This paper presents the development of a graph autoencoder architecture capable of performing projection-based model-order reduction (PMOR) using a nonlinear manifold least-squares Petrov–Galerkin (LSPG) projection scheme. The architecture is particularly useful for advection-dominated flows modeled by unstructured meshes, as it provides a robust nonlinear mapping that can be leveraged in a PMOR setting. The presented graph autoencoder is constructed with a two-part process that consists of (1) generating a hierarchy of reduced graphs to emulate the compressive abilities of convolutional neural networks (CNNs) and (2) training a message passing operation at each step in the hierarchy of reduced graphs to emulate the filtering process of a CNN. The resulting framework provides improved flexibility over traditional CNN-based autoencoders because it is readily extendable to unstructured meshes. We provide an analysis of the interpretability of the graph autoencoder’s latent state variables, where we find that the Jacobian of the decoder for the proposed graph autoencoder provides interpretable mode shapes akin to traditional proper orthogonal decomposition modes. To highlight the capabilities of the proposed framework, which is named geometric deep least-squares Petrov–Galerkin (GD-LSPG), we benchmark the method on a one-dimensional Burgers’ model with a structured mesh and demonstrate the flexibility of GD-LSPG by deploying it on two test cases for two-dimensional Euler equations that use an unstructured mesh. The proposed framework is more flexible than using a traditional CNN-based autoencoder and provides considerable improvement in accuracy for very low-dimensional latent spaces in comparison with traditional affine projections.

This article proposes a local projection (LP) residual bootstrap method to construct confidence intervals for impulse response coefficients of AR(1) models. Our bootstrap method is based on the LP approach and involves a residual bootstrap procedure applied to AR(1) models. We present theoretical results for our bootstrap method and proposed confidence intervals. First, we prove the uniform consistency of the LP-residual bootstrap over a large class of AR(1) models that allow for a unit root, conditional heteroskedasticity of unknown form, and martingale difference shocks. Then, we prove the asymptotic validity of our confidence intervals over the same class of AR(1) models. Finally, we show that the LP-residual bootstrap provides asymptotic refinements for confidence intervals on a restricted class of AR(1) models relative to those required for the uniform consistency of our bootstrap.

This paper presents a comprehensive analysis of the frequency and severity of accidents involving electric vehicles (EVs) in comparison to internal combustion engine vehicles (ICEVs). It draws on extensive data from Norway from 2020 to 2023, a period characterised by significant EV adoption. We examine over two million registered EVs that collectively account for 28 billion kilometres of travel. In total we have analysed 139 billion kilometres of travel and close to 14,0000 accidents across all fuel types. We supplement this data with data from the Highway Loss Data Institute in the US and Association of British Insurers data in the UK as well as information from the Guy Carpenter large loss motor database.

A thorough analysis comparing accident frequency and severity of EVs with ICEVs in the literature to date has yet to be conducted, which this paper aims to address. This research will assist actuaries and analysts across various domains, including pricing, reserving and reinsurance considerations.

Our findings reveal a notable reduction in the frequency of accidents across all fuel types over time. Specifically, EVs demonstrate a lower accident frequency compared to ICEVs, a trend that may be attributed more to advancements in technology rather than the inherent characteristics of the fuel type, even when adjusted for COVID. Furthermore, our analysis indicates that EVs experience fewer accidents involving single units relative to non-EV and suggests a decrease in driver error and superior performance on regular road types.

Reduction in EV accident frequency of 17% and a change in the distribution of average severity with higher damage costs and lower injury costs leading to an overall reduction of 11%

However, it is important to note that when accidents do occur, the number of units involved as a proxy for severity involving EVs is marginally higher than those involving ICEVs. The average claim cost profile for EVs changes significantly with property damage claims being more expensive and bodily injury claims being less expensive for EVs.

Overall, our research concludes that EVs present a lower risk profile compared to their ICEV counterparts, highlighting the evolving landscape of vehicle safety in the context of increasing EV utilisation.

We study two continuous-time, time-inconsistent problems for an individual who purchases life annuities and invests her wealth in a risky asset under the mean-variance criterion. In the first problem, the buyer may only purchase life annuities at a bounded, continuous rate, while in the second problem, the buyer may purchase any amount of life annuity income at any time, which results in a singular control problem. We find the individual’s time-consistent equilibrium control strategies explicitly for the two life-annuity problems by solving the corresponding extended Hamilton–Jacobi–Bellman systems of equations. We also discuss the effects of parameters on the equilibrium strategies of the two life-annuity problems.

Assessing systemic risk presents a significant challenge in finance and insurance, where conditional risk measures are essential for capturing contagion effects. This paper introduces two novel systemic risk measures – conditional interval value-at-risk (CoIVaR) and conditional interval expected shortfall (CoIES) – which extend traditional metrics by incorporating interval-based uncertainty. A formal theoretical framework is developed for both measures, offering a detailed characterization of their key properties and risk contributions. We then propose a comprehensive comparison methodology for systemic risk assessment, leveraging stochastic orders, dependence structures, and marginal distributions to establish conditions for ranking risk vectors. Finally, through numerical experiments and real-world stock market applications, we demonstrate the practical utility of CoIVaR and CoIES in quantifying systemic risk under uncertainty. The findings provide valuable insights into systemic risk propagation and establish a robust foundation for risk management in interconnected financial systems.

Low-dimensional representation and clustering of network data are tasks of great interest across various fields. Latent position models are routinely used for this purpose by assuming that each node has a location in a low-dimensional latent space and by enabling node clustering. However, these models fall short through their inability to simultaneously determine the latent space dimension and number of clusters. Here we introduce the latent shrinkage position cluster model (LSPCM), which addresses this limitation. The LSPCM posits an infinite-dimensional latent space and assumes a Bayesian nonparametric shrinkage prior on the latent positions’ variance parameters resulting in higher dimensions having increasingly smaller variances, aiding the identification of dimensions with non-negligible variance. Further, the LSPCM assumes the latent positions follow a sparse finite Gaussian mixture model, allowing for automatic inference on the number of clusters related to non-empty mixture components. As a result, the LSPCM simultaneously infers the effective dimension of the latent space and the number of clusters, eliminating the need to fit and compare multiple models. The performance of the LSPCM is assessed via simulation studies and demonstrated through application to two real Twitter network datasets from sporting and political contexts. Open-source software is available to facilitate widespread use of the LSPCM.

Effectively controlling systems governed by partial differential equations (PDEs) is crucial in several fields of applied sciences and engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement learning (RL), particularly deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges, including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these challenges, we propose a data-efficient, interpretable, and scalable Dyna-style model-based RL framework specifically tailored for PDE control. Our approach integrates Sparse Identification of Nonlinear Dynamics with Control within an Autoencoder-based dimensionality reduction scheme for PDE states and actions (AE+SINDy-C). This combination enables fast rollouts with significantly fewer environment interactions while providing an interpretable latent space representation of the PDE dynamics, facilitating insight into the control process. We validate our method on two PDE problems describing fluid flows—namely, the 1D Burgers equation and 2D Navier–Stokes equations—comparing it against a model-free baseline. Our extensive analysis highlights improved sample efficiency, stability, and interpretability in controlling complex PDE systems.

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. This approach is predicated on the assumption of monotonicity in the propensity score function, a condition that can be justified in many economic applications. We show that the nature of the isotonic estimator can help us to fix many problems of existing matching methods, including efficiency, choice of the number of matches, choice of tuning parameters, robustness to propensity score misspecification, and bootstrap validity. As a by-product, a uniformly consistent isotonic estimator is developed for our proposed matching method.

We consider an inhomogeneous Erdős–Rényi random graph ensemble with exponentially decaying random disconnection probabilities determined by an independent and identically distributed field of variables with heavy tails and infinite mean associated with the vertices of the graph. This model was recently investigated in the physics literature (Garuccio, Lalli, and Garlaschelli 2023) as a scale-invariant random graph within the context of network renormalization. From a mathematical perspective, the model fits in the class of scale-free inhomogeneous random graphs whose asymptotic geometrical features have recently attracted interest. While for this type of graph several results are known when the underlying vertex variables have finite mean and variance, here instead we consider the case of one-sided stable variables with necessarily infinite mean. To simplify our analysis, we assume that the variables are sampled from a Pareto distribution with parameter $\alpha\in(0,1)$. We start by characterizing the asymptotic distributions of the typical degrees and some related observables. In particular, we show that the degree of a vertex converges in distribution, after proper scaling, to a mixed Poisson law. We then show that correlations among degrees of different vertices are asymptotically non-vanishing, but at the same time a form of asymptotic tail independence is found when looking at the behavior of the joint Laplace transform around zero. Moreover, we present some findings concerning the asymptotic density of wedges and triangles, and show a cross-over for the existence of dust (i.e. disconnected vertices).

The use of large language models (LLMs) has exploded since November 2022, but there is sparse evidence regarding LLM use in health, medical, and research contexts. We aimed to summarise the current uses of and attitudes towards LLMs across our campus’ clinical, research, and teaching sites. We administered a survey about LLM uses and attitudes. We conducted summary quantitative analysis and inductive qualitative analysis of free text responses. In August–September 2023, we circulated the survey amongst all staff and students across our three campus sites (approximately n = 7500), comprising a paediatric academic hospital, research institute, and paediatric university department. We received 281 anonymous survey responses. We asked about participants’ knowledge of LLMs, their current use of LLMs in professional or learning contexts, and perspectives on possible future uses, opportunities, and risks of LLM use. Over 90% of respondents have heard of LLM tools and about two-thirds have used them in their work on our campus. Respondents reported using LLMs for various uses, including generating or editing text and exploring ideas. Many, but not necessarily all, respondents seem aware of the limitations and potential risks of LLMs, including privacy and security risks. Various respondents expressed enthusiasm about the opportunities of LLM use, including increased efficiency. Our findings show LLM tools are already widely used on our campus. Guidelines and governance are needed to keep up with practice. Insights from this survey were used to develop recommendations for the use of LLMs on our campus.

Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is often infeasible due to epistemic uncertainty, cost, or time constraints, resulting in models that fail to accurately describe the behavior of the system. On the other hand, data-driven machine learning models such as variational autoencoders are not guaranteed to identify a parsimonious representation. As a result, they can suffer from poor generalization performance and reconstruction accuracy in the regime of limited and noisy data. We propose a physics-informed variational autoencoder architecture that combines the interpretability of physics-based models with the flexibility of data-driven models. To promote disentanglement of the known physics and confounding influences, the latent space is partitioned into physically meaningful variables that parametrize a physics-based model, and data-driven variables that capture variability in the domain and class of the physical system. The encoder is coupled with a decoder that integrates physics-based and data-driven components, and constrained by an adversarial training objective that prevents the data-driven components from overriding the known physics, ensuring that the physics-grounded latent variables remain interpretable. We demonstrate that the model is able to disentangle features of the input signal and separate the known physics from confounding influences using supervision in the form of class and domain observables. The model is evaluated on a series of synthetic case studies relevant to engineering structures, demonstrating the feasibility of the proposed approach.

A meta-conjecture of Coulson, Keevash, Perarnau, and Yepremyan [12] states that above the extremal threshold for a given spanning structure in a (hyper-)graph, one can find a rainbow version of that spanning structure in any suitably bounded colouring of the host (hyper-)graph. We solve one of the most pertinent outstanding cases of this conjecture by showing that for any $1\leq j\leq k-1$, if $G$ is a $k$-uniform hypergraph above the $j$-degree threshold for a loose Hamilton cycle, then any globally bounded colouring of $G$ contains a rainbow loose Hamilton cycle.

Political polarization is a group phenomenon in which opposing factions, often of unequal size, exhibit asymmetrical influence and behavioral patterns. Within these groups, elites and masses operate under different motivations and levels of influence, challenging simplistic views of polarization. Yet, existing methods for measuring polarization in social networks typically reduce it to a single value, assuming homogeneity in polarization across the entire system. While such approaches confirm the rise of political polarization in many social contexts, they overlook structural complexities that could explain its underlying mechanisms. We propose a method that decomposes existing polarization and alignment measures into distinct components. These components separately capture polarization processes involving elites and masses from opposing groups. Applying this method to Twitter discussions surrounding the 2019 and 2023 Finnish parliamentary elections, we find that (1) opposing groups rarely have a balanced contribution to observed polarization, and (2) while elites strongly contribute to structural polarization and consistently display greater alignment across various topics, the masses, too, have recently experienced a surge in alignment. Our method provides an improved analytical lens through which to view polarization, explicitly recognizing the complexity of and need to account for elite-mass dynamics in polarized environments.

We show that the Potts model on a graph can be approximated by a sequence of independent and identically distributed spins in terms of Wasserstein distance at high temperatures. We prove a similar result for the Curie–Weiss–Potts model on the complete graph, conditioned on being close enough to any of its equilibrium macrostates, in the low-temperature regime. Our proof technique is based on Stein’s method for comparing the stationary distributions of two Glauber dynamics with similar updates, one of which is rapid mixing and contracting on a subset of the state space. Along the way, we prove a new upper bound on the mixing time of the Glauber dynamics for the conditional measure of the Curie–Weiss–Potts model near an equilibrium macrostate.

In this paper we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$. We interpret these equations either in the sense of Young ($H>1/2$) or Stratonovich ($H=1/2$). In particular, fractional Young differential equations are well suited to modeling real-world phenomena as they capture memory effects, unlike other frameworks. Although it is very complex to solve them in high dimensions, model reduction schemes for Young or Stratonovich settings have not yet been much studied. To address this gap, we analyze important features of fundamental solutions associated with the underlying systems. We prove a weak type of semigroup property which is the foundation of studying system Gramians. From the Gramians introduced, a dominant subspace can be identified, which is shown in this paper as well. The difficulty for fractional drivers with $H>1/2$ is that there is no link between the corresponding Gramians and algebraic equations, making the computation very difficult. Therefore we further propose empirical Gramians that can be learned from simulation data. Subsequently, we introduce projection-based reduced-order models using the dominant subspace information. We point out that such projections are not always optimal for Stratonovich equations, as stability might not be preserved and since the error might be larger than expected. Therefore an improved reduced-order model is proposed for $H=1/2$. We validate our techniques conducting numerical experiments on some large-scale stochastic differential equations driven by fBm resulting from spatial discretizations of fractional stochastic PDEs. Overall, our study provides useful insights into the applicability and effectiveness of reduced-order methods for stochastic systems with fractional noise, which can potentially aid in the development of more efficient computational strategies for practical applications.

This article introduces a blockchain-based insurance scheme that integrates parametric and collaborative elements. A pool of investors, referred to as surplus providers, locks funds in a smart contract, enabling blockchain users to underwrite parametric insurance contracts. These contracts automatically trigger compensation when predefined conditions are met. The collaborative aspect is embodied in the generation of tokens, which are distributed to surplus providers. These tokens represent each participant’s share of the surplus and grant voting rights for management decisions. The smart contract is developed in Solidity, a high-level programming language for the Ethereum blockchain, and deployed on the Sepolia testnet, with data processing and analysis conducted using Python. In addition, open-source code is provided and main research challenges are identified, so that further research can be carried out to overcome limitations of this first proof of concept.

Detecting multiple structural breaks at unknown dates is a central challenge in time-series econometrics. Step-indicator saturation (SIS) addresses this challenge during model selection, and we develop its asymptotic theory for tuning parameter choice. We study its frequency gauge—the false detection rate—and show it is consistent and asymptotically normal. Simulations suggest that a smaller gauge minimizes bias in post-selection regression estimates. For the small gauge situation, we develop a complementary Poisson theory. We compare the local power of SIS to detect shifts with that of Andrews’ break test. We find that SIS excels when breaks are near the sample end or closely spaced. An application to U.K. labor productivity reveals a growth slowdown after the 2008 financial crisis.

Measure of uncertainty in past lifetime distribution plays an important role in the context of information theory, forensic science and other related fields. In the present work, we propose non-parametric kernel type estimator for generalized past entropy function, which was introduced by Gupta and Nanda [9], under $\alpha$-mixing sample. The resulting estimator is shown to be weak and strong consistent and asymptotically normally distributed under certain regularity conditions. The performance of the estimator is validated through simulation study and a real data set.