An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions

Graphs with multiple edge costs arise naturally in the route planning domain when apart from travel time other criteria like fuel consumption or positive height difference are also objectives to be minimized. In such a scenario, this paper investigates the number of extreme shortest paths between a given source-target pair s, t. We show that for a fixed but arbitrary number of cost types d ? 1 the number of extreme shortest paths is in n^O(log^{d-1}n) in graphs G with n nodes. This is a generalization of known upper bounds for d = 2 and d = 3

Preference-Based Trajectory Clustering - An Application of Geometric Hitting Sets

In a road network with multicriteria edge costs we consider the problem of computing a minimum number of driving preferences such that a given set of paths/trajectories is optimal under at least one of these preferences. While the exact formulation and solution of this problem appears theoretically hard, we show that in practice one can solve the problem exactly even for non-homeopathic instance sizes of several thousand trajectories in a road network of several million nodes. We also present a parameterized guaranteed-polynomial-time scheme with very good practical performance

Visualization and thermodynamic encoding of single-molecule partition functions

Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and enthalpy at finite-temperatures are challenging to determine with ensemble-averaging alone. Here, we provide a method to access single-molecule thermodynamics, by confining an individual molecule to a nanoscopic pore of a two-dimensional metal-organic nanomesh, where we directly record finite-temperature time-averaged statistical weights using temperature-controlled scanning tunneling microscopy. The obtained patterns represent a real space equilibrium probability distribution. We associate this distribution with a partition function projection to assess spatially resolved thermodynamic quantities, by means of computational modeling. The presented molecular dynamics based Boltzmann weighting model is able to reproduce experimentally observed molecular states with high accuracy. By an in-silico customized energy landscape we demonstrate that distinct probability distributions can be encrypted at different temperatures. Such modulation provides means to encode and decode information into position-temperature space or to realize nanoscopic thermal probes.Comment: 20 Pages Main text, 5 Figures. 10 Pages Annexed tex

Superconducting CH Cavities for Heavy Ion Acceleration

To demonstrate the operation ability of superconducting (sc) Crossbar-H-mode (CH) cavity technology a 217 MHz structure of this type is under development at the Institute for Applied Physics (IAP) of Frankfurt University. The cavity has 15 accelerating cells and a design beta of 0.059. It will be equipped with all necessary auxiliaries like a 10 kW power coupler and a tuning system. Currently, the cavity is under construction. Furthermore, this cavity will serve as demonstrator for a sc continuous wave (cw) LINAC at GSI. The proposed cw LINAC is highly requested to fulfil the requirements of nuclear chemistry and especially for a competitive production of new Super Heavy Elements (SHE) in the future. A full performance test by injecting and accelerating a beam from the GSI High Charge Injector (HLI) is planned in 2014. The current status of the sc CH cavity and the demonstrator project is presented