For the measurement of flow-induced microrotations in flows utilizing the depolarization of phosphorescence anisotropy, suitable luminophores are crucial. The present work examines dyes of the xanthene family, namely Rhodamine B, Eosin Y and Erythrosine B. Both in solution and incorporated in particles, the dyes are examined regarding their luminescent lifetimes and their quantum yield. In an oxygen-rich environment at room temperature, all dyes exhibit lifetimes in the sub-microsecond range and a low intensity signal, making them suitable for sensing fast rotations with sensitive acquisition systems.

We analyse the behaviour of the Euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field $\mathbb{F}_{q}$ of q elements when the highest degree polynomial g is fixed. Considering all the elements f of fixed degree, we establish asymptotically optimal bounds in terms of q for the number of elements f that are relatively prime with g and for the average degree of $\gcd(g,f)$. We also exhibit asymptotically optimal bounds for the average-case complexity of the Euclidean algorithm applied to pairs (g,f) as above.

We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call ‘extender’ and ‘hypershallow’ graph sequences, respectively. Our main result is a probabilistic construction of non-hypershallow graph sequences.

Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton–Watson trees. For example, let $\mathcal{T}_1$ be the event that a Galton–Watson tree is infinite and let $\mathcal{T}_2$ be the event that it contains an infinite binary tree starting from its root. These events satisfy similar recursive properties: $\mathcal{T}_1$ holds if and only if $\mathcal{T}_1$ holds for at least one of the trees initiated by children of the root, and $\mathcal{T}_2$ holds if and only if $\mathcal{T}_2$ holds for at least two of these trees. The probability of $\mathcal{T}_1$ has a continuous phase transition, increasing from 0 when the mean of the child distribution increases above 1. On the other hand, the probability of $\mathcal{T}_2$ has a first-order phase transition, jumping discontinuously to a non-zero value at criticality. Given the recursive property satisfied by the event, we describe the critical child distributions where a continuous phase transition takes place. In many cases, we also characterise the event undergoing the phase transition.

Between 19 May and 12 June 2020, employees of the UZ Brussel were recruited in this study aiming to document the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) seroprevalence, to investigate the potential work-related risk factors for SARS-CoV-2 infection and to estimate the proportion of asymptomatic infections. In total, 2662 participants were included of whom 7.4% had immunoglobulin G antibodies against SARS-CoV-2. Of the participants reporting a positive polymerase chain reaction for SARS-CoV-2, 89% had antibodies at the time of blood sampling. Eleven per cent of the antibody positive participants reported no recent symptoms suggestive of coronavirus disease 2019 (COVID-19). Participants reporting fever, chest pain and/or anosmia/ageusia were significantly more frequently associated with the presence of antibodies against SARS-CoV-2. The presence of antibodies was highest in the group that had had contact with COVID-19-infected individuals outside the hospital with or without using appropriate personnel protective equipment (PPE) (P < 0.001). Inside the hospital, a statistically significant difference was observed for the employees considered as low-risk exposure compared to the intermediate-risk exposure group (P = 0.005) as well as the high-risk exposure group compared to the intermediate exposure risk group (P < 0.001). These findings highlight the importance of using correct PPE.

Like a hydra, fraudsters adapt and circumvent increasingly sophisticated barriers erected by public or private institutions. Among these institutions, banks must quickly take measures to avoid losses while guaranteeing the satisfaction of law-abiding customers. Facing an expanding flow of operations, effective banking relies on data analytics to support established risk control processes, but also on a better understanding of the underlying fraud mechanism. In addition, fraud being a criminal offence, the evidential aspect of the process must also be considered. These legal, operational, and strategic constraints lead to compromises on the means to be implemented for fraud management. This paper first focuses on the translation of practical questions raised in the banking industry at each step of the fraud management process into performance evaluation required to design a fraud detection model. Secondly, it considers a range of machine learning approaches that address these specificities: the imbalance between fraudulent and nonfraudulent operations, the lack of fully trusted labels, the concept-drift phenomenon, and the unavoidable trade-off between accuracy and interpretability of detection. This state-of-the-art review sheds some light on a technology race between black box machine learning models improved by post-hoc interpretation and intrinsic interpretable models boosted to gain accuracy. Finally, it discusses how concrete and promising hybrid approaches can provide pragmatic, short-term answers to banks and policy makers without swallowing up stakeholders with economical and ethical stakes in this technological race.

Catastrophe insurance markets fail to provide sufficient protections against natural catastrophes, whereas they have the capacity to absorb the losses. In this paper, we assume the catastrophic risks are dependent and extremely heavy-tailed, and insurers have limited liability to cover losses up to a certain amount. We provide a comprehensive study to show that the diversification in the catastrophe insurance markets can be transited from suboptimal to preferred by increasing the number of insurers in the market. This highlights the importance of coordination among insurers and the government intervention in encouraging insurers to participate in the catastrophe insurance market to exploit risk sharing. Simulation studies are provided to illuminate the key findings of our results.

This paper shows that if the errors in a multiple regression model are heavy-tailed, the ordinary least squares (OLS) estimators for the regression coefficients are tail-dependent. The tail dependence arises, because the OLS estimators are stochastic linear combinations of heavy-tailed random variables. Moreover, tail dependence also exists between the fitted sum of squares (FSS) and the residual sum of squares (RSS), because they are stochastic quadratic combinations of heavy-tailed random variables.

We consider a competition involving $r$ teams, where each individual game involves two teams, and where each game between teams $i$ and $j$ is won by $i$ with probability $P_{i,j} = 1 - P_{j,i}$. We suppose that $i$ and $j$ are scheduled to play $n(i,j)$ games and say that the team that wins the most games is the winner of the competition. We show that the conditional probability that $i$ is the winner, given that $i$ wins $k$ games, is increasing in $k$. We bound the tail probability of the number of wins of the winning team. We consider the special case where $P_{i,j} = {v_i}/{(v_i + v_j)}$, and obtain structural results on the probability that team $i$ is the winner. We give efficient simulation approaches for computing the probability that team $i$ is the winner, and the conditional probability given the number of wins of $i$.

There is a paucity of evidence about the prevalence and risk factors for symptomatic infection among children. This study aimed to describe the prevalence of symptomatic coronavirus disease 2019 (COVID-19) and its risk factors in children and adolescents aged 0–18 years in Qatar. We conducted a cross-sectional study of all children aged 0–18 years diagnosed with COVID-19 using polymerase chain reaction in Qatar during the period 1st March to 31st July 2020. A generalised linear model with a binomial family and identity link was used to assess the association between selected factors and the prevalence of symptomatic infection. A total of 11 445 children with a median age of 8 years (interquartile range (IQR) 3–13 years) were included in this study. The prevalence of symptomatic COVID-19 was 36.6% (95% confidence interval (CI) 35.7–37.5), and it was similar between children aged <5 years (37.8%), 5–9 years (34.3%) and 10 + years (37.3%). The most frequently reported symptoms among the symptomatic group were fever (73.5%), cough (34.8%), headache (23.2%) and sore throat (23.2%). Fever (82.8%) was more common in symptomatic children aged <5 years, while cough (38.7%) was more prevalent in those aged 10 years or older, compared to other age groups. Variables associated with an increased risk of symptomatic infection were; contact with confirmed cases (RD 0.21; 95% CI 0.20–0.23; P = 0.001), having visited a health care facility (RD 0.54; 95% CI 0.45–0.62; P = 0.001), and children aged under 5 years (RD 0.05; 95% CI 0.02–0.07; P = 0.001) or aged 10 years or older (RD 0.04; 95% CI 0.02–0.06; P = 0.001). A third of the children with COVID-19 were symptomatic with a higher proportion of fever in very young children and a higher proportion of cough in those between 10 and 18 years of age.

The prevalence of human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) is increasing day by day in the region, including Turkey. The study aimed to examine AIDS-related deaths in Turkey between 2009 and 2018 according to the national death registration system records. In this descriptive study, data on AIDS-related deaths were obtained from the Turkish Statistical Institute. The data consist of the cause of death codes, year of death, age and gender. Findings were presented using numbers and percentages. Seven hundred twenty-one AIDS-related deaths were reported in Turkey between 2009 and 2018. AIDS-related deaths in Turkey increased more than twice at the end of 10 years. The male/female death ratio is 4.5. Deaths under the age of 15 were 4.2% in total; however, they were increased to 10.2% in 2018. AIDS-related deaths are decreasing in the world but increasing in Turkey. The data from the Ministry of Health do not match the data of the national death registration system. Establishing a strong and accurate HIV/AIDS reporting system and identifying the causes and risk groups of this increase in AIDS-related deaths are critical.

We estimate the delay-adjusted all-cause excess deaths across 53 US jurisdictions. Using provisional data collected from September through December 2020, we first identify a common mean reporting delay of 2.8 weeks, whereas four jurisdictions have prolonged reporting delays compared to the others: Connecticut (mean 5.8 weeks), North Carolina (mean 10.4 weeks), Puerto Rico (mean 4.7 weeks) and West Virginia (mean 5.5 weeks). After adjusting for reporting delays, we estimate the percent change in all-cause excess mortality from March to December 2020 with range from 0.2 to 3.6 in Hawaii to 58.4 to 62.4 in New York City. Comparing the March–December with September–December 2020 periods, the highest increases in excess mortality are observed in South Dakota (36.9–54.0), North Dakota (33.9–50.7) and Missouri (27.8–33.9). Our findings indicate that analysis of provisional data requires caution in interpreting the death counts in recent weeks, while one needs also to account for heterogeneity in reporting delays of excess deaths among US jurisdictions.

Two general practitioners (GPs) with SARS-CoV-2 infection provided in-person patient care to patients of their joint medical practice before and after symptom onset, up until SARS-CoV-2 laboratory confirmation. Through active contact tracing, the local public health authorities recruited the cohort of patients that had contact with either GP in their putative infectious period. In this cohort of patient contacts, we assess the frequency and determinants of SARS-CoV-2-transmission from GPs to patients. We calculated incidence rate ratios (IRR) to explore the type of contact as an explanatory variable for COVID-19 cases. Among the cohort of 83 patient contacts, we identified 22 (27%) COVID-19 cases including 17 (21%) possible, three (4%) probable and two (2%) confirmed cases. All 22 cases had contact with a GP when the GP did not wear a mask, and/or when contact was ≥10 min. Importantly, patients who had contact <10 min with a GP wearing a facemask were at reduced risk (IRR 0.21; 95% CI 0.01–0.99) of COVID-19. This outbreak investigation adds to the body of evidence in supporting current guidelines on measures at preventing the transmission of SARS-CoV-2 in an outpatient setting.

Clinical and genetic risk factors for severe coronavirus disease 2019 (COVID-19) are often considered independently and without knowledge of the magnitudes of their effects on risk. Using severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) positive participants from the UK Biobank, we developed and validated a clinical and genetic model to predict risk of severe COVID-19. We used multivariable logistic regression on a 70% training dataset and used the remaining 30% for validation. We also validated a previously published prototype model. In the validation dataset, our new model was associated with severe COVID-19 (odds ratio per quintile of risk = 1.77, 95% confidence interval (CI) 1.64–1.90) and had acceptable discrimination (area under the receiver operating characteristic curve = 0.732, 95% CI 0.708–0.756). We assessed calibration using logistic regression of the log odds of the risk score, and the new model showed no evidence of over- or under-estimation of risk (α = −0.08; 95% CI −0.21−0.05) and no evidence or over-or under-dispersion of risk (β = 0.90, 95% CI 0.80–1.00). Accurate prediction of individual risk is possible and will be important in regions where vaccines are not widely available or where people refuse or are disqualified from vaccination, especially given uncertainty about the extent of infection transmission among vaccinated people and the emergence of SARS-CoV-2 variants of concern.

We compute the large N limit of the partition function of the Euclidean Yang–Mills measure on orientable compact surfaces with genus $g\geqslant 1$ and non-orientable compact surfaces with genus $g\geqslant 2$, with structure group the unitary group ${\mathrm U}(N)$ or special unitary group ${\mathrm{SU}}(N)$. Our proofs are based on asymptotic representation theory: more specifically, we control the dimension and Casimir number of irreducible representations of ${\mathrm U}(N)$ and ${\mathrm{SU}}(N)$ when N tends to infinity. Our main technical tool, involving ‘almost flat’ Young diagram, makes rigorous the arguments used by Gross and Taylor (1993, Nuclear Phys. B 400(1–3) 181–208) in the setting of QCD, and in some cases, we recover formulae given by Douglas (1995, Quantum Field Theory and String Theory (Cargèse, 1993), Vol. 328 of NATO Advanced Science Institutes Series B: Physics, Plenum, New York, pp. 119–135) and Rusakov (1993, Phys. Lett. B 303(1) 95–98).

This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

This study aimed to investigate the environmental contamination of nucleic acid at 2019 novel coronavirus (2019-nCOV) vaccination site and to evaluate the effect of improvement to the vaccination process. Nucleic acid samples were collected from the surface of the objects in 2019-nCOV vaccination point A (used between 15 November 2020 and 25 December 2020) and point B (used after 27 December 2020) in a comprehensive tertiary hospital. Samples were collected from point A before improvement to the vaccination process, and from point B (B1 and B2) after improvement to the vaccination process. The real-time fluorescence polymerase chain reaction method was used for detection. The positive rate of vaccination room was 47.06% (24/51) at point A. No positive result was found in point B1 both at working hours (0/27) and after terminal disinfection (0/27). In point B2, the positive results were found in vaccine's outer packaging and staff gloves at working hours, with a positive rate of 7.41% (2/27). The positive rate was 0 (0/27) after terminal disinfection in point B2. The nucleic acid contamination in the vaccination room of 2019-nCOV vaccine nucleic acid sampling point is serious, which can be avoided through the improvement and intervention (such as personal protection, vaccination operation and disinfection methods).

It is well known that for any integers k and g, there is a graph with chromatic number at least k and girth at least g. In 1960s, Erdös and Hajnal conjectured that for any k and g, there exists a number h(k,g), such that every graph with chromatic number at least h(k,g) contains a subgraph with chromatic number at least k and girth at least g. In 1977, Rödl proved the case when $g=4$, for arbitrary k. We prove the fractional chromatic number version of Rödl’s result.