We propose a discrete-time discrete-space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of curvilinear boundaries and diffusion processes, we prove the convergence of the constructed approximations in the form of products of the respective substochastic matrices to the boundary crossing probabilities for the process as the time grid used to construct the Markov chains is getting finer. Numerical results indicate that the convergence rate for the proposed approximation with the Brownian bridge correction is $O(n^{-2})$ in the case of $C^2$ boundaries and a uniform time grid with n steps.

The basic idea of voting protocols is that nodes query a sample of other nodes and adjust their own opinion throughout several rounds based on the proportion of the sampled opinions. In the classic model, it is assumed that all nodes have the same weight. We study voting protocols for heterogeneous weights with respect to fairness. A voting protocol is fair if the influence on the eventual outcome of a given participant is linear in its weight. Previous work used sampling with replacement to construct a fair voting scheme. However, it was shown that using greedy sampling, i.e., sampling with replacement until a given number of distinct elements is chosen, turns out to be more robust and performant.

In this paper, we study fairness of voting protocols with greedy sampling and propose a voting scheme that is asymptotically fair for a broad class of weight distributions. We complement our theoretical findings with numerical results and present several open questions and conjectures.

We study the distribution of the consensus formed by a broadcast-based consensus algorithm for cases in which the initial opinions of agents are random variables. We first derive two fundamental equations for the time evolution of the average opinion of agents. Using the derived equations, we then investigate the distribution of the consensus in the limit in which agents do not have any mutual trust, and show that the consensus without mutual trust among agents is in sharp contrast to the consensus with complete mutual trust in the statistical properties if the initial opinion of each agent is integrable. Next, we provide the formulation necessary to mathematically discuss the consensus in the limit in which the number of agents tends to infinity, and derive several results, including a central limit theorem concerning the consensus in this limit. Finally, we study the distribution of the consensus when the initial opinions of agents follow a stable distribution, and show that the consensus also follows a stable distribution in the limit in which the number of agents tends to infinity.

This study aims to understand the time-to-treatment initiation pre and post DAA access to inform strategies to improve HCV care. The data for our study were derived from the SuperMIX cohort study of people who inject drugs in Melbourne, Australia. Time-to-event analysis using Weibull accelerated failure time was performed for data collected between 2009 and 2021, among a cohort of HCV-positive participants. Among 223 participants who tested positive for active hepatitis C infection, 102 people (45.7%) reported treatment initiation, with a median time-to-treatment of 7 years. However, the median time-to-treatment reduced to 2.3 years for those tested positive after 2016. The study found that treatment with Opioid Agonist Therapy (TR 0.7, 95% CI 0.6–0.9), engagement with health or social services (TR 0.7, 95% CI 0.6–0.9), and having a first positive HCV RNA test after March 2016 (TR 0.3, 95% CI 0.2–0.3) were associated with a reduced time-to-treatment initiation. The study highlights the need for strategies to improve engagement with health services, including drug treatment services into routine HCV care to achieve timely treatment.

Relational event models (REMs) for the analysis of social interaction were first introduced 15 years ago. Since then, a number of important substantive and methodological contributions have produced their progressive refinement and hence facilitated their increased adoption in studies of social and other networks. Today REMs represent a well-established class of statistical models for relational processes. This special issue of Network Science demonstrates the standing and recognition that REMs have achieved within the network analysis and networks science communities. We wrote this brief introductory editorial essay with four main objectives in mind: (i) positioning relational event data and models in the larger context of contemporary network science and social network research; (ii) reviewing some of the most important recent developments; (iii) presenting the innovative studies collected in this special issue as evidence of the empirical value of REMs, and (iv) identifying open questions and future research directions.

In this paper, we consider a financial or insurance system with a finite number of individual risks described by real-valued random variables. We focus on two kinds of risk measures, referred to as the tail moment (TM) and the tail central moment (TCM), which are defined as the conditional moment and conditional central moment of some individual risk in the event of system crisis. The first-order TM and the second-order TCM coincide with the popular risk measures called the marginal expected shortfall and the tail variance, respectively. We derive asymptotic expressions for the TM and TCM with any positive integer orders, when the individual risks are pairwise asymptotically independent and have distributions from certain classes that contain both light-tailed and heavy-tailed distributions. The formulas obtained possess concise forms unrelated to dependence structures, and hence enable us to estimate the TM and TCM efficiently. To demonstrate the wide application of our results, we revisit some issues related to premium principles and optimal capital allocation from the asymptotic point of view. We also give a numerical study on the relative errors of the asymptotic results obtained, under some specific scenarios when there are two individual risks in the system. The corresponding asymptotic properties of the degenerate univariate versions of the TM and TCM are discussed separately in an appendix at the end of the paper.

The hypothesis that violence—especially gang violence—behaves like a contagious disease has grown in popularity in recent years. Scholars have long observed the tendency for violence to cluster in time and space, but little research has focused on empirically unpacking the mechanisms that make violence contagious. In the context of gang violence, retaliation is the prototypical mechanism to explain why violence begets violence. In this study, we leverage relational event models (REMs)—an underutilized yet particularly well-suited modeling technique to study the dynamics of inter-gang violence. We use REMs to examine gang violence’s tendency to replicate—for which retaliation is but one plausible mechanism—and its tendency to diffuse to other groups. We rely on data on conflicts between gangs in a region of Los Angeles over 3 years. We consider how the characteristics of gangs, their spatial proximity, networks of established rivalries, and the evolving history, directionality, and structure of conflicts predict future inter-gang conflicts. While retaliation is an important mechanism for the replication of violence, established rivalries, and inertia—a gang’s tendency to continue attacking the same group—are more important drivers of future violence. We also find little evidence for an emerging pecking order or status hierarchy between gangs suggested by other scholars. However, we find that gangs are more likely to attack multiple gangs in quick succession. We propose that gang violence is more likely to diffuse to other groups because of the boost of internal group processes an initial attack provides.

This study aims to understand the epidemiological characteristics of SARS-CoV-2 infection in the paediatric population during the outbreak of the Omicron variant in Shanghai. We retrospectively analysed the population-based epidemiological characteristics and clinical outcome of SARS-CoV-2 Omicron variant infection in children in Minhang District, Shanghai, based on the citywide surveillance system during the outbreak period in 2022 (March to May). During this time, a total of 63,969 cases of SARS-CoV-2 infection were notified in Minhang District, out of which 4,652 (7.3%) were children and adolescents <18 years. The incidence rate of SARS-CoV-2 infections in children was 153 per 10,000. Of all paediatric cases, 50% reported to be clinically symptomatic within 1–3 days after PCR confirmation by parents or themselves, with 36.3% and 18.9% of paediatric cases reporting fever and cough. Also, 58.4% of paediatric cases had received at least one dose of the COVID-19 vaccine and 52.1% had received two doses of the COVID-19 vaccination. Our findings are informative for the implementation of appropriate measures to protect children from the threat of SARS-CoV-2 infection.

This work presents a $\textsf{Python}$ EMD package named AdvEMDpy that is both more flexible and generalises existing empirical mode decomposition (EMD) packages in $\textsf{Python}$, $\textsf{R}$, and $\textsf{MATLAB}$. It is aimed specifically for use by the insurance and financial risk communities, for applications such as return modelling, claims modelling, and life insurance applications with a particular focus on mortality modelling. AdvEMDpy both expands upon the EMD options and methods available, and improves their statistical robustness and efficiency, providing a robust, usable, and reliable toolbox. Unlike many EMD packages, AdvEMDpy allows customisation by the user, to ensure that a broader class of linear, non-linear, and non-stationary time series analyses can be performed. The intrinsic mode functions (IMFs) extracted using EMD contain complex multi-frequency structures which warrant maximum algorithmic customisation for effective analysis. A major contribution of this package is the intensive treatment of the EMD edge effect which is the most ubiquitous problem in EMD and time series analysis. Various EMD techniques, of varying intricacy from numerous works, have been developed, refined, and, for the first time, compiled in AdvEMDpy. In addition to the EMD edge effect, numerous pre-processing, post-processing, detrended fluctuation analysis (localised trend estimation) techniques, stopping criteria, spline methods, discrete-time Hilbert transforms (DTHT), knot point optimisations, and other algorithmic variations have been incorporated and presented to the users of AdvEMDpy. This paper and the supplementary materials provide several real-world actuarial applications of this package for the user’s benefit.

We study site and bond percolation in simple directed random graphs with a given degree distribution. We derive the percolation threshold for the giant strongly connected component and the fraction of vertices in this component as a function of the percolation probability. The results are obtained for degree sequences in which the maximum degree may depend on the total number of nodes n, being asymptotically bounded by $n^{\frac{1}{9}}$.