A Chebychev propagator for inhomogeneous Schr\"odinger equations

We present a propagation scheme for time-dependent inhomogeneous Schr\"odinger equations which occur for example in optimal control theory or in reactive scattering calculations. A formal solution based on a polynomial expansion of the inhomogeneous term is derived. It is subjected to an approximation in terms of Chebychev polynomials. Different variants for the inhomogeneous propagator are demonstrated and applied to two examples from optimal control theory. Convergence behavior and numerical efficiency are analyzed.Comment: explicit description of algorithm and two appendices added version accepted by J Chem Phy

Parallel Graph Partitioning for Complex Networks

Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for these networks. This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsened graph. The resulting system is both more scalable and achieves higher quality than state-of-the-art systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. For example, our algorithm can partition a web graph with 3.3 billion edges in less than sixteen seconds using 512 cores of a high performance cluster while producing a high quality partition -- none of the competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach arXiv:1402.328

Semi-Quantitative Comparative Analysis And Its Application

SQCA is an implemented technique for the semi-quantitative comparative analysis of dynamical systems. It is both able to deal with incompletely specified models and make precise predictions by exploiting semi-quantitative information in the form of numerical bounds on the variables and functions occuring in the models. The technique has a solid mathematical foundation which facilitates proofs of correctness and convergence properties. SQCA represents the core of a method for the automated prediction of experimental results

Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems

We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction. We investigate their phase diagram at zero temperature using the survey propagation formalism and the interpolation method. We prove that the SAT-UNSAT phase transition threshold of an infinite chain is identical to the one of the individual standard model, and is therefore not affected by spatial coupling. We compute the survey propagation complexity using population dynamics as well as large degree approximations, and determine the survey propagation threshold. We find that a clustering phase survives coupling. However, as one increases the range of the coupling window, the survey propagation threshold increases and saturates towards the phase transition threshold. We also briefly discuss other aspects of the problem. Namely, the condensation threshold is not affected by coupling, but the dynamic threshold displays saturation towards the condensation one. All these features may provide a new avenue for obtaining better provable algorithmic lower bounds on phase transition thresholds of the individual standard model

On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in the particular case of partially decimated random constraint satisfaction problems. This allows to develop a theoretical understanding of a class of algorithms for solving constraint satisfaction problems, in which elementary degrees of freedom are sequentially assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.Comment: 32 pages, 24 figure

Survey propagation at finite temperature: application to a Sourlas code as a toy model

In this paper we investigate a finite temperature generalization of survey propagation, by applying it to the problem of finite temperature decoding of a biased finite connectivity Sourlas code for temperatures lower than the Nishimori temperature. We observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation, as suggested recently by Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state

A Robotic CAD System using a Bayesian Framework

We present in this paper a Bayesian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how esian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how to take this propagation into account when solving inverse problems. We describe the methodology we use to represent and handle uncertainties using probability distributions on the system's parameters and sensor measurements. It may be seen as a generalization of constraint-based approaches where we express a constraint as a probability distribution instead of a simple equality or inequality. Appropriate numerical algorithms used to apply this methodology are also described. Using an example, we show how to apply our approach by providing simulation results using our CAD system

Multiobjective Tactical Planning under Uncertainty for Air Traffic Flow and Capacity Management

We investigate a method to deal with congestion of sectors and delays in the tactical phase of air traffic flow and capacity management. It relies on temporal objectives given for every point of the flight plans and shared among the controllers in order to create a collaborative environment. This would enhance the transition from the network view of the flow management to the local view of air traffic control. Uncertainty is modeled at the trajectory level with temporal information on the boundary points of the crossed sectors and then, we infer the probabilistic occupancy count. Therefore, we can model the accuracy of the trajectory prediction in the optimization process in order to fix some safety margins. On the one hand, more accurate is our prediction; more efficient will be the proposed solutions, because of the tighter safety margins. On the other hand, when uncertainty is not negligible, the proposed solutions will be more robust to disruptions. Furthermore, a multiobjective algorithm is used to find the tradeoff between the delays and congestion, which are antagonist in airspace with high traffic density. The flow management position can choose manually, or automatically with a preference-based algorithm, the adequate solution. This method is tested against two instances, one with 10 flights and 5 sectors and one with 300 flights and 16 sectors.Comment: IEEE Congress on Evolutionary Computation (2013). arXiv admin note: substantial text overlap with arXiv:1309.391