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.

Climate change is likely to increase the frequency, severity, and duration of heat waves in many countries. To plan mitigation, adaptation, and resilience strategies, it is necessary to quantify heat wave risk at both the local level and the country level. A new, more granular methodology is proposed in order to integrate the impact of heat waves in hexagonal France on mortality with a short-term stress scenario. Based on open data and reproducible methodology, the approach can be used as a starting point to investigate other effects, such as urban heat islands. The present application is based on in situ observational weather data and environmental vulnerability data to construct adapted geographical clusters without relying on the administrative division of the territory. Excess mortality is modeled as a function of weather using machine learning. Using recent knowledge of climatology, we construct extreme weather scenarios to calculate a shock to mortality. Short-term shocks are compared, and their respective merits are discussed. The methodology has been shown to generate mortality shocks up to five times greater than those estimated by the French regulatory authority.

We propose a matrix-based factor analysis model for predicting the probability of insurance claims. The model employs projected principal component analysis (PPCA), which enhances the estimation of unobserved latent factors by projecting a data matrix onto a linear space spanned by insured-specific features. This approach addresses the overparameterization problem when the number of insured-specific features and insurance coverages is large, enabling more accurate estimation of claim probability than conventional methods. Using a large-scale health insurance dataset from a leading life insurer in South Korea, we demonstrate that the proposed model outperforms conventional and machine-learning benchmarks, such as logistic regression and XGBoost, in predicting claim probabilities. We further determine that our model can reduce computational time by approximately 86% and 98% compared to logistic regression and XGBoost, respectively. The proposed model provides a unified and scalable framework for modeling high-dimensional claim probabilities, offering practical value for underwriting, risk management, and personalized insurance product design.

Accurate and internally coherent crop-yield forecasts are important for agricultural risk management, crop-insurance ratemaking, and regional risk assessment under climate variability. However, crop yields are influenced by high-dimensional and strongly correlated weather conditions, while forecasts produced at different spatial levels often violate aggregation constraints. Existing studies focus on yield prediction within individual regions and pay limited attention to weather-informed forecasting, hierarchical coherence, and insurance-oriented risk measurement. This paper develops an integrated framework for hierarchical crop-yield forecasting and risk assessment by combining dimensionality reduction for high-dimensional weather variables, probabilistic forecasting, and forecast reconciliation. Using county- and state-level spring and winter wheat yields in Montana from 1982 to 2022, we compare alternative base forecasting models and reconciliation methods under scenarios with and without weather information. Forecast performance is evaluated using point and probabilistic scoring rules, and the reconciled predictive distributions are used to construct scenario-based measures of downside yield risk. The results show that incorporating weather information and hierarchical reconciliation improves the quality and coherence of hierarchical yield forecasts. The resulting probabilistic forecasts provide a basis for loss-rate estimation, cross-county risk comparison, and spatial risk mapping and also support crop-insurance ratemaking under a retain–cede game between private insurers and the government.