In early March 2020, a COVID-19-outbreak occurred in the district of Tirschenreuth, Germany. The outbreak was characterised by a rapid increase in case numbers and a comparatively high crude case fatality ratio (CFR; 11%). Until the beginning of May 2020, 1122 cases were reported in the district. To investigate the outbreak, we analysed surveillance and other data available at the district health department, including data on cases living in care facilities and public health measures applied. Furthermore, we compared the number of tests performed in Tirschenreuth and in Germany as a whole. We interviewed the first 110 cases in order to investigate potential exposures at the beginning of the outbreak. We found that returning ski-travellers from Austria and Italy and early undetected community transmission likely initiated the outbreak which was then accelerated by Bavarian beer festivities. Testing of mainly acute cases in the district of Tirschenreuth resulted in a higher rate of positive tests compared to the whole of Germany. Despite adjustment for age, the CFR continued to exceed the German mean which was due to spread to vulnerable populations. Strict public health measures likely contributed to control the outbreak by mid-April 2020.

A k-uniform tight cycle $C_s^k$ is a hypergraph on s > k vertices with a cyclic ordering such that every k consecutive vertices under this ordering form an edge. The pair (k, s) is admissible if gcd (k, s) = 1 or k / gcd (k,s) is even. We prove that if $s \ge 2{k^2}$ and H is a k-uniform hypergraph with minimum codegree at least (1/2 + o(1))|V(H)|, then every vertex is covered by a copy of $C_s^k$. The bound is asymptotically sharp if (k, s) is admissible. Our main tool allows us to arbitrarily rearrange the order in which a tight path wraps around a complete k-partite k-uniform hypergraph, which may be of independent interest.

For hypergraphs F and H, a perfect F-tiling in H is a spanning collection of vertex-disjoint copies of F. For $k \ge 3$, there are currently only a handful of known F-tiling results when F is k-uniform but not k-partite. If s ≢ 0 mod k, then $C_s^k$ is not k-partite. Here we prove an F-tiling result for a family of non-k-partite k-uniform hypergraphs F. Namely, for $s \ge 5{k^2}$, every k-uniform hypergraph H with minimum codegree at least (1/2 + 1/(2s) + o(1))|V(H)| has a perfect $C_s^k$-tiling. Moreover, the bound is asymptotically sharp if k is even and (k, s) is admissible.

We employ the absorbing-path method in order to prove two results regarding the emergence of tight Hamilton cycles in the so-called two-path or cherry-quasirandom 3-graphs.

Our first result asserts that for any fixed real α > 0, cherry-quasirandom 3-graphs of sufficiently large order n having minimum 2-degree at least α(n – 2) have a tight Hamilton cycle.

Our second result concerns the minimum 1-degree sufficient for such 3-graphs to have a tight Hamilton cycle. Roughly speaking, we prove that for every d, α > 0 satisfying d + α > 1, any sufficiently large n-vertex such 3-graph H of density d and minimum 1-degree at least $\alpha \left({\matrix{{n - 1} \cr 2 \cr } } \right)$ has a tight Hamilton cycle.

von Neumann [(1951). Various techniques used in connection with random digits. National Bureau of Standards Applied Math Series 12: 36–38] introduced a simple algorithm for generating independent unbiased random bits by tossing a (possibly) biased coin with unknown bias. While his algorithm fails to attain the entropy bound, Peres [(1992). Iterating von Neumann's procedure for extracting random bits. The Annals of Statistics 20(1): 590–597] showed that the entropy bound can be attained asymptotically by iterating von Neumann's algorithm. Let $b(n,p)$ denote the expected number of unbiased bits generated when Peres’ algorithm is applied to an input sequence consisting of the outcomes of $n$ tosses of the coin with bias $p$. With $p=1/2$, the coin is unbiased and the input sequence consists of $n$ unbiased bits, so that $n-b(n,1/2)$ may be referred to as the cost incurred by Peres’ algorithm when not knowing $p=1/2$. We show that $\lim _{n\to \infty }\log [n-b(n,1/2)]/\log n =\theta =\log [(1+\sqrt {5})/2]$ (where $\log$ is the logarithm to base $2$), which together with limited numerical results suggests that $n-b(n,1/2)$ may be a regularly varying sequence of index $\theta$. (A positive sequence $\{L(n)\}$ is said to be regularly varying of index $\theta$ if $\lim _{n\to \infty }L(\lfloor \lambda n\rfloor )/L(n)=\lambda ^\theta$ for all $\lambda > 0$, where $\lfloor x\rfloor$ denotes the largest integer not exceeding $x$.) Some open problems on the asymptotic behavior of $nh(p)-b(n,p)$ are briefly discussed where $h(p)=-p\log p- (1-p)\log (1-p)$ denotes the Shannon entropy of a random bit with bias $p$.

For a real constant α, let $\pi _3^\alpha (G)$ be the minimum of twice the number of K2’s plus α times the number of K3’s over all edge decompositions of G into copies of K2 and K3, where Kr denotes the complete graph on r vertices. Let $\pi _3^\alpha (n)$ be the maximum of $\pi _3^\alpha (G)$ over all graphs G with n vertices.

The extremal function $\pi _3^3(n)$ was first studied by Győri and Tuza (Studia Sci. Math. Hungar. 22 (1987) 315–320). In recent progress on this problem, Král’, Lidický, Martins and Pehova (Combin. Probab. Comput. 28 (2019) 465–472) proved via flag algebras that$\pi _3^3(n) \le (1/2 + o(1)){n^2}$. We extend their result by determining the exact value of $\pi _3^\alpha (n)$ and the set of extremal graphs for all α and sufficiently large n. In particular, we show for α = 3 that Kn and the complete bipartite graph ${K_{\lfloor n/2 \rfloor,\lceil n/2 \rceil }}$ are the only possible extremal examples for large n.

In this paper, we develop the lower–upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding “capped (barrier) option” with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.

During summer 2020, observations of the mesosphere using a 53.5 MHz radar on Svalbard, at 78.2°N 15.1°E, revealed the well-known Polar Mesospheric Summer Echoes (PMSE). At the same time, a co-located meteor detection radar, operating at 31 MHz detected corresponding echoes very distinct from those associated with meteor trails. Comparing as many days as possible during 2020, incontestable evidence arose to demonstrate that the meteor detection radar was capable of observing PMSE, although not in the optimised fashion of the 53.5 MHz system. We present examples of results from both systems, supplementing the earlier findings of Swarnalingam et al. (2009), and simultaneously show very first results from this particular geographical location.

Denture-related stomatitis caused by Candida spp. affects elderly individuals using partial/total prosthesis, provoking several discomforts including burning sensation and altered taste. Herein, we have studied 52 denture-wearing individuals (>60 years-old), attended at the dentistry clinic of UNIVALE, aiming to isolate Candida spp. directly from the stomatitis lesions and to evaluate their potential to produce virulence attributes. A low prevalence of denture-related stomatitis was reported in these patients (4/52; 7.7%). Candida albicans was isolated in the 4 selected patients, with the ability to form biofilm over a polystyrene surface and to produce aspartic protease, esterase and hemolysin. However, neither phospholipase nor caseinase activities were detected. Planktonic-growing yeasts were susceptible to amphotericin B and caspofungin, while the susceptibility to azoles (fluconazol, itraconazole and voriconazole) varied depending on either the isolate or antifungal. Relevantly, biofilm-forming C. albicans cells exhibited resistance to all studied antifungals. So, new effective drugs against resistant C. albicans isolates causing denture-related stomatitis are urgently required.

A compartmental model is proposed to predict the coronavirus 2019 (Covid-19) spread. It considers: detected and undetected infected populations, social sequestration, release from sequestration, plus reinfection. This model, consisting of seven coupled equations, has eight coefficients which are evaluated by fitting data for eight US states that make up 43% of the US population. The evolution of Covid-19 is fairly similar among the states: variations in contact and undetected recovery rates remain below 5%; however, variations are larger in recovery rate, death rate, reinfection rate, sequestration adherence and release rate from sequestration. Projections based on the current situation indicate that Covid-19 will become endemic. If lockdowns had been kept in place, the number of deaths would most likely have been significantly lower in states that opened up. Additionally, we predict that decreasing contact rate by 10%, or increasing testing by approximately 15%, or doubling lockdown compliance (from the current ~15% to ~30%) will eradicate infections in Texas within a year. Extending our fits for all of the US states, we predict about 11 million total infections (including undetected), and 8 million cumulative confirmed cases by 1 November 2020.

In this article, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, allowing for the time span to increase as well as the sampling interval to decrease, and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by simulation and provide some illustrative empirical analyses.

A Canadian outbreak investigation into a cluster of Escherichia coli O121 was initiated in late 2016. When initial interviews using a closed-ended hypothesis-generating questionnaire did not point to a common source, cases were centrally re-interviewed using an open-ended approach. The open-ended interviews led cases to describe exposures with greater specificity, as well as food preparation activities. Data collected supported hypothesis generation, particularly with respect to flour exposures. In March 2017, an open sample of Brand X flour from a case home, and a closed sample collected at retail of the same brand and production date, tested positive for the outbreak strain of E. coli O121. In total, 76% (16/21) of cases reported that they used or probably used Brand X flour or that it was used or probably was used in the home during their exposure period. Crucial hypothesis-generating techniques used during the course of the investigation included a centralised open-ended interviewing approach and product sampling from case homes. This was the first outbreak investigation in Canada to identify flour as the source of infection.

Toxoplasmosis is a worldwide zoonotic infectious disease caused by Toxoplasma gondii. This infection is estimated to affect about a third of the world's population. The aim of this study was to evaluate the knowledge of Italian women about toxoplasmosis and its forms of transmission, clinical manifestations, diagnosis and prevention through two different modalities (e-research and traditional research). In a cross-sectional study, 808 Italian women were interviewed, using a self-administered questionnaire, through two different modalities: an e-research or web survey and a traditional paper research and 84% reported to have heard about toxoplasmosis, but from most of the sample, it resulted that the knowledge of the protozoan disease was superficial and incomplete.

The assessment of the dimensionality related to the toxoplasmosis knowledge's instrument showed that the scale is composed by two stable and reliable factors which explain 58.6% of the variance: (a) the basic knowledge (α = 0.83), which explains the 45.2% of the variance and (b) the specialist knowledge (α = 0.71), which explains the 13.4% of the variance. The variance and the multiple linear regression data analysis showed significant predictors of correct basic knowledge of toxoplasmosis: the highest age, the highest degree of study, to have previously contracted illness or to know someone who had contracted it, to be working or to be housewives. In conclusion, this study showed limited awareness of toxoplasmosis and suggested the implementation of effective education and learning programs. The results also showed that online data collection, in academic research, might be a valid alternative to more traditional (paper-and-pencil) surveys.

The current pandemic is defined by the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that can lead to coronavirus disease 2019 (COVID-19). How is SARS-CoV-2 transmitted? In this review, we use a global lens to examine the sociological contexts that are potentially and systematically involved in high rates of SARS-CoV-2 transmission, including lack of personal protective equipment, population density and confinement. Altogether, this review provides an in-depth conspectus of the current literature regarding how SARS-CoV-2 disproportionately impacts many minority communities. By contextualising and disambiguating transmission risks that are particularly prominent for disadvantaged populations, this review can assist public health efforts throughout and beyond the COVID-19 pandemic.

Forecasting the epidemics of the diseases is very valuable in planning and supplying resources effectively. This study aims to estimate the epidemiological trends of the coronavirus disease 2019 (COVID-19) prevalence and mortality using the advanced α-Sutte Indicator, and its prediction accuracy level was compared with the most frequently adopted autoregressive integrated moving average (ARIMA) method. Time-series analysis was performed based on the total confirmed cases and deaths of COVID-19 in the world, Brazil, Peru, Canada and Chile between 27 February 2020 and 30 June 2020. By comparing the prediction reliability indices, including the root mean square error, mean absolute error, mean error rate, mean absolute percentage error and root mean square percentage error, the α-Sutte Indicator was found to produce lower forecasting error rates than the ARIMA model in all data apart from the prevalence testing set globally. The α-Sutte Indicator can be recommended as a useful tool to nowcast and forecast the COVID-19 prevalence and mortality of these regions except for the prevalence around the globe in the near future, which will help policymakers to plan and prepare health resources effectively. Also, the findings of our study may have managerial implications for the outbreak in other countries.

The magnitude and consistency of the sex differences in meningococcal disease incidence rates (IR) have not been systematically examined in different age groups, countries and time periods. We obtained national data on meningococcal disease IR by sex, age group and time period, from 10 countries. We used meta-analytic methods to combine the male to female incidence rate ratios (IRRs) by country and year for each age group. Meta-regression analysis was used to assess the contribution of age, country and time period to the variation in the IRRs. The pooled male to female IRRs (with 95% CI) for ages 0–1, 1–4, 5–9, 10–14 and 15–44, were 1.25 (1.19–1.32), 1.24 (1.20–1.29), 1.13 (1.07–1.20), 1.21 (1.13–1.29) and 1.15 (1.10–1.21), respectively. In the age groups 45−64 and over 65, the IR were lower in males with IRRs of 0.83 (0.78–0.88) and 0.64 (0.60–0.69), respectively. Sensitivity analysis and meta-regression confirmed that the results were robust. The excess meningococcal IR in young males and the higher rates in females at older ages were consistent in all countries, except the Czech Republic. While behavioural factors could explain some of the sex differences in the older age groups, the excess rates in very young males suggest that genetic and hormonal differences could be important.

Agricultural intensification within forage systems has reduced grassland floral diversity by promoting ryegrass (Lolium spp.), damaging soil functionality which underpins critical ecosystem services. Diverse forage mixtures may enhance environmental benefits of pastures by decreasing nutrient leaching, increasing soil carbon storage, and with legume inclusion, reduce nitrogen fertilizer input. This UK study reports on how species-rich forage mixtures affect soil carbon, phosphorus, and nitrogen at dry, medium and wet soil moisture sites, compared to ryegrass monoculture. Increasing forage mixture diversity (from 1 to 17 species) affected soil carbon at the dry site. No effect of forage mixture on soil phosphorus was found, while forage mixture and site did interact to affect soil nitrate/nitrite availability. Results suggest that forage mixtures could be used to improve soil function, but longer-term studies are needed to conclusively demonstrate environmental and production benefits of high-diversity forages.

We develop a model that successfully learns social and organizational human network structure using ambient sensing data from distributed plug load energy sensors in commercial buildings. A key goal for the design and operation of commercial buildings is to support the success of organizations within them. In modern workspaces, a particularly important goal is collaboration, which relies on physical interactions among individuals. Learning the true socio-organizational relational ties among workers can therefore help managers of buildings and organizations make decisions that improve collaboration. In this paper, we introduce the Interaction Model, a method for inferring human network structure that leverages data from distributed plug load energy sensors. In a case study, we benchmark our method against network data obtained through a survey and compare its performance to other data-driven tools. We find that unlike previous methods, our method infers a network that is correlated with the survey network to a statistically significant degree (graph correlation of 0.46, significant at the 0.01 confidence level). We additionally find that our method requires only 10 weeks of sensing data, enabling dynamic network measurement. Learning human network structure through data-driven means can enable the design and operation of spaces that encourage, rather than inhibit, the success of organizations.