Given partially ordered sets (posets) $(P, \leq _P\!)$ and $(P^{\prime}, \leq _{P^{\prime}}\!)$, we say that $P^{\prime}$ contains a copy of $P$ if for some injective function $f\,:\, P\rightarrow P^{\prime}$ and for any $X, Y\in P$, $X\leq _P Y$ if and only if $f(X)\leq _{P^{\prime}} f(Y)$. For any posets $P$ and $Q$, the poset Ramsey number $R(P,Q)$ is the least positive integer $N$ such that no matter how the elements of an $N$-dimensional Boolean lattice are coloured in blue and red, there is either a copy of $P$ with all blue elements or a copy of $Q$ with all red elements. We focus on a poset Ramsey number $R(P, Q_n)$ for a fixed poset $P$ and an $n$-dimensional Boolean lattice $Q_n$, as $n$ grows large. We show a sharp jump in behaviour of this number as a function of $n$ depending on whether or not $P$ contains a copy of either a poset $V$, that is a poset on elements $A, B, C$ such that $B\gt C$, $A\gt C$, and $A$ and $B$ incomparable, or a poset $\Lambda$, its symmetric counterpart. Specifically, we prove that if $P$ contains a copy of $V$ or $\Lambda$ then $R(P, Q_n) \geq n +\frac{1}{15} \frac{n}{\log n}$. Otherwise $R(P, Q_n) \leq n + c(P)$ for a constant $c(P)$. This gives the first non-marginal improvement of a lower bound on poset Ramsey numbers and as a consequence gives $R(Q_2, Q_n) = n + \Theta \left(\frac{n}{\log n}\right)$.

In this paper, we study the estimation of a scale parameter from a sample of lifetimes of coherent systems with a fixed structure. We assume that the components are independent and identically distributed having a common distribution which belongs to a scale parameter family. Some results are obtained as well for dependent (exchangeable) components. To this end, we will use the representations for the distribution function of a coherent system based on signatures. We prove that the efficiency of the estimators depends on the structure of the system and on the scale parameter family. In the dependence case, it also depends on the baseline copula function.

This study aimed to assess human papillomavirus (HPV) vaccine effectiveness (VE) against both vaccine-type and nonvaccine-type high-risk HPV (hrHPV) infection, and duration of protection in United States. The study population was female participants aged 18–35 years with an HPV vaccination history and genital testing for HPV from the National Health and Nutrition Examination Survey, 2007–2016. Participants vaccinated before sexual debut were assessed against 13 nonvaccine-type hrHPV infection including 31/33/35/39/45/51/52/56/58/59/68/73/82. Multivariable logistic regression was used to estimate VE overall, by age at diagnosis, time since vaccination and lifetime sexual partners. A total of 3866 women were included in the analysis, with 23.3% (95% CI 21.3%–25.4%) having been vaccinated (≥1 dose). VE against vaccine-type HPV18/16/11/6 infection was 58% overall, which was mainly driven by those aged 18–22 years (VE = 64%) and 23–27 years (65%). Among participants aged 18–22 years vaccinated before sexual debut, the VE was 47% (23%–64%) against 13 nonvaccine-type hrHPV and 61% (95% CI 36%–77%) against 5 selected nonvaccine-type hrHPV35/39/52/58/59. Both direct effectiveness and cross-protection maintained effective for 5–10 years post vaccination. We also found the prevalence of ever diagnosed cervical cancer among vaccinated was significantly lower (0.46%, 4/874) than that among unvaccinated participants (1.27%, 38/2992). These findings highlight the potential of significant reduction of cervical cancer following the universal HPV vaccination programme.

After the winter of 2021/2022, the coronavirus disease 2019 (COVID-19) pandemic had reached a phase where a considerable number of people in Germany have been either infected with a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, vaccinated or both, the full extent of which was difficult to estimate, however, because infection counts suffer from under-reporting, and the overlap between the vaccinated and recovered subpopulations is unknown. Yet, reliable estimates regarding population-wide susceptibility were of considerable interest: Since both previous infection and vaccination reduce the risk of severe disease, a low share of immunologically naïve individuals lowers the probability of further severe outbreaks, given that emerging variants do not escape the acquired susceptibility reduction. Here, we estimate the share of immunologically naïve individuals by age group for each of the sixteen German federal states by integrating an infectious-disease model based on weekly incidences of SARS-CoV-2 infections in the national surveillance system and vaccine uptake, as well as assumptions regarding under-ascertainment. We estimate a median share of 5.6% of individuals in the German population have neither been in contact with vaccine nor any variant up to 31 May 2022 (quartile range [2.5%–8.5%]). For the adult population at higher risk of severe disease, this figure is reduced to 3.8% [1.6%–5.9%] for ages 18–59 and 2.1% [1.0%–3.4%] for ages 60 and above. However, estimates vary between German states mostly due to heterogeneous vaccine uptake. Excluding Omicron infections from the analysis, 16.3% [14.1%–17.9%] of the population in Germany, across all ages, are estimated to be immunologically naïve, highlighting the large impact the first two Omicron waves had until the beginning of summer in 2022. The method developed here might be useful for similar estimations in other countries or future outbreaks of other infectious diseases.

Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover time of multiple walks has been investigated for many natural networks, the problem of finding a general characterisation of multiple cover times for worst-case start vertices (posed by Alon, Avin, Koucký, Kozma, Lotker and Tuttle in 2008) remains an open problem. First, we improve and tighten various bounds on the stationary cover time when $k$ random walks start from vertices sampled from the stationary distribution. For example, we prove an unconditional lower bound of $\Omega ((n/k) \log n)$ on the stationary cover time, holding for any $n$-vertex graph $G$ and any $1 \leq k =o(n\log n )$. Secondly, we establish the stationary cover times of multiple walks on several fundamental networks up to constant factors. Thirdly, we present a framework characterising worst-case cover times in terms of stationary cover times and a novel, relaxed notion of mixing time for multiple walks called the partial mixing time. Roughly speaking, the partial mixing time only requires a specific portion of all random walks to be mixed. Using these new concepts, we can establish (or recover) the worst-case cover times for many networks including expanders, preferential attachment graphs, grids, binary trees and hypercubes.

The COVID-19 pandemic has presented a unique opportunity to understand how real-time pathogen genomics can be used for large-scale outbreak investigations. On 12 August 2021, the Australian Capital Territory (ACT) detected an incursion of the SARS-CoV-2 Delta (B.1.617.2) variant. Prior to this date, SARS-CoV-2 had been eliminated locally since 7 July 2020. Several public health interventions were rapidly implemented in response to the incursion, including a territory-wide lockdown and comprehensive contact tracing. The ACT has not previously used pathogen genomics at a population level in an outbreak response; therefore, this incursion also presented an opportunity to investigate the utility of genomic sequencing to support contact tracing efforts in the ACT. Sequencing of >75% of the 1793 laboratory-confirmed cases during the 3 months following the initial notification identified at least 13 independent incursions with onwards spread in the community. Stratification of cases by genomic cluster revealed that distinct cohorts were affected by the different incursions. Two incursions resulted in most of the community transmission during the study period, with persistent transmission in vulnerable sections of the community. Ultimately, both major incursions were successfully mitigated through public health interventions, including COVID-19 vaccines. The high rates of SARS-CoV-2 sequencing in the ACT and the relatively small population size facilitated detailed investigations of the patterns of virus transmission, revealing insights beyond those gathered from traditional contact tracing alone. Genomic sequencing was critical to disentangling complex transmission chains to target interventions appropriately.

For a random binary noncoalescing feedback shift register of width $n$, with all $2^{2^{n-1}}$ possible feedback functions $f$ equally likely, the process of long cycle lengths, scaled by dividing by $N=2^n$, converges in distribution to the same Poisson–Dirichlet limit as holds for random permutations in $\mathcal{S}_N$, with all $N!$ possible permutations equally likely. Such behaviour was conjectured by Golomb, Welch and Goldstein in 1959.

We examine urn models under random replacement schemes, and the related distributions, by using generating functions. A fundamental isomorphism between urn models and a certain system of differential equations has previously been established. We study the joint distribution of the numbers of balls in the urn, and determined recurrence relations for the probability generating functions. The associated partial differential equation satisfied by the generating function is derived. We develop analytical methods for the study of urn models that can lead to perspectives on urn-related problems from analytic combinatorics. The results presented here provide a broader framework for the study of exactly solvable urns than the existing framework. Finally, we examine several applications and their numerical results in order to demonstrate how our theoretical results can be employed in the study of urn models.

The bacterium Neisseria meningitidis causes life-threatening disease worldwide, typically with a clinical presentation of sepsis or meningitis, but can be carried asymptomatically as part of the normal human oropharyngeal microbiota. The aim of this study was to examine N. meningitidis carriage with regard to prevalence, risk factors for carriage, distribution of meningococcal lineages and persistence of meningococcal carriage. Throat samples and data from a self-reported questionnaire were obtained from 2744 university students (median age: 23 years) at a university in Sweden on four occasions during a 12-month period. Meningococcal isolates were characterised using whole-genome sequencing. The carriage rate among the students was 9.1% (319/3488; 95% CI 8.2–10.1). Factors associated with higher carriage rate were age ≤22 years, previous tonsillectomy, cigarette smoking, drinking alcohol and attending parties, pubs and clubs. Female gender and sharing a household with children aged 0–9 years were associated with lower carriage. The most frequent genogroups were capsule null locus (cnl), group B and group Y and the most commonly identified clonal complexes (cc) were cc198 and cc23. Persistent carriage with the same meningococcal strain for 12 months was observed in two students. Follow-up times exceeding 12 months are recommended for future studies investigating long-term carriage of N. meningitidis.

In this paper, we answer the multiple calls for systematic analysis of paradigms and subdisciplines in political science—the search for coherence within a fragmented field. We collected a large dataset of over seven hundred thousand writings in political science from Web of Science since 1946. We found at least two waves of political science development, from behaviorism to new institutionalism. Political science appeared to be more fragmented than literature suggests—instead of ten subdisciplines, we found 66 islands. However, despite fragmentation, there is also a tendency for integration in contemporary political science, as revealed by co-existence of several paradigms and coherent and interconnected topics of the “canon of political science,” as revealed by the core-periphery structure of topic networks. This was the first large-scale investigation of the entire political science field, possibly due to newly developed methods of bibliometric network analysis: temporal bibliometric analysis and island methods of clustering. Methodological contribution of this work to network science is evaluation of islands method of network clustering against a hierarchical cluster analysis for its ability to remove misleading information, allowing for a more meaningful clustering of large weighted networks.

We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees—the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.

While the incidence of infections with the human immunodeficiency virus largely remained unchanged in Germany, an increase of other sexually transmitted infections (STIs) was observed. The aim was to analyse the effectiveness of our sexual education lecture for students in improving the awareness, knowledge and prevention of STIs. We conducted a cross-sectional survey after students had attended our extra-curricular lecture at the Department of Dermatology of the Ludwig-Maximilians-University of Munich, Germany (LMU). We compared the data with a previously performed study in which the same survey was carried out before the lecture had started. A total of 5866 questionnaires were included in the analysis. After attending the lecture significantly more students were aware of STIs (syphilis: 36.8% (before) vs. 63.5% (after); chlamydia: 30.5% vs. 49.3%; gonorrhoea: 22.4% vs. 38.2%; human papillomaviruses (HPV): 17.7% vs. 30.2%), the transmission pathways of STIs (oral: 36.6% vs. 82.6%; vaginal: 81.8% vs. 97.3%; anal: 42.8% vs. 94.0%; penile: 68.7% vs. 92.1%), knew that the HPV vaccination is directed against a virus (36.8% vs. 56.9%) and were interested in receiving a vaccination (57.7% vs. 78.8%). This study demonstrates the positive educative effects of our lecture for awareness and improved knowledge of STIs. To satisfy the need for a comprehensive sexual education, a combination of school and health facility-based programmes should be implemented as one single lecture cannot convey the entire information about STIs.

The temperature of maximum pyrolysis yield (known as Tmax) can be used to determine the level of thermal alteration in sedimentary organic matter; higher Tmax values represent higher thermal alteration. Tmax is commonly measured on petroleum source rocks or similar sediments with high organic carbon contents. It would be desirable to measure the Tmax of volcanic sediments because they can have complex patterns of thermal alteration. However, volcanic sediments often have low total organic carbon contents and consequently are susceptible to analytical interferences. Despite this, it can be shown that meaningful Tmax measurements can still be made in sediment with organic carbon contents as low as 0.2% and that interference caused by bitumen or ionizable salts can be mitigated by solvent extraction and rinsing with water. Thus, it is reasonable to use temperature programmed pyrolysis to assess levels of thermal alteration in even low total organic carbon volcanoclastic sediments.

Barriers to suicide cluster detection and monitoring include requiring advanced software and statistical knowledge. We tested face validity of a simple method using readily accessible household software, Excel 3D Maps, to identify suicide clusters in this county, years 2014–2019. For spatial and temporal clusters, respectively, we defined meaningful thresholds of suicide density as 1.39/km2 and 33.9/yearly quarter, defined as the 95th percentile of normal logarithmic and normal scale distributions of suicide density per area in each ZIP Code Tabulated Area and 24 yearly quarters from all years. We generated heat maps showing suicide densities per 2.5 km viewing diameter. We generated a one-dimensional temporal map of 3-month meaningful cluster(s). We identified 21 total population spatial clusters and one temporal cluster. For greater accessibility, we propose an alternative method to traditional scan statistics using Excel 3D Maps potentially broadly advantageous in detecting, monitoring, and intervening at suicide clusters.