Hip-joint simulator accurately duplicates human walking pattern

Device simulates all three motions of walking and provides realistic variable loading during each step. Simulator will enable laboratory evaluation of all known types of total hip prostheses

Subgraphs and Colourability of Locatable Graphs

We study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked whether there exists a characterisation of the graph property of locatable graphs by either forbidden or forbidden induced subgraphs, both of which we answer in the negative. We then proceed to show that such a characterisation does exist for graphs of diameter at most 2, stating it explicitly, and note that this is not true for higher diameter. Exploring a different direction of topic, we also start research in the direction of colourability of locatable graphs, we also show that every locatable graph is 4-colourable, but not necessarily 3-colourable.Comment: 25 page

Fluid thermal actuator

Operational characteristics of actuator for spacecraft thermal control syste

Subdivisions in the Robber Locating Game

We consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m \geqslant n$. They conjectured that this bound was best possible for complete graphs, but the present authors showed that in fact the cop wins on $K^{1/m}$ if and only if $m \geqslant n/2$, for all but a few small values of $n$. In this paper we extend this result to general graphs by proving that the cop has a winning strategy on $G^{1/m}$ provided $m \geqslant n/2$ for all but a few small values of $n$; this bound is best possible. We also consider replacing the edges of $G$ with paths of varying lengths.Comment: 13 Page

Locating a robber with multiple probes

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m\geq n$. The present authors showed that, for all but a few small values of $n$, this bound may be improved to $m\geq n/2$, which is best possible. In this paper we consider the natural extension in which the cop probes a set of $k$ vertices, rather than a single vertex, at each turn. We consider the relationship between the value of $k$ required to ensure victory on the original graph and the length of subdivisions required to ensure victory with $k=1$. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of $k$ for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree $\Delta$, which is best possible up to a factor of $(1-o(1))$.Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to infinite graphs. Accepted for publication in Discrete Mathematic