University of Paderborn

About: University of Paderborn is a education organization based out in Paderborn, Nordrhein-Westfalen, Germany. It is known for research contribution in the topics: Computer science & Context (language use). The organization has 6684 authors who have published 16929 publications receiving 323154 citations.

StreamKM++: A clustering algorithm for data streams

Abstract: We develop a new k-means clustering algorithm for data streams of points from a Euclidean space. We call this algorithm StreamKM++. Our algorithm computes a small weighted sample of the data stream and solves the problem on the sample using the k-means++ algorithm of Arthur and Vassilvitskii (SODA '07). To compute the small sample, we propose two new techniques. First, we use an adaptive, nonuniform sampling approach similar to the k-means++ seeding procedure to obtain small coresets from the data stream. This construction is rather easy to implement and, unlike other coreset constructions, its running time has only a small dependency on the dimensionality of the data. Second, we propose a new data structure, which we call coreset tree. The use of these coreset trees significantly speeds up the time necessary for the adaptive, nonuniform sampling during our coreset construction.We compare our algorithm experimentally with two well-known streaming implementations: BIRCH [Zhang et al. 1997] and StreamLS [Guha et al. 2003]. In terms of quality (sum of squared errors), our algorithm is comparable with StreamLS and significantly better than BIRCH (up to a factor of 2). Besides, BIRCH requires significant effort to tune its parameters. In terms of running time, our algorithm is slower than BIRCH. Comparing the running time with StreamLS, it turns out that our algorithm scalesmuch better with increasing number of centers. We conclude that, if the first priority is the quality of the clustering, then our algorithm provides a good alternative to BIRCH and StreamLS, in particular, if the number of cluster centers is large. We also give a theoretical justification of our approach by proving that our sample set is a small coreset in low-dimensional spaces.

Color-Tuned Electroluminescence from Columnar Liquid Crystalline Alkyl Arenecarboxylates.

Abstract: Simple ester derivatives of polycyclic arenes offer access to light-emitting diodes of nearly any visible color by making use of the good charge-transport properties of the columnar liquid crystals of these derivatives. The picture shows the orange-red electroluminescence of a light-emitting diode containing the perylene 3,4,9,10-tetracarboxylic acid ethyl ester (structure shown, R=Et). Through use of multiple layers of different esters light-emitting diodes with almost white luminescence can be obtained.

Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system

Abstract: The chemotaxis-Navier-Stokes system linking the chemotaxis equations \[ n_t + u\cdot abla n = \Delta n - abla \cdot (n\chi(c) abla c) \] and \[ c_t + u\cdot abla c = \Delta c-nf(c) \] to the incompressible Navier-Stokes equations, \[ u_t + (u\cdot abla)u = \Delta u + abla P + n abla \Phi, \qquad abla \cdot u = 0, \] is considered under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of Dirichlet type for $u$, in a bounded convex domain $\Omega\subset R^3$ with smooth boundary, where $\Phi\in W^{1,\infty}(\Omega)$, and where $f\in C^1([0,\infty))$ and $\chi\in C^2([0,\infty))$ are nonnegative with $f(0)=0$. Problems of this type have been used to describe the mutual interaction of populations of swimming aerobic bacteria with the surrounding fluid. Up to now, however, global existence results seem to be available only for certain simplified variants such as e.g.the two-dimensional analogue, or the associated chemotaxis-Stokes system obtained on neglecting the nonlinear convective term in the fluid equation. The present work gives an affirmative answer to the question of global solvability in the following sense: Under mild assumptions on the initial data, and under modest structural assumptions on $f$ and $\chi$, inter alia allowing for the prototypical case when \[ f(s)=s \quad {for all} s\ge 0 \qquad {and} \qquad \chi \equiv const., \] the corresponding initial-boundary value problem is shown to possess a globally defined weak solution.