Abstract
We address the problem of dynamically switching the topology of a formation of a number of undistinguishable agents. Given the current and the final topologies, each with n agents, there are n! possible allocations between the initial and final positions of the agents. Given the agents maximum velocities, there is still a degree of freedom in the trajectories that might be used in order to avoid collisions. We seek an allocation and corresponding agent trajectories minimizing the maximum time required by all agents to reach the final topology, avoiding collisions. Collision avoidance is guaranteed through an appropriate choice of trajectories, which might have consequences in the choice of an optimal permutation. We propose here a dynamic programming approach to optimally solve problems of small dimension. We report computational results for problems involving formations with up to 12 agents. © Springer Science+Business Media, LLC 2010.

Abstract
In this work we propose a new problem, that we have named hop-constrained minimum cost flow spanning tree problem, and develop an exact solution methodology. This problem is an extension of the well know NP-hard hop-constrained Minimum Spanning Tree problem (MST), since in addition to finding the arcs to be used we also must find the amount of flow that is to be routed through each arc. The hop-constrained MST has numerous practical applications in the design of communication networks. The hop constraints are usually used to guarantee a certain quality of service with respect to availability, reliability and lower delays, since they limit the number of arcs in each path from the central service provider. Including the flows, as we propose, allows for different levels of service requirements. A further extension is considered: the cost functions may have any type or form, may be neither convex nor concave, and need not to be differentiable or continuous. We develop a dynamic programming approach, which extends the scope of application of a previous work, to solve to optimality such problems. Computational experiments are performed using randomly generated test problems. Results showing the robustness of the method are reported.

Abstract
We compute the analytic expression of the probability distributions F(AEX,+) and F(AEX,-) of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the alpha re-scaled AEX daily index positive returns r(t)(alpha) and negative returns (-r(t))(alpha), which we call, after normalization, the alpha positive fluctuations and alpha negative fluctuations. We use the Kolmogorov-Smirnov statistical test as a method to find the values of alpha that optimize the data collapse of the histogram of the alpha fluctuations with the Bramwell-Holdsworth-Pinton (BHP) probability density function. The optimal parameters that we found are alpha(+) = 0.46 and alpha(-) = 0.43. Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of stock exchange markets.

Abstract
We study the European river Danube and the South American river Negro daily water levels. We present a fit for the Negro daily water level period and standard deviation. Unexpectedly, we discover that the river Negro and Danube are mirror rivers in the sense that the daily water levels fluctuations histograms are close to the universal non-parametric BHP and reversed BHP, respectively. Hence, the probability of a certain positive fluctuation range in the river Negro is, approximately, equal to the probability of the corresponding symmetric negative fluctuation range in the river Danube.

Abstract
We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Abstract
Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.