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

Comparing verbal media for alarm handling: Speech versus textual displays

The rise of computers in command and control domains has meant that control operations can be performed via desk-based visual display terminals. This trend has also produced the potential to display information to operators in a variety of formats. Of particular interest has been the use of text-based displays for alarm presentation. There are possible limitations to the use of text for alarm presentation, not least of which is the need for a dedicated alarms display screen (or, at least, a display page). Given the capability of computers to synthesize speech, it is possible that speech-based alarms could generate the same information as text-based displays without the need for dedicated screen space. In this paper an experimental comparison of speech-based and text-based displays for presentation of alarms is reported. The findings show that speech leads to longer response times than text displays, but that it has minimal effect on the efficacy of fault handling. The results are discussed within the alarm initiated activities framework and implications for alarm system design are outlined

Advanced Supersonic Technology concept AST-100 characteristics developed in a baseline-update study

The advanced supersonic technology configuration, AST-100, is described. The combination of wing thickness reduction, nacelle recontouring for minimum drag at cruise, and the use of the horizontal tail to produce lift during climb and cruise resulted in an increase in maximum lift-to-drag ratio. Lighter engines and lower fuel weight associated with this resizing result in a six percent reduction in takeoff gross weight. The AST-100 takeoff maximum effective perceived noise at the runway centerline and sideline measurement stations was 114.4 decibels. Since 1.5-decibels tradeoff is available from the approach noise, the required engine noise supression is 4.9 decibels. The AST-100 largest maximum overpressure would occur during transonic climb acceleration when the aircraft was at relatively low altitude. Calculated standard +8 C day range of the AST-100, with a 292 passenger payload, is 7348 km (3968 n.mi). Fuel price is the largest contributor to direct operating cost. However, if the AST-100 were flown subsonically (M = 0.9), direct operating costs would increase approximately 50 percent because of time related costs

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

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