In this paper, we consider the friendship paradox in the context of random walks and paths. Among our results, we give an equality connecting long-range degree correlation, degree variability, and the degree-wise effect of additional steps for a random walk on a graph. Random paths are also considered, as well as applications to acquaintance sampling in the context of core-periphery structure.

Finite state Markov processes and their aggregated Markov processes have been extensively studied, especially in ion channel modeling and reliability modeling. In reliability field, the asymptotic behaviors of repairable systems modeled by both processes have been paid much attention to. For a Markov process, it is well-known that limiting measures such as availability and transition probability do not depend on the initial state of the process. However, for an aggregated Markov process, it is difficult to directly know whether this conclusion holds true or not from the limiting measure formulas expressed by the Laplace transforms. In this paper, four limiting measures expressed by Laplace transforms are proved to be independent of the initial state through Tauber’s theorem. The proof is presented under the assumption that the rank of transition rate matrix is one less than the dimension of state space for the Markov process, which includes the case that all states communicate with each other. Some numerical examples and discussions based on these are presented to illustrate the results directly and to show future related research topics. Finally, the conclusion of the paper is given.

We conducted a retrospective cross-sectional population-based survey among recovered COVID-19 cases in Uganda to establish the case presentations of the second wave SARS-CoV-2 infections. We interviewed 1,120 recovered COVID-19 cases from 10 selected districts in Uganda. We further conducted 38 key informant interviews with members of the COVID-19 District Taskforce and 19 in-depth interviews among COVID-19 survivors from March to June 2021. Among them, 62% were aged 39 years and below and 51.5% were female with 90.9% under home-based care management. Cases were more prevalent among businesspeople (25.9%), students (16.2%), farmers (16.1%), and health workers (12.4%). Being asymptomatic was found to be associated with not seeking healthcare (APR 2, P < 0.001). The mortality rate was 3.6% mostly among the elderly (6.3%) and 31.3% aged 40 years and above had comorbidities of high blood pressure, diabetes, and asthma. Being asymptomatic, or under home-based care management (HBCM), working/operating/studying at schools, and not being vaccinated were among the major drivers of the second wave of the resurgence of COVID19 in Uganda. Managing future COVID-19 waves calls for proactive efforts for improving homebased care services, ensuring strict observation of SOPs in schools, and increasing the uptake of COVID-19 vaccination.

Polarization makes it difficult to form positive relationships across existing groups. Decreasing polarization may improve political discourse around the world. Polarization can be modeled on a social network as structural balance, where the network is composed of groups with positive links between all individuals in the group and negative links with all others. Previous work shows that incorporating attributes of individuals usually makes structural balance, and hence polarization, harder to achieve. That work examines only a limited number and types of attributes. We present a generalized model and a simulation framework to analyze the effect of any type of attribute, including analytically as long as an expected value can be written for the type of attribute. As attributes, we consider people’s (approximately) immutable characteristics (e.g., race, wealth) and such opinions that change more slowly than relationships (e.g., political preferences). We detail and analyze five classes of attributes, recapitulating the results of previous work in this framework and extending it. While it is easier to prevent than to destabilize polarization, we find that usually the most effective at both are continuous attributes, followed by ordered attributes and, finally, binary attributes. The effectiveness of unordered attributes varies depending on the magnitude of negative impact of having differing attributes but is smaller than of continuous ones. Testing the framework on network structures containing communities revealed that destroying polarization may require introducing local tensions. This model could be used by policymakers, among others, to prevent and design effective interventions to counteract polarization.

A graph is called $k$-critical if its chromatic number is $k$ but every proper subgraph has chromatic number less than $k$. An old and important problem in graph theory asks to determine the maximum number of edges in an $n$-vertex $k$-critical graph. This is widely open for every integer $k\geq 4$. Using a structural characterisation of Greenwell and Lovász and an extremal result of Simonovits, Stiebitz proved in 1987 that for $k\geq 4$ and sufficiently large $n$, this maximum number is less than the number of edges in the $n$-vertex balanced complete $(k-2)$-partite graph. In this paper, we obtain the first improvement in the above result in the past 35 years. Our proofs combine arguments from extremal graph theory as well as some structural analysis. A key lemma we use indicates a partial structure in dense $k$-critical graphs, which may be of independent interest.

We create a framework to analyze the timing and frequency of instantaneous interactions between pairs of entities. This type of interaction data is especially common nowadays and easily available. Examples of instantaneous interactions include email networks, phone call networks, and some common types of technological and transportation networks. Our framework relies on a novel extension of the latent position network model: we assume that the entities are embedded in a latent Euclidean space and that they move along individual trajectories which are continuous over time. These trajectories are used to characterize the timing and frequency of the pairwise interactions. We discuss an inferential framework where we estimate the individual trajectories from the observed interaction data and propose applications on artificial and real data.

A new COVID-19 vaccine was introduced in a remarkably short period of time. Public and healthcare workers (HCWs) were concerned about the safety of the vaccine, especially in light of the use of new technologies. A review regarding attitudes towards COVID-19 vaccination found a 22.5% hesitancy rate among HCWs. Online anonymous questionnaires were delivered using a web-based surveying platform to community HCWs in a central district in Israel from 3 to 19 January 2021. The real COVID-19 vaccination data were collected between the beginning of the vaccination rollout and the end of the month after the survey as well as the real vaccination rate among the general population. Of the 3,172 HCWs, 549 (17%) responded to the questionnaire. The highest positive attitude towards the vaccine was among physicians (95%), while nurses showed the highest level of hesitation (14%) for a specific sector (P < 0.05). However, the real vaccination rates were similar among physicians (63%) and nurses (62%). Surprisingly, the total vaccination rate of HCWs was substantially lower (52%) than that of the general population (71%). The main vaccination motivators were the social and economic effects of the COVID-19 epidemic. Focused strategies to reduce the level of hesitancy among HCWs are needed.

An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

This work concerns Markov decision chains on a denumerable state space endowed with a bounded cost function. The performance of a control policy is assessed by a long-run average criterion as measured by a risk-seeking decision maker with constant risk-sensitivity. Besides standard continuity–compactness conditions, the framework of the paper is determined by the following conditions: (i) the state process is communicating under each stationary policy, and (ii) the simultaneous Doeblin condition holds. Within this framework it is shown that (i) the optimal superior and inferior limit average value functions coincide and are constant, and (ii) the optimal average cost is characterized via an extended version of the Collatz–Wielandt formula in the theory of positive matrices.

Varicella vaccination is optional and requires self-payment. On 1 December 2018, Wuxi City launched a free varicella vaccination program for children. This study aimed to evaluate the changes in varicella incidence before and after the implementation of the policy. The data were obtained from official information systems and statistical yearbooks. We divided the period into chargeable (January 2017 to November 2018) and free (December 2018 to December 2021) periods. Interrupt time series analysis was used to conduct a generalised least-squares regression analysis for the two periods. A total of 51,071 varicella cases were reported between January 2017 and December 2021. After the implementation of the policy, there was a statistically significant decrease in the incidence of varicella (β2 = −0.140, P = 0.017), and the slope of the incidence also decreased by 0.012 (P = 0.015). Following policy implementation, the incidence decreased in all age groups, with the largest decline observed among children aged 8–14 years (β2 = −1.109, P = 0.009), followed by children aged ≤7 years (β2 = −0.894, P = 0.013). Our study found a significant reduction in the incidence of varicella in the total population after the introduction of free varicella vaccination in Wuxi City.

This work aimed to study the role of different SARS-CoV-2 lineages in the epidemiology of multiple waves of the COVID-19 pandemic in Ribeirão Preto (São Paulo state), with comparison within Brazil and globally. Viral genomic sequencing was combined with clinical and sociodemographic information of 2,379 subjects at a large Brazilian hospital. On the whole 2,395 complete SARS-CoV-2 genomes were obtained from April 2020 to January 2022. We report variants of concern (VOC) and interest (VOI) dynamics and the role of Brazilian lineages. We identified three World Health Organization VOCs (Gamma, Delta, Omicron) and one VOI (Zeta), which caused distinct waves in this cohort. We also identified 47 distinct Pango lineages. Consistent with the high prevalence of Gamma in Brazil, Pango lineage P.1 dominated infections in this cohort for half of 2021. Each wave of infection largely consisted of a single variant group, with each new group quickly and completely rising to dominance. Despite increasing vaccination in Brazil starting in 2021, this pattern was observed throughout the study and is consistent with the hypothesis that herd immunity tends to be SARS-CoV-2 variant-specific and does not broadly protect against COVID-19.

In this paper we study a variation of the random $k$-SAT problem, called polarised random $k$-SAT, which contains both the classical random $k$-SAT model and the random version of monotone $k$-SAT another well-known NP-complete version of SAT. In this model there is a polarisation parameter $p$, and in half of the clauses each variable occurs negated with probability $p$ and pure otherwise, while in the other half the probabilities are interchanged. For $p=1/2$ we get the classical random $k$-SAT model, and at the other extreme we have the fully polarised model where $p=0$, or 1. Here there are only two types of clauses: clauses where all $k$ variables occur pure, and clauses where all $k$ variables occur negated. That is, for $p=0$, and $p=1$, we get an instance of random monotone $k$-SAT.

We show that the threshold of satisfiability does not decrease as $p$ moves away from $\frac{1}{2}$ and thus that the satisfiability threshold for polarised random $k$-SAT with $p\neq \frac{1}{2}$ is an upper bound on the threshold for random $k$-SAT. Hence the satisfiability threshold for random monotone $k$-SAT is at least as large as for random $k$-SAT, and we conjecture that asymptotically, for a fixed $k$, the two thresholds coincide.

Cyclosporiasis results from an infection of the small intestine by Cyclospora parasites after ingestion of contaminated food or water, often leading to gastrointestinal distress. Recent developments in temporally linking genetically related Cyclospora isolates demonstrated effectiveness in supporting epidemiological investigations. We used ‘temporal-genetic clusters’ (TGCs) to investigate reported cyclosporiasis cases in the United States during the 2021 peak-period (1 May – 31 August 2021). Our approach split 655 genotyped isolates into 55 genetic clusters and 31 TGCs. We linked two large multi-state epidemiological clusters (Epidemiologic Cluster 1 [n = 136 cases, 54 genotyped] and Epidemiologic Cluster 2 [n = 42 cases, 15 genotyped]) to consumption of lettuce varieties; however, product traceback did not identify a specific product for either cluster due to the lack of detailed product information. To evaluate the utility of TGCs, we performed a retrospective case study comparing investigation outcomes of outbreaks first detected using epidemiological methods with those of the same outbreaks had TGCs been used to first detect them. Our study results indicate that adjustments to routine epidemiological approaches could link additional cases to epidemiological clusters of cyclosporiasis. Overall, we show that CDC’s integrated genotyping and epidemiological investigations provide valuable insights into cyclosporiasis outbreaks in the United States.

A register-based retrospective observational study was conducted to describe SARS-CoV-2 cases and case-clusters in schoolchildren of Danish primary and lower secondary schools and identify which factors were associated with the occurrence of case-clusters in schools. The study period was the autumn school semester 2021. Clusters were defined as three or more cases in a school-class level within 14 days. Descriptive analysis was carried out and multivariable logistic regression analysis was performed to determine which factors were associated with case introductions (i.e., primary case) being linked to a cluster. More cases and clusters were identified in lower than in higher class levels. Out of 21,497 cases introduced into a school, 41.6% started a cluster. A higher assumed immunity level in a class level was significantly reducing the odds of a case introduction being linked to a cluster (e.g., assumed immunity of ≥80% vs <20%: OR: 0.28; 95%CI: 0.17–0.44). A previous infection (in the primary case) had a protective effect (OR: 0.58; 95%CI: 0.33–0.99). This study suggests that most cases appearing in schools did not induce clusters, but that once cluster occur sizes can be large. It further indicates that vaccination of children markedly reduces the risk of secondary infections.

The aim of this cross-sectional study was to identify post-COVID-19 condition (PCC) phenotypes and to investigate the health-related quality of life (HRQoL) and healthcare use per phenotype. We administered a questionnaire to a cohort of PCC patients that included items on socio-demographics, medical characteristics, health symptoms, healthcare use, and the EQ-5D-5L. A principal component analysis (PCA) of PCC symptoms was performed to identify symptom patterns. K-means clustering was used to identify phenotypes. In total, 8630 participants completed the survey. The median number of symptoms was 18, with the top 3 being fatigue, concentration problems, and decreased physical condition. Eight symptom patterns and three phenotypes were identified. Phenotype 1 comprised participants with a lower-than-average number of symptoms, phenotype 2 with an average number of symptoms, and phenotype 3 with a higher-than-average number of symptoms. Compared to participants in phenotypes 1 and 2, those in phenotype 3 consulted significantly more healthcare providers (median 4, 6, and 7, respectively, p < 0.001) and had a significantly worse HRQoL (p < 0.001). In conclusion, number of symptoms rather than type of symptom was the driver in the identification of PCC phenotypes. Experiencing a higher number of symptoms is associated with a lower HRQoL and more healthcare use.

HIV-1 molecular surveillance provides a new approach to explore transmission risks and targeted interventions. From January to June 2021, 663 newly reported HIV-1 cases were recruited in Zhaotong City, Yunnan Province, China. The distribution characteristics of HIV-1 subtypes and HIV-1 molecular network were analysed. Of 542 successfully subtyped samples, 12 HIV-1 strains were identified. The main strains were CRF08_BC (47.0%, 255/542), CRF01_AE (17.0%, 92/542), CRF07_BC (17.0%, 92/542), URFs (8.7%, 47/542), and CRF85_BC (6.5%, 35/542). CRF08_BC was commonly detected among Zhaotong natives, illiterates, and non-farmers and was mostly detected in Zhaoyang County. CRF01_AE was frequently detected among married and homosexual individuals and mostly detected in Weixin and Zhenxiong counties. Among the 516 pol sequences, 187 (36.2%) were clustered. Zhaotong natives, individuals aged ≥60 years, and illiterate individuals were more likely to be found in the network. Assortativity analysis showed that individuals were more likely to be genetically associated when stratified by age, education level, occupation, and reporting area. The genetic diversity of HIV-1 reflects the complexity of local HIV epidemics. Molecular network analyses revealed the subpopulations to focus on and the characteristics of the risk networks. The results will help optimise local prevention and control strategies.

In pricing insurance contracts based on the individual policyholder’s aggregate losses for non-life insurers, the literature has mainly focused on using detailed information from policies and closed claims. However, the information on open claims can reflect shifts in the distribution of the expected claim payments better than closed claims. Such shifts may be needed to be reflected in the ratemaking process earlier rather than later, especially when insurers are experiencing environmental changes. In practice, actuaries use ad hoc techniques to adjust data to current levels to determine premiums. This paper presents an intuitive ratemaking model, employing a marked Poisson process framework, which ensures that the multivariate risk analysis is done more routinely using all reported claims and makes an adjustment for Incurred But Not Reported claims. Utilizing data from the Wisconsin Local Government Property Insurance Fund, we find that by determining rates based on current data, the proposed ratemaking model leads to better alignment of premiums and provides insurers with a more financially sound portfolio.

The use of artificial intelligence and algorithmic decision-making in public policy processes is influenced by a range of diverse drivers. This article provides a comprehensive view of 13 drivers and their interrelationships, identified through empirical findings from the taxation and social security domains in Belgium. These drivers are organized into five hierarchical layers that policy designers need to focus on when introducing advanced analytics in fraud detection: (a) trust layer, (b) interoperability layer, (c) perceived benefits layer, (d) data governance layer, and (e) digital governance layer. The layered approach enables a holistic view of assessing adoption challenges concerning new digital technologies. The research uses thematic analysis and interpretive structural modeling.

Bribery for access to public goods and services remains a widespread and seemingly innocuous practice which disproportionately targets the poor and helps keep them poor. Furthermore, its aggregate effects erode the legitimacy of government institutions and their capacity to fairly administer public goods and services as well as protection under the law. Drawing on original evidence using social norms methodology, this research tests underlying beliefs and expectations which sustain persistent forms of bribery and draws attention to the presence of pluralistic ignorance and consequent collective action problems. With examples focused on bribery in traffic law enforcement, healthcare, and education—three critical areas where bribery is often identified as an entrenched practice—this article contributes new evidence of: (a) the presence of pluralistic ignorance, a common social comparison error, surrounding bribery behavior; (b) differing social evaluations of bribe-solicitation; and finally, (c) how this context might exacerbate collective action problems. This empirical case study of Nigeria shows that even though more people are likely to be directly affected by bribery during routine interactions with public officials and institutions and many believe this practice is wrong, most people incorrectly believe that others in their community tolerate or even accept bribery behavior.