We seek to understand the factors that drive mortality in the contiguous United States using data that are indexed by county and year and grouped into 18 different age bins. We propose a model that adds two important contributions to existing mortality studies. First, we treat age as a random effect. This is an improvement over previous models because it allows the model in one age group to borrow information from other age groups. Second, we utilize Gaussian Processes to create nonlinear covariate effects for predictors such as unemployment rate, race, and education level. This allows for a more flexible relationship to be modeled between mortality and these predictors. Understanding that the United States is expansive and diverse, we allow for many of these effects to vary by location. The flexibility in how predictors relate to mortality has not been used in previous mortality studies and will result in a more accurate model and a more complete understanding of the factors that drive mortality. Both the multivariate nature of the model as well as the spatially varying non-linear predictors will advance the study of mortality and will allow us to better examine the relationships between the predictors and mortality.

The Erdős–Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erdős–Simonovits type stability theorem in multi-partite graphs. Different from the Erdős–Simonovits stability theorem, our stability theorem in multi-partite graphs says that if the number of edges of an $H$-free graph $G$ is close to the extremal graphs for $H$, then $G$ has a well-defined structure but may be far away from the extremal graphs for $H$. As applications, we strengthen a theorem of Bollobás, Erdős, and Straus and solve a conjecture in a stronger form posed by Han and Zhao concerning the maximum number of edges in multi-partite graphs which does not contain vertex-disjoint copies of a clique.

We consider the hypergraph Turán problem of determining $ex(n, S^d)$, the maximum number of facets in a $d$-dimensional simplicial complex on $n$ vertices that does not contain a simplicial $d$-sphere (a homeomorph of $S^d$) as a subcomplex. We show that if there is an affirmative answer to a question of Gromov about sphere enumeration in high dimensions, then $ex(n, S^d) \geq \Omega (n^{d + 1 - (d + 1)/(2^{d + 1} - 2)})$. Furthermore, this lower bound holds unconditionally for 2-LC (locally constructible) spheres, which includes all shellable spheres and therefore all polytopes. We also prove an upper bound on $ex(n, S^d)$ of $O(n^{d + 1 - 1/2^{d - 1}})$ using a simple induction argument. We conjecture that the upper bound can be improved to match the conditional lower bound.

QuickSelect (also known as Find), introduced by Hoare ((1961) Commun. ACM 4 321–322.), is a randomized algorithm for selecting a specified order statistic from an input sequence of $n$ objects, or rather their identifying labels usually known as keys. The keys can be numeric or symbol strings, or indeed any labels drawn from a given linearly ordered set. We discuss various ways in which the cost of comparing two keys can be measured, and we can measure the efficiency of the algorithm by the total cost of such comparisons.

We define and discuss a closely related algorithm known as QuickVal and a natural probabilistic model for the input to this algorithm; QuickVal searches (almost surely unsuccessfully) for a specified population quantile $\alpha \in [0, 1]$ in an input sample of size $n$. Call the total cost of comparisons for this algorithm $S_n$. We discuss a natural way to define the random variables $S_1, S_2, \ldots$ on a common probability space. For a general class of cost functions, Fill and Nakama ((2013) Adv. Appl. Probab. 45 425–450.) proved under mild assumptions that the scaled cost $S_n / n$ of QuickVal converges in $L^p$ and almost surely to a limit random variable $S$. For a general cost function, we consider what we term the QuickVal residual:

\begin{equation*} \rho _n \,{:\!=}\, \frac {S_n}n - S. \end{equation*}

The residual is of natural interest, especially in light of the previous analogous work on the sorting algorithm QuickSort (Bindjeme and Fill (2012) 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Mathematics, and Theoretical Computer Science Proceedings, AQ, Association: Discrete Mathematics and Theoretical Computer Science, Nancy, pp. 339–348; Neininger (2015) Random Struct. Algorithms 46 346–361; Fuchs (2015) Random Struct. Algorithms 46 677–687; Grübel and Kabluchko (2016) Ann. Appl. Probab. 26 3659–3698; Sulzbach (2017) Random Struct. Algorithms 50 493–508). In the case $\alpha = 0$ of QuickMin with unit cost per key-comparison, we are able to calculate–àla Bindjeme and Fill for QuickSort (Bindjeme and Fill (2012) 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Mathematics and Theoretical Computer Science Proceedings, AQ, Association: Discrete Mathematics and Theoretical Computer Science, Nancy, pp. 339–348.)–the exact (and asymptotic) $L^2$-norm of the residual. We take the result as motivation for the scaling factor $\sqrt {n}$ for the QuickVal residual for general population quantiles and for general cost. We then prove in general (under mild conditions on the cost function) that $\sqrt {n}\,\rho _n$ converges in law to a scale mixture of centered Gaussians, and we also prove convergence of moments.

Achieving Zero Hunger by 2030, a United Nations Sustainable Development Goal, requires resilient food systems capable of securely feeding billions. This article introduces the Food Systems Resilience Score (FSRS), a novel framework that adapts a proven resilience measurement approach to the context of food systems. The FSRS builds on the success of the Community Flood Resilience Measurement Tool, which has been used in over 110 communities, by applying its five capitals (natural, human, social, financial, and manufactured) and four qualities (robustness, redundancy, resourcefulness, and rapidity) framework to food systems. We define food system resilience as the capacity to ensure adequate, appropriate, and accessible food supply to all, despite various disturbances and unforeseen disruptions. The FSRS measures resilience across multiple dimensions using carefully selected existing indicators, ensuring broad applicability and comparability. Our methodology includes rigorous technical validation to ensure reliability, including optimal coverage analysis, stability checks, and sensitivity testing. By providing standardized metrics and a comprehensive assessment of food system resilience, this framework not only advances research but also equips policymakers with valuable tools for effective interventions. The FSRS enables comparative analysis between countries and temporal tracking of resilience changes, facilitating targeted strategies to build and maintain resilient national food systems. This work contributes to the global effort toward long-term food security and sustainability.

Reduction in mobility due to gait impairment is a critical consequence of diseases affecting the neuromusculoskeletal system, making detecting anomalies in a person’s gait a key area of interest. This challenge is compounded by within-subject and between-subject variability, further emphasized in individuals with multiple sclerosis (MS), where gait patterns exhibit significant heterogeneity. This study introduces a novel perspective on modeling kinematic gait patterns, recognizing the inherent hierarchical structure of the data, which is gathered from contralateral limbs, individuals, and groups of individuals comprising a population, using wearable sensors. Rather than summarizing features, this approach models the entire gait cycle functionally, including its variation. A Hierarchical Variational Sparse Heteroscedastic Gaussian Process was used to model the shank angular velocity across 28 MS and 28 healthy individuals. The utility of this methodology was underscored by its granular analysis capabilities. This facilitated a range of quantifiable comparisons, spanning from group-level assessments to patient-specific analyses, addressing the complexity of pathological gait patterns and offering a robust methodology for kinematic pattern characterization for large datasets. The group-level analysis highlighted notable differences during the swing phase and towards the end of the stance phase, aligning with previously established literature findings. Moreover, the study identified the heteroscedastic gait pattern variability as a distinguishing feature of MS gait. Additionally, a novel approach for lower limb gait asymmetry quantification has been proposed. The use of probabilistic hierarchical modeling facilitated a better understanding of the impaired gait pattern, while also expressing potential for extrapolation to other pathological conditions affecting gait.

We investigate state-level age-specific mortality trends based on the United States Mortality Database (USMDB) published by the Human Mortality Database. In tandem with looking at the longevity experience across all the states, we also consider a collection of socio-demographic, economic, and educational covariates that correlate with mortality trends. To obtain smoothed mortality surfaces for each state, we implement the machine learning framework of Multi-Output Gaussian Process regression (Huynh & Ludkovski, AAS, 2021) on targeted groupings of 3–6 states. Our detailed exploratory analysis shows that the mortality experience is highly inhomogeneous across states in terms of respective Age structures. We moreover document multiple divergent trends between best and worst states, between Females and Males, and between younger and older Ages. The comparisons across the 50+ fitted models offer opportunities for rich insights about drivers of mortality in the U.S. and are visualized through numerous figures and an online interactive dashboard.

Following the large-scale Russian invasion in February 2022, policymakers and humanitarian actors urgently sought to anticipate displacement flows within Ukraine. However, existing internal displacement data systems had not been adapted to contexts as dynamic as a full-fledged war marked by uneven trigger events. A year and a half later, policymakers and practitioners continue to seek forecasts, needing to anticipate how many internally displaced persons (IDPs) can be expected to return to their areas of origin and how many will choose to stay and seek a durable solution in their place of displacement. This article presents a case study of an anticipatory approach deployed by the International Organization for Migration (IOM) Mission in Ukraine since March 2022, delivering nationwide displacement figures less than 3 weeks following the invasion alongside near real-time data on mobility intentions as well as key data anticipating the timing, direction, and volume of future flows and needs related to IDP return and (re)integration. The authors review pre-existing mobility forecasting approaches, then discuss practical experiences with mobility prediction applications in the Ukraine response using the Ukraine General Population Survey (GPS), including in program and policy design related to facilitating durable solutions to displacement. The authors focus on the usability and ethics of the approach, already considered for replication in other displacement contexts.

In this work, we focus on stochastic modeling for sustainable systems and introduce the family of r-modified reliability systems. This new family generalizes classical reliability systems studied in the literature by considering the components in the system to exhibit a kind of dependence that relaxes the component operating requirements and provides energy and resource efficiency. From a theoretical viewpoint, such a dependence is modeled with the use of a modified binary sequence. We then derive the reliability of two members of the family, i.e., the r-modified-k-out-of-n:F system and the r-modified-consecutive-k-out-of-n:F system, under different assumptions on the component reliabilities by using a variety of approaches, including Markov chains, combinatorial methods, and simple probabilistic arguments. We finally give some examples of real-life systems wherein the developed models and results are applicable and present the corresponding numerical results.

Governments all over the world are struggling to control the spiralling costs of healthcare – the UK government is no exception. Its long-term strategy includes a much greater focus on prevention: to keep people as healthy and productive as possible for longer. This paper asks whether a greater focus on prevention is a possible lifeline for the National Health Service (NHS) as is often claimed, but it also examines other benefits to society. After considering various examples of prevention and the metrics used to measure their effectiveness, we use tobacco consumption as a case study to evaluate the costs to the public purse and to wider society. We give further examples, including obesity, but in less depth. We find that whilst there are significant benefits to public expenditure, including the NHS, in both cases, these are dwarfed by wider benefits to society both in terms of tangible economic benefits and improved well-being. We offer several suggestions for improving our understanding of the effectiveness of prevention policies in general and how the Actuarial profession can contribute to this debate.

This paper investigates time-varying risk sharing between annuity buyer and provider. It explores Pareto optimal (PO) and viable Pareto optimal (VPO) risk-sharing designs, in which the share of the reserve deviation transferred to the policyholder varies over time. The optimization problem, based on a weighted average of mean-variance preferences, results in a complex quartic objective function. Such optimization problems are difficult to solve, and checking their convexity is known to be NP-hard. A heuristic method is introduced to simplify the problem, providing a closed-form solution that closely approximates the numerical results. The paper also highlights factors influencing the existence of VPO designs, with age playing a critical role, thereby suggesting the suitability of these designs as retirement products.

Investigating risk factors for mpox’s infectious period is vital for preventing this emerging disease, yet evidence remains scarce. This study aimed to identify risk factors associated with the duration of mpox infectiousness among mpox cases in Vietnam. The primary outcome was the duration of the mpox infectiousness, defined between symptom onset and the first negative test result for the mpox virus. Fine and Gray’s regression models were employed to assess the associations between the infectious period and several risk factors while accounting for competing risks of death by mpox. Most mpox cases recovered within 30 days. Patients with HIV or treated at multiple facilities for mpox had lower incidence rates of cleared infection compared to those who were HIV-negative or treated at a single facility. In regression models, patients with mpox symptoms of rash or mucosal lesions (sub-distribution hazard ratios = 0.62, 95% confidence interval = 0.46–0.83), ulcers (0.57, 0.41–0.80), or fever (0.62, 0.46–0.83) had significantly prolonged infectious periods than those without such symptoms. Our findings provided insights for managing mpox cases, especially those vulnerable to prolonged infectious periods in settings with sporadic cases reported.

The Alpha, Delta, and Omicron variants of the SARS-CoV-2 virus have been deemed as variants of concern (VOCs) by the WHO due to their increased transmissibility, severity of illness, and resilience against treatments. Geographically tracking the spread of these variants can help us implement effective control measures. RNA from 8,154 SARS-CoV-2 positive nasal swab samples from a Central Texas hospital collected between March 2020 and April 2023 were sequenced in Temple, TX. Global and U.S. sequencing metadata was obtained from the GISAID database on 3 April 2023. Using sequencing metadata, the growth rate of Alpha, Delta, and the first subvariant of Omicron (BA.1) were obtained as 0.27, 0.3, and 1.08 each. The average time in days to penetrate the US for Alpha, Delta, and Omicron were 269.2, 326.2, and 27.3 days, respectively. Viral sequencing data can be a useful tool to examine the spread of viruses. Each emerging SARS-CoV-2 variant penetrated cities more rapidly as the pandemic progressed. With a high logarithmic growth rate, the Omicron variant penetrated the US more rapidly as the pandemic progressed.

Inequality is a critical global issue, particularly in the United States, where economic disparities are among the most pronounced. Social justice research traditionally studies attitudes towards inequality—perceptions, beliefs, and judgments—using latent variable approaches. Recent scholarship adopts a network perspective, showing that these attitudes are interconnected within inequality belief systems. However, scholars often compare belief systems using split-sample approaches without examining how emotions, such as anger, shape these systems. Moreover, they rarely investigate Converse’s seminal idea that changes in central attitudes can lead to broader shifts in belief systems. Addressing these gaps, we applied a tripartite analytical strategy using U.S. data from the 2019 ISSP Social Inequality module. First, we used a mixed graphical model to demonstrate that inequality belief systems form cohesive small-world networks, with perception of large income inequality and belief in public redistribution as central nodes. Second, a moderated network model revealed that anger towards inequality moderates nearly one-third of network edges, consolidating the belief system by polarizing associations. Third, Ising model simulations showed that changes to central attitudes produce broader shifts across the belief system. This study advances belief system research by introducing innovative methods for comparing structures and testing dynamics of attitude change. It also contributes to social justice research by integrating emotional dynamics and highlighting anger’s role in structuring inequality belief systems.

We define the generalized equilibrium distribution, that is the equilibrium distribution of a random variable with support in $\mathbb{R}$. This concept allows us to prove a new probabilistic generalization of Taylor’s theorem. Then, the generalized equilibrium distribution of two ordered random variables is considered and a probabilistic analog of the mean value theorem is proved. Results regarding distortion-based models and mean-median-mode relations are illustrated as well. Conditions for the unimodality of such distributions are obtained. We show that various stochastic orders and aging classes are preserved through the proposed equilibrium transformations. Further applications are provided in actuarial science, aiming to employ the new unimodal equilibrium distributions for some risk measures, such as Value-at-Risk and Conditional Tail Expectation.

We show that on every affine Weyl group natural random walks are noise sensitive in total variation.

As the global elderly population expands, the associated risks of longevity intensify, presenting significant challenges to traditional retirement security systems. We study actuarial fairness in tontines under the Volterra mortality framework, integrating long-range dependence mortality models rates with tontine structures. Initially, we establish an optimal tontine model for a homogeneous tontine under this framework. However, according only to individual actuarial fairness can neglect the collective nature of tontines. So we propose a hybrid optimization model that accounts for age and wealth discrepancies affecting payment amounts and the collective fairness. Specially, we first apply the f-value fairness measure in age-heterogeneous tontines for assessing fairness. Our results reveal that while the model ensures actuarial fairness at the group level, relative payments are lower for older age groups. By incorporating dynamic mortality modeling through the Volterra mortality framework, our work demonstrates that this comprehensive scheme significantly enhances the robustness and sustainability of retirement security systems. These findings provide valuable insights for the future integration of dynamic mortality models with innovative retirement income structures.

Hepatitis B virus vaccination is currently recommended in Australia for adults at an increased risk of acquiring infection or at high risk of complications from infection. This retrospective cohort study used data from an Australian sentinel surveillance system to assess the proportion of individuals who had a recorded test that indicated being susceptible to hepatitis B infection in six priority populations, as well as the proportion who were then subsequently vaccinated within six months of being identified as susceptible. Priority populations included in this analysis were people born overseas in a hepatitis B endemic country, people living with HIV, people with a recent hepatitis C infection, gay, bisexual and other men who have sex with men, people who have ever injected drugs, and sex workers. Results of the study found that in the overall cohort of 43,335 individuals, 14,140 (33%) were identified as susceptible to hepatitis B, and 5,255 (37%) were subsequently vaccinated. Between 26% and 33% of individuals from priority populations were identified as susceptible to hepatitis B infection, and the proportion of these subsequently vaccinated within six months was between 28% and 42% across the groups. These findings suggest further efforts are needed to increase the identification and subsequent vaccination of susceptible individuals among priority populations recommended for hepatitis B vaccination, including among people who are already engaged in hepatitis B care.