The sleekest link algorithm

How does Google decide which web sites are important? It uses an ingenious algorithm that exploits the structure of the web and is resistant to hacking. Here, we describe this PageRank algorithm, illustrate it by example, and show how it can be interpreted as a Jacobi iteration and a teleporting random walk. We also ask the algorithm to rank the undergraduate mathematics classes offered at the University of Strathclyde. PageRank draws upon ideas from linear algebra, graph theory and stochastic processes, and it throws up research-level challenges in scientific computing. It thus forms an exciting and modern application area that could brighten up many a mathematics class syllabus

Discovering bipartite substructure in directed networks

Bipartivity is an important network concept that can be applied to nodes, edges and communities. Here we focus on directed networks and look for subnetworks made up of two distinct groups of nodes, connected by “one-way” links. We show that a spectral approach can be used to find hidden substructure of this form. Theoretical support is given for the idealised case where there is limited overlap between subnetworks. Numerical experiments show that the approach is robust to spurious and missing edges. A key application of this work is in the analysis of high-throughput gene expression data, and we give an example where a biologically meaningful directed bipartite subnetwork is found from a cancer microarray dataset

The Gedanken Ball-and-Stick Construction Problem: What is the Most Simple Structure that it is Possible to Construct?

A very simple question is posed: Employing a ball-and-stick modelling system, and given a supply of the component balls and rods, then, treating it as a gedanken experiment, what is the most simple structure that it is possible to construct

A Structuralist Proposal for the Foundations of the Natural Numbers

This paper introduces a novel object that has less structure than, and is ontologically prior to the natural numbers. As such it is a candidate model of the foundation that lies beneath the natural numbers. The implications for the construction of mathematical objects built upon that foundation are discussed

A review of selection criteria used by medical scheme advisers to approve or deny procedures with a cosmetic component

Objective. To review and apply statistical tests to the selection criteria used by two medical advisers to approve or deny applications for three common cosmetic or reconstructive procedures within a large group of medical schemes.Design. A retrospective descriptive study which applied multiple regression analysis, frequency analysis, comparison of means and simple correlations to the data sets for three procedures.Setting. Administrative records from the clinical files of medical advisers and the administrator's claims database.Subjects. Data were reviewed for 1 143 members who, between January and December 1996, submitted applications for breast reduction, excimer laser refractive surgery, or otoplasty.Main outcome measures. The primary outcome measure was the statistical relationship between medical advisers' selection criteria and final decision. In addition, the financial implications of these cosmetic/reconstructive procedures were assessed.Results. For the three procedures reviewed there was a statistically significant relationship behveen 5 of 13 preoperative criteria requested and the medical advisers' opinion. Excimer laser surgery was generally approved on the basis of the refractive error (myopia> -3.00; astigmatism > -1.5 dioptres); otoplasty was generally approved for children aged :≤ 12.years; and breast reduction was usually covered for women with a sternal-nipple distance > 29.0 cm and with a cup size ≥ DD. The other data submitted were similarly distributed between the approved and denied groups.Conclusions. Review of medical advisers' decisions is important in an era of protocols, guidelines and 'standard operating procedures'. Selection criteria for approval of applications for medically necesssary cosmetic/reconstructive surgery must be reviewed and revised to provide a reliable, reproducible and statistically valid process

CONTEST : a Controllable Test Matrix Toolbox for MATLAB

Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models have been proposed that capture key properties of real-life networks. These models provide realistic, parametrized matrices for testing linear system and eigenvalue solvers. CONTEST (CONtrollable TEST matrices) is a random network toolbox for MATLAB that implements nine models. The models produce unweighted directed or undirected graphs; that is, symmetric or unsymmetric matrices with elements equal to zero or one. They have one or more parameters that affect features such as sparsity and characteristic pathlength and all can be of arbitrary dimension. Utility functions are supplied for rewiring, adding extra shortcuts and subsampling in order to create further classes of networks. Other utilities convert the adjacency matrices into real-valued coefficient matrices for naturally arising computational tasks that reduce to sparse linear system and eigenvalue problems

Protocol of a cost-effectiveness analysis of a combined intervention for depression and parenting compared with enhanced standard of care for perinatally depressed, HIV-positive women and their infants in rural South Africa

Introduction: Poverty, HIV and perinatal depression represent a triple threat to public health in sub-Saharan Africa because of their combined negative effects on parenting and child development. In the resource-constrained context of low-income and middle-income countries, a lay-counsellor-delivered intervention that combines a psychological and parenting intervention could offer the potential to mitigate the consequences of perinatal depression while also optimising scarce resources for healthcare. Measuring the cost-effectiveness of such a novel intervention will help decision-makers to better understand the relative costs and effects associated with replicating the intervention, thereby supporting evidence-based decision-making. This protocol sets out the methodological framework for analysing the cost-effectiveness of a cluster randomised controlled trial (RCT) that compares a combined intervention to enhanced standard of care when treating depressed, HIV-positive pregnant women and their infants in rural South Africa. Methods and analysis: This cost-effectiveness analysis (CEA) protocol complies with the Consolidated Health Economic Evaluation Reporting Standards 2022 checklist. A societal perspective will be chosen. The proposed methods will determine the cost and efficiency of implementing the intervention as per the randomised control trial protocol, as well as the cost of replicating the intervention in a non-research setting. The costs will be calculated using an appropriately adjusted version of the Standardised Early Childhood Development Costing Tool. Primary health outcomes will be used in combination with costs to determine the cost per improvement in maternal perinatal depression at 12 months postnatal and the cost per improvement in child cognitive development at 24 months of age. To facilitate priority setting, the incremental cost-effectiveness ratios for improvements in child cognitive development will be ranked against six other child cognitive-development interventions according to Verguet et al’s methodology (2022). A combination of activity-based and ingredient-based costing approaches will be used to identify, measure and value activities and inputs for all alternatives. Outcomes data will be sourced from the RCT team. Ethics and dissemination: The University of Oxford is the sponsor of the CEA. Ethics approval has been obtained from the Human Sciences Research Council (HSRC, #REC 5/23/08/17), South Africa and the Oxford Tropical Research Ethics Committee (OxTREC #31–17), UK. Consent for publication is not applicable since no participant data are used in this protocol. We plan to disseminate the CEA results to key policymakers and researchers in the form of a policy brief, meetings and academic papers. Trial registration details: ISRCTN registry #11 284 870 (14/11/2017) and SANCTR DOH-27-102020-9097 (17/11/2017)

Exclusive breastfeeding and cognition, executive function, and behavioural disorders in primary school-aged children in rural South Africa: A cohort analysis

Background Exclusive breastfeeding (EBF) is associated with early child health; its longer-term benefits for child development remain inconclusive. We examine the associations between EBF, HIV exposure, and other maternal/child factors and the cognitive and emotional-behavioural development of children aged 7–11 y. Methods and Findings The Vertical Transmission Study (VTS) supported EBF in HIV-positive and HIV-negative women; between 2012 and 2014, HIV-negative VTS children (332 HIV exposed, 574 HIV unexposed) were assessed in terms of cognition (Kaufman Assessment Battery for Children Second Edition [KABC-II]), executive function (Developmental Neuropsychological Assessment Second Edition [NEPSY-II]), and emotional-behavioural functioning (parent-reported Child Behaviour Checklist, [CBCL]). We developed population means by combining the VTS sample with 629 same-aged HIV-negative children from the local demographic platform. For each outcome, we split the VTS sample into scores above or at/below each population mean and modelled each outcome using logistic regression analyses, overall and stratified by child sex. There was no demonstrated effect of EBF on overall cognitive functioning. EBF was associated with fewer conduct disorders overall (adjusted odds ratio [aOR] 0.44 [95% CI 0.3–0.7], p ≤ 0.01), and there was weak evidence of better cognition in boys who had been exclusively breastfed for 2–5 mo versus ≤1 mo (Learning subscale aOR 2.07 [95% CI 1.0–4.3], p = 0.05). Other factors associated with better child cognition were higher maternal cognitive ability (aOR 1.43 [95% CI 1.1–1.9], p = 0.02, Sequential; aOR 1.74 [95% CI 1.3–2.4], p < 0.001, Planning subscales) and crèche attendance (aOR 1.96 [95% CI 1.1–3.5], p = 0.02, Sequential subscale). Factors positively associated with executive function were home stimulation (aOR 1.36 [95% CI 1.0–1.8], p = 0.04, Auditory Attention; aOR 1.35 [95% CI 1.0–1.8], p = 0.05, Response Set) and crèche (aOR 1.74 [95% CI 1.0–3.0], p = 0.05, Animal Sorting). Maternal mental health problems and parenting stress were associated with increased emotional-behavioural problems on the total CBCL (aOR 2.44 [95% CI 1.3–4.6], p = 0.01; aOR 7.04 [95% CI 4.2–11.9], p < 0.001, respectively). Maternal HIV status was not associated with any outcomes in the overall cohort. Limitations include the nonrandomised study design and lack of maternal mental health assessment at the child’s birth. Conclusions EBF was associated with fewer than average conduct disorders and weakly associated with improved cognitive development in boys. Efforts to improve stimulation at home, reduce maternal stress, and enable crèche attendance are likely to improve executive function and emotional-behavioural development of children