On the complexity of the chip-firing reachability problem

In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a special case when the reachability problem can be decided in polynomial time for general digraphs: if the target distribution is recurrent restricted to each strongly connected component. As a further positive result, we show that the chip-firing reachability problem is in co-NP for general digraphs. We also show that the chip-firing halting problem is in co-NP for Eulerian digraphs

Strongly trapped two-dimensional quantum walks

Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum systems. DTQWs usually spread ballistically due to their quantumness. In some cases, however, they can remain localized at their initial state (trapping). The trapping and other fundamental properties of DTQWs are determined by the choice of the coin operator. We introduce and analyze an up to now uncharted type of walks driven by a coin class leading to strong trapping, complementing the known list of walks. This class of walks exhibit a number of exciting properties with the possible applications ranging from light pulse trapping in a medium to topological effects and quantum search.Comment: 5 pages, 4 figures, Accepted for publication in Physical Review

The formation of carbonaceous layer from ethylene over various transition metal catalysts – an FT-IR study

The ethylene-derived carbonaceous overlayers were studied over silica-supported Pt, Pd, Rh and Cu catalysts by FT-IR spectroscopy under desorption conditions. As a general feature it was observed over all catalysts that upon increasing the desorption temperature the overlayer gradually became poor in hydrogen. The structure of the overlayers was similar over the silica-supported Pt, Pd and Rh. On increasing the reaction temperature the σ-adsorbed half-hydrogenated species are transformed to adsorbed ethylidyne. On the Cu catalyst prepared with ion exchange a similar picture emerged, while on those prepared with precipitation ethylidyne soon became the predominant species. Hydrogen swept off the carbonaceous species from the transition metals, however, copper retained large portions of it

Discrete time quantum walks on percolation graphs

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear and disappear randomly in each step during the time evolution. The resulting open system dynamics is hard to treat numerically in general. We shortly review the literature on this problem. We then present our method to solve the evolution on finite percolation graphs in the long time limit, applying the asymptotic methods concerning random unitary maps. We work out the case of one dimensional chains in detail and provide a concrete, step by step numerical example in order to give more insight into the possible asymptotic behavior. The results about the case of the two-dimensional integer lattice are summarized, focusing on the Grover type coin operator.Comment: 22 pages, 3 figure

New approach for estimation of incident energy on high voltage level

Abstract The purpose of this paper is to show a new calculation model, which is able to calculate the incident energy in any places near an electric arc in case of high voltage, without neglecting of length and position of the electric arc. This method is developed especially for the electric transmission network above 35 kV and several meters of gap distances. It would be used to estimate the thermal load of a power line worker close an initiated electric arc during live-line maintenance by bare-hand and hot stick method as well

A Collaborative Graph-based SLAM Framework Using a Computationally Effective Measurement Algebra

Simultaneous localization and mapping (SLAM) is an essential task for autonomous rover navigation in an unknown environment, especially if no absolute location information is available. This paper presents a computationally lightweight framework to enable agents with limited processing power to carry out the SLAM cooperatively and without absolute onboard localization sensors in a 2D environment. The proposed solution is built on a graph-based map representation, where nodes (resp. edges) represent landmarks (resp. odometry-based relative measurements), a measurement algebra with embedded uncertainty, and a compact database format that could be stored on a server in a centralized manner. The operations required by the agents to insert a new landmark in the graph, update landmark positions and combine measurements as a loop is closed in the graph are detailed. The resulting framework was tested in a laboratory environment and on a public dataset with encouraging results; hence our method can be used for cost-effective indoor mobile agents with limited computational resources and onboard sensors to achieve a mapping while keeping track of the agent's position. The method can also be easily generalized for a 3D scenario

Robust Trajectory Tracking Control of a Differentially Flat Overhead Crane Using Sliding Mode

The control of overhead cranes is a benchmark problem, since it is an underactuated mechanism and its mathematical model is nonlinear. During operation the mass of the load is unknown, representing an uncertainty in the inertial parameters, which requires robustness of the controlled system. Our paper proposes a novel robust control method, that combines the differentially flat property of the dynamics with the robustness of the sliding mode control. The sliding surface is constructed to ensure the tracking of the configuration variables whose accelerations is calculated using the flatness property of the dynamic model. This formulation also allows achieving the matching conditions of the parameter uncertainties. Considering a simplified overhead crane model where the load motion is restricted in a vertical plane, two sliding surfaces are defined for the rope angle and rope length, since the cart position can be calculated from the previous two. The suggested control method is successfully validated in simulations as well as using a reduced-size overhead crane. For the real crane, the rope angle was estimated by utilizing the dynamical model, which uses the estimated cart acceleration

Motion planning algorithms for stratified kinematic systems with application to the hexapod robot

The paper addresses the motion planning problem of legged robots. Kinematic models of these robots are stratified, i.e. the equations of motion differ on different strata. An improved version of the motion planning algorithm proposed in the literature is compared with two alternative solutions via the example of the six-legged (hexapod) robot. The first alternative solution uses explicit integration of the vector fields while the second one exploits the flatness of a restricted subsystem