Physics-informed neural networks (PINNs) are a promising alternative for extracting additional time-averaged (mean) flow quantities from experimental data. In the case of particle image velocimetry (PIV), for example, the measured mean flow field is contaminated by noise, has a limited field of view, is restricted to a uniform grid, and does not provide the pressure field. To overcome these limitations, we present a methodology in which PINNs are first trained on a Reynolds-averaged Navier–Stokes (RANS) simulation such that it learns all states at every location in the domain. We then apply transfer learning, which updates the PINN using sub-sampled PIV data. The resulting predictions are in significantly better agreement with the full PIV dataset than PINNs, which are trained on experimental data only. This work builds on the recent literature by integrating a Spalart-Allmaras turbulence model and applying hard constraints to the no-slip wall boundary condition. We apply this methodology to a two-dimensional NACA 0012 airfoil inclined at an angle of attack, $ \alpha $ = 15°, for two Reynolds numbers of Re = 10,000 and 75,000. The proposed methodology is initially validated using large eddy simulation (LES) data and then demonstrated on experimental PIV data. Our transfer learning approach results in improved predictions and a reduction in training time when compared to using a random network initialization.

Let $\{Y_{n}$, $n \geq 1\}$ be a critical branching process with immigration having finite variance for the offspring number of particles and finite mean for the immigrating number of particles. In this paper we study lower deviation probabilities for $Y_{n}$. More precisely, assuming that $k,n \to \infty$ so that $k={\mathrm{o}} (n)$, we investigate the asymptotics of $\mathbb P(Y_{n} \leq k )$ and $\mathbb P(Y_{n} = k )$. Our results clarify the role of the moment conditions in the local limit theorem for $Y_n$ proved by Mellein (1982).

This research sought to update understanding following improvements to treatment and deepen the understanding of the mortality risk associated with Type 1 or Type 2 diabetes, including relative risk in the presence of co-morbidities. Specifically, we developed a model to provide mortality predictions at a granular level for lives with and without diabetes. The model is tailored for use by the insurance industry to provide an updated source from which to appreciate the risk posed when underwriting people with diabetes. By providing an updated and deeper understanding of mortality risk, the research’s aim is to improve access to insurance for those individuals living with diabetes. The model combines industry standard underwriting risk factors, such as age, gender, deprivation index, body mass index (BMI), smoker status, blood pressure (BP) and cholesterol level, with various co-morbidities related to diabetes. A comprehensive analysis of mortality risk factors, between 2010 and 2019, for people with and without diabetes is undertaken on over 1.2 million records based on Clinical Practice Research Datalink (CPRD), Hospital Episode Statistics (HES) and Office for National Statistics (ONS) death registrations data. Cox proportional hazards models are used to estimate the probability of death, stratified by gender across three distinct populations: Type 1 diabetes, Type 2 diabetes and a general population sample. The model outputs produced are permutations of the following: gender; population split by general sample, Type 1 and Type 2 diabetes; and a time-dependent exponential model and a time-invariant homogeneous model. A Shiny model application allows interaction with the model outputs (https://0jv7e6-scott-reid.shinyapps.io/diabmdl/) and spreadsheets provide additional explanation. Useful insights were obtained through industry discussions on the variation of existing market practice against that implied by the results. Key rating factors were generally aligned with market practice, such as age, BMI, BP, cholesterol and years since a diabetes diagnosis. However, for a few significant mortality risks impacting co-morbidities, the results did not adhere to prior expectations. Exploratory work suggested that the order and sequencing of key co-morbidities for diabetes must be included in future model development.

While Structural Health Monitoring (SHM) has been widely studied, its reliability in real-world applications remains challenged by pronounced operational variability, particularly when system behavior changes discretely between operating regimes. Such methods generally rely on baseline comparisons; however, under multiple operating regimes, the baseline becomes distributed across several distinct regions, each associated with a specific regime. This multi-baseline behavior complicates anomaly detectability, as variations induced by changing operating conditions may mask the subtle changes caused by structural degradation. The challenge is particularly pronounced for systems exhibiting regime-dependent behavior, where transitions between approximately stationary conditions occur frequently and are difficult to isolate. To address this, an efficient probabilistic multi-model framework is proposed, in which each operating regime is represented by a locally Vector Autoregressive (VAR) model. A Bayesian formulation is adopted to account for parameter uncertainty explicitly and to enable sequential updating, allowing the regime models to adapt as additional data become available—an important feature for early-stage SHM. New observations are evaluated against the ensemble of regime-specific VAR models using the marginal likelihood, enabling assessment of statistical consistency with the learned reference behavior. Persistently low consistency is interpreted as indicative of anomalies, which may reflect structural changes or evolving degradation. The proposed method is demonstrated using vibration data from gearboxes onboard a Crew Transfer Vessel operating under multiple regimes. Despite the limitations and uncertainties inherent to early-phase SHM, the framework successfully identifies deviations from the learned reference behavior within consistent operating conditions, demonstrating its potential for SHM under realistic, time-varying operation.

We relate the expected hyperbolic length of the perimeter of the convex hull of the trajectory of Brownian motion in the hyperbolic plane to an expectation of a certain exponential functional of a one-dimensional real-valued Brownian motion, and hence derive small- and large-time asymptotics for the expected hyperbolic perimeter. In contrast to the case of Euclidean Brownian motion with non-zero drift, the large-time asymptotics are a factor of two greater than the lower bound implied by the fact that the convex hull includes the hyperbolic line segment from the origin to the endpoint of the hyperbolic Brownian motion. We also obtain an exact expression for the expected perimeter length after an independent exponential random time.

We develop a continuous-time stochastic model for optimal cybersecurity investment under the threat of cyberattacks. The arrival of attacks is modeled using a Hawkes process, capturing the empirically relevant feature of clustering in cyberattacks. Extending the Gordon–Loeb model, each attack may result in a breach, with breach probability depending on the system’s vulnerability. We aim at determining the optimal cybersecurity investment to reduce vulnerability. The problem is cast as a two-dimensional Markovian stochastic optimal control problem and solved using dynamic programming methods. Numerical results illustrate how accounting for attack clustering leads to more responsive and effective investment policies, offering significant improvements over static and Poisson-based benchmark strategies. Our findings underscore the value of incorporating realistic threat dynamics into cybersecurity risk management.

Since stochastic differential equations (SDEs) driven by G-Brownian motion are of great importance in modeling situations that incorporate ambiguity, it is essential to address efficient numerical schemes to approximate the solution of such equations. The stream of research related to the numerical solutions of G-SDEs under standard assumptions is to some extent well understood. In this note, we are interested in designing an implicit $\theta$-Euler–Maruyama scheme to approximate the solution of G-SDEs under locally Lipschitz continuous coefficients. The convergence of the proposed scheme is established using the stopping time technique. In addition, we investigate the exponentially/quasi-surely asymptotic stability property of the scheme.

In 2017–2018, New South Wales (NSW), Australia, experienced a hepatitis A virus (HAV) outbreak predominantly affecting men who have sex with men (MSM). We aimed to estimate immunity and identify immunity gaps among MSM in NSW. We triangulated four data sources. We tested 409 residual sera collected from males undergoing syphilis testing between August and October 2017 for anti-HAV IgG. We surveyed all publicly funded sexual health clinics about HAV testing and vaccine provision for the preceding financial year. We conducted a convenience behavioural survey of 50 men at a sex-on-premises venue in October 2017, and we analysed community survey data from 2018 to 2019 (n = 5,924). Descriptive statistics and logistic regression ere used to examine associations with immunity and vaccination. Overall serological immunity was 62.8% (257/409) and increased with age, from 50.0% in those aged under 26 years to 79.0% in those over 45 years. Clinic immunity and community survey estimates were higher (74.5% and 76.8%). Immunity gaps were identified among bisexual men, those less connected to the gay community, and people born outside Australia. NSW Health implemented targeted vaccination and community engagement in response. Multisource assessment provided actionable evidence to guide targeted vaccination and outbreak response.

In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following results.

1. (i) There are constants $C\gt 0$ and $c\in (0,1]$ such that, whenever $d/\lambda \ge C$, every $(n,d,\lambda )$-graph contains a spanning subdivision of $K_t$ for all $2\le t \le \min \{cd,c\sqrt {\frac {n}{\log n}}\}$.

2. (ii) There are constants $C\gt 0$ and $c\in (0,1]$ such that, whenever $d/\lambda \ge C\log ^3n$, every $(n,d,\lambda )$-graph contains a spanning nearly balanced subdivision of $K_t$ for all $2\le t \le \min \{cd,c\sqrt {\frac {n}{\log ^3n}}\}$.

3. (iii) For every $\mu \gt 0$, there are constants $c,\varepsilon \in (0,1]$ and $n_0\in \mathbb N$ such that, whenever $n\ge n_0$, every $n$-vertex graph with minimum degree at least $\mu n$ and no bipartite holes of size $\varepsilon n$ contains a spanning nearly balanced subdivision of $K_t$ for all $2\le t \le c\sqrt {n}$.

We study random integer-valued Lipschitz functions on regular trees. It was shown by Peled, Samotij, and Yehudayoff [22] that such functions are localized; however, finer questions about the structure of Gibbs measures remain unanswered. Our main result is that the weak limit of a uniformly chosen 1-Lipschitz function with 0 boundary condition on a $d$-ary tree of height $n$ exists as $n \to \infty$ if $2 \le d \le 7$, but not if $d \ge 8$, thereby partially answering a question posed by Peled, Samotij and Yehudayoff. For large $d$, the value at the root alternates between being almost entirely concentrated on 0 for even $n$ and being roughly uniform on $\{-1,0,1\}$ for odd $n$, leading to different limits as $n$ approaches infinity along evens or odds. For $d \ge 8$, the essence of this phenomenon is preserved, which obstructs the convergence. For $d \le 7$, this phenomenon ceases to exist, and the law of the value at the root loses its connection with the parity of $n$. Along the way, we also obtain an alternative proof of localization. The key idea is a fixed point convergence result for a related operator on $\ell ^\infty$ and a procedure to show that the iterations get into a ‘basin of attraction’ of the fixed point. We also prove some accompanying analogous ‘even-odd phenomenon’ type results about $M$-Lipschitz functions on general non-amenable graphs with high enough expansion (this includes for example the large $d$ case for regular trees). We also prove a convergence result for 1-Lipschitz functions with $\{0,1\}$ boundary condition. This last result relies on an absolute value FKG for uniform 1-Lipschitz functions when shifted by $1/2$.

Ethical considerations in social network studies are grounded in the general principles of human subjects’ research, including avoidance of harm, promotion of justice, equitable distribution of burdens and benefits, respect for human dignity, and protection of confidentiality. To help navigate these challenges, this article presents recommendations for conducting ethical network research, developed by a multi-disciplinary and multi-national working group. The article is divided in three main sections where there are certain recommendations identified for each one of them: data collections, use, and availability. Discovering how others addressed and solved problems can be a way for all of us to improve our capacity to stand up to the scrutiny of ethical governance bodies, while also increasing our capacity to responsibly address novel, rare, or otherwise difficult situations for which institutions provide limited guidance. We see this as a first step toward a virtuous circle, or a form of “generalized indirect reciprocity” whereby researchers share information that may be relevant for others, and benefit at the same time from the information given by other members of the social networks analysis community. Our goal is to continue to produce and promote scientifically solid, ethical social network research.

This article introduces the global Women’s Safety Index (WSI), outlining its rationale, purpose, and potential applications. The Index consist of three dimensions: Equity, Protection, and Resources, identified as foundational to women’s safety. Key indicators within each dimension are selected based on theoretical relevance and empirical evidence. We detail the statistical methodology and framework used to construct the Index and present validation analyses demonstrating its ability to capture changes in women’s safety, particularly in response to external disruptions. The WSI is available on an interactive digital platform, enabling users to explore, visualize, and compare women’s safety data across regions and over time.

The infection fatality risk indicates the probability of death among infected individuals. The age-dependent heterogeneity of infection fatality risk is crucial for severity assessment and prioritization of countermeasures. However, infection fatality risk estimation requires infection data from a large-scale seroepidemiological survey combined with either direct ascertainment of deaths caused by infection or excess mortality estimates. To overcome the difficulty in ascertaining death, we propose an alternative approach to estimating the age-specific infection fatality risk for SARS-CoV-2 using medicolegal death investigation data in Tokyo with systematic post-mortem polymerase chain reaction testing. We integrated (i) polymerase chain reaction positivity among all deceased individuals at the Tokyo Medical Examiner’s Office, (ii) age-specific all-cause mortality risks from vital statistics, and (iii) age-stratified cumulative infection risks derived from seroepidemiological surveys. Infection fatality risk was computed using Bayes’ theorem. Results showed that infection fatality risk increased steeply with age. Our estimates (0.02% for ages 0–39 years, 0.30%–0.50% for ages 40–64 years, and 3.8%–4.2% for those aged ≥65 years) were consistent with published pre-vaccination meta-analytic estimates. Systematic testing within medicolegal death investigation systems can provide rapid, age-resolved severity assessments, improving the timeliness and comparability of infection fatality risk estimation across jurisdictions.