We consider the problem of controlling the drift and diffusion rate of the endowment processes of two firms such that the joint survival probability is maximized. We assume that the endowment processes are continuous diffusions, driven by independent Brownian motions, and that the aggregate endowment is a Brownian motion with constant drift and diffusion rate. Our results reveal that the maximal joint survival probability depends only on the aggregate risk-adjusted return and on the maximal risk-adjusted return that can be implemented in each firm. Here the risk-adjusted return is understood as the drift rate divided by the squared diffusion rate.

We introduce a formula for translating any upper bound on the percolation threshold of a lattice $G$ into a lower bound on the exponential growth rate of lattice animals $a(G)$ and vice versa. We exploit this in both directions. We obtain the rigorous lower bound ${\dot{p}_c}({\mathbb{Z}}^3)\gt 0.2522$ for 3-dimensional site percolation. We also improve on the best known asymptotic bounds on $a({\mathbb{Z}}^d)$ as $d\to \infty$. Our formula remains valid if instead of lattice animals we enumerate certain subspecies called interfaces. Enumerating interfaces leads to functional duality formulas that are tightly connected to percolation and are not valid for lattice animals, as well as to strict inequalities for the percolation threshold.

Incidentally, we prove that the rate of the exponential decay of the cluster size distribution of Bernoulli percolation is a continuous function of $p\in (0,1)$.

Routine blood examination is an easy way to examine infectious diseases. This study is aimed to develop a model to diagnose serious bacterial infections (SBI) in ICU neonates based on routine blood parameters. This was a cross-sectional study, and data were extracted from the Medical Information Mart for Intensive Care III (MIMIC-III). SBI was defined as suffering from one of the following: pyelonephritis, bacteraemia, bacterial meningitis, sepsis, pneumonia, cellulitis, and osteomyelitis. Variables with statistical significance in the univariate logistic regression analysis and log systemic immune–inflammatory index (SII) were used to develop the model. The area under the curve (AUC) was calculated to assess the performance of the model. A total of 1,880 participants were finally included for analysis. Weight, haemoglobin, mean corpuscular volume, white blood cell, monocyte, premature delivery, and log SII were selected to develop the model. The developed model showed a good performance to diagnose SBI for ICU neonates, with an AUC of 0.812 (95% confidence interval (CI): 0.737–0.888). A nomogram was developed to make this model visualise. In conclusion, our model based on routine blood parameters performed well in the diagnosis of neonatal SBI, which may be helpful for clinicians to improve treatment recommendations.

In this note, we give a precise description of the limiting empirical spectral distribution for the non-backtracking matrices for an Erdős-Rényi graph $G(n,p)$ assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then, we use Tao and Vu’s replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum.

We study the problem of detecting the community structure from the generalized stochastic block model with two communities (G2-SBM). Based on analysis of the Stieljtes transform of the empirical spectral distribution, we prove a Baik–Ben Arous–Péché (BBP)-type transition for the largest eigenvalue of the G2-SBM. For specific models, such as a hidden community model and an unbalanced stochastic block model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.

Over the past two decades, the incidence of legionellosis has been steadily increasing in the United States though there is noclear explanation for the main factors driving the increase. While legionellosis is the leading cause of waterborne outbreaks in the US, most cases are sporadic and acquired in community settings where the environmental source is never identified. This scoping review aimed to summarise the drivers of infections in the USA and determine the magnitude of impact each potential driver may have. A total of 1,738 titles were screened, and 18 articles were identified that met the inclusion criteria. Strong evidence was found for precipitation as a major driver, and both temperature and relative humidity were found to be moderate drivers of incidence. Increased testing and improved diagnostic methods were classified as moderate drivers, and the ageing U.S. population was a minor driver of increasing incidence. Racial and socioeconomic inequities and water and housing infrastructure were found to be potential factors explaining the increasing incidence though they were largely understudied in the context of non-outbreak cases. Understanding the complex relationships between environmental, infrastructure, and population factors driving legionellosis incidence is important to optimise mitigation strategies and public policy.

We prove that certain differential operators of the form $ DLD $ with $ L $ hypergeometric and $ D=z\frac{\partial }{dz} $ are of Picard–Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi–Yau motives presumed to be of analytic rank 1. We compare their values numerically to the first derivative of the $ L $-functions of the respective motives at $ s=2 $.

A variable annuity is a modern life insurance product that offers its policyholders participation in investment with various guarantees. To address the computational challenge of valuing large portfolios of variable annuity contracts, several data mining frameworks based on statistical learning have been proposed in the past decade. Existing methods utilize regression modeling to predict the market value of most contracts. Despite the efficiency of those methods, a regression model fitted to a small amount of data produces substantial prediction errors, and thus, it is challenging to rely on existing frameworks when highly accurate valuation results are desired or required. In this paper, we propose a novel hybrid framework that effectively chooses and assesses easy-to-predict contracts using the random forest model while leaving hard-to-predict contracts for the Monte Carlo simulation. The effectiveness of the hybrid approach is illustrated with an experimental study.

A third nationally representative serosurvey was performed to study the changes in Toxoplasma gondii (T. gondii) seroprevalence in the Netherlands over a 20-year time span and to identify and confirm risk factors for acquired toxoplasmosis. This cross-sectional study (conducted in 2016/2017) was designed similarly to the previous two studies (1995/1996 and 2006/2007) and included a questionnaire and serum sampling among Dutch residents. Factors associated with seropositivity for T. gondii were determined using multivariable analysis of the questionnaire-derived data. The earlier observed decrease in T. gondii seroprevalence between 1995/1996 and 2006/2007 (from 40.5% to 26.0%) did not continue into 2016/2017 (29.9%). Similarly to the previous studies, the seroprevalence increased with age and varied among regions. In all studies, higher T. gondii seropositivity was associated with increasing age, lower educational level, not living in the Southeast, and eating raw or semi-cooked pork. The incidence of congenital toxoplasmosis was estimated at 1.3/1000 (95% CI 0.9–1.8) live-born children in 2017. As the seroprevalence of T. gondii in the Netherlands did not decrease over the last decade, an increase in public health awareness is needed and prevention measures may need to be taken to achieve a further reduction in T. gondii infections in the Netherlands.

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.