The flip-graph of the 4-dimensional cube is connected

Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92 487 256 triangulations, partitioned into 247 451 symmetry classes.Comment: 20 pages, 3 figures, revised proofs and notation

Three-dimensional distinct element simulation of spherocylinder crystallization

Abstract.: We present a three-dimensional distinct element model (DEM) able to handle populations of spherocylinders. We report on granular crystallization occurring when vibrating mono-disperse assemblies of spherocylinders that faithfully reproduce the corresponding results of physical experiments from the literatur

About the influence of friction and polydispersity on the jamming behavior of bead assemblies

We study the jamming of bead assemblies placed in a cylindrical container whose bottom is pierced with a circular hole. Their jamming behavior is quantified here by the mean critical diameter, that is the diameter of the hole for which the jamming probability is 0.5. Mean critical diameters of monodisperse assemblies are obtained numerically using Distinct Element Method and experimentally with steel beads. We obtain good agreement between numerical and experimental results. The influence of friction is then investigated. In particular, the formation of concentric bead rings is observed for low frictions. We identify this phenomenon as a boundary effect and study its influence on jamming. Relying on measures obtained from simulation runs, the mean critical diameter of bidisperse bead assemblies is finally found to depend only on the volume-average diameter of their constituting beads. We formulate this as a tentative law and validate it using bidisperse assemblies of steel beads

Neighborhoods of trees in circular orderings

In phylogenetics, a common strategy used to construct an evolutionary tree for a set of species X is to search in the space of all such trees for one that optimizes some given score function (such as the minimum evolution, parsimony or likelihood score). As this can be computationally intensive, it was recently proposed to restrict such searches to the set of all those trees that are compatible with some circular ordering of the set X. To inform the design of efficient algorithms to perform such searches, it is therefore of interest to find bounds for the number of trees compatible with a fixed ordering in the neighborhood of a tree that is determined by certain tree operations commonly used to search for trees: the nearest neighbor interchange (nni), the subtree prune and regraft (spr) and the tree bisection and reconnection (tbr) operations. We show that the size of such a neighborhood of a binary tree associated with the nni operation is independent of the tree’s topology, but that this is not the case for the spr and tbr operations. We also give tight upper and lower bounds for the size of the neighborhood of a binary tree for the spr and tbr operations and characterize those trees for which these bounds are attained

Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Safety of Levetiracetam in paediatrics: a systematic review

Objective To identify adverse events (AEs) associated with Levetiracetam (LEV) in children. Methods Databases EMBASE (1974-February 2015) and Medline (1946-February 2015) were searched for articles in which paediatric patients (≤18 years) received LEV treatment for epilepsy. All studies with reports on safety were included. Studies involving adults, mixed age population (i.e. children and adults) in which the paediatric subpopulation was not sufficiently described, were excluded. A meta-analysis of the RCTs was carried out and association between the commonly reported AEs or treatment discontinuation and the type of regimen (polytherapy or monotherapy) was determined using Chi2 analysis. Results Sixty seven articles involving 3,174 paediatric patients were identified. A total of 1,913 AEs were reported across studies. The most common AEs were behavioural problems and somnolence, which accounted for 10.9% and 8.4% of all AEs in prospective studies. 21 prospective studies involving 1120 children stated the number of children experiencing AEs. 47% of these children experienced AEs. Significantly more children experienced AEs with polytherapy (64%) than monotherapy (22%) (p<0.001). Levetiracetam was discontinued in 4.5% of all children on polytherapy and 0.9% on monotherapy (p<0.001), the majority were due to behavioural problems. Conclusion Behavioural problems and somnolence were the most prevalent adverse events to LEV and the most common causes of treatment discontinuation. Children on polytherapy have a greater risk of adverse events than those receiving monotherapy