We consider the following question: given information on individual policyholder characteristics, how can we ensure that insurance prices do not discriminate with respect to protected characteristics, such as gender? We address the issues of direct and indirect discrimination, the latter resulting from implicit learning of protected characteristics from nonprotected ones. We provide rigorous mathematical definitions for direct and indirect discrimination, and we introduce a simple formula for discrimination-free pricing, that avoids both direct and indirect discrimination. Our formula works in any statistical model. We demonstrate its application on a health insurance example, using a state-of-the-art generalized linear model and a neural network regression model. An important conclusion is that discrimination-free pricing in general requires collection of policyholders’ discriminatory characteristics, posing potential challenges in relation to policyholder’s privacy concerns.

We define a new ribbon group action on ribbon graphs that uses a semidirect product of a permutation group and the original ribbon group of Ellis-Monaghan and Moffatt to take (partial) twists and duals, or twuals, of ribbon graphs. A ribbon graph is a fixed point of this new ribbon group action if and only if it is isomorphic to one of its (partial) twuals. This extends the original ribbon group action, which only used the canonical identification of edges, to the more natural setting of self-twuality up to isomorphism. We then show that every ribbon graph has in its orbit an orientable embedded bouquet and prove that the (partial) twuality properties of these bouquets propagate through their orbits. Thus, we can determine (partial) twualities via these one vertex graphs, for which checking isomorphism reduces simply to checking dihedral group symmetries. Finally, we apply the new ribbon group action to generate all self-trial ribbon graphs on up to seven edges, in contrast with the few, large, very high-genus, self-trial regular maps found by Wilson, and by Jones and Poultin. We also show how the automorphism group of a ribbon graph yields self-dual, -petrial or –trial graphs in its orbit, and produce an infinite family of self-trial graphs that do not arise as covers or parallel connections of regular maps, thus answering a question of Jones and Poulton.

Telematicsdevices installed in insured vehicles provide actuaries with new risk factors, such as the time of the day, average speeds, and other driving habits. This paper extends the multivariate mixed model describing the joint dynamics of telematics data and claim frequencies proposed by Denuit et al. (2019a) by allowing for signals with various formats, not necessarily integer-valued, and by replacing the estimation procedure with the Expected Conditional Maximization algorithm. A numerical study performed on a database related to Pay-How-You-Drive, or PHYD motor insurance illustrates the relevance of the proposed approach for practice.

This paper introduces a framework for understanding complex temporal interaction patterns in large-scale scientific collaboration networks. In particular, we investigate how two key concepts in science studies, scientific collaboration and scientific mobility, are related and possibly differ between fields. We do so by analyzing multilayer temporal motifs: small recurring configurations of nodes and edges.

Driven by the problem that many papers share the same publication year, we first provide a methodological contribution: an efficient counting algorithm for multilayer temporal motifs with concurrent edges. Next, we introduce a systematic categorization of the multilayer temporal motifs, such that each category reflects a pattern of behavior relevant to scientific collaboration and mobility. Here, a key question concerns the causal direction: does mobility lead to collaboration or vice versa? Applying this framework to scientific collaboration networks extracted from Web of Science (WoS) consisting of up to 7.7 million nodes (authors) and 94 million edges (collaborations), we find that international collaboration and international mobility reciprocally influence one another. Additionally, we find that Social sciences & Humanities (SSH) scholars co-author to a greater extent with authors at a distance, while Mathematics & Computer science (M&C) scholars tend to continue to collaborate within the established knowledge network and organization.

The network Laplacian spectral density calculation is critical in many fields, including physics, chemistry, statistics, and mathematics. It is highly computationally intensive, limiting the analysis to small networks. Therefore, we present two efficient alternatives: one based on the network’s edges and another on the degrees. The former gives the exact spectral density of locally tree-like networks but requires iterative edge-based message-passing equations. In contrast, the latter obtains an approximation of the spectral density using only the degree distribution. The computational complexities are 𝒪(|E|log(n)) and 𝒪(n), respectively, in contrast to 𝒪(n3) of the diagonalization method, where n is the number of vertices and |E| is the number of edges.

Vertebral osteomyelitis (VO) represents 4–10% of bone and joint infections. In Western countries, its incidence seems to increase, simultaneously with an increasing number of comorbidities among an ageing population. This study aimed to assess the evolution of VO epidemiology in France over the 2010–2019 decade. A nationwide cross-sectional study was conducted using the French hospital discharge data collected through the French diagnosis-related groups ‘Programme de Médicalisation des Systèmes d'Information’. VOs were detected with a previously validated case definition using International Classification of Diseases 10 (ICD-10) codes, implemented with the French current procedural terminology codes. The study population included all patients hospitalised in France during the 2010–2019 decade, aged 15 years old and more. Patient and hospital stay characteristics and their evolutions were described. During the study period, 42 105 patients were hospitalised for VO in France involving 60 878 hospital stays. The mean VO incidence was 7.8/100 000 over the study period, increasing from 6.1/100 000 in 2010 to 11.3/100 000 in 2019. The mean age was 64.8 years old and the sex ratio was 1.56. There were 31 341 (74.4%) patients with at least one comorbidity and 3059 (7.3%) deceased during their hospital stay. Even if rare, device-associated VOs (4450 hospital stays, 7.3%) highly increased over the period. The reliability of the method, based upon an exhaustive database and a validated case definition, provided an effective tool to compare data over time in real-life conditions to regularly update the epidemiology of VO.

As the corona virus disease 2019 (COVID-19) pandemic continues around the world, understanding the transmission characteristics of COVID-19 is vital for prevention and control. We conducted the first study aiming to estimate and compare the relative risk of secondary attack rates (SARs) of COVID-19 in different contact environments. Until 26 July 2021, epidemiological studies and cluster epidemic reports of COVID-19 were retrieved from SCI, Embase, PubMed, CNKI, Wanfang and CBM in English and Chinese, respectively. Relative risks (RRs) were estimated in pairwise comparisons of SARs between different contact environments using the frequentist NMA framework, and the ranking of risks in these environments was calculated using the surface under the cumulative ranking curve (SUCRA). Subgroup analysis was performed by regions. Thirty-two studies with 68 260 participants were identified. Compared with meal or gathering, transportation (RR 10.55, 95% confidence interval (CI) 1.43–77.85), medical care (RR 11.68, 95% CI 1.58–86.61) and work or study places (RR 10.15, 95% CI 1.40–73.38) had lower risk ratios for SARs. Overall, the SUCRA rankings from the highest to the lowest were household (95.3%), meal or gathering (81.4%), public places (58.9%), daily conversation (50.1%), transportation (30.8%), medical care (18.2%) and work or study places (15.3%). Household SARs were significantly higher than other environments in the subgroup of mainland China and sensitive analysis without small sample studies (<100). In light of the risks, stratified personal protection and public health measures need to be in place accordingly, so as close contacts categorising and management.

Spatial data are a rich source of information for actuarial applications: knowledge of a risk’s location could improve an insurance company’s ratemaking, reserving or risk management processes. Relying on historical geolocated loss data is problematic for areas where it is limited or unavailable. In this paper, we construct spatial embeddings within a complex convolutional neural network representation model using external census data and use them as inputs to a simple predictive model. Compared to spatial interpolation models, our approach leads to smaller predictive bias and reduced variance in most situations. This method also enables us to generate rates in territories with no historical experience.

Reliable hepatitis C prevalence estimates are crucial for a good follow-up of the indicators to eliminate hepatitis by 2030 as set by the World Health Organization. In Belgium, no recent national population-based hepatitis C virus (HCV) seroprevalence estimate is available. The current study estimated HCV prevalence as part of the first Belgian Health Examination Survey, which was organized in 2018 as a second stage of the sixth Belgian Health Interview Survey. This national population-based cross-sectional study resulted in a weighted national HCV seroprevalence of 0.02% (95% CI 0.00–0.07%). The results show a much lower HCV seroprevalence compared to previous studies.

The COVID-19 pandemic has accelerated the use of mobile operator data to support public policy, although without a universal governance framework for its application. This article describes five principles to guide and assist statistical agencies, mobile network operators and intermediary service providers, who are actively working on projects using mobile operator data to support governments in monitoring the effectiveness of its COVID-19 related interventions. These are principles of necessity and proportionality, of professional independence, of privacy protection, of commitment to quality, and of international comparability. Compliance with each of these principles can help maintain public trust in the handling of these sensitive data and their results, and therefore keep citizen support for government policies. Three projects (in Estonia, Ghana, and the Gambia) were described and reviewed with respect to the compliance and applicability of the five principles. Most attention was placed on privacy protection, somewhat at the expense of the quality of the compiled indicators. The necessity and proportionality in the choice of mobile operator data can be very well justified given the need for timely, frequent and granular indicators. Explicitly addressing the five principles in the preparation of a project should give confidence to the statistical agency and its partners, that enough care has been exercised in the set up and implementation of the project, and should convey trust to public and government in the use mobile operator data for policy purposes.

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin represents the monitored system as accurately as possible. One way this is achieved is by calibration of simulation models, whether data-derived or physics-based, or a combination of both. Traditional manual calibration is not possible in this context; hence, new methods are required for continuous calibration. In this paper, a particle filter methodology for continuous calibration of the physics-based model element of a digital twin is presented and applied to an example of an underground farm. The methodology is applied to a synthetic problem with known calibration parameter values prior to being used in conjunction with monitored data. The proposed methodology is compared against static and sequential Bayesian calibration approaches and compares favourably in terms of determination of the distribution of parameter values and analysis run times, both essential requirements. The methodology is shown to be potentially useful as a means to ensure continuing model fidelity.

A case of listeriosis occurred in a hospitalised patient in England in July 2017. Analysis by whole genome sequencing of the Listeria monocytogenes from the patient's blood culture was identified as clonal complex (CC) 121. This culture was indistinguishable to isolates from sandwiches, salads and the maufacturing environment of Company X which supplied these products widely to the National Health Service. Whilst an inpatient, the case was served sandwiches produced by this company on 12 occasions. No other cases infected by this type were detected in the UK between 2016 and 2020. Between 2016 and 2020, more than 3000 samples of food, food ingredients and environmental swabs from this company were tested. Listeria monocytogenes contamination rates declined after July 2017 from 31% to 0.3% for salads and 3% to 0% for sandwiches. A monophyletic group of 127 L. monocytogenes CC121 isolates was recovered during 2016–2019 and was used to estimate the time of the most recent common ancestor as 2014 (95% CI of between 2012 and 2016). These results represent persistent contamination of equipment, food contact surfaces and foods at a food manufacturer by a single L. monocytogenes strain. Colonisation and persistent contamination of food and production environments are risks for public health.