Compositional data, which is data consisting of fractions or probabilities, is common in many fields including ecology, economics, physical science and political science. If these data would otherwise be normally distributed, their spread can be conveniently represented by a multivariate normal distribution truncated to the non-negative space under a unit simplex. Here this distribution is called the simplex-truncated multivariate normal distribution. For calculations on truncated distributions, it is often useful to obtain rapid estimates of their integral, mean and covariance; these quantities characterising the truncated distribution will generally possess different values to the corresponding non-truncated distribution.

In the paper "Adams, Matthew (2022) Integral, mean and covariance of the simplex-truncated multivariate normal distribution. PLoS One, 17(7), Article number: e0272014. ", three different approaches that can estimate the integral, mean and covariance of any simplex-truncated multivariate normal distribution are described and compared. These three approaches are (1) naive rejection sampling, (2) a method described by Gessner et al. that unifies subset simulation and the Holmes-Diaconis-Ross algorithm with an analytical version of elliptical slice sampling, and (3) a semi-analytical method that expresses the integral, mean and covariance in terms of integrals of hyperrectangularly-truncated multivariate normal distributions, the latter of which are readily computed in modern mathematical and statistical packages. Strong agreement is demonstrated between all three approaches, but the most computationally efficient approach depends strongly both on implementation details and the dimension of the simplex-truncated multivariate normal distribution.

This dataset consists of all code and results for the associated article.

In this paper, we present a mathematical model to assess the impact of reducing the quarantine period and lifting the indoor mask mandate on the spread of Coronavirus Disease 2019 (COVID-19) in Korea. The model incorporates important epidemiological parameters, such as transmission rates and mortality rates, to simulate the transmission of the virus under different scenarios. Our findings reveal that the impact of mask wearing fades in the long term, which highlights the crucial role of quarantine in controlling the spread of the disease. In addition, balancing the confirmed cases and costs, the lifting of mandatory indoor mask wearing is cost-effective; however, maintaining the quarantine period remains essential. A relationship between the disease transmission rate and vaccine efficiency was also apparent, with higher transmission rates leading to a greater impact of the vaccine efficiency. Moreover, our findings indicate that a higher disease transmission rate exacerbates the consequences of early quarantine release.

This text aims to understand how the experiences with pedagogical workshops on taching mathematics in rural areas favored the teaching and learning of geometry by undergraduate in Pedagogy and by elementary school students. The text reflects the contexts of the countryside, showing how this can be enhanced as a locus for valuing actions in teaching that go beyond the school walls and expand by the contexts of life of their students. The methodology of this work comprises the realization of a pedagogical workshop with a course load of 12 hours, held at Sítio Mata da Lua by graduates of the Pedagogy Course in the Teaching of Mathematics discipline, given to students of the 9th grade of Elementary School II and the High school. The workshop was the research device used to enable reflections on the development of teaching practices that aim to theorize and value the students' context through a study on the concepts of trigonometry, plane geometry and surface measurements in situations and experiences in the fields. We take the reports of teachers and students who participated in this workshop as an element of analysis. It is concluded that the teaching of mathematics generates meanings for the student when the context in which he lives is taken into consideration for the construction of school knowledge. The countryside was understood as a locus of teaching in mathematics, enabling students to create connections between th knowledge of the countryside and the knowledge of trigonometry, in a construction of significant learning about mathematical knowledge.

R scripts and data used to generate figures and supplementary materials for manuscript.

Supplementary Information files for The impact of a lack of mathematical education on brain development and future attainmentFormal education has a long-term impact on an individual’s life. However, our knowledge of the effect of a specific lack of education, such as in mathematics, is currently poor but is highly relevant given the extant differences between countries in their educational curricula and the differences in opportunities to access education. Here we examined whether neurotransmitter concentrations in the adolescent brain could classify whether a student is lacking mathematical education. Decreased γ-aminobutyric acid (GABA) concentration within the middle frontal gyrus (MFG) successfully classified whether an adolescent studies math and was negatively associated with frontoparietal connectivity. In a second experiment, we uncovered that our findings were not due to preexisting differences before a mathematical education ceased. Furthermore, we showed that MFG GABA not only classifies whether an adolescent is studying math or not, but it also predicts the changes in mathematical reasoning ∼19 mo later. The present results extend previous work in animals that has emphasized the role of GABA neurotransmission in synaptic and network plasticity and highlight the effect of a specific lack of education on MFG GABA concentration and learning-dependent plasticity. Our findings reveal the reciprocal effect between brain development and education and demonstrate the negative consequences of a specific lack of education during adolescence on brain plasticity and cognitive functions.

Abstract Paper aims This paper portrays three examples of system dynamics modes applied to social good. Originality System dynamics has a strong tradition of applied research addressing complex social issues ranging from world and urban dynamics to the spread of infectious diseases. System dynamics can provide insight and inform long-term policy in complex social systems. This paper describes system dynamics applications in three important social challenges facing humanity. Research method In this article, we present three applications of system dynamics research addressing important social challenges, such as HIV/AIDS policy, the eradication of infectious diseases, and capacity building at humanitarian organizations. Main findings The examples illustrate how system dynamics can effectively capture key elements of complex dynamic systems allowing managers to understand the behavior of such environments over time. Implications for theory and practice This paper contributes to Jay Forrester's bold vision of aiming system dynamics to model important social challenges faced by humanity.

The SARS-CoV-2 Omicron outbreak is ongoing in Shanghai, home to 25 million population. Here, we presented a novel mathematical model to evaluate the Omicron spread and Zero-COVID strategy. Our model provided important parameters, the average quarantine ratio, the detection interval from being infected to being tested positive, and the spreading coefficient to understand the epidemic progression better. Moreover, we found that the key to a relatively accurate long-term forecast was to take the variation/relaxation of the parameters into consideration based on the flexible execution of the quarantine policy. This allowed us to propose the criteria for estimating the parameters and outcome for the ending stage that is likely to take place in late May. Altogether, this model helped to give a correct mathematical appraisal of the SARS-CoV-2 Omicron outbreak under the strict Zero-COVID policy in China.

Outbreak response strategies and notation used.

In 2024, 9.3 percent of students in the United Kingdom achieved the highest possible grade (an A*) in their A-Levels, with more than a quarter of entries achieving an B, the most common individual grade level in this year. Grades in 2020 and 2021 were generally a lot higher than in previous years due to the different grading circumstances brought on by the COVID-19 pandemic.

Mean and standard deviation of the normalised summary statistics for experimental images, where the normalisation is based on Eq (7).

The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model’s estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations.

The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model’s estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations.

Evolvability by means of simple sequence repeat (SSR) instability is a feature under the constant influence of opposing selective pressures to expand and compress the repeat tract and is mechanistically influenced by factors that affect genetic instability. In addition to direct selection for protein expression and structural integrity, other factors that influence tract length evolution were studied. The genetic instability of SSRs that switch the expression of antibiotic resistance ON and OFF was modelled mathematically and monitored in a panel of live meningococcal strains. The mathematical model showed that the SSR length of a theoretical locus in an evolving population may be shaped by direct selection of expression status (ON or OFF), tract length dependent (α) and tract length independent factors (β). According to the model an increase in α drives the evolution towards shorter tracts. An increase in β drives the evolution towards a normal distribution of tract lengths given that an upper and a lower limit are set. Insertion and deletion biases were shown to skew allelic distributions in both directions. The meningococcal SSR model was tested in vivo by monitoring the frequency of spectinomycin resistance OFF→ON switching in a designed locus. The instability of a comprehensive panel of the homopolymeric SSRs, constituted of a range of 5–13 guanine nucleotides, was monitored in wildtype and mismatch repair deficient backgrounds. Both the repeat length itself and mismatch repair deficiency were shown to influence the genetic instability of the homopolymeric tracts. A possible insertion bias was observed in tracts ≤G10. Finally, an inverse correlation between the number of tract-encoded amino acids and growth in the presence of ON-selection illustrated a limitation to SSR expansion in an essential gene associated with the designed model locus and the protein function mediating antibiotic resistance.

Mathematical and statistical models can be used to make predictions of how epidemics may progress in the near future and form a central part of outbreak mitigation and control. Renewal equation based models allow inference of epidemiological parameters from historical data and forecast future epidemic dynamics without requiring complex mechanistic assumptions. However, these models typically ignore interaction between age groups, partly due to challenges in parameterising a time varying interaction matrix. Social contact data collected regularly during the COVID-19 epidemic provide a means to inform interaction between age groups in real-time. We developed an age-specific forecasting framework and applied it to two age-stratified time-series: incidence of SARS-CoV-2 infection, estimated from a national infection and antibody prevalence survey; and, reported cases according to the UK national COVID-19 dashboard. Jointly fitting our model to social contact data from the CoMix study, we inferred a time-varying next generation matrix which we used to project infections and cases in the four weeks following each of 29 forecast dates between October 2020 and November 2021. We evaluated the forecasts using proper scoring rules and compared performance with three other models with alternative data and specifications alongside two naive baseline models. Overall, incorporating age interaction improved forecasts of infections and the CoMix-data-informed model was the best performing model at time horizons between two and four weeks. However, this was not true when forecasting cases. We found that age group interaction was most important for predicting cases in children and older adults. The contact-data-informed models performed best during the winter months of 2020–2021, but performed comparatively poorly in other periods. We highlight challenges regarding the incorporation of contact data in forecasting and offer proposals as to how to extend and adapt our approach, which may lead to more successful forecasts in future.

Addressing global environmental crises such as anthropogenic climate change requires the consistent adoption of proenvironmental behavior by a large part of a population. Here, we develop a mathematical model of a simple behavior-environment feedback loop to ask how the individual assessment of the environmental state combines with social interactions to influence the consistent adoption of proenvironmental behavior, and how this feeds back to the perceived environmental state. In this stochastic individual-based model, individuals can switch between two behaviors, ‘active’ (or actively proenvironmental) and ‘baseline’, differing in their perceived cost (higher for the active behavior) and environmental impact (lower for the active behavior). We show that the deterministic dynamics and the stochastic fluctuations of the system can be approximated by ordinary differential equations and a Ornstein-Uhlenbeck type process. By definition, the proenvironmental behavior is adopted consistently when, at population stationary state, its frequency is high and random fluctuations in frequency are small. We find that the combination of social and environmental feedbacks can promote the spread of costly proenvironmental behavior when neither, operating in isolation, would. To be adopted consistently, strong social pressure for proenvironmental action is necessary but not sufficient—social interactions must occur on a faster timescale compared to individual assessment, and the difference in environmental impact must be small. This simple model suggests a scenario to achieve large reductions in environmental impact, which involves incrementally more active and potentially more costly behavior being consistently adopted under increasing social pressure for proenvironmentalism.

The COVID-19 pandemic is the first to be rapidly and sequentially measured by nation-wide PCR community testing for the presence of the viral RNA at a global scale. We take advantage of the novel "natural experiment" where diverse nations and major subnational regions implemented various policies including social distancing and vaccination at different times with different levels of stringency and adherence. Initially, case numbers expand exponentially with doubling times of ~1–2 weeks. In the nations where interventions were not implemented or perhaps lees effectual, case numbers increased exponentially but then stabilized around 102-to-103 new infections (per km2 built-up area per day). Dynamics under effective interventions were perturbed and infections decayed to low levels. They rebounded concomitantly with the lifting of social distancing policies or pharmaceutical efficacy decline, converging on a stable equilibrium setpoint. Here we deploy a mathematical model which captures this V-shape behavior, incorporating a direct measure of intervention efficacy. Importantly, it allows the derivation of a maximal estimate for the basic reproductive number Ro (mean 1.6–1.8). We were able to test this approach by comparing the approximated "herd immunity" to the vaccination coverage observed that corresponded to rapid declines in community infections during 2021. The estimates reported here agree with the observed phenomena. Moreover, the decay (0.4–0.5) and rebound rates (0.2–0.3) were similar throughout the pandemic and among all the nations and regions studied. Finally, a longitudinal analysis comparing multiple national and regional results provides insights on the underlying epidemiology of SARS-CoV-2 and intervention efficacy, as well as evidence for the existence of an endemic steady state of COVID-19.