Many algorithms can nd optimal bipartitions for various objectives including minimizing the maximum cluster diameter (\min-diameter"); these algorithms are often applied iteratively in top-down fashion to derive a partition P k consisting of k clusters, with k > 2. Bottom-up agglomerative approaches are also commonly used to construct partitions, and we discuss these in terms of worst-case perf...

In the beginning of the eighties, M. Shub and S. Smale developed a quantitative analysis of Newton’s method for multivariate analytic maps. In particular, their α-theory gives an effective criterion that ensures safe convergence to a simple isolated zero. This criterion requires only information concerning the map at the initial point of the iteration. Generalizing this theory to multiple zeros...

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

The thermal behavior of iron nanoclusters on a porous substrate has been studied using classical molecular dynamics simulations. The substrate has been modeled with a simple Morse potential and pores with different shapes have been modeled in order to mimic the porous substrates used for carbon nanotube growth. It has been confirmed that the presence of the substrate increases the cluster melti...

The energy transfer in 3He and 4He clusters electronically excited by monochromatic synchrotron radiation is investigated by luminescence spectroscopy. Depending on the cluster size and the isotopic constitution, either sharp, broadened, or shifted emission bands of single He molecules are observed. The spectral features show that He molecules emit light either within a bubble inside the cluste...

Breeding blueberry cultivars with enhanced fruit quality requires simple, accurate, and cost-effective assays to select individuals from segregating populations. In this study, berry diameter, weight, firmness, pH, total polyphenol, acids, D-glucose, D-fructose, glucose, sugar content were quantified in 188 southern highbush selections over 2 years. Significant variation between years, genotype...

Single-walled carbon nanotubes (SWNTs) [1] is now recognized as the most fascinating material of so-called nano-technology in this century. Despite the expectation of future applications, it is still difficult to obtain large amount of pure SWNTs, because the generation process is still not clear. It is well known that transition metals such as La, Y and Sc can be encapsulated inside the fuller...

Rodent somatosensory barrel cortex is organized both physiologically and anatomically in columns with a cross-sectional diameter of 100-400 microm. The underlying anatomical correlate of physiologically defined, much narrower minicolumns (20-60 microm in diameter) remains unclear. The minicolumn has been proposed to be a fundamental functional unit in the cortex, and one anatomical component of...

We report on BV I CCD photometry of a field centered in the region of the Galactic star cluster Whiting 1 down to V = 23.0. This cluster has never been studied insofar, and we provide for the first time estimates of its fundamental parameters, namely, radial extent, age, distance and reddening. Whiting 1 turns out to be a compact star cluster with a diameter of about 1. We find that the cluster...

Given a weighted and complete graph G = (V, E), V denotes the set of n objects to be clustered, and the weight d(u, v) associated with an edge (u, v) ∈ E denotes the dissimilarity between objects u and v. The diameter of a cluster is the maximum dissimilarity between pairs of objects in the cluster, and the split of a cluster is the minimum dissimilarity between objects within the cluster and o...