costs increase with the number of ensembles. In this work, we propose Ensemble Distillation as a robust alternative to commonly used uncertainty estimation techniques by distilling the knowledge of multiple ensemble models into a single model. Through extensive experiments on the DRIVE and FIVES datasets, we demonstrate that Ensemble Distillation achieves comparable performance via calibration and segmentation metrics, while significantly reducing computational complexity. These findings suggest that Ensemble distillation provides an efficient and reliable approach for uncertainty estimation in the segmentation of the retinal vessels, making it a promising tool for medical imaging applications.

Dynamic resource allocation in heterogeneous wireless networks (HetNets) is challenging for traditional methods under varying user loads and channel conditions. We propose a deep reinforcement learning (DRL) framework that jointly optimises transmit power, bandwidth, and scheduling via a multi-objective reward balancing throughput, energy efficiency, and fairness. Using real base station coordinates, we compare Proximal Policy Optimisation (PPO) and Twin Delayed Deep Deterministic Policy Gradient (TD3) against three heuristic algorithms in multiple network scenarios. Our results show that DRL frameworks outperform heuristic algorithms in optimising resource allocation in dynamic networks. These findings highlight key trade-offs in DRL design for future HetNets.

Numerical simulations are a versatile tool providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant force on large scales. To date, a century after the formulation of general relativity, numerical codes for structure formation still employ Newton's law of gravitation. This approximation relies on the two assumptions that gravitational fields are weak and that they are only sourced by non-relativistic matter. While the former appears well justified on cosmological scales, the latter imposes restrictions on the nature of the "dark" components of the Universe (dark matter and dark energy) which are, however, poorly understood. Here we present the first simulations of cosmic structure formation using equations consistently derived from general relativity. We study in detail the small relativistic effects for a standard {\Lambda}CDM cosmology which cannot be obtained within a purely Newtonian framework. Our particle-mesh N-body code computes all six degrees of freedom of the metric and consistently solves the geodesic equation for particles, taking into account the relativistic potentials and the frame-dragging force. This conceptually clean approach is very general and can be applied to various settings where the Newtonian approximation fails or becomes inaccurate, ranging from simulations of models with dynamical dark energy or warm/hot dark matter to core collapse supernova explosions.

The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a new 400-800MHz radio interferometer under development for deployment in South Africa. HIRAX will comprise 1024 six meter parabolic dishes on a compact grid and will map most of the southern sky over the course of four years. HIRAX has two primary science goals: to constrain Dark Energy and measure structure at high redshift, and to study radio transients and pulsars. HIRAX will observe unresolved sources of neutral hydrogen via their redshifted 21-cm emission line (`hydrogen intensity mapping'). The resulting maps of large-scale structure at redshifts 0.8-2.5 will be used to measure Baryon Acoustic Oscillations (BAO). HIRAX will improve upon current BAO measurements from galaxy surveys by observing a larger cosmological volume (larger in both survey area and redshift range) and by measuring BAO at higher redshift when the expansion of the universe transitioned to Dark Energy domination. HIRAX will complement CHIME, a hydrogen intensity mapping experiment in the Northern Hemisphere, by completing the sky coverage in the same redshift range. HIRAX's location in the Southern Hemisphere also allows a variety of cross-correlation measurements with large-scale structure surveys at many wavelengths. Daily maps of a few thousand square degrees of the Southern Hemisphere, encompassing much of the Milky Way galaxy, will also open new opportunities for discovering and monitoring radio transients. The HIRAX correlator will have the ability to rapidly and eXperimentciently detect transient events. This new data will shed light on the poorly understood nature of fast radio bursts (FRBs), enable pulsar monitoring to enhance long-wavelength gravitational wave searches, and provide a rich data set for new radio transient phenomena searches. This paper discusses the HIRAX instrument, science goals, and current status.

Neural Machine Translation models are extremely data and compute-hungry. However, not all data points contribute equally to model training and generalization. Data pruning to remove the low-value data points has the benefit of drastically reducing the compute budget without significant drop in model performance. In this paper, we propose a new data pruning technique: Checkpoints Across Time (CAT), that leverages early model training dynamics to identify the most relevant data points for model performance. We benchmark CAT against several data pruning techniques including COMET-QE, LASER and LaBSE. We find that CAT outperforms the benchmarks on Indo-European languages on multiple test sets. When applied to English-German, English-French and English-Swahili translation tasks, CAT achieves comparable performance to using the full dataset, while pruning up to 50% of training data. We inspect the data points that CAT selects and find that it tends to favour longer sentences and sentences with unique or rare words.

Radio weak lensing, while a highly promising complementary probe to optical weak lensing, will require incredible precision in the measurement of galaxy shape parameters. In this paper, we extend the Bayesian Inference for Radio Observations model fitting approach to measure galaxy shapes directly from visibility data of radio continuum surveys, instead of from image data. We apply a Hamiltonian Monte Carlo (HMC) technique for sampling the posterior, which is more efficient than the standard Monte Carlo Markov Chain method when dealing with a large dimensional parameter space. Adopting the exponential profile for galaxy model fitting allows us to analytically calculate the likelihood gradient required by HMC, allowing a faster and more accurate sampling. The method is tested on SKA1-MID simulated observations at 1.4 GHz of a field containing up to 1000 star-forming galaxies. It is also applied to a simulated observation of the weak lensing precursor survey SuperCLASS. In both cases we obtain reliable measurements of the galaxies' ellipticity and size for all sources with SNR $\ge 10$, and we also find relationships between the convergence properties of the HMC technique and some source parameters. Direct shape measurement in the visibility domain achieves high accuracy at the expected source number densities of the current and next SKA precursor continuum surveys. The proposed method can be easily extended for the fitting of other galaxy and scientific parameters, as well as simultaneously marginalising over systematic and instrumental effects.

We present the full Hubble diagram of photometrically-classified Type Ia supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN). DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic redshifts of 7,000 host galaxies. Based on the light-curve quality, we select 1635 photometrically-identified SNe Ia with spectroscopic redshift 0.10< z <1.13, which is the largest sample of supernovae from any single survey and increases the number of known z>0.5 supernovae by a factor of five. In a companion paper, we present cosmological results of the DES-SN sample combined with 194 spectroscopically-classified SNe Ia at low redshift as an anchor for cosmological fits. Here we present extensive modeling of this combined sample and validate the entire analysis pipeline used to derive distances. We show that the statistical and systematic uncertainties on cosmological parameters are $\sigma_{\Omega_M,{\rm stat+sys}}^{\Lambda{\rm CDM}}=$0.017 in a flat $\Lambda$CDM model, and $(\sigma_{\Omega_M},\sigma_w)_{\rm stat+sys}^{w{\rm CDM}}=$(0.082, 0.152) in a flat $w$CDM model. Combining the DES SN data with the highly complementary CMB measurements by Planck Collaboration (2020) reduces uncertainties on cosmological parameters by a factor of 4. In all cases, statistical uncertainties dominate over systematics. We show that uncertainties due to photometric classification make up less than 10% of the total systematic uncertainty budget. This result sets the stage for the next generation of SN cosmology surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time.

The management of future AI-native Next-Generation (NextG) Radio Access Networks (RANs), including 6G and beyond, presents a challenge of immense complexity that exceeds the capabilities of traditional automation. In response, we introduce the concept of the LLM-RAN Operator. In this paradigm, a Large Language Model (LLM) is embedded into the RAN control loop to translate high-level human intents into optimal network actions. Unlike prior empirical studies, we present a formal framework for an LLM-RAN operator that builds on earlier work by making guarantees checkable through an adapter aligned with the Open RAN (O-RAN) standard, separating strategic LLM-driven guidance in the Non-Real-Time (RT) RAN intelligent controller (RIC) from reactive execution in the Near-RT RIC, including a proposition on policy expressiveness and a theorem on convergence to stable fixed points. By framing the problem with mathematical rigor, our work provides the analytical tools to reason about the feasibility and stability of AI-native RAN control. It identifies critical research challenges in safety, real-time performance, and physical-world grounding. This paper aims to bridge the gap between AI theory and wireless systems engineering in the NextG era, aligning with the AI4NextG vision to develop knowledgeable, intent-driven wireless networks that integrate generative AI into the heart of the RAN.

New time-domain surveys, such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), will observe millions of transient alerts each night, making standard approaches of visually identifying new and interesting transients infeasible. We present two novel methods of automatically detecting anomalous transient light curves in real-time. Both methods are based on the simple idea that if the light curves from a known population of transients can be accurately modelled, any deviations from model predictions are likely anomalies. The first modelling approach is a probabilistic neural network built using Temporal Convolutional Networks (TCNs) and the second is an interpretable Bayesian parametric model of a transient. We demonstrate our methods' ability to provide anomaly scores as a function of time on light curves from the Zwicky Transient Facility. We show that the flexibility of neural networks, the attribute that makes them such a powerful tool for many regression tasks, is what makes them less suitable for anomaly detection when compared with our parametric model. The parametric model is able to identify anomalies with respect to common supernova classes with high precision and recall scores, achieving area under the precision-recall curves (AUCPR) above 0.79 for most rare classes such as kilonovae, tidal disruption events, intermediate luminosity transients, and pair-instability supernovae. Our ability to identify anomalies improves over the lifetime of the light curves. Our framework, used in conjunction with transient classifiers, will enable fast and prioritised followup of unusual transients from new large-scale surveys.

This study presents a mathematical model formulated as a system of first-order non-linear ordinary differential equations, aimed at examining the effects of different factors, classified as local and systemic factors on a wound healing process. Specifically, the model incorporates pathogens, inflammatory cells, fibroblast cells, collagen, and the initial wound size. The variables utilized in the model lack specific units since they represent combined responses of different cell types. As such, these variables serve as indicators of the relative behaviors of these cellular populations. The feasibility of the model solution is examined through the demonstration of its positivity. A threshold, denoted $R_w$, is established to determine the conditions necessary for the existence of a wound-free equilibrium. Sensitivity analysis is carried out to determine the contribution of parameters to the behavior of fibroblast cells and $R_w$, which are crucial to the wound healing process. Through numerical simulations, it is demonstrated that factors such as oxygen levels, pathogen activity, inflammatory cell activity, age, smoking, alcoholism, and stress exert considerable influence on the behaviors of these cells, thereby contributing to delayed wound healing and the occurrence of chronic wounds.

Language-agnostic sentence embeddings generated by pre-trained models such as LASER and LaBSE are attractive options for mining large datasets to produce parallel corpora for low-resource machine translation. We test LASER and LaBSE in extracting bitext for two related low-resource African languages: Luhya and Swahili. For this work, we created a new parallel set of nearly 8000 Luhya-English sentences which allows a new zero-shot test of LASER and LaBSE. We find that LaBSE significantly outperforms LASER on both languages. Both LASER and LaBSE however perform poorly at zero-shot alignment on Luhya, achieving just 1.5% and 22.0% successful alignments respectively (P@1 score). We fine-tune the embeddings on a small set of parallel Luhya sentences and show significant gains, improving the LaBSE alignment accuracy to 53.3%. Further, restricting the dataset to sentence embedding pairs with cosine similarity above 0.7 yielded alignments with over 85% accuracy.

This paper reviews the topological groundwork for the study of reinforcement learning (RL) by focusing on the structure of state, action, and policy spaces. We begin by recalling key mathematical concepts such as complete metric spaces, which form the foundation for expressing RL problems. By leveraging the Banach contraction principle, we illustrate how the Banach fixed-point theorem explains the convergence of RL algorithms and how Bellman operators, expressed as operators on Banach spaces, ensure this convergence. The work serves as a bridge between theoretical mathematics and practical algorithm design, offering new approaches to enhance the efficiency of RL. In particular, we investigate alternative formulations of Bellman operators and demonstrate their impact on improving convergence rates and performance in standard RL environments such as MountainCar, CartPole, and Acrobot. Our findings highlight how a deeper mathematical understanding of RL can lead to more effective algorithms for decision-making problems.

Multi-view data from the same source often exhibit correlation. This is mirrored in correlation between the latent spaces of separate variational autoencoders (VAEs) trained on each data-view. A multi-view VAE approach is proposed that incorporates a joint prior with a non-zero correlation structure between the latent spaces of the VAEs. By enforcing such correlation structure, more strongly correlated latent spaces are uncovered. Using conditional distributions to move between these latent spaces, missing views can be imputed and used for downstream analysis. Learning this correlation structure involves maintaining validity of the prior distribution, as well as a successful parameterization that allows end-to-end learning.