A dynamical systems model of unorganised segregation

We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative analysis of the system for the case of a linear tolerance schedule in both populations. In doing so, we recover and generalise Schelling's qualitative results. For the case of unlimited population movement, we derive exact formulae for regions in parameter space where stable integrated population mixes can occur. We show how neighbourhood tipping can be adequately explained in terms of basins of attraction. For the case of limiting population movement, we derive exact criteria for the occurrence of new population mixes and identify the stable cases. We show how to apply our methodology to nonlinear tolerance schedules, illustrating our approach with numerical simulations. We associate each term in our Schelling dynamical system with a social meaning. In particular we show that the dynamics of one population in the presence of another can be summarised as follows {rate of population change} = {intrinsic popularity of neighbourhood} - {finite size of neighbourhood} - {presence of other population} By approaching the dynamics from this perspective, we have a complementary approach to that of the tolerance schedule.Comment: 17 pages (inc references), 9 figure

A dynamical systems model of unorganised segregation in two neighbourhoods

We present a complete analysis of the Schelling dynamical system [Haw2018] of two connected neighbourhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable integration is only possible when the minority is small and combined tolerance is large. Unlike the case of the single neighbourhood, limiting one population does not necessarily produce stable integration and may destroy it. We conclude that a growing minority can only remain integrated if the majority increases its own tolerance. Our results show that an integrated single neighbourhood may not remain so when a connecting neighbourhood is created.Comment: 26 pages, 13 figure

A neutron scattering study of the interplay between structure and magnetism in Ba(Fe1−x_{1-x}Cox_{x})2_2As2_2

Single crystal neutron diffraction is used to investigate the magnetic and structural phase diagram of the electron doped superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. Heat capacity and resistivity measurements have demonstrated that Co doping this system splits the combined antiferromagnetic and structural transition present in BaFe$_2$As$_2$ into two distinct transitions. For $x$=0.025, we find that the upper transition is between the high-temperature tetragonal and low-temperature orthorhombic structures with ($T_{\mathrm{TO}}=99 \pm 0.5$ K) and the antiferromagnetic transition occurs at $T_{\mathrm{AF}}=93 \pm 0.5$ K. We find that doping rapidly suppresses the antiferromagnetism, with antiferromagnetic order disappearing at $x \approx 0.055$. However, there is a region of co-existence of antiferromagnetism and superconductivity. The effect of the antiferromagnetic transition can be seen in the temperature dependence of the structural Bragg peaks from both neutron scattering and x-ray diffraction. We infer from this that there is strong coupling between the antiferromagnetism and the crystal lattice

An Introduction to the Hyperspace of Hargreaves-Samani Reference Evapotranspiration

Climate change has been shown to directly influence evapotranspiration, which is one of the crucial watershed processes. The common approach to its calculation is via mathematical equations, such as 1985 Hargreaves-Samani (HS85). It computes reference evapotranspiration (ETo) through three climatic variables and one constant: RA (extra-terrestrial radiation), TC (mean temperature), TR (temperature range) and KR (empirical coefficient). To make HS85 more accurate, one of its authors proposed an equation for KR as a function of TR in 2000 (HS00). Both models are 4D and their internal behaviours are difficult to understand, hence, the data driven applications prevalent among experts and managers. In this study, we introduce an innovative research by trying to respond to two questions. What are the relationships between TC and TR? What are the internal patterns of HS hyperspace (4D domain) and the changes in ETo possibilities of the two models? In the proposed approach, thresholds for the four variables are utilized to cover majority of the agroclimatic situations in the world and the hyperspace is discretized with more than 50,000 calculation nodes. The ETo results show that under various climatic conditions, the behaviour of HS is nonlinear (more for HS00) leading to an increased uncertainty particularly for data driven applications. TC and TR show patterns useful for regions with less data.This work was partially financed by (a) the Portuguese Foundation for Science and Technology (FCT) under the contract UID/ECI/04047/2013 for the Centre of Territory, Environment and Construction(CTAC) of the University of Minho, (b) project POCI-01-0145-FEDER-028247 - funded by FEDER funds throughCOMPETE2020—Programa Operacional Competitividade e Internacionalização (POCI) and by national funds (PIDDAC) through FCT/MCTES. Acknowledgments: The authors appreciate the cooperation of the Cluster computing facilities of the University of Minho developed under the Project ‘Search-ON2: Revitalization of HPC infrastructure of UMinho’ (NORTE-07-0162-FEDER-000086), co-funded by the North Portugal Regional Operational Programme (ON.2—O Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF).info:eu-repo/semantics/publishedVersio

Impact of Scottish smoke-free legislation on smoking quit attempts and prevalence

<p><b>Objectives:</b> In Scotland, legislation was implemented in March 2006 prohibiting smoking in all wholly or partially enclosed public spaces. We investigated the impact on attempts to quit smoking and smoking prevalence.</p> <p><b>Methods:</b> We performed time series models using Box-Jenkins autoregressive integrated moving averages (ARIMA) on monthly data on the gross ingredient cost of all nicotine replacement therapy (NRT) prescribed in Scotland in 2003–2009, and quarterly data on self-reported smoking prevalence between January 1999 and September 2010 from the Scottish Household Survey.</p> <p><b>Results:</b> NRT prescription costs were significantly higher than expected over the three months prior to implementation of the legislation. Prescription costs peaked at £1.3 million in March 2006; £292,005.9 (95% CI £260,402.3, £323,609, p<0.001) higher than the monthly norm. Following implementation of the legislation, costs fell exponentially by around 26% per month (95% CI 17%, 35%, p<0.001). Twelve months following implementation, the costs were not significantly different to monthly norms. Smoking prevalence fell by 8.0% overall, from 31.3% in January 1999 to 23.7% in July–September 2010. In the quarter prior to implementation of the legislation, smoking prevalence fell by 1.7% (95% CI 2.4%, 1.0%, p<0.001) more than expected from the underlying trend.</p> <p><b>Conclusions:</b> Quit attempts increased in the three months leading up to Scotland's smoke-free legislation, resulting in a fall in smoking prevalence. However, neither has been sustained suggesting the need for additional tobacco control measures and ongoing support.</p&gt

Does gravity cause load-bearing bridges in colloidal and granular systems?

We study structures which can bear loads, "bridges", in particulate packings. To investigate the relationship between bridges and gravity, we experimentally determine bridge statistics in colloidal packings. We vary the effective magnitude and direction of gravity, volume fraction, and interactions, and find that the bridge size distributions depend only on the mean number of neighbors. We identify a universal distribution, in agreement with simulation results for granulars, suggesting that applied loads merely exploit preexisting bridges, which are inherent in dense packings

Breast cancer in high-risk Afrikaner families: Is BRCA founder mutation testing sufficient?

Background. Germline pathogenic mutations in cancer susceptibility genes result in inherited cancer syndromes. In the Afrikaner population of South Africa (SA), three founder mutations in the BRCA genes that lead to hereditary breast and ovarian cancer syndrome (HBOCS) have been identified.Objectives. To investigate the uptake and type of molecular testing performed on patients for HBOCS, to determine the prevalence of the three Afrikaner founder BRCA mutations as well as non-founder BRCA mutations in the study population, and to analyse the utility of two mutation prediction models (Breast and Ovarian Analysis of Disease Incidence and Carrier Estimation Algorithm (BOADICEA) and Manchester scoring method) in assisting with the decision for the most cost-effective testing option.Methods. A retrospective file review was performed on counsellees of self reported Afrikaner ancestry from Johannesburg, SA (2001 - 2014), with a personal or family history of breast and/or ovarian cancer. Demographic and family history information was recorded and Manchester and BOADICEA scores were calculated for each patient.Results. Of 86 unrelated counsellees whose files were reviewed, 54 (62.8%) underwent BRCA genetic testing; 18 (33.3%) tested positive for a mutation, and 14 of these (77.8%) for an Afrikaner founder mutation. Twelve counsellees had the BRCA2 c.7934delG mutation. Four non-founder mutations were identified. BOADICEA scores were significantly higher in counsellees who tested positive for a mutation than in those who tested negative.Conclusions. Founder mutation testing should be performed as a first-line option. BOADICEA is very useful in identifying counsellees at high risk for a BRCA mutation and also assists with the decision to pursue further testing following a negative founder mutation result. These findings assist in guiding an informed genetic counselling service for at-risk individuals with an Afrikaner background