Lex-Partitioning: A New Option for BDD Search

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n) ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n). The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

Turbulence evolution in MHD plasmas

Turbulence in the interstellar medium has been an active field of research in the last decade. Numerical simulations are the tool of choice in most cases. But while there are a number of simulations on the market some questions have not been answered finally. In this paper we are going to examine the influence of compressible and incompressible driving on the evolution of turbulent spectra in a number of possible interstellar medium scenarios. We conclude that the driving not only has an influence on the ratio of compressible to incompressible component but also on the anisotropy of turbulence.Comment: Accepted for publication in Journal of Plasma Physic

Symbolic Search in Planning and General Game Playing

Search is an important topic in many areas of AI. Search problems often result in an immense number of states. This work addresses this by using a special datastructure, BDDs, which can represent large sets of states efficiently, often saving space compared to explicit representations. The first part is concerned with an analysis of the complexity of BDDs for some search problems, resulting in lower or upper bounds on BDD sizes for these. The second part is concerned with action planning, an area where the programmer does not know in advance what the search problem will look like. This part presents symbolic algorithms for finding optimal solutions for two different settings, classical and net-benefit planning, as well as several improvements to these algorithms. The resulting planner was able to win the International Planning Competition IPC 2008. The third part is concerned with general game playing, which is similar to planning in that the programmer does not know in advance what game will be played. This work proposes algorithms for instantiating the input and solving games symbolically. For playing, a hybrid player based on UCT and the solver is presented

Propagation in 3D spiral-arm cosmic-ray source distribution models and secondary particle production using PICARD

We study the impact of possible spiral-arm distributions of Galactic cosmic-ray sources on the flux of various cosmic-ray nuclei throughout our Galaxy. We investigate model cosmic-ray spectra at the nominal position of the sun and at different positions within the Galaxy. The modelling is performed using the recently introduced numerical cosmic ray propagation code \textsc{Picard}. Assuming non-axisymmetric cosmic ray source distributions yields new insights on the behaviour of primary versus secondary nuclei. We find that primary cosmic rays are more strongly confined to the vicinity of the sources, while the distribution of secondary cosmic rays is much more homogeneous compared to the primaries. This leads to stronger spatial variation in secondary to primary ratios when compared to axisymmetric source distribution models. A good fit to the cosmic-ray data at Earth can be accomplished in different spiral-arm models, although leading to decisively different spatial distributions of the cosmic-ray flux. This results in very different cosmic ray anisotropies, where even a good fit to the data becomes possible. Consequently, we advocate directions to seek best fit propagation parameters that take into account the higher complexity introduced by the spiral-arm structure on the cosmic-ray distribution. We specifically investigate whether the flux at Earth is representative for a large fraction of the Galaxy. The variance among possible spiral-arm models allows us to quantify the spatial variation of the cosmic-ray flux within the Galaxy in presence of non-axisymmetric source distributions.Comment: 38 pages, 16 figures, accepted for publication in Astroparticle Physic