Motivated by problems in percolation theory, we study the following two-player positional game. Let Λm×n be a rectangular grid-graph with m vertices in each row and n vertices in each column. Two players, Maker and Breaker, play in alternating turns. On each of her turns, Maker claims p (as yet unclaimed) edges of the board Λm×n, while on each of his turns Breaker claims q (as yet unclaimed) edges of the board and destroys them. Maker wins the game if she manages to claim all the edges of a crossing path joining the left-hand side of the board to its right-hand side, otherwise Breaker wins. We call this game the (p, q)-crossing game on Λm×n.

Given m, n ∈ ℕ, for which pairs (p, q) does Maker have a winning strategy for the (p, q)-crossing game on Λm×n? The (1, 1)-case corresponds exactly to the popular game of Bridg-it, which is well understood due to it being a special case of the older Shannon switching game. In this paper we study the general (p, q)-case. Our main result is to establish the following transition.

• If p ≥ 2q, then Maker wins the game on arbitrarily long versions of the narrowest board possible, that is, Maker has a winning strategy for the (2q, q)-crossing game on Λm×(q+1) for any m ∈ ℕ.

• If p ≤ 2q − 1, then for every width n of the board, Breaker has a winning strategy for the (p, q)-crossing game on Λm×n for all sufficiently large board-lengths m.

Our winning strategies in both cases adapt more generally to other grids and crossing games. In addition we pose many new questions and problems.

Although the African continent is, for the moment, less impacted than the rest of the world, it still faces the risk of a spread of COVID-19. In this study, we have conducted a systematic review of the information available in the literature in order to provide an overview of the epidemiological and clinical features of COVID-19 pandemic in West Africa and of the impact of risk factors such as comorbidities, climatic conditions and demography on the pandemic. Burkina Faso is used as a case study to better describe the situation in West Africa. The epidemiological situation of COVID-19 in West Africa is marked by a continuous increase in the numbers of confirmed cases. This geographic area had on 29 July 2020, 131 049 confirmed cases by polymerase chain reaction, 88 305 recoveries and 2102 deaths. Several factors may influence the SARS-CoV-2 circulation in Africa: (i) comorbidities: diabetes mellitus and high blood pressure could lead to an increase in the number of severe cases of SARS-CoV-2; (ii) climatic factors: the high temperatures could be a factor contributing to slow the spread of the virus and (iii) demography: the West Africa population is very young and this could be a factor limiting the occurrence of severe forms of SARS-CoV-2 infection. Although the spread of the SARS-CoV-2 epidemic in West Africa is relatively slow compared to European countries, vigilance must remain. Difficulties in access to diagnostic tests, lack of hospital equipment, but also the large number of people working in the informal sector (such as trading, businesses, transport and restoration) makes it difficult to apply preventive measures, namely physical distancing and containment.

In this paper, we consider finite mixture models with components having distributions from the location-scale family. We then discuss the usual stochastic order and the reversed hazard rate order of such finite mixture models under some majorization conditions on location, scale and mixing probabilities as model parameters.

Teenagers are important carriers of Neisseria meningitidis, which is a leading cause of invasive meningococcal disease. In China, the carriage rate and risk factors among teenagers are unclear. The present study presents a retrospective analysis of epidemiological data for N. meningitidis carriage from 2013 to 2017 in Suizhou city, China. The carriage rates were 3.26%, 2.22%, 3.33%, 3.53% and 9.88% for 2013, 2014, 2015, 2016 and 2017, respectively. From 2014 to 2017, the carriage rate in the 15- to 19-year-old age group (teenagers) was the highest and significantly higher than that in remain age groups. Subsequently, a larger scale survey (December 2017) for carriage rate and relative risk factors (population density, time spent in the classroom, gender and antibiotics use) were investigated on the teenagers (15- to 19-year-old age) at the same school. The carriage rate was still high at 33.48% (223/663) and varied greatly from 6.56% to 52.94% in a different class. Population density of the classroom was found to be a significant risk factor for carriage, and 1.4 persons/m2 is recommended as the maximum classroom density. Further, higher male gender ratio and more time spent in the classroom were also significantly associated with higher carriage. Finally, antibiotic use was associated with a significantly lower carriage rate. All the results imply that attention should be paid to the teenagers and various measures can be taken to reduce the N. meningitidis carriage, to prevent and control the outbreak of IMD.

Ecologic studies investigating COVID-19 mortality determinants, used to make predictions and design public health control measures, generally focused on population-based variable counterparts of individual-based risk factors. Influenza is not causally associated with COVID-19, but shares population-based determinants, such as similar incidence/mortality trends, transmission patterns, efficacy of non-pharmaceutical interventions, comorbidities and underdiagnosis. We investigated the ecologic association between influenza mortality rates and COVID-19 mortality rates in the European context. We considered the 3-year average influenza (2014–2016) and COVID-19 (31 May 2020) crude mortality rates in 34 countries using EUROSTAT and ECDC databases and performed correlation and regression analyses. The two variables – log transformed, showed significant Spearman's correlation ρ = 0.439 (P = 0.01), and regression coefficients, b = 0.743 (95% confidence interval, 0.272–1.214; R2 = 0.244; P = 0.003), b = 0.472 (95% confidence interval, 0.067–0.878; R2 = 0.549; P = 0.02), unadjusted and adjusted for confounders (population size and cardiovascular disease mortality), respectively. Common significant determinants of both COVID-19 and influenza mortality rates were life expectancy, influenza vaccination in the elderly (direct associations), number of hospital beds per population unit and crude cardiovascular disease mortality rate (inverse associations). This analysis suggests that influenza mortality rates were independently associated with COVID-19 mortality rates in Europe, with implications for public health preparedness, and implies preliminary undetected SARS-CoV-2 spread in Europe.

Graphlet counting is a widely explored problem in network analysis and has been successfully applied to a variety of applications in many domains, most notatbly bioinformatics, social science, and infrastructure network studies. Efficiently computing graphlet counts remains challenging due to the combinatorial explosion, where a naive enumeration algorithm needs O(Nk) time for k-node graphlets in a network of size N. Recently, many works introduced carefully designed combinatorial and sampling methods with encouraging results. However, the existing methods ignore the fact that graphlet counts and the graph structural information are correlated. They always consider a graph as a new input and repeat the tedious counting procedure on a regular basis even if it is similar or exactly isomorphic to previously studied graphs. This provides an opportunity to speed up the graphlet count estimation procedure by exploiting this correlation via learning methods. In this paper, we raise a novel graphlet count learning (GCL) problem: given a set of historical graphs with known graphlet counts, how to learn to estimate/predict graphlet count for unseen graphs coming from the same (or similar) underlying distribution. We develop a deep learning framework which contains two convolutional neural network models and a series of data preprocessing techniques to solve the GCL problem. Extensive experiments are conducted on three types of synthetic random graphs and three types of real-world graphs for all 3-, 4-, and 5-node graphlets to demonstrate the accuracy, efficiency, and generalizability of our framework. Compared with state-of-the-art exact/sampling methods, our framework shows great potential, which can offer up to two orders of magnitude speedup on synthetic graphs and achieve on par speed on real-world graphs with competitive accuracy.

The objective of this study was to describe the epidemiology of COVID-19 in Nigeria with a view of generating evidence to enhance planning and response strategies. A national surveillance dataset between 27 February and 6 June 2020 was retrospectively analysed, with confirmatory testing for COVID-19 done by real-time polymerase chain reaction (RT-PCR). The primary outcomes were cumulative incidence (CI) and case fatality (CF). A total of 40 926 persons (67% of total 60 839) had complete records of RT-PCR test across 35 states and the Federal Capital Territory, 12 289 (30.0%) of whom were confirmed COVID-19 cases. Of those confirmed cases, 3467 (28.2%) had complete records of clinical outcome (alive or dead), 342 (9.9%) of which died. The overall CI and CF were 5.6 per 100 000 population and 2.8%, respectively. The highest proportion of COVID-19 cases and deaths were recorded in persons aged 31–40 years (25.5%) and 61–70 years (26.6%), respectively; and males accounted for a higher proportion of confirmed cases (65.8%) and deaths (79.0%). Sixty-six per cent of confirmed COVID-19 cases were asymptomatic at diagnosis. In conclusion, this paper has provided an insight into the early epidemiology of COVID-19 in Nigeria, which could be useful for contextualising public health planning.

Antibiotic-resistant Gram-negative bacteraemias (GNB) are increasing in incidence. We aimed to investigate the impact of empirical antibiotic therapy on clinical outcomes by carrying out an observational 6-year cohort study of patients at a teaching hospital with community-onset Escherichia coli bacteraemia (ECB), Klebsiella pneumoniae bacteraemia (KPB) and Pseudomonas aeruginosa bacteraemia (PsAB). Antibiotic therapy was considered concordant if the organism was sensitive in vitro and discordant if resistant. We estimated the association between concordant vs. discordant empirical antibiotic therapy on odds of in-hospital death and ICU admission for KPB and ECB. Of 1380 patients, 1103 (79.9%) had ECB, 189 (13.7%) KPB and 88 (6.4%) PsAB. Discordant therapy was not associated with increased odds of either outcome. For ECB, severe illness and non-urinary source were associated with increased odds of both outcomes (OR of in-hospital death for non-urinary source 3.21, 95% CI 1.73–5.97). For KPB, discordant therapy was associated with in-hospital death on univariable but not multivariable analysis. Illness severity was associated with increased odds of both outcomes. These findings suggest broadening of therapy for low-risk patients with community-onset GNB is not warranted. Future research should focus on the relationship between patient outcomes, clinical factors, infection focus and causative organism and resistance profile.

COVID-19 has spread across the globe with higher burden placed in Europe and North America. However, the rate of transmission has recently picked up in low- and middle-income countries, particularly in the Indian subcontinent. There is a severe underreporting bias in the existing data available from these countries mostly due to the limitation of resources and accessibility. Most studies comparing cross-country cases or fatalities could fail to account for this systematic bias and reach erroneous conclusions. This paper provides several recommendations on how to effectively tackle these issues regarding data quality, test coverage and case counts.

A new method of forecasting mortality is introduced. The method is based on the continuous-time dynamics of the Lexis diagram, which given weak assumptions implies that the death count data are Poisson distributed. The underlying mortality rates are modelled with a hidden Markov model (HMM) which enables a fully likelihood-based inference. Likelihood inference is done by particle filter methods, which avoids approximating assumptions and also suggests natural model validation measures. The proposed model class contains as special cases many previous models with the important difference that the HMM methods make it possible to estimate the model efficiently. Another difference is that the population and latent variable variability can be explicitly modelled and estimated. Numerical examples show that the model performs well and that inefficient estimation methods can severely affect forecasts.

TLR3 and IL-10 play a crucial role in antiviral defence. However, there is a controversy between TLR3 rs3775291 and IL-10 rs1800871 polymorphisms and the risk of hepatitis B virus (HBV) infection. The purpose of this study is to explore the relationship between the two single nucleotide mutations and the risk of HBV infection by meta-analysis. Medline, EMBASE, Web of Science, CNKI, China Wanfang database were searched for the case-control studies on the relationship between TLR3 rs3775291 and IL-10 rs1800871 polymorphism and susceptibility to HBV, updated to June 2020. The data were analysed by Stata 15.0 software. A total of 22 articles were included. The results showed that in the analysis of IL10 rs1800871 polymorphism and the risk of HBV infection, the pooled OR was 1.21 (95% CI 1.06–1.37), 1.28 (95% CI 1.04–1.56) and 1.20 (95% CI 1.06–1.37) and 1.40 (95% CI 1.07–1.83) in the allele model (C vs. T), dominant model (CC+CT vs. TT), recessive model (CC vs. CT+TT) and homozygous model (CC vs. TT), respectively. There was no statistical significance in the heterozygote model. A subgroup analysis of the Asian population showed similar results. The analysis of TLR3 rs3775291 polymorphism and the risk of HBV showed that in the allele model (T vs. C), the pooled OR was 1.30 (95% CI 1.05–1.61). Except for the recessive model, no significances were found in other genetic models. In conclusion, TLR3 rs3775291 and IL-10 rs1800871 polymorphisms are associated with the risk of HBV. Allele C and genotype CC at IL10 rs1800871 loci, as well as allele T and genotype TT at TLR rs3775291 loci, may increase susceptibility to Hepatitis B infection.

Internet and Communication Technology/electrical and electronic equipment (ICT/EEE) form the bedrock of today’s knowledge economy. This increasingly interconnected web of products, processes, services, and infrastructure is often invisible to the user, as are the resource costs behind them. This ecosystem of machine-to-machine and cyber-physical-system technologies has a myriad of (in)direct impacts on the lithosphere, biosphere, atmosphere, and hydrosphere. As key determinants of tomorrow’s digital world, academic institutions are critical sites for exploring ways to mitigate and/or eliminate negative impacts. This Report is a self-deliberation provoked by the question How do we create more resilient and healthier computer science departments: living laboratories for teaching and learning about resource-constrained computing, computation, and communication? Our response for University College London (UCL) Computer Science is to reflect on how, when, and where resources—energy, (raw) materials including water, space, and time—are consumed by the building (place), its occupants (people), and their activities (pedagogy). This perspective and attendant first-of-its-kind assessment outlines a roadmap and proposes high-level principles to aid our efforts, describing challenges and difficulties hindering quantification of the Department’s resource footprint. Qualitatively, we find a need to rematerialise the ICT/EEE ecosystem: to reveal the full costs of the seemingly intangible information society by interrogating the entire life history of paraphernalia from smartphones through servers to underground/undersea cables; another approach is demonstrating the corporeality of commonplace phrases and Nature-inspired terms such as artificial intelligence, social media, Big Data, smart cities/farming, the Internet, the Cloud, and the Web. We sketch routes to realising three interlinked aims: cap annual power consumption and greenhouse gas emissions, become a zero waste institution, and rejuvenate and (re)integrate the natural and built environments.

The Coronavirus Disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a public health emergency of international concern. The current study aims to explore whether the neutrophil-to-lymphocyte ratio (NLR) and platelet-to-lymphocyte ratio (PLR) are associated with the development of death in patients with COVID-19. A total of 131 patients diagnosed with COVID-19 from 13 February 2020 to 14 March 2020 in a hospital in Wuhan designated for treating COVID-19 were enrolled in the current study. These 131 patients had a median age of 64 years old (interquartile range: 56–71 years old). Furthermore, among these patients, 111 (91.8%) patients were discharged and 12 (9.2%) patients died in the hospital. The pooled analysis revealed that the NLR at admission was significantly elevated for non-survivors, when compared to survivors (P < 0.001). The NLR of 3.338 was associated with all-cause mortality, with a sensitivity of 100.0% and a specificity of 84.0% (area under the curve (AUC): 0.963, 95% confidence interval (CI) 0.911–1.000; P < 0.001). In view of the small number of deaths (n = 12) in the current study, NLR of 2.306 might have potential value for helping clinicians to identify patients with severe COVID-19, with a sensitivity of 100.0% and a specificity of 56.7% (AUC: 0.729, 95% CI 0.563–0.892; P = 0.063). The NLR was significantly associated with the development of death in patients with COVID-19. Hence, NLR is a useful biomarker to predict the all-cause mortality of COVID-19.

We investigate a covering problem in 3-uniform hypergraphs (3-graphs): Given a 3-graph F, what is c1(n, F), the least integer d such that if G is an n-vertex 3-graph with minimum vertex-degree $\delta_1(G)>d$ then every vertex of G is contained in a copy of F in G?

We asymptotically determine c1(n, F) when F is the generalized triangle $K_4^{(3)-}$, and we give close to optimal bounds in the case where F is the tetrahedron $K_4^{(3)}$ (the complete 3-graph on 4 vertices).

This latter problem turns out to be a special instance of the following problem for graphs: Given an n-vertex graph G with $m> n^2/4$ edges, what is the largest t such that some vertex in G must be contained in t triangles? We give upper bound constructions for this problem that we conjecture are asymptotically tight. We prove our conjecture for tripartite graphs, and use flag algebra computations to give some evidence of its truth in the general case.

The search space for new thermoelectric oxides has been limited to the alloys of a few known systems, such as ZnO, SrTiO3, and CaMnO3. Notwithstanding the high power factor, their high thermal conductivity is a roadblock in achieving higher efficiency. In this paper, we apply machine learning (ML) models for discovering novel transition metal oxides with low lattice thermal conductivity ($ {k}_L $). A two-step process is proposed to address the problem of small datasets frequently encountered in material informatics. First, a gradient-boosted tree classifier is learnt to categorize unknown compounds into three categories of $ {k}_L $: low, medium, and high. In the second step, we fit regression models on the targeted class (i.e., low $ {k}_L $) to estimate $ {k}_L $ with an $ {R}^2>0.9 $. Gradient boosted tree model was also used to identify key material properties influencing classification of $ {k}_L $, namely lattice energy per atom, atom density, band gap, mass density, and ratio of oxygen by transition metal atoms. Only fundamental materials properties describing the crystal symmetry, compound chemistry, and interatomic bonding were used in the classification process, which can be readily used in the initial phases of materials design. The proposed two-step process addresses the problem of small datasets and improves the predictive accuracy. The ML approach adopted in the present work is generic in nature and can be combined with high-throughput computing for the rapid discovery of new materials for specific applications.

The Poisson process is an essential building block to move up to complicated counting processes, such as the Cox (“doubly stochastic Poisson”) process, the Hawkes (“self-exciting”) process, exponentially decaying shot-noise Poisson (simply “shot-noise Poisson”) process and the dynamic contagion process. The Cox process provides flexibility by letting the intensity not only depending on time but also allowing it to be a stochastic process. The Hawkes process has self-exciting property and clustering effects. Shot-noise Poisson process is an extension of the Poisson process, where it is capable of displaying the frequency, magnitude and time period needed to determine the effect of points. The dynamic contagion process is a point process, where its intensity generalises the Hawkes process and Cox process with exponentially decaying shot-noise intensity. To facilitate the usage of these processes in practice, we revisit the distributional properties of the Poisson, Cox, Hawkes, shot-noise Poisson and dynamic contagion process and their compound processes. We provide simulation algorithms for these processes, which would be useful to statistical analysis, further business applications and research. As an application of the compound processes, numerical comparisons of value-at-risk and tail conditional expectation are made.

In this note we study the emergence of Hamiltonian Berge cycles in random r-uniform hypergraphs. For $r\geq 3$ we prove an optimal stopping time result that if edges are sequentially added to an initially empty r-graph, then as soon as the minimum degree is at least 2, the hypergraph with high probability has such a cycle. In particular, this determines the threshold probability for Berge Hamiltonicity of the Erdős–Rényi random r-graph, and we also show that the 2-out random r-graph with high probability has such a cycle. We obtain similar results for weak Berge cycles as well, thus resolving a conjecture of Poole.

The test-negative design (TND) has become a standard approach for vaccine effectiveness (VE) studies. However, previous studies suggested that it may be more vulnerable than other designs to misclassification of disease outcome caused by imperfect diagnostic tests. This could be a particular limitation in VE studies where simple tests (e.g. rapid influenza diagnostic tests) are used for logistical convenience. To address this issue, we derived a mathematical representation of the TND with imperfect tests, then developed a bias correction framework for possible misclassification. TND studies usually include multiple covariates other than vaccine history to adjust for potential confounders; our methods can also address multivariate analyses and be easily coupled with existing estimation tools. We validated the performance of these methods using simulations of common scenarios for vaccine efficacy and were able to obtain unbiased estimates in a variety of parameter settings.

The Office for National Statistics (ONS) is currently undertaking a substantial research program into using price information scraped from online retailers in the Consumer Prices Index including occupiers’ housing costs (CPIH). In order to make full use of these data, we must classify it into the product types that make up the basket of goods and services used in the current collection. It is a common problem that the amount of labeled training data is limited and it is either impossible or impractical to manually increase the size of the training data, as is the case with web-scraped price data. We make use of a semi-supervised machine learning (ML) method, Label Propagation, to develop a pipeline to increase the number of labels available for classification. In this work, we use several techniques in succession and in parallel to enable higher confidence in the final increased labeled dataset to be used in training a traditional ML classifier. We find promising results using this method on a test sample of data achieving good precision and recall values for both the propagated labels and the classifiers trained from these labels. We have shown that through combining several techniques together and averaging the results, we are able to increase the usability of a dataset with limited labeled training data, a common problem in using ML in real world situations. In future work, we will investigate how this method can be scaled up for use in future CPIH calculations and the challenges this brings.