A solution to the 2/3 conjecture

We prove a vertex domination conjecture of Erd\H os, Faudree, Gould, Gy\'arf\'as, Rousseau, and Schelp, that for every n-vertex complete graph with edges coloured using three colours there exists a set of at most three vertices which have at least 2n/3 neighbours in one of the colours. Our proof makes extensive use of the ideas presented in "A New Bound for the 2/3 Conjecture" by Kr\'al', Liu, Sereni, Whalen, and Yilma.Comment: 12 pages, 4 figures, 2 data files and proof checking code. Revised version to appear in SIAM Journal on Discrete Mathematic

Hypergraphs do jump

We say that $\alpha\in [0,1)$ is a jump for an integer $r\geq 2$ if there exists $c(\alpha)>0$ such that for all $\epsilon >0$ and all $t\geq 1$ any $r$-graph with $n\geq n_0(\alpha,\epsilon,t)$ vertices and density at least $\alpha+\epsilon$ contains a subgraph on $t$ vertices of density at least $\alpha+c$. The Erd\H os--Stone--Simonovits theorem implies that for $r=2$ every $\alpha\in [0,1)$ is a jump. Erd\H os showed that for all $r\geq 3$, every $\alpha\in [0,r!/r^r)$ is a jump. Moreover he made his famous "jumping constant conjecture" that for all $r\geq 3$, every $\alpha \in [0,1)$ is a jump. Frankl and R\"odl disproved this conjecture by giving a sequence of values of non-jumps for all $r\geq 3$. We use Razborov's flag algebra method to show that jumps exist for $r=3$ in the interval $[2/9,1)$. These are the first examples of jumps for any $r\geq 3$ in the interval $[r!/r^r,1)$. To be precise we show that for $r=3$ every $\alpha \in [0.2299,0.2316)$ is a jump. We also give an improved upper bound for the Tur\'an density of $K_4^-=\{123,124,134\}$: $\pi(K_4^-)\leq 0.2871$. This in turn implies that for $r=3$ every $\alpha \in [0.2871,8/27)$ is a jump.Comment: 11 pages, 1 figure, 42 page appendix of C++ code. Revised version including new Corollary 2.3 thanks to an observation of Dhruv Mubay

Rewritable routines in human interaction with public technology

In this paper, the cognitive ergonomics of using public technology is investigated. A methodology for predicting human error with technology has been developed. Predictions from the method (combined with observation of user performance) form the foundation of the concept of ‘rewritable routines’. This is in keeping with the tradition of building models of user cognition on the basis of observed and predicted errors. The concept is introduced and illustrated with examples. Implications for cognitive ergonomics are discussed

An Exploration of the Perspectives of Neuropsychologists Working With Clients From Ethnically, Culturally and Linguistically Diverse Backgrounds

The ethnic minority population of the UK is growing rapidly. Research has shown that factors such as, culture, language and ethnicity can influence cognitive functioning and performance on neuropsychological tests. Most neuropsychological assessment measures have been standardised on individuals from Euro-American, English-speaking backgrounds and have therefore little relevance to people from diverse backgrounds. This can place neuropsychologists in a difficult dilemma, who are required to conduct an adequate assessment and interpretation of a client’s cognitive function but are presented with unique challenges when working with diverse populations. Little is known about the neuropsychological assessment and practices involving ethnic minority groups in the U.K. Thus, the current study aimed to explore the experiences and practices of clinicians working in cross-cultural and cross- linguistic neuropsychology. A cross-sectional research design was utilised, and a sample of professionals working in neuropsychology were recruited from various forums through purposive sampling. The study sample was representative of clinical neuropsychologists in the U.K based on the BPS Division of Neuropsychology (DoN) membership. Respondents (N= 78) completed a self-report questionnaire consisting of open (quantitative) and closed-ended (qualitative) questions via an online survey platform. Frequencies were reported for quantitative data whereas qualitative data were subjected to two waves of analysis. Content analysis was firstly used to tabulate and summarize open-ended responses. Recurring themes from this data were then abstracted using thematic analysis. Several themes emerged from the data including: a lack of training, challenges of working across culture, awareness of culture, neuropsychological tests and norms, clinical interview and interpreters. Overall, the quantitative data supported findings from the qualitative data. The findings were analysed in order to draw overall conclusions relating to neuropsychologists’ assessment practices, challenges faced by them and the wider profession and recommendations for improving cross-cultural and cross-linguistic neuropsychology. It is hoped that the results from this study stimulate research in the area of culture and language in neuropsychological practice as well as improve cultural competence at an individual and organisational level

Task analysis for error identification: Theory, method and validation

This paper presents the underlying theory of Task Analysis for Error Identification. The aim is to illustrate the development of a method that has been proposed for the evaluation of prototypical designs from the perspective of predicting human error. The paper presents the method applied to representative examples. The methodology is considered in terms of the various validation studies that have been conducted, and is discussed in the light of a specific case study

WESTT (Workload, Error, Situational Awareness, Time and Teamwork): An analytical prototyping system for command and control

Modern developments in the use of information technology within command and control allow unprecedented scope for flexibility in the way teams deal with tasks. These developments, together with the increased recognition of the importance of knowledge management within teams present difficulties for the analyst in terms of evaluating the impacts of changes to task composition or team membership. In this paper an approach to this problem is presented that represents team behaviour in terms of three linked networks (representing task, social network structure and knowledge) within the integrative WESTT software tool. In addition, by automating analyses of workload and error based on the same data that generate the networks, WESTT allows the user to engage in the process of rapid and iterative “analytical prototyping”. For purposes of illustration an example of the use of this technique with regard to a simple tactical vignette is presented