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.

On Cluster Validity and the Information Need of Users

Abstract: In the field of information retrieval, clustering algorithms are used to analyze large collections of documents with the objective to form groups of similar documents. Clustering a document collection is an ambiguous task: A clustering, i. e. a set of document groups, depends on the chosen clustering algorithm as well as on the algorithm’s parameter settings. To find the best among several clusterings, it is common practice to evaluate their internal structures with a cluster validity measure. A clustering is considered to be useful to a user if particular structural properties are well developed. Nevertheless, the presence of certain structural properties may not guarantee usefulness from an information retrieval standpoint, say, whether or not the found document groups resemble the classification of a human editor. The paper in hand investigates this point: Based on already classified document collections we generate clusterings and compare the predicted quality to their real quality. Our analysis includes the classical cluster validity measures from Dunn and Davies-Bouldin as well as the new graph-based measures Λ (weighted edge connectivity) and ρ (expected edge density). The experiments show interesting results: The classical measures behave in a consistent manner insofar as mediocre and poor clusterings are identified as such. On real-world document clustering data, however, they are definitely outperformed by the expected edge density ρ. This superiority of the graph-based measures can be explained by their independence of cluster forms and distances.

Dislocations in diamond: Core structures and energies

Abstract: The structures and core energies of dislocations in diamond are calculated using both isotropic and anisotropic elasticity theory combined with ab initio-based tight-binding total energy calculations. Perfect and dissociated 60° and screw dislocations are considered. Their possible dissociation reactions are investigated through a consideration of the calculated elastic energy factors and core energies. Dissociation into partials is energetically favored. We find that the double-period reconstruction of the 90° glide partial dislocation is more stable than the single-period reconstruction and that the glide set of 60° perfect dislocations is more stable than the shuffle set. Shuffle partials containing interstitials are less likely than those containing vacancies.

Direct Characterization of Ultrafast Energy-Time Entangled Photon Pairs.

Abstract: Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast time scales, making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast time scales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.

Stabilization in a chemotaxis model for tumor invasion

Abstract: This paper deals with the chemotaxis system \[ \begin{cases} u_t=\Delta u - abla \cdot (u abla v), \qquad x\in \Omega, \ t>0, \\ v_t=\Delta v + wz, \qquad x\in \Omega, \ t>0, \\ w_t=-wz, \qquad x\in \Omega, \ t>0, \\ z_t=\Delta z - z + u, \qquad x\in \Omega, \ t>0, \end{cases} \] in a smoothly bounded domain $\Omega \subset \mathbb{R}^n$, $n \le 3$, that has recently been proposed as a model for tumor invasion in which the role of an active extracellular matrix is accounted for. It is shown that for any choice of nonnegative and suitably regular initial data $(u_0,v_0,w_0,z_0)$, a corresponding initial-boundary value problem of Neumann type possesses a global solution which is bounded. Moreover, it is proved that whenever $u_0 ot\equiv 0$, these solutions approach a certain spatially homogeneous equilibrium in the sense that as $t\to\infty$, $u(x,t)\to \overline{u_0}$ ,   $v(x,t) \to \overline{v_0} + \overline{w_0}$,   $w(x,t) \to 0$   and   $z(x,t) \to \overline{u_0}$,   uniformly with respect to $x\in\Omega$, where $\overline{u_0}:=\frac{1}{|\Omega|} \int_{\Omega} u_0$, $\overline{v_0}:=\frac{1}{|\Omega|} \int_{\Omega} v_0$  and   $\overline{w_0}:=\frac{1}{|\Omega|} \int_{\Omega} w_0$.

An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF

Abstract: We consider the minimal unsatisfiability problem for propositional formulas over n variables with n+k clauses for fixed k. We will show that in case of at most n clauses no formula is minimal unsatisfiable. For n+1 clauses the minimal unsatisfiability problem is solvable in quadratic time. Further, we present a characterization of minimal unsatisfiable formulas with n+1 clauses in terms of a certain form of matrices.