In this paper we focus on modelling formations of non-holonomic mobile robots using non-linear attractor dynamics (see video). The benefit is that the behavior of each robot is generated by time series of asymptotically stable states which therefore contribute to the robustness against environmental perturbations. This study extends our previous work [10]. Here we develop a set of decentralized...

Recent development of the user-friendly software package “Co-registration of Optically Sensed Images and Correlation” (COSI-Corr), which allows for automatic and precise ortho-rectification, co-registration, and sub-pixel correlation of pushbroom satellite and aerial images, has enabled Earth’s surface dynamics to be accurately monitored using optical imagery [1]. This technique compares two im...

We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N , which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M .

1 Let there be given n points in the plane. Denote by t i the number of lines which contain exactly i of the points (2 < i < n). The properties of the set {ti } have been studied a great deal. For example, there is the classical result of Gallai and Sylvester : Assume to = 0 (i .e ., the points are not all on one line) ; then t2 > 0. For the history of this problem see, e.g ., Motzkin [6] and E...

We give a detailed description of the Veldkamp space of the smallest slim dense near hexagon. This space is isomorphic to PG(7, 2) and its 2 − 1 = 255 Veldkamp points (that is, geometric hyperplanes of the near hexagon) fall into five distinct classes, each of which is uniquely characterized by the number of points/lines as well as by a sequence of the cardinalities of points of given orders an...

The C60 molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact calculations. The fragments of C60 studied are pyracylene, fluoranthene and corannulene. The energies, bond orders, spin– spin and charge–correla...