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Long COVID, a long-lasting disorder following an acute infection of COVID-19, represents a significant public health burden at present. In this paper, we propose a new mechanistic model based on differential equations to investigate the population dynamics of long COVID. By connecting long COVID with acute infection at the population level, our modeling framework emphasizes the interplay between COVID-19 transmission, vaccination, and long COVID dynamics. We conducted a detailed mathematical analysis of the model. We also validated the model using numerical simulation with real data from the US state of Tennessee and the UK. [ABSTRACT FROM AUTHOR]

We consider the problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers. We find an approximate solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes an upper bound to its exact solution. This upper bound allows direct structure-epidemic dynamic relations via the total communicability function. Using this approach we propose a strategy to remove edges in a network that significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers. We apply this strategy to the analysis of the UK airport transportation network weighted by the number of passengers transported in 2003. We find that the removal of all flights connecting four origin-destination pairs in the UK delays the propagation of a disease by more than 300%, with a minimal deterioration of the transportation capacity of this network. These time delays in the propagation of a disease represent an important non-pharmaceutical intervention to confront an epidemic, allowing for better preparations of the health systems, while keeping the economy moving with minimal disruptions. [ABSTRACT FROM AUTHOR]

In this survey, we trace the interplay between the Hardy-Littlewood school of analysis, prominent in the UK in the first half of the last century, and probability theory, barely known in the UK at that time. [ABSTRACT FROM AUTHOR]

Abstract: The first national target for reducing road accident casualties in Great Britain was set in 1987, the target year being 2000. As the year 2000 approached, preparations were made for setting a subsequent target, the target year being 2010. A major part of the preparation consisted of forecasting the number of casualties that might be expected in 2010, conditional upon predictions about how the volume of road travel by the various transport modes might change and the type of new road safety measures that the Government might introduce. The forecasts provided the numerical context for the casualty reduction target that the Government announced in March 2000. This paper summarises the statistical analyses of accident data from 1983 to 1998 upon which the forecasts were based, and compares the approach with alternatives that have been adopted elsewhere. It also describes how progress towards the target has been monitored annually, allowing the Government to judge whether additional efforts might be needed to achieve the target. This examination of the actual data from 1999 to 2007 shows how far the original forecasts have proved to be successful. The improvement of car secondary safety over the past 15years has probably been the development that has had the most significant effect on the national casualty total. A statistical model is used to quantify this effect by analysis of accident data, and the results of the most recent analyses are included. [Copyright &y& Elsevier]

Abstract: This study investigates property securities bubbles and crashes by using a dynamic mathematical methodology developed from the previous research (Watanabe et al. 2007a, b ). The improved model is used to detect the bubble and crash periods in five international countries/cities (namely, United States, United Kingdom, Japan, Hong Kong and Singapore) from Jan, 2000 to Oct, 2008. By this model definition, we are able to detect the beginning of each bubble period even before it bursts. Meanwhile, the empirical results show that most of property securities markets experienced bubble periods between 2003 and 2007, and crashes happened in Apr 2008 triggered by the Subprime Mortgage Crisis of US. In contrast, Japan suffered the shortest bubble period and no evidence has documented the existence of crash there. [Copyright &y& Elsevier]

Abstract: The carbonaceous components of Particulate Matter samples form a substantial fraction of their total mass, but their quantification depends strongly on the instruments and methods used. United Kingdom monitoring networks have provided many relevant data sets that are already in the public domain. Specifically, hourly organic carbon (OC) and elemental carbon (EC) were determined at four sites between 2003 and 2007 using Rupprecht and Pattashnik (R & P) 5400 automatic instruments. Since 2007, daily OC/EC measurements have been made by manual thermo-optical analysis of filter samples using a Sunset Laboratory Carbon Aerosol Analysis instrument. In parallel, long term daily measurements of Black Smoke, a quantity directly linked to black carbon (measured by aethalometers) and indirectly related to elemental carbon, have been made at many sites. The measurement issues associated with these techniques are evaluated in the context of UK measurements, making use of several sets of parallel data, with the aim of aiding the interpretation of network results. From the results available, the main conclusions are that the R & P 5400 instruments greatly under-read EC and total carbon (TC=OC+EC) at kerbside sites, probably due to the fact that the smaller particles are not sampled by the instrument; the R & P 5400 instrument is inherently difficult to characterise, so that all quantitative results need to be treated with caution; both aethalometer and Black Smoke (converted to black carbon) measurements can show reasonable agreement with elemental carbon results; and manual thermo-optical OC/EC results may under-read EC (and hence over-read OC), whether either transmittance or reflectance is used for the pyrolysis correction, and this effect is significant at rural sites. [Copyright &y& Elsevier]

Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study. [ABSTRACT FROM AUTHOR]

This article considers the role John Playfair (1748-1819) played in creating and popularizing the myth that mathematical development halted in Great Britain in the eighteenth century due to mathematicians' irrational attachment to a geometrical approach to the calculus. By the turn of the nineteenth century, Playfair had established his reputation as an energetic teacher, gifted expositor, and skilled natural philosopher. He served as joint professor of mathematics at the University of Edinburgh and as general secretary of the Royal Society of Edinburgh, editing the Society's Transactions, while his written accomplishments included Elements of geometry (1795) and Illustrations of the Huttonian theory of the earth (1802). He then contributed his talents to the opinionated journal, Edinburgh Review, where his assessments of the contemporary state of mathematics reached a wide audience of intellectuals, gentlemen, and merchants, albeit anonymously. The article expands upon a section of a talk delivered to the Fourth Joint Meeting of the BSHM and CSHPM in Montreal, 27-29 July 2007 (see also Ackerberg-Hastings 2007). [ABSTRACT FROM AUTHOR]

This paper will consider the range of British participation in mathematics internationally during the nineteenth century through an analysis of British mathematical contributions to scientific journals outside of Britain. Viewing scientific papers contained in journals as significant indicators of research, we consider scientists who authored or read and responded in print to papers in a given area within a given group of journals to constitute a publication community. The extent of publication by British mathematicians in these journals can help characterize the role of foreign publication in nineteenth-century British mathematics. Moreover, the isolation of educational, societal, and personal circumstances which motivated British mathematicians to present their work to foreign journals highlights limited but concentrated groups of mathematicians committed to developing and strengthening international mathematical ties with Britain. [ABSTRACT FROM AUTHOR]

The results of a survey of the mathematics provision within UK university computer science departments are presented. In particular it is found that many academics are dissatisfied with the level of ‘mathematical preparedness’ of their students. A number of recommendations and resources are suggested to address this. [ABSTRACT FROM AUTHOR]

Electoral analysis using aggregate data relies on the availability of accurate voting statistics. One vital piece of information, often missing from official electoral returns, particularly British local government elections, is the total number of valid ballot papers. This figure is essential for the calculation of electoral turnout. When voters have a single vote and official information about the number of ballot papers issued is missing, a figure for the total vote can still be derived. However, local elections in Britain frequently use a system of multiple-member wards, where voters have as many votes as there are seats to be filled. In such cases, calculating the total vote and, hence, the turnout does present a real problem. It cannot be assumed that all voters will use their full quota of votes or that voters will cast a ballot in favour of a single party. This paper develops and tests diff erent algorithms for calculating the total vote in such circumstances. We conclude that the accuracy of an algorithm is closely related to the structure of party competition. The findings of this paper have a number of important implications. First, the difficulties in calculating the turnout in multiple-member wards are identified. This will inform the debate about public participation in the local electoral process. Second, the method for deriving a figure for the total vote has an important bearing on a number of other statistics widely employed in electoral analysis. [ABSTRACT FROM AUTHOR]

Examines the true place of astrology among the mathematical arts of England in the late Tudor period. Legitimation of the celestial art; Alignment of astrology with the mathematical arts; Practice of astrology alongside other mathematical arts.

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK. [ABSTRACT FROM AUTHOR]

The article reports on a study by Kirsten Pfeiffer related to students' method of evaluating and comparing alternative mathematical proofs in Great Britain. The author of the study discusses students' performance, criteria and behavior when evaluating mathematical proofs. It presents an overview of written tasks and interviews conducted with a total of 141 first year mathematics students in response to algebras, mathematical notation, and visual tests. However it concludes that oral exercises of different proofs can be used as an appropriate method to make the nature of proof visible to the students. Also it suggests that 'mathematical-looking' formalism and the appearance of a proof seem to carry more significance to students than its content.

The article focuses on the research project Increasing Student Competence and Confidence in Algebra and Multiplicative Structures (ICCAMS), aimed at finding ways to enhance students' attainment and participation in various fields including mathematics, science, and engineering. The research is being done in England and it consists of two phases. The first phase involves a survey on the accomplishment of multiplicative reasoning and algebra in students of 11-14 years of age while the second phase focuses on a collaborative study to improve their attainment. The project also compares children's current attainment with that during the 1970s.

The article reports on the findings of a study related to the mathematical competence of adults who are returning to learning on a university foundation programme in Great Britain. The study, which involves 157 adult students and 46 international students, uses mathematics questions that are based on the ideas from the Concepts in Secondary Mathematics and Science (CSMS) study. Questions which likely identify some of the most common mathematical misconceptions were included. The study seeks to identify differences in hierarchies which suggest interaction between school learning and other processes.

The article discusses a study related to the use of representations in mathematics teaching by elementary teachers in Great Britain. The study examines how subject matter knowledge (SMK) and pedagogical content knowledge (PCK) can support the pedagogical decisions made by prospective teachers. Results show that beginning teachers prefer representations based on superficial attractiveness and aesthetic appeal rather than how mathematics can be mediated through such representation. Teacher respondents are found to think more conceptually about their use of iconic representations.

The article focuses on the use of context in post-16 pure mathematics questions set by the Examination Boards for national assessment in Great Britain. The study uses the grounded theory approach with six items from each specification analyzing and re-analyzing for identifying categories and relationships. Base from these questions, a framework analysis with three components is proposed. The accessibility of the context to all students is the first framework component. The second component pertains to its realistic appearance in the modeling experience and in test specific mathematics. The authenticity of the context in mathematical content is the third component. Further research is conducted for the verification of the framework result.