BIOMECHANICAL PROFILE OF SOCCER GOALKEEPERS

Although the soccer goalkeeper often plays a decisive role in the outcome of a match, research on the goalkeeper’s actions or the qualities required of a top class goalkeeper is scarce. With this study we attempted to define a biomechanical profile of the goalkeeper. We tested whether the skill level of 6 goalkeepers, determined by the league they played in, correlated with a number of biomechanical tests. The tests were devised as standardized measurements of typical goalkeeper actions; they comprised various jumps, a short sprint and a leg strength measurement. We found no correlation between the goalkeepers’ skill level and their score in any of the tests. Thus, with reservation for the limited number of subjects, we conclude that the measured biomechanical parameters are of minor importance compared to skills as tactical understanding, perception and anticipation

Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free intersection graph. We show that such rectangle arrangements are in bijection with the 4-orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Moreover, we prove that every triangle-free planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.Comment: 15 pages, 13 figures, extended version of a paper to appear at the International Symposium on Graph Drawing and Network Visualization (GD) 201

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

Social isolation affects intra-specific interaction behaviour and reduces the size of the cerebellar brain region in juvenile Atlantic salmon Salmo salar

The social environment can affect the development of behavioural phenotypes in fish, and it is important to understand such effects when rearing fish in artificial environments. Here, the authors test the effects of spatial isolation on social interaction propensity and brain development in hatchery-reared Atlantic salmon Salmo salar L. Salmon reared in isolation generally stayed further away from a conspecific in a standardized intruder test than conspecifics reared together in groups. Isolated salmon also tended to be more active in an intruder test, albeit non-significantly so, but this pattern was not detected in open-field tests without an intruding conspecific. The cerebellar brain region was relatively smaller in isolated salmon, suggesting that the brain was developing differently in these fish. Therefore, some features of the behavioural and neural phenotype are affected by rearing in isolation. These effects should be considered when rearing salmon, particularly for experimental purposes as it may affect results of laboratory studies on behavioural expression and brain size

Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time

Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988]. In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedding preserves the same set of pairs of crossing edges. We give a linear-time algorithm for finding a straight-line drawable 1-plane re-embedding or the forbidden configuration.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016). This is an extended abstract. For a full version of this paper, see Hong S-H, Nagamochi H.: Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time, Technical Report TR 2016-002, Department of Applied Mathematics and Physics, Kyoto University (2016