Factor probabilistic distance clustering (FPDC): a new clustering method

Factor clustering methods have been developed in recent years thanks to improvements in computational power. These methods perform a linear transformation of data and a clustering of the transformed data, optimizing a common criterion. Probabilistic distance (PD)-clustering is an iterative, distribution free, probabilistic clustering method. Factor PD-clustering (FPDC) is based on PD-clustering and involves a linear transformation of the original variables into a reduced number of orthogonal ones using a common criterion with PD-clustering. This paper demonstrates that Tucker3 decomposition can be used to accomplish this transformation. Factor PD-clustering alternatingly exploits Tucker3 decomposition and PD-clustering on transformed data until convergence is achieved. This method can significantly improve the PD-clustering algorithm performance; large data sets can thus be partitioned into clusters with increasing stability and robustness of the results. Real and simulated data sets are used to compare FPDC with its main competitors, where it performs equally well when clusters are elliptically shaped but outperforms its competitors with non-Gaussian shaped clusters or noisy data.     

A simple,efficient, regioselective and one-pot preparation of N-hydroxy- and N–O-protected hydroxyindoles via cycloaddition of nitrosoarenes with alkynes. Synthetic scope,applications and novel by-products

The thermal reaction between nitrosoarenes and alkynes under alkylating conditions produces N-alkoxyindoles as the major products in moderate to good yields and excellent regioselectivity. Various electrophiles are used affording different N–O-protected hydroxyindoles in a multi-component fashion. Privileged acetylenic substrates used in reactions with substituted nitrosoarenes are arylalkynes or propiolates. Potentially bioactive compounds and other classes of highly functionalizable indole products were prepared. Reactions between o-carbomethoxy-nitrosoarenes and arylacetylenes provided tricyclic compounds containing an acylaziridine indoline skeleton.     

Conformally invariant tensors of an almost Hermitian manifold associated with the holomorphic curvature tensor

We consider an almost Hermitian manifold and apply the conformal change of metric to its holomorphic curvature tensor. In such a way we find that the generalized Bochner curvature tensor can be expressed as a linear combination of B ₁, B ₂, and B ₃ such that (6.4) holds. Each of the tensors B ₁, B ₂, B ₃ is conformally invariant and satisfies the condition (1.2) of K?hler type.     

Scalar mesons moving in a finite volume and the role of partial wave mixing

Phase shifts and resonance parameters can be obtained from finite-volume lattice spectra for interacting pairs of particles, moving with non-zero total momentum. We present a simple derivation of the method that is subsequently applied to obtain the ?Ц? and ??K phase shifts in the sectors with total isospin I = 0 and I = 1/2 , respectively. Considering different total momenta, one obtains extra data points for a given volume that allow for a very efficient extraction of the resonance parameters in the infinite-volume limit. Corrections due to the mixing of partial waves are provided. We expect that our results will help to optimize the strategies in lattice simulations, which aim at an accurate determination of the scattering and resonance properties.