General-purpose large language models (LLMs), despite their broad capabilities, often struggle with specialized domain knowledge. This gap hinders their deployment as reliable research agents in demanding fields such as astronomy. Building on our prior work with AstroSage-Llama-3.1-8B, this study introduces AstroSage-Llama-3.1-70B, a 70-billion parameter domain-specialized natural-language AI assistant. It is designed for research and education across astronomy, astrophysics, space science, astroparticle physics, cosmology, and astronomical instrumentation. Developed from the Meta-Llama-3.1-70B foundation, AstroSage-Llama-3.1-70B underwent extensive continued pre-training (CPT) on a vast corpus of astronomical literature, followed by supervised fine-tuning (SFT) and model merging. We integrated reasoning chains into the SFT dataset, enabling AstroSage-Llama-3.1-70B to either answer the user query immediately, or first emit a human-readable thought process. Evaluated on a validated subset of 3,846 questions from the AstroMLab-1 benchmark (Ting et al., 2024) -- derived from literature withheld during training -- AstroSage-Llama-3.1-70B achieves top-tier performance (89.0%), matching GPT-5.2, Claude-4.5-Opus, and Gemini-3-Pro while being more cost-efficient. This work demonstrates that domain specialization, when applied to large-scale models, can enable them to outperform generalist counterparts in specialized knowledge areas like astronomy, thereby advancing the frontier of AI capabilities in the field.

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable, which is crucial for determining an individual's potential to further spread the infection. While final statuses are hidden, intermediate indicators such as symptoms of infection are observable and provide useful representations of the underlying diffusion process. We propose a partial observability-aware Machine Learning framework to learn the characteristics of the spreading model. We term the method Distribution Classification, which utilizes the power of classifiers to infer the underlying transmission dynamics. Through extensive benchmarking against Approximate Bayesian Computation and GNN-based baselines, our framework consistently outperforms these state-of-the-art methods, delivering accurate parameter estimates across diverse diffusion settings while scaling efficiently to large networks. We validate the method on synthetic networks and extend the study to a real-world insider trading network, demonstrating its effectiveness in analyzing spreading phenomena where direct observation of individual statuses is not possible.

IoT networks often face conflicting routing goals such as maximizing packet delivery, minimizing delay, and conserving limited battery energy. These priorities can also change dynamically: for example, an emergency alert requires high reliability, while routine monitoring prioritizes energy efficiency to prolong network lifetime. Existing works, including many deep reinforcement learning approaches, are typically centralized and assume static objectives, making them slow to adapt when preferences shift. We propose a dynamic and fully distributed multi-objective Q-learning routing algorithm that learns multiple per-preference Q-tables in parallel and introduces a novel greedy interpolation policy to act near-optimally for unseen preferences without retraining or central coordination. A theoretical analysis further shows that the optimal value function is Lipschitz-continuous in the preference parameter, ensuring that the proposed greedy interpolation policy yields provably near-optimal behavior. Simulations show that our approach adapts in real time to shifting priorities and achieves up to 80-90\% lower energy consumption and more than 2-5x higher cumulative rewards and packet delivery compared to six baseline protocols, under dynamic and distributed settings. Sensitivity analysis across varying preference window lengths confirms that the proposed DPQ framework consistently achieves higher composite reward than all baseline methods, demonstrating robustness to changes in operating conditions.

Exploration remains a fundamental challenge in reinforcement learning, as many existing methods either lack theoretical guarantees or fall short in practical effectiveness. In this paper, we propose CAE, i.e., the Critic as an Explorer, a lightweight approach that repurposes the value networks in standard deep RL algorithms to drive exploration, without introducing additional parameters. CAE leverages multi-armed bandit techniques combined with a tailored scaling strategy, enabling efficient exploration with provable sub-linear regret bounds and strong empirical stability. Remarkably, it is simple to implement, requiring only about 10 lines of code. For complex tasks where learning reliable value networks is difficult, we introduce CAE+, an extension of CAE that incorporates an auxiliary network. CAE+ increases the parameter count by less than 1% while preserving implementation simplicity, adding roughly 10 additional lines of code. Extensive experiments on MuJoCo, MiniHack, and Habitat validate the effectiveness of CAE and CAE+, highlighting their ability to unify theoretical rigor with practical efficiency.

Recent developments in large language models (LLMs) have facilitated autonomous AI agents capable of imitating human-generated content, raising fundamental questions about how AI may reshape democratic information environments such as news. We develop a large-scale simulation framework to examine the system-level effects of AI-based imitation, using the full population of Danish digital news articles published in 2022. Varying imitation strategies and AI prevalence across information environments with different baseline structures, we show that the effects of AI-driven imitation are strongly context-dependent: imitating AI agents increase semantic diversity in initially homogeneous environments but can reduce diversity in heterogeneous ones. This pattern is qualitatively consistent across multiple LLMs. However, this diversity arises primarily through stylistic differentiation and variance compression rather than factual enrichment, as AI-generated articles tend to omit information while remaining semantically distinct. These findings indicate that AI-driven imitation produces ambivalent transformations of information environments that may shape collective intelligence in democratic societies.

Machine learning algorithms permeate the day-to-day aspects of our lives and therefore studying the fairness of these algorithms before implementation is crucial. One way in which bias can manifest in a dataset is through missing values. Missing data are often assumed to be missing completely randomly; in reality the propensity of data being missing is often tied to the demographic characteristics of individuals. There is limited research into how missing values and the handling thereof can impact the fairness of an algorithm. Most researchers either apply listwise deletion or tend to use simpler methods of imputation (e.g. mean or mode) compared to more advanced approaches (e.g. multiple imputation). This study considers the fairness of various classification algorithms after a range of missing data handling strategies is applied. Missing values are generated (i.e. amputed) in three popular datasets for classification fairness, by creating a high percentage of missing values using three missing data mechanisms. The results show that the missing data mechanism does not significantly impact fairness; across the missing data handling techniques listwise deletion gives the highest fairness on average and amongst the classification algorithms random forests leads to the highest fairness on average. The interaction effect of the missing data handling technique and the classification algorithm is also often significant.

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited. GNNs can encounter difficulties in gathering information from nodes that are far apart by iterated aggregation steps. This situation is partly caused by so-called oversmoothing; and overcoming it is one of the practically motivated challenges. We consider the situation where information is aggregated by multiple steps of convolution, leading to graph convolutional networks (GCNs). We analyze the generalization performance of a basic GCN, trained for node classification on data generated by the contextual stochastic block model. We predict its asymptotic performance by deriving the free energy of the problem, using the replica method, in the high-dimensional limit. Calling depth the number of convolutional steps, we show the importance of going to large depth to approach the Bayes-optimality. We detail how the architecture of the GCN has to scale with the depth to avoid oversmoothing. The resulting large depth limit can be close to the Bayes-optimality and leads to a continuous GCN. Technically, we tackle this continuous limit via an approach that resembles dynamical mean-field theory (DMFT) with constraints at the initial and final times. An expansion around large regularization allows us to solve the corresponding equations for the performance of the deep GCN. This promising tool may contribute to the analysis of further deep neural networks.

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By complying with physical laws, PINNs provide advantages over purely data-driven models in limited-data regimes and present as a promising route towards Physical AI. This feature has propelled them to the forefront of scientific machine learning, a domain characterized by scarce and costly data. However, the vision of accurate physics-informed learning comes with significant challenges. This work examines PINNs in terms of model optimization and generalization, shedding light on the need for new algorithmic advances to overcome issues pertaining to the training speed, precision, and generalizability of today's PINN models. Of particular interest are gradient-free evolutionary algorithms (EAs) for optimizing the uniquely complex loss landscapes arising in PINN training. Methods synergizing gradient descent and EAs for discovering bespoke neural architectures and balancing multiple terms in physics-informed learning objectives are positioned as important avenues for future research. Another exciting track is to cast EAs as a meta-learner of generalizable PINN models. To substantiate these proposed avenues, we further highlight results from recent literature to showcase the early success of such approaches in addressing the aforementioned challenges in PINN optimization and generalization.

Causal inference in observational studies with high-dimensional covariates presents significant challenges. We introduce CausalBGM, an AI-powered Bayesian generative modeling approach that captures the causal relationship among covariates, treatment, and outcome. The core innovation is to estimate the individual treatment effect (ITE) by learning the individual-specific distribution of a low-dimensional latent feature set (e.g., latent confounders) that drives changes in both treatment and outcome. This individualized posterior representation yields estimates of the individual treatment effect (ITE) together with well-calibrated posterior intervals while mitigating confounding effect. CausalBGM is fitted through an iterative algorithm to update the model parameters and the latent features until convergence. This framework leverages the power of AI to capture complex dependencies among variables while adhering to the Bayesian principles. Extensive experiments demonstrate that CausalBGM consistently outperforms state-of-the-art methods, particularly in scenarios with high-dimensional covariates and large-scale datasets. By addressing key limitations of existing methods, CausalBGM emerges as a robust and promising framework for advancing causal inference in a wide range of modern applications. The code for CausalBGM is available at https://github.com/liuq-lab/bayesgm. The document for using CausalBGM is available at https://bayesgm.readthedocs.io.

Website fingerprinting (WF) attacks, which covertly monitor user communications to identify the web pages they visit, pose a serious threat to user privacy. Existing WF defenses attempt to reduce attack accuracy by disrupting traffic patterns, but attackers can retrain their models to adapt, making these defenses ineffective. Meanwhile, their high overhead limits deployability. To overcome these limitations, we introduce a novel controllable website fingerprinting defense called TrapFlow based on backdoor learning. TrapFlow exploits the tendency of neural networks to memorize subtle patterns by injecting crafted trigger sequences into targeted website traffic, causing the attacker model to build incorrect associations during training. If the attacker attempts to adapt by training on such noisy data, TrapFlow ensures that the model internalizes the trigger as a dominant feature, leading to widespread misclassification across unrelated websites. Conversely, if the attacker ignores these patterns and trains only on clean data, the trigger behaves as an adversarial patch at inference time, causing model misclassification. To achieve this dual effect, we optimize the trigger using a Fast Levenshtein like distance to maximize both its learnability and its distinctiveness from normal traffic. Experiments show that TrapFlow significantly reduces the accuracy of the RF attack from 99 percent to 6 percent with 74 percent data overhead. This compares favorably against two state of the art defenses: FRONT reduces accuracy by only 2 percent at a similar overhead, while Palette achieves 32 percent accuracy but with 48 percent more overhead. We further validate the practicality of our method in a real Tor network environment.

Physics-informed neural networks (PINNs) are at the forefront of scientific machine learning, making possible the creation of machine intelligence that is cognizant of physical laws and able to accurately simulate them. However, today's PINNs are often trained for a single physics task and require computationally expensive re-training for each new task, even for tasks from similar physics domains. To address this limitation, this paper proposes a pioneering approach to advance the generalizability of PINNs through the framework of Baldwinian evolution. Drawing inspiration from the neurodevelopment of precocial species that have evolved to learn, predict and react quickly to their environment, we envision PINNs that are pre-wired with connection strengths inducing strong biases towards efficient learning of physics. A novel two-stage stochastic programming formulation coupling evolutionary selection pressure (based on proficiency over a distribution of physics tasks) with lifetime learning (to specialize on a sampled subset of those tasks) is proposed to instantiate the Baldwin effect. The evolved Baldwinian-PINNs demonstrate fast and physics-compliant prediction capabilities across a range of empirically challenging problem instances with more than an order of magnitude improvement in prediction accuracy at a fraction of the computation cost compared to state-of-the-art gradient-based meta-learning methods. For example, when solving the diffusion-reaction equation, a 70x improvement in accuracy was obtained while taking 700x less computational time. This paper thus marks a leap forward in the meta-learning of PINNs as generalizable physics solvers. Sample codes are available at https://github.com/chiuph/Baldwinian-PINN.

Modern biomedical image analysis using deep learning often encounters the challenge of limited annotated data. To overcome this issue, deep generative models can be employed to synthesize realistic biomedical images. In this regard, we propose an image synthesis method that utilizes denoising diffusion probabilistic models (DDPMs) to automatically generate retinal optical coherence tomography (OCT) images. By providing rough layer sketches, the trained DDPMs can generate realistic circumpapillary OCT images. We further find that more accurate pseudo labels can be obtained through knowledge adaptation, which greatly benefits the segmentation task. Through this, we observe a consistent improvement in layer segmentation accuracy, which is validated using various neural networks. Furthermore, we have discovered that a layer segmentation model trained solely with synthesized images can achieve comparable results to a model trained exclusively with real images. These findings demonstrate the promising potential of DDPMs in reducing the need for manual annotations of retinal OCT images.

From deciding on a PhD program to buying a new camera, unfamiliar decisions--decisions without domain knowledge--are frequent and significant. The complexity and uncertainty of such decisions demand unique approaches to information seeking, understanding, and decision-making. Our formative study highlights that users want to start by discovering broad and relevant domain information evenly and simultaneously, quickly address emerging inquiries, and gain personalized standards to assess information found. We present ChoiceMates, an interactive multi-agent system designed to address these needs by enabling users to engage with a dynamic set of LLM agents each presenting a unique experience in the domain. Unlike existing multi-agent systems that automate tasks with agents, the user orchestrates agents to assist their decision-making process. Our user evaluation (n=12) shows that ChoiceMates enables a more confident, satisfactory decision-making with better situation understanding than web search, and higher decision quality and confidence than a commercial multi-agent framework. This work provides insights into designing a more controllable and collaborative multi-agent system.

This study uses domain randomization to generate a synthetic RGB-D dataset for training multimodal instance segmentation models, aiming to achieve colour-agnostic hand localization in cluttered industrial environments. Domain randomization is a simple technique for addressing the "reality gap" by randomly rendering unrealistic features in a simulation scene to force the neural network to learn essential domain features. We provide a new synthetic dataset for various hand detection applications in industrial environments, as well as ready-to-use pretrained instance segmentation models. To achieve robust results in a complex unstructured environment, we use multimodal input that includes both colour and depth information, which we hypothesize helps to improve the accuracy of the model prediction. In order to test this assumption, we analyze the influence of each modality and their synergy. The evaluated models were trained solely on our synthetic dataset; yet we show that our approach enables the models to outperform corresponding models trained on existing state-of-the-art datasets in terms of Average Precision and Probability-based Detection Quality.

We propose a neural network-based framework to optimize the perceptions simulated by the in silico retinal implant model pulse2percept. The overall pipeline consists of a trainable encoder, a pre-trained retinal implant model and a pre-trained evaluator. The encoder is a U-Net, which takes the original image and outputs the stimulus. The pre-trained retinal implant model is also a U-Net, which is trained to mimic the biomimetic perceptual model implemented in pulse2percept. The evaluator is a shallow VGG classifier, which is trained with original images. Based on 10,000 test images from the MNIST dataset, we show that the convolutional neural network-based encoder performs significantly better than the trivial downsampling approach, yielding a boost in the weighted F1-Score by 36.17% in the pre-trained classifier with 6x10 electrodes. With this fully neural network-based encoder, the quality of the downstream perceptions can be fine-tuned using gradient descent in an end-to-end fashion.

Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and under-represented in others. This paper defines a novel $\ell_1$-regularized pseudo-likelihood approach for fair graphical model selection. In particular, we assume there is some community or clustering structure in the true underlying graph, and we seek to learn a sparse undirected graph and its communities from the data such that demographic groups are fairly represented within the communities. In the case when the graph is known a priori, we provide a convex semidefinite programming approach for fair community detection. We establish the statistical consistency of the proposed method for both a Gaussian graphical model and an Ising model for, respectively, continuous and binary data, proving that our method can recover the graphs and their fair communities with high probability.

Fovea localization is one of the most popular tasks in ophthalmic medical image analysis, where the coordinates of the center point of the macula lutea, i.e. fovea centralis, should be calculated based on color fundus images. In this work, we treat the localization problem as a classification task, where the coordinates of the x- and y-axis are considered as the target classes. Moreover, the combination of the softmax activation function and the cross entropy loss function is modified to its multiscale variation to encourage the predicted coordinates to be located closely to the ground-truths. Based on color fundus photography images, we empirically show that the proposed multiscale softmax cross entropy yields better performance than the vanilla version and than the mean squared error loss with sigmoid activation, which provides a novel approach for coordinate regression.

We present X-ray proper motion (PM) measurements of 19 pulsars using new and archival data from the Chandra X-ray Observatory, including pulsar wind trails and X-ray filaments. Precise X-ray PMs are often limited by uncertainties in aligning observations to a common reference frame. Our analysis uses unresolved X-ray flux from stars in the Gaia catalog in addition to X-ray bright point sources for alignment, improving uncertainties. We obtain absolute positions referenced to Gaia with typical astrometric precision $\sim$10 mas and PM statistical uncertainties down to 1.3 mas yr$^{-1}$, the most precise X-ray PM achieved to date. With our improved frame alignment, PM accuracies are now limited by the pulsar flux in most cases. These results reveal a new X-ray filament and illuminate the wind nebula structures and origins of several of these pulsars.

We analyze the existence of Brownian motion tilted by a potential of full support on hyperbolic spaces $\mathbb{H}^d$. On compact spaces, it is classical that these path limits, called Q-processes, exist and can be directly defined using the ground state of the corresponding Schrödinger operator. On non-compact spaces like $\mathbb{H}^d$, the existence fails in general. We show that for \emph{stationary random} potentials on $\mathbb{H}^d$ with suitable spectral and sup norm bounds, the Q-processes exist a.s. For potentials that are factors of a Poisson point process, the method works up to sup norm $(d-1)^2/8$. In this case, we also show that the path limit can be approximated by periodic potentials. As a tool, we use the foliated space defined by the point process. It turns out that the global ground state of this foliated space serves as a substitute for the non-existing $L^2$ ground states on the leaves of the foliation. Restricting the global ground state to a leaf gives a generalized eigenwave that can be plugged into the usual machinery to get the Q-process.

The spatial distribution and morphology of precipitates formed during aging are key factors that determine the precipitation hardening response of various magnesium-rare earth alloys. In recent years, the use of high-performance computing clusters and massively parallel frameworks has enabled quantitative simulations of the evolution of individual and multiple precipitates at relevant length and time scales. However, predictive modeling of precipitate evolution remains challenging, in part because many key thermodynamic and kinetic parameters governing the underlying physics are either unknown or have a high degree of uncertainty. In this work, we developed a workflow in which experimental data were used to parameterize a phase-field model to perform two-dimensional (2D) simulations of concurrent nucleation and evolution of $β_1$ precipitates in magnesium-neodymium alloy during aging. Matrix composition and precipitate number density at different aging times were obtained from atom probe tomography and transmission electron microscopy measurements, respectively. We applied a stereological method to estimate the three-dimensional (3D) number densities from experimental cross-sectional transmission electron micrographs. The estimated 3D number density data were then converted to effective 2D number densities. The effective 2D number density and composition data were used to determine the required model parameters by minimizing the discrepancy between simulation and experimental results. The parameterized model allows for quantitative phase-field simulations of nucleation and growth of $β_1$ precipitates, which can be employed to optimize aging time to achieve a target number density of precipitates. This work highlights an approach to overcome the challenges associated with parameterizing a coupled phase-field and nucleation model.

We investigate the convex hulls of the eight dihedral symmetry classes of $n \times n$ alternating sign matrices, i.e., ASMs invariant under a subgroup of the symmetry group of the square. Extending the prefix-sum description of the ASM polytope, we develop a uniform core--assembly framework: each symmetry class is encoded by a set of core positions and an affine assembly map that reconstructs the full matrix from its core. This reduction transfers polyhedral questions to lower-dimensional core polytopes, which are better suited to the tool set of polyhedral combinatorics, while retaining complete information about the original symmetry class. For the vertical, vertical--horizontal, half-turn, diagonal, diagonal--antidiagonal, and total symmetry classes, we give explicit polynomial-size linear inequality descriptions of the associated polytopes. In these cases, we also determine the dimension and provide facet descriptions. The quarter-turn symmetry class behaves differently: the natural relaxation admits fractional vertices, and we need to extend the system with a structured family of parity-type Chvátal--Gomory inequalities to obtain the quarter-turn symmetric ASM polytope. Our framework leads to efficient algorithms for computing minimum-cost ASMs in each symmetry class and provides a direct link between the combinatorics of symmetric ASMs and tools from polyhedral combinatorics and combinatorial optimization.

The leading singularities of one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory are known to factorise into products of tree-level amplitudes, and this can be seen from a number of different perspectives e.g. generalised unitarity or on-shell diagrams. Here we investigate the leading singularities from the perspective of the Wilson loop expectation values to which these amplitudes are dual, in particular making use of the twistor Wilson loop formalism. We show that the factorisation of one-loop leading singularities of a null Wilson loop's expectation value into a product of tree-level objects is manifest at the level of twistor Wilson loop diagrams, and is a simple consequence of planarity, without appeal to e.g. unitarity on the amplitude side of the duality. We then use the same approach to derive compact formulae for the one-loop leading singularities of correlators of multiple light-like Wilson loop operators in terms of tree-level objects. Via the chiral box expansion, these formulae provide a simple route to writing down the $O(g^2)$ correlation function of any number of Wilson loops at any MHV degree.

Phase matching is essential for efficient energy transfer in nonlinear wave-mixing processes. Traditional methods, such as birefringent and quasi-phase matching, have remained conceptually unchanged since their discovery over 60 years ago, each posing inherent constraints and limitations. Here, we demonstrate the concept of geometric phase matching as a new paradigm for tunable nonlinear wave mixing, based on a multilayered platform of nonlinear thin-film crystals. We leverage this concept to experimentally show reconfigurable and spin-controlled phase matching for second-harmonic generation (SHG), opening new avenues for real-time manipulation of nonlinear interactions in photonic devices. We specifically demonstrate full modulation of SHG from a bilayer structure, nearly perfect and tunable geometric phase matching from an eight-layer structure, and polarization tomography that reveals the evolution of the spin dependent interaction. This approach not only expands the design space for nonlinear optical processes but also paves the way for highly robust, tunable and efficient frequency conversion, for next-generation adaptive nonlinear photonic, quantum photonic and nonlinear optical metamaterial technologies based on thin-film crystals.

Designing robust trajectories under uncertainties is an emerging technology that may represent a key paradigm shift in space mission design. As we pursue more ambitious scientific goals (e.g., multi-moon tours, missions with extensive components of autonomy), it becomes more crucial that missions are designed with navigation (Nav) processes in mind. The effect of Nav processes is statistical by nature, as they consist of orbit determination (OD) and flight-path control (FPC). Thus, this mission design paradigm calls for techniques that appropriately quantify statistical effects of Nav, evaluate associated risks, and design missions that ensure sufficiently low risk while minimizing a statistical performance metric; a common metric is Delta-V99: worst-case (99%-quantile) Delta-V expenditure including statistical FPC efforts. In response to the need, this paper develops an algorithm for risk-constrained trajectory optimization under operational uncertainties due to initial state dispersion, navigation error, maneuver execution error, and imperfect dynamics modeling. We formulate it as a nonlinear stochastic optimal control problem and develop a computationally tractable algorithm that combines optimal covariance steering and sequential convex programming (SCP). Specifically, the proposed algorithm takes a block-Cholesky approach for convex formulation of optimal covariance steering, and leverages a recent SCP algorithm, SCvx*, for reliable numerical convergence. We apply the developed algorithm to risk-constrained, statistical trajectory optimization for exploration of dwarf planet Ceres with a Mars gravity assist, and demonstrate the robustness of the statistically-optimal trajectory and FPC policies via nonlinear Monte Carlo simulation.

The transition matrix (T-matrix) is a complete description of an object's linear scattering response. As such, it has found wide adoption for the theoretical and computational description of multiple-scattering phenomena. In its original form, the T-matrix describes the interaction of a scatterer with a monochromatic source. In practice, however, information about the T-matrix is usually needed in an extended spectral domain. To access the frequency-dispersion, one might naively sample T-matrices over a finely resolved set of discrete frequencies and store one T-matrix per frequency. This approach has multiple drawbacks: it is computationally expensive, requires excessive memory, and it disregards the physical origin of the spectral features, weakening physical interpretability. To overcome these major limitations, we leverage a pole-expansion technique to represent the T-matrix with arbitrary frequency resolution within a selected frequency domain via a set of resonant contributions. A matrix-valued variant of the recently established adaptive Antoulas-Anderson (AAA) algorithm for rational approximation enables us to compute the pole-expansion at minimal computational cost using only a small number of direct evaluations. We demonstrate the benefits of such a representation with examples ranging from semi-analytically accessible scatterers to quasi-dual bound states in the continuum. To allow the wider community to capitalize on these findings, we provide open-source tools to perform the presented pole-expansion of the T-matrix.

This article explores Rota-Baxter operators on finite-dimensional $ω$-Lie algebras over a field of characteristic not 2. We provide several methods for constructing left-symmetric algebras, $ω$-Lie algebras, and Hom-Lie algebras via compatible Rota-Baxter operators on a given $ω$-Lie algebra. We also study the geometric structures of compatible Rota-Baxter operators of weight $0$ and isometric Rota-Baxter operators of weight $1$ over the field of complex numbers. In particular, we prove that the affine variety of all isometric Rota-Baxter operators of weight $1$ on any finite-dimensional non-Lie complex simple $ω$-Lie algebra is $1$-dimensional. Furthermore, we show that for every $4$-dimensional non-Lie complex $ω$-Lie algebra, there always exists a nilpotent compatible Rota-Baxter operator of weight $0$ such that the induced Hom-Lie algebra is nonabelian but solvable.

This paper investigates a uncrewed aerial vehicles (UAV)-assisted cell-free architecture for vehicular networks in road-constrained environments. Roads are modeled using a Poisson Line Process (PLP), with multi-layer roadside access points (APs) deployed via 1-D Poisson Point Process (PPP). Each user forms a localized cell-free cluster by associating with the nearest AP in each layer along its corresponding road. This forms a road-constrained cell-free architecture. To enhance coverage, UAV act as an aerial tier, extending access from 1-D road-constrained layouts (embedded in 2-D) to 3-D. We employ a Matérn Hard-Core (MHC) point process to model the spatial distribution of UAV base stations, ensuring a minimum safety distance between them. In order to enable tractable analysis of the aggregate signal from multiple APs, a distance-based power control scheme is introduced. Leveraging tools from stochastic geometry, we have studied the coverage probability. Furthermore, we analyze the impact of key system parameters on coverage performance, providing useful insights into the deployment and optimization of UAV-assisted cell-free vehicular networks.

We introduce two reconstruction schemes that enable the recovery of a function in the entire Euclidean space $\mathbb{R}^n$ from local data $(u|_W, [(-Δ)^s u]|_W)$, where $W$ is an arbitrarily small nonempty open subset of $\mathbb R^n$ and $(-Δ)^s$ denotes the fractional Laplace operator of order $s\in (0,1)$. These procedures rely crucially on the weak Unique Continuation Property (UCP) for the fractional Laplacian. We apply these schemes to two distinct inverse problems. Following the seminal work from Ghosh et al., the first one concerns the recovery of a potential (Calderón-type problem) from the fractional Schrödinger equation under nonlocal Robin-type exterior conditions. The second one involves recovering the solution of the space-fractional heat equation in $\mathbb{R}^n$ from localized time-dependent measurements within a ball. To tackle these problems, we introduce new analytical tools such as a generalized weak Kelvin transform and a fractional Robin-to-Robin map. Finally, we provide numerical simulations for one of the reconstruction methods, illustrating the stability issues and the severe ill-posedness inherent to such inverse problems.

The information bottleneck (IB) method seeks a compressed representation of data that preserves information relevant to a target variable for prediction while discarding irrelevant information from the original data. In its classical formulation, the IB method employs mutual information to evaluate the compression between the original and compressed data and the utility of the representation for the target variable. In this study, we investigate a generalized IB problem, where the evaluation of utility is based on the $\mathcal{H}$-mutual information that satisfies the concave (\texttt{CV}) and averaging (\texttt{AVG}) conditions. This class of information measures admits a statistical decision-theoretic interpretation via its equivalence to the expected value of sample information. Based on this interpretation, we derive an alternating optimization algorithm to assess the tradeoff between compression and utility in the generalized IB problem.

Time-fractional parabolic equations with a Caputo time derivative of order $α\in(0,1)$ are discretised in time using collocation methods, which assume that the Caputo derivative of the computed solution is piecewise-polynomial. For such discretisations of any order $m\ge 0$, with any choice of collocation points, we give sufficient conditions for existence and uniqueness of collocation solutions. Furthermore, we investigate the applicability and performance of such schemes in the context of the a-posteriori error estimation and adaptive time stepping algorithms.