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In this chapter we investigate the small-world structure in rank-1 and general inhomogeneous random graphs. For this, we develop path-counting techniques that are interesting in their own right.
In this chapter we discuss local convergence, which describes the intuitive notion that a finite graph, seen from the perspective of a typical vertex, looks like a certain limiting graph. Local convergence plays a profound role in random graph theory. We give general definitions of local convergence in several probabilistic senses. We then show that local convergence in its various forms is equivalent to the appropriate convergence of subgraph counts. We continue by discussing several implications of local convergence, concerning local neighborhoods, clustering, assortativity, and PageRank. We further investigate the relation between local convergence and the size of the giant, making the statement that the giant is “almost local” precise.
This study examined the association between the number of nursing staff in intensive care units (ICUs) and hospital-acquired pneumonia (HAP) among surgical patients in South Korea. Data were obtained between 2008 and 2019 from the Korean National Health Insurance Service Cohort Database; 37,706 surgical patients who received critical care services were included in the analysis. Patients with a history of pneumonia 1 year prior to surgery or those who had undergone lung-related surgery were excluded. The ICU nursing management fee is an admission fee that varies based on the grading determined by nurse-to-bed ratio. Using this grading system, we classified four groups from the highest to the lowest level based on the proportion of beds to nurses (high, high-mid, mid-low, and low group). HAP was defined by the International Classification of Disease, 10th revision (ICD-10) code. Multilevel logistic regression was used to investigate the relationship between the level of ICU nurse staffing and pneumonia, controlling for variables at the individual and hospital levels. Lower levels of nurse staffing were associated with a greater incidence of HAP than higher levels of nurse staffing (mid-high, OR: 1.33, 95% CI: 1.12–1.57; mid-low, OR: 1.61, 95% CI: 1.27–2.04; low, OR: 2.13, 95% CI: 1.67–2.71). The intraclass correlation coefficient value was 0.177, and 17.7% of the variability in HAP was accounted for by the hospital. Higher ICU nursing management fee grades (grade 5 and above) in general and hospital settings were significantly associated with an increased risk of HAP compared to grade 1 admissions. Similarly, in tertiary hospitals, grade 2 and higher ICU nursing management fees were significantly associated with an increased risk of HAP compared to grade 1 admissions. Especially, a lower level of nurse staffing was associated with bacterial pneumonia but not pneumonia due to aspiration. In conclusion, this study found an association between the level of ICU nurse staffing and HAP among surgical patients. A lower level of nurse staffing in the ICU was associated with increased rates of HAP among surgical patients. This indicates that having fewer beds assigned to nurses in the ICU setting is a significant factor in preventing HAP, regardless of the size of the hospital.
In this chapter we investigate the local limit of the configuration model, we identify when it has a giant component and find its size and degree structure. We give two proofs, one based on a “the giant is almost local” argument, and another based on a continuous-time exploration of the connected components in the configuration model. Further results include its connectivity transition.
We formulate a centrally planned portfolio selection problem with the investor and the manager having S-shaped utilities under a recently popular first-loss contract. We solve for the closed-form optimal portfolio, which shows that a first-loss contract can sometimes behave like an option contract. We propose an asymptotic approach to investigate the portfolio. This approach can be adopted to illustrate economic insights, including the fact that the portfolio under a convex contract becomes more conservative when the market state is better. Furthermore, we discover a means of Pareto improvement by simultaneously considering the investor’s utility and increasing the manager’s incentive rate. This is achieved by establishing the collection of Pareto points of a single contract, proving that it is a strictly decreasing and strictly concave frontier, and comparing the Pareto frontiers of different contracts. These results may be helpful for the illustration of risk choices and the design of Pareto-optimal contracts.
In this chapter we introduce the general setting of inhomogeneous random graphs that are generalizations of the Erdos–Rényi and generalized random graphs. In inhomogeneous random graphs, the status of edges is independent with unequal edge-occupation probabilities. While these edge probabilities are moderated by vertex weights in generalized random graphs, in the general setting they are described in terms of a kernel. The main results in this chapter concern the degree structure, the multi-type branching process local limits, and the phase transition in these inhomogeneous random graphs. We also discuss various examples, and indicate that they can have rather different structure.
In this chapter we discuss some related random graph models that have been studied in the literature. We explain their relevance, as well as some of the properties in them. We discuss directed random graphs, random graphs with local and global community structures, as well as spatial random graphs.
We provide general expressions for the joint distributions of the k most significant b-ary digits and of the k leading continued fraction (CF) coefficients of outcomes of arbitrary continuous random variables. Our analysis highlights the connections between the two problems. In particular, we give the general convergence law of the distribution of the jth significant digit, which is the counterpart of the general convergence law of the distribution of the jth CF coefficient (Gauss-Kuz’min law). We also particularise our general results for Benford and Pareto random variables. The former particularisation allows us to show the central role played by Benford variables in the asymptotics of the general expressions, among several other results, including the analogue of Benford’s law for CFs. The particularisation for Pareto variables—which include Benford variables as a special case—is especially relevant in the context of pervasive scale-invariant phenomena, where Pareto variables occur much more frequently than Benford variables. This suggests that the Pareto expressions that we produce have wider applicability than their Benford counterparts in modelling most significant digits and leading CF coefficients of real data. Our results may find practical application in all areas where Benford’s law has been previously used.
This study sought to establish the elements that constitute comprehensive legal and regulatory landscape for successful digital identity system establishment and implementation. Subsequently, the study sought to assess whether these elements were present in the establishment and implementation of the National Integrated Identity Management System (NIIMS) in Kenya. The study adopted a qualitative approach, data was obtained firstly, through literature review that provided background information to the study. Secondly, semi structured interviews were undertaken on purposively selected key informants. The study established that the elements that constitute a robust legal and regulatory framework for digital identity (ID) establishment and implementation include presence of a constitutional provision on the right to privacy; existence of a digital ID law governing the establishment of the system; amendment of laws relating to the registration of persons; existence of a data protection law; existence of an overarching law governing the digital economy among others. Largely, most of these elements were present in Kenya. However, the legislative approach adopted in crafting digital ID law in Kenya was wanting. This has undermined effective implementation of the NIIM system by among other things eroding public confidence in the system. The study concluded that effective operation of the system hinged on the existence of a robust and comprehensive legal and regulatory framework that will engender users’ trust in the system. In this regard, the study recommended review of the existing legal framework to ensure that it underpins both the foundational and functional aspects of the NIIM system.
There is limited information on the antibody responses against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in subjects from developing countries with populations having a high incidence of co-morbidities. Here, we analysed the immunogenicity of homologous schemes using the ChAdOx1-S, Sputnik V, or BNT162b2 vaccines and the effect of a booster dose with ChAdOx1-S in middle-aged adults who were seropositive or seronegative to the SARS-CoV-2 spike protein before vaccination. The study was conducted post-vaccination with a follow-up of 4 months for antibody titre using enzyme-linked immunosorbent assay (ELISA) and pseudovirus (PV) neutralization assays (PNAs). All three vaccines elicited a superior IgG anti-receptor-binding domain (RBD) and neutralization response against the Alpha and Delta variants when administered to individuals with a previous infection by SARS-CoV-2. The booster dose spiked the neutralization activity among individuals with and without a prior SARS-CoV-2 infection. The ChAdOx1-S vaccine induced weaker antibody responses in infection-naive subjects. A follow-up of 4 months post-vaccination showed a drop in antibody titre, with about 20% of the infection-naive and 100% of SARS-CoV-2 pre-exposed participants with detectable neutralization capacity against Alpha pseudovirus (Alpha-PV) and Delta PV (Delta-PV). Our observations support the use of different vaccines in a country with high seroprevalence at the vaccination time.
C.coli is a significant cause of foodborne gastroenteritis worldwide, with the majority of cases attributed to C.jejuni. Although most clinical laboratories do not typically conduct antimicrobial susceptibility testing for C.coli, the rise in resistant strains has underscored the necessity for such testing and epidemiological surveillance. The current study presents clinical isolate characteristics and demographics of 221 patients with C.coli (coli and jejuni) infections in Northern Israel, between 2015 and 2021. Clinical and demographic data were collected from patient medical records. Susceptibility to erythromycin, tetracycline, ciprofloxacin, and gentamicin was assessed using the standard E-test. No significant correlations were found between bacterial species and patient ethnicity, patient gender, or duration of hospitalization. In contrast, significant differences were found between infecting species and patient age and age subgroup (P < 0.001). Furthermore, erythromycin resistance was observed in only 0.5% of the study population, while resistance to ciprofloxacin, tetracycline, and gentamicin was observed in 95%, 93%, and 2.3% of the population, respectively. The presented study underscores the need for routine surveillance of C.coli antibiotic resistance.
We outline a theory of algorithmic attention rents in digital aggregator platforms. We explore the way that as platforms grow, they become increasingly capable of extracting rents from a variety of actors in their ecosystems—users, suppliers, and advertisers—through their algorithmic control over user attention. We focus our analysis on advertising business models, in which attention harvested from users is monetized by reselling the attention to suppliers or other advertisers, though we believe the theory has relevance to other online business models as well. We argue that regulations should mandate the disclosure of the operating metrics that platforms use to allocate user attention and shape the “free” side of their marketplace, as well as details on how that attention is monetized.
Women infected during pregnancy with TORCH (Toxoplasmosis, Other, Rubella, Cytomegalovirus, and Herpes simplex viruses) pathogens have a higher risk of adverse birth outcomes including stillbirth / miscarriage because of mother-to-child transmission. To investigate these risks in pregnant women in Kenya, we analyzed serum specimens from a pregnancy cohort study at three healthcare facilities. A sample of 481 participants was selected for TORCH pathogen antibody testing to determine seroprevalence. A random selection of 285 from the 481 participants was selected to measure seroconversion. These sera were tested using an IgG enzyme-linked immunosorbent assay against 10 TORCH pathogens. We found that the seroprevalence of all but three of the 10 TORCH pathogens at enrollment was >30%, except for Bordetella pertussis (3.8%), Treponema pallidum (11.4%), and varicella zoster virus (0.5%). Conversely, very few participants seroconverted during their pregnancy and were herpes simplex virus type 2 (n = 24, 11.2%), parvovirus B19 (n = 14, 6.2%), and rubella (n = 12, 5.1%). For birth outcomes, 88% of the participant had live births and 12% had stillbirths or miscarriage. Cytomegalovirus positivity at enrolment had a statistically significant positive association with a live birth outcome (p = 0.0394). Of the 10 TORCH pathogens tested, none had an association with adverse pregnancy outcome.
A significant challenge of structural health monitoring (SHM) is the lack of labeled data collected from damage states. Consequently, the collected data can be incomplete, making it difficult to undertake machine learning tasks, to detect or predict the full range of damage states a structure may experience. Transfer learning is a helpful solution, where data from (source) structures containing damage labels can be used to transfer knowledge to (target) structures, for which damage labels do not exist. Machine learning models are then developed that generalize to the target structure. In practical applications, it is unlikely that the source and the target structures contain the same damage states or experience the same environmental and operational conditions, which can significantly impact the collected data. This is the first study to explore the possibility of transfer learning for damage localisation in SHM when the damage states and the environmental variations in the source and target datasets are disparate. Specifically, using several domain adaptation methods, this article localizes severe damage states at a target structure, using labeled information from minor damage states at a source structure. By minimizing the distance between the marginal and conditional distributions between the source and the target structures, this article successfully localizes damage states of disparate severities, under varying environmental and operational conditions. The effect of partial and universal domain adaptation—where the number of damage states in the source and target datasets differ—is also explored in order to mimic realistic industrial applications of these methods.
In this paper, we explore how to design the optimal insurance contracts when the insured faces insurable, counterparty, and additive background risk simultaneously. The target is to minimize the mean-variance of the insured’s loss. By utilizing the calculus of variations, an implicit characterization of the optimal ceded loss function is given. An explicit structure of the optimal ceded loss function is also provided by making full use of its implicit characterization. We further derive a much simpler solution when these three kinds of risk have some special dependence structures. Finally, we give a numerical example to illustrate our results.
Crimean–Congo haemorrhagic fever virus (CCHFV) is an emerging viral pathogen with pandemic potential that is often misdiagnosed. Case fatality in low-resource settings could be up to 40% due to close contact between animals and humans. A two-year cross-sectional study was conducted in Fagge abattoir, Kano State, Nigeria, to estimate the seropositivity of CCHFV in camels using a commercial multi-species competitive enzyme-linked immunosorbent assay (ELISA). A closed-ended questionnaire was administered to the abattoir workers to assess their awareness, mitigation, and behavioural practices associated with CCHF. Of the 184 camels tested, 179 (97%) were seropositive for CCHFV (95% confidence interval (CI): 93.77, 99.11). The median (interquartile range (IQR)) age of respondents was 41 (35–52), with 62% having no education. Respondents had little knowledge about CCHFV and the concept of zoonotic disease. In this study, the high estimated prevalence of antibodies to CCHFV in camels highlights the heightened risk of transmission of CCHFV in Nigeria. Similarly, a concerning lack of knowledge and inadequate preventive practices, alongside a prevalence of high-risk behaviours associated with CCHF among abattoir workers, were noted in this study. Thus, there is an urgent need for comprehensive public health education and collaborative One Health strategies to avert the threats of spillover events.