Moderate deviations for stabilizing functionals in geometric probability

The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a certain control over the growth of the moments of the functional and its radius of stabilization. Our proof techniques rely on cumulant expansions and cluster measures and yield completely explicit bounds on deviation probabilities. In addition, we establish a new criterion for the limiting variance to be non-degenerate. Moreover, our main result provides a new central limit theorem, which, though stated under strong moment assumptions, does not require bounded support of the intensity of the Poisson input. We apply our results to three groups of examples: random packing models, geometric functionals based on Euclidean nearest neighbors and the sphere of influence graphs.Comment: 52 page

Cut Size Statistics of Graph Bisection Heuristics

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by ``local'' algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also available at http://ipnweb.in2p3.fr/~martin

Competitiveness of milk and wine production and processing in Albania

This study provides an empirical assessment of the competitiveness of Albanian dairy and wine production, based on specifically collected survey data. For both product groups, the analysis is carried out on two levels: farm level production of raw material and processing and manufacturing of the final product in the food industry. In a third step, both levels are aggregated to analyse the competitiveness of the entire production chain for each product group. Overall, the wine sector appears in an economically more favourable situation than the milk sector. Although there is currently no relevant export of wine, there has been considerable in-vestment activity at the farm level and the harmonisation of quality standards with EU legislation is currently pursued. Grape processing is currently profitable. Small farm and herd sizes limit the profitability and efficiency of dairy farming. Fragmented and dispersed production units increase the costs of milk collection. International quality standards are by far not met. This is partially due to the high share of informally traded milk and the importance of direct sales to consumers. It is therefore unlikely that Albanian dairy products will become internationally competitive in the near future. -- G E R M A N V E R S I O N: Die vorliegende Studie beinhaltet eine Einschätzung der Wettbewerbsfähigkeit der albanischen Milch- und Weinproduktion, die sich auf spezifisch gesammelte Betriebsdaten stützt. Für beide Produktgruppen wird eine Analyse auf zwei Ebenen durchgeführt: Erzeugung der Rohprodukte und Verarbeitungsstufe. In einem dritten Schritt werden die Teilergebnisse der beiden Ebenen zu einer Gesamtbewertung der Wettbewerbsfähigkeit der jeweiligen Produktions- und Verarbei-tungskette zusammengeführt. Insgesamt präsentiert sich der albanische Weinsektor in ökono-misch günstigerer Verfassung als der Milchsektor. Auch wenn der Export von albanischem Wein derzeit keine Rolle spielt, werden die notwendigen rechtlichen Rahmenbedingungen für die Sicherung von Qualität und Herkunftsbezeichnung bei Wein werden derzeit geschaffen. Auf der Erzeugerebene wurden in den vergangenen Jahren bereits größere Investitionen durchge-führt. Die Verarbeitungsstufe weist positive wirtschaftliche Ergebnisse auf. Milchproduktion und -verarbeitung leiden unter mangelnden Hygienestandards und einem stark informell ge-prägten, untransparenten Markt für Frischprodukte. Unter diesen Bedingungen fällt es den Mol-kereien schwer, sich wirtschaftlich zu behaupten. Es ist daher nicht zu erwarten, dass albanische Milchprodukte in nächster Zeit international wettbewerbsfähig sein werden.Agricultural sector,competitiveness,milk,wine,Albania,Agrarsektor,Wettbewerbsfähigkeit,Milch,Wein,Albanien

A Decentralized Parallelization-in-Time Approach with Parareal

With steadily increasing parallelism for high-performance architectures, simulations requiring a good strong scalability are prone to be limited in scalability with standard spatial-decomposition strategies at a certain amount of parallel processors. This can be a show-stopper if the simulation results have to be computed with wallclock time restrictions (e.g.\,for weather forecasts) or as fast as possible (e.g. for urgent computing). Here, the time-dimension is the only one left for parallelization and we focus on Parareal as one particular parallelization-in-time method. We discuss a software approach for making Parareal parallelization transparent for application developers, hence allowing fast prototyping for Parareal. Further, we introduce a decentralized Parareal which results in autonomous simulation instances which only require communicating with the previous and next simulation instances, hence with strong locality for communication. This concept is evaluated by a prototypical solver for the rotational shallow-water equations which we use as a representative black-box solver

Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the coordination numbers that qualitatively change the properties of continuous and first-order phase transitions. To determine whether or not these unusual features also influence Anderson localization, we study the electronic wave functions by multifractal analysis and finite-size scaling. We observe only localized states for all energies in the two-dimensional system. In three dimensions, we find two Anderson transitions between localized and extended states very close to the band edges. The critical exponent of the localization length is about 1.6. All these results agree with the usual orthogonal universality class. Additional generic energetic randomness introduced via random potentials does not lead to qualitative changes but allows us to obtain a phase diagram by varying the strength of these potentials

Time Inconsistent Preferences and the Annuitization Decision

Good news can involve difficult decisions. For example winning a lottery jackpot can go along with the decision, whether to have the jackpot paid out immediately as a lump sum or as periodic annual payments. Also when entering retirement most people face the decision whether they want their defined contribution account balance paid as a lump sum or to annuitize that amount. The fact that people tend to choose the lump sum even if economic reasons suggest that they should choose the annuity is called the annuity paradox. In a large online survey we find that people behave time inconsistent: older people have a stronger tendency to choose the lump sum than younger people when they are asked to predict today what to choose when they retire. This effect is considerably stronger for participants that answer simple time preference questions inconsistently. Our findings suggest to think about precommitment devices for the annuitization decision, in the retirement case, already at the time when the defined benefit plan is started