08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Debris flow susceptibility mapping for initiation areas at medium scale: a case study in Western Norway

In recent years, rapid mass movements such as debris flow and debris avalanches resulted in a significant impact on Norwegian society and economy. The need for dispelling the uncertainty inherent in landslide risk assessment has encouraged the development of hazard and susceptibility maps. Different statistically-based modelling methods, in combination with geographic information systems (GIS), have been extensively used to ascertain landslide susceptibility in quantitative terms. This thesis proposes a bivariate statistical method (Weights of Evidence) for assessing the spatial proneness of debris flows within Førde and Jølster municipalities (Western Norway), where emphasis is put on the critical conditions of initiation. Since no feasible landslide database could be exploited for susceptibility mapping at medium scale, this thesis addressed the realisation of a new inventory. By coupling pre-existing data from remote sensing and field observations, circa 1100 debris flow initiation areas were outlined and differentiated in four categories with geomorphological repeatable features. Simple topography-based parameters such as slope, upslope contributing area, curvature and roughness were used to find significant statistical differences between the initiation areatypes. Moreover, they were employed together with other thematic maps as informative layers for landslide modelling. In order to test the model fitting performance, the ROC curves method is used in this thesis. The evaluation of different discretization schemes and combinations of the above-mentioned variables led to individuate models with different performances in terms of success rates. The best model is obtained by using only a combination of slope, flow accumulation and elevation (82% true positive rate), while the manual adjustment of the classification scheme did not lead to significant improvements

Emergence of Network Motifs in Deep Neural Networks

Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called "network motifs". In this article we show that network science tools can be successfully applied also to the study of artificial neural networks operating according to self-organizing (learning) principles. In particular, we study the emergence of network motifs in multi-layer perceptrons, whose initial connectivity is defined as a stack of fully-connected, bipartite graphs. Our simulations show that the final network topology is primarily shaped by learning dynamics, but can be strongly biased by choosing appropriate weight initialization schemes. Overall, our results suggest that non-trivial initialization strategies can make learning more effective by promoting the development of useful network motifs, which are often surprisingly consistent with those observed in general transduction networks

(Global) Optimization: Historical notes and recent developments

Recent developments in (Global) Optimization are surveyed in this paper. We collected and commented quite a large number of recent references which, in our opinion, well represent the vivacity, deepness, and width of scope of current computational approaches and theoretical results about nonconvex optimization problems. Before the presentation of the recent developments, which are subdivided into two parts related to heuristic and exact approaches, respectively, we briefly sketch the origin of the discipline and observe what, from the initial attempts, survived, what was not considered at all as well as a few approaches which have been recently rediscovered, mostly in connection with machine learning

Subdivision schemes with general dilation in the geometric and nonlinear setting

AbstractWe establish results on convergence and smoothness of subdivision rules operating on manifold-valued data which are based on a general dilation matrix. In particular we cover irregular combinatorics. For the regular grid case results are not restricted to isotropic dilation matrices. The nature of the results is that intrinsic subdivision rules which operate on geometric data inherit smoothness properties of their linear counterparts

Approximation orders of shift-invariant subspaces of W2s(Rd)W^s_2({\Bbb R}^d)

We extend the existing theory of approximation orders provided by shift-invariant subspaces of $L_2$ to the setting of Sobolev spaces, provide treatment of $L_2$ cases that have not been covered before, and apply our results to determine approximation order of solutions to a refinement equation with a higher-dimensional solution space.Comment: 49 page

Functional trait variation related to gap dynamics in tropical moist forests: a vegetation modelling perspective

The conventional representation of Plant Functional Types (PFTs) in Dynamic Global Vegetation Models (DGVMs) is increasingly recognized as simplistic and lacking in predictive power. Key ecophysiological traits, including photosynthetic parameters, are typically assigned single values for each PFT while the substantial trait variation within PFTs is neglected. This includes continuous variation in response to environmental factors, and differences linked to spatial and temporal niche differentiation within communities. A much stronger empirical basis is required for the treatment of continuous plant functional trait variation in DGVMs. We analyse 431 sets of measurements of leaf and plant traits, including photosynthetic measurements, on evergreen angiosperm trees in tropical moist forests of Australia and China. Confining attention to tropical moist forests, our analysis identifies trait differences that are linked to vegetation dynamic roles. Coordination theory predicts that Rubisco- and electron-transport limited rates of photosynthesis are co-limiting under field conditions. The least-cost hypothesis predicts that air-to-leaf CO2 drawdown minimizes the combined costs per unit carbon assimilation of maintaining carboxylation and transpiration capacities. Aspects of these predictions are supported for within-community trait variation linked to canopy position, just as they are for variation along spatial environmental gradients. Trait differences among plant species occupying different structural and temporal niches may provide a basis for the ecophysiological representation of vegetation dynamics in next-generation DGVMs