There are many clustering techniques presented in the literature. The particularity of single-link clustering is that it rather discovers the clusters as chains. We aim to identify a method to apply the single link clustering technique so that: it discovers the first level clusters and the user doesn’t have to provide any sort of a parameter. We focuses on clusters that are well separated, and ...

Let M n be a complete Riemannian manifold of bounded curvature, say IKI ~ 1. Given a small number, e > 0, we put M n = SWn(e) u ~n(e), where SW n (e) consists of those points at which the injectivity radius of the exponential map is ~ e. The complementary set, ~n (e) is called the e-collapsed part of Mn. If x E SWn(e) , r ~ e, then the metric ball BJr) is quasi-isometric, with small distortion,...

Among the various clustering algorithms, DBSCAN is an effective clustering algorithm used in many applications. It has various advantages like no a priori assumption needed about the number of clusters, can find arbitrarily shaped clusters and can perform well even in the presence of outliers. However, the performance is seriously affected when the dataset size becomes large. Moreover, the sele...

The detailed topological or ‘connectivity’ properties of the clusters formed in diffusion limited aggregation (DLA) and cluster-cluster aggregation (CCA) are considered for spatial dimensions d = 2,3 and 4. Specifically, for both aggregation phenomena we calculate the fractal dimension d,,, = i-’ defined by e R d m l n where e is the shortest path between two points separated by a Pythagorean d...

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024(3) collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, E(R)k=|E(M)k - E(K)k|, and total energy, Ek=E(K)k+E(M)k, are observed to scale self-similarly in the inertial range as E(R)k...

Suprem e Court Justice William O. D ouglas w ill speak on “The Conservation of M an” at 8 p.m. Thursday (March 11) in Stepan Center. The controversial justice is the author of “ Points of R e b e llio n ” and is a noted champion of civil rights and conservation. A ppoin ted to the n a tio n ’s h ig h e s t cou rt by P r e s id e n t Franklin D. R oosevelt in 1939, Douglas has authored 20 books ...

An intuitive method for distributing N points on a manifold A ⊂ Rd is to consider minimal s-energy arrangements of points that interact through a power law (Riesz) potential V = 1/r, where s > 0 and r is Euclidean distance in R 0 . Under what conditions will these points be “uniformly” distributed on A for large N? In this talk I will present recent results characterizing asymptotic properties ...

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