Function Spaces on Singular Manifolds

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the singularities, are introduced. These results are of importance for the study of partial differential equations on piece-wise smooth domains.Comment: 37 pages, 1 figure, final version, augmented by additional references; to appear in Math. Nachrichte

Collective classification for labeling of places and objects in 2D and 3D range data

In this paper, we present an algorithm to identify types of places and objects from 2D and 3D laser range data obtained in indoor environments. Our approach is a combination of a collective classification method based on associative Markov networks together with an instance-based feature extraction using nearest neighbor. Additionally, we show how to select the best features needed to represent the objects and places, reducing the time needed for the learning and inference steps while maintaining high classification rates. Experimental results in real data demonstrate the effectiveness of our approach in indoor environments

Homogeneous Equations of Algebraic Petri Nets

Algebraic Petri nets are a formalism for modeling distributed systems and algorithms, describing control and data flow by combining Petri nets and algebraic specification. One way to specify correctness of an algebraic Petri net model "N" is to specify a linear equation "E" over the places of "N" based on term substitution, and coefficients from an abelian group "G". Then, "E" is valid in "N" iff "E" is valid in each reachable marking of "N". Due to the expressive power of Algebraic Petri nets, validity is generally undecidable. Stable linear equations form a class of linear equations for which validity is decidable. Place invariants yield a well-understood but incomplete characterization of all stable linear equations. In this paper, we provide a complete characterization of stability for the subclass of homogeneous linear equations, by restricting ourselves to the interpretation of terms over the Herbrand structure without considering further equality axioms. Based thereon, we show that stability is decidable for homogeneous linear equations if "G" is a cyclic group

A New Approach to Function Spaces on Quasi-Metric Spaces

Sin resumenA d-space X = (X, , µ) is a compact set X with respect to a quasi-metric and a Borel measure µ such that the measure of a ball of radius r is equivalent to rd , where d > 0. The paper deals with spaces Bp (X ; H ) of Besov type where s 1 < p < and s R. Here H is a bi-Lipschitzian map of the snowflaked version (X, , µ) of X for some 0 < < 1, onto a fractal d/-set = H X in s/ some Rn , reducing the spaces Bp (X ; H ) to the better known spaces Bp ().

Optimal intrinsic descriptors for non-rigid shape analysis

We propose novel point descriptors for 3D shapes with the potential to match two shapes representing the same object undergoing natural deformations. These deformations are more general than the often assumed isometries, and we use labeled training data to learn optimal descriptors for such cases. Furthermore, instead of explicitly defining the descriptor, we introduce new Mercer kernels, for which we formally show that their corresponding feature space mapping is a generalization of either the Heat Kernel Signature or the Wave Kernel Signature. I.e. the proposed descriptors are guaranteed to be at least as precise as any Heat Kernel Signature or Wave Kernel Signature of any parameterisation. In experiments, we show that our implicitly defined, infinite-dimensional descriptors can better deal with non-isometric deformations than state-of-the-art methods