ar X iv : 0 90 5 . 44 41 v 1 [ cs . C G ] 2 7 M ay 2 00 9 Reverse nearest neighbor queries in fixed dimension ∗

ar X iv : 0 70 5 . 31 41 v 1 [ as tr o - ph ] 2 2 M ay 2 00 7 The SARG Planet Search

ar X iv : 0 80 5 . 24 44 v 1 [ m at h . A G ] 1 6 M ay 2 00 8 Symmetry and holomorphy of the second member of the second Painlevé hierarchy

We study symmetry and holomorphy of the second member of the second Painlevé hierarchy P (2) II .

ar X iv : 0 90 5 . 25 85 v 1 [ m at h . C O ] 1 5 M ay 2 00 9 CHARACTERISTIC POINTS OF RECURSIVE SYSTEMS

Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.

ar X iv : 0 80 1 . 27 93 v 2 [ cs . C G ] 9 M ay 2 00 8 Algorithms for ε - approximations of Terrains ∗

Consider a point set D with a measure function μ : D → R. Let A be the set of subsets of D induced by containment in a shape from some geometric family (e.g. axis-aligned rectangles, half planes, balls, k-oriented polygons). We say a range space (D,A) has an ε-approximation P if max R∈A ∣

ar X iv : 0 90 3 . 28 70 v 1 [ cs . L G ] 1 6 M ar 2 00 9 ON p - ADIC CLASSIFICATION

A p-adic modification of the split-LBG classification method is presented in which first clusterings and then cluster centers are computed which locally minimise an energy function. The outcome for a fixed dataset is independent of the prime number p with finitely many exceptions. In the end, the methods are applied to the construction of p-adic classifiers in the context of learning.