We study the $R_\beta$-positivity and the existence of zero-temperature limits for a sequence of infinite-volume Gibbs measures $(\mu_{\beta}(\!\cdot\!))_{\beta \geq 0}$ at inverse temperature $\beta$ associated to a family of nearest-neighbor matrices $(Q_{\beta})_{\beta \geq 0}$ reflected at the origin. We use a probabilistic approach based on the continued fraction theory previously introduced in Ferrari and Martínez (1993) and sharpened in Littin and Martínez (2010). Some necessary and sufficient conditions are provided to ensure (i) the existence of a unique infinite-volume Gibbs measure for large but finite values of $\beta$, and (ii) the existence of weak limits as $\beta \to \infty$. Some application examples are revised to put in context the main results of this work.

Despite being a vaccine-preventable disease for decades, pertussis control is still a public health challenge. A pertussis outbreak emerged in Jerusalem (n = 257 cases, January to June 2023). Most cases were young children (median age 1.5 years), and 100 were infants under 1 year. The hospitalisation rate of infants was 24%, which was considerably higher than that of cases aged 1 year and above (3.8%). There was one fatality in an unvaccinated, 10-week-old infant whose mother had not received pertussis vaccination during pregnancy. Most children were unvaccinated and resided in Jewish ultra-orthodox neighbourhoods in Jerusalem district. An intervention programme and vaccination campaign are ongoing.

Fertility, particularly at its current low level in many developed countries and high level in some less developed countries, is a key factor driving demographic, economic, and societal changes at local, national, and global levels. Population ageing due to low fertility and increasing longevity represents one of the most significant global megatrends and risks. Many countries are already experiencing population decline and rapid growth of their elderly populations, with implications for workforce size, economic development, health and pension schemes, and social security arrangements. Actuaries are well known for their work on mortality and morbidity, but they have rarely considered fertility and its proximate determinants, despite their demographic and economic effects. This paper explores key explanations and outcomes of past and projected future fertility trends, and the implications for actuaries and for political and economic decision-makers.

Wind derivatives are financial instruments designed to mitigate losses caused by adverse wind conditions. With the rapid growth of wind power capacity due to efforts to reduce carbon emissions, the demand for wind derivatives to manage uncertainty in wind power production is expected to increase. However, existing wind derivative literature often assumes normally distributed wind speed, despite the presence of skewness and leptokurtosis in historical wind speed data. This paper investigates how the misspecification of wind speed models affects wind derivative prices and proposes the use of the generalized hyperbolic distribution to account for non-normality. The study develops risk-neutral approaches for pricing wind derivatives using the conditional Esscher transform, which can accommodate stochastic processes with any distribution, provided the moment-generating function exists. The analysis demonstrates that model risk varies depending on the choice of the underlying index and the derivative’s payoff structure. Therefore, caution should be exercised when choosing wind speed models. Essentially, model risk cannot be ignored in pricing wind speed derivatives.

We study the locations of complex zeroes of independence polynomials of bounded-degree hypergraphs. For graphs, this is a long-studied subject with applications to statistical physics, algorithms, and combinatorics. Results on zero-free regions for bounded-degree graphs include Shearer’s result on the optimal zero-free disc, along with several recent results on other zero-free regions. Much less is known for hypergraphs. We make some steps towards an understanding of zero-free regions for bounded-degree hypergaphs by proving that all hypergraphs of maximum degree $\Delta$ have a zero-free disc almost as large as the optimal disc for graphs of maximum degree $\Delta$ established by Shearer (of radius $\sim 1/(e \Delta )$). Up to logarithmic factors in $\Delta$ this is optimal, even for hypergraphs with all edge sizes strictly greater than $2$. We conjecture that for $k\ge 3$, $k$-uniform linear hypergraphs have a much larger zero-free disc of radius $\Omega (\Delta ^{- \frac{1}{k-1}} )$. We establish this in the case of linear hypertrees.

Industrial materials images are an important application domain for content-based image retrieval. Users need to quickly search databases for images that exhibit similar appearance, properties, and/or features to reduce analysis turnaround time and cost. The images in this study are 2D images of millimeter-scale rock samples acquired at micrometer resolution with light microscopy or extracted from 3D micro-CT scans. Labeled rock images are expensive and time-consuming to acquire and thus are typically only available in the tens of thousands. Training a high-capacity deep learning (DL) model from scratch is therefore not practicable due to data paucity. To overcome this “few-shot learning” challenge, we propose leveraging pretrained common DL models in conjunction with transfer learning. The “similarity” of industrial materials images is subjective and assessed by human experts based on both visual appearance and physical qualities. We have emulated this human-driven assessment process via a physics-informed neural network including metadata and physical measurements in the loss function. We present a novel DL architecture that combines Siamese neural networks with a loss function that integrates classification and regression terms. The networks are trained with both image and metadata similarity (classification), and with metadata prediction (regression). For efficient inference, we use a highly compressed image feature representation, computed offline once, to search the database for images similar to a query image. Numerical experiments demonstrate superior retrieval performance of our new architecture compared with other DL and custom-feature-based approaches.

Bovine tuberculosis (bTB) is prevalent among livestock and wildlife in many countries including New Zealand (NZ), a country which aims to eradicate bTB by 2055. This study evaluates predictions related to the numbers of livestock herds with bTB in NZ from 2012 to 2021 inclusive using both statistical and mechanistic (causal) modelling. Additionally, this study made predictions for the numbers of infected herds between 2022 and 2059. This study introduces a new graphical method representing the causal criteria of strength of association, such as R2, and the consistency of predictions, such as mean squared error. Mechanistic modelling predictions were, on average, more frequently (3 of 4) unbiased than statistical modelling predictions (1 of 4). Additionally, power model predictions were, on average, more frequently (3 of 4) unbiased than exponential model predictions (1 of 4). The mechanistic power model, along with annual updating, had the highest R2 and the lowest mean squared error of predictions. It also exhibited the closest approximation to unbiased predictions. Notably, significantly biased predictions were all underestimates. Based on the mechanistic power model, the biological eradication of bTB from New Zealand is predicted to occur after 2055. Disease eradication planning will benefit from annual updating of future predictions.