New RuII(arene) complexes with halogen-substituted bis- and tris(pyrazol-1-YL)borate ligands

[RuCl(arene)(-Cl)](2) dimers were treated in a 1:2 molar ratio with sodium or thallium salts of bis- and tris(pyrazolyl)borate ligands [Na(BpBr3)], [Tl(TpBr3)], and [Tl(Tp(iPr,4Br))]. Mononuclear neutral complexes [RuCl(arene)((2)-BpBr3)] (1: arene=p-cymene (cym); 2: arene=hexamethylbenzene (hmb); 3: arene=benzene (bz)), [RuCl(arene)((2)-TpBr3)] (4: arene=cym; 6: arene=bz), and [RuCl(arene)((2)-Tp(iPr,4Br))] (7: arene=cym, 8: arene=hmb, 9: arene=bz) have been always obtained with the exception of the ionic [Ru-2(hmb)(2)(-Cl)(3)][TpBr3] (5), which formed independently of the ratio of reactants and reaction conditions employed. The ionic [Ru(CH3OH)(cym)((2)-BpBr3)][X] (10: X=PF6, 12: X=O3SCF3) and the neutral [Ru(O2CCF3)(cym)((2)-BpBr3)] (11) have been obtained by a metathesis reaction with corresponding silver salts. All complexes 1-12 have been characterized by analytical and spectroscopic data (IR, ESI-MS, H-1 and (CNMR)-C-13 spectroscopy). The structures of the thallium and calcium derivatives of ligand TpBr3, [Tl(TpBr3)] and [Ca(dmso)(6)][TpBr3](2)2DMSO, of the complexes 1, 4, 5, 6, 11, and of the decomposition product [RuCl(cym)(Hpz(iPr,4Br))(2)][Cl] (7) have been confirmed by using single-crystal X-ray diffraction. Electrochemical studies showed that 1-9 and 11 undergo a single-electron (RuRuIII)-Ru-II oxidation at a potential, measured by cyclic voltammetry, which allows comparison of the electron-donor characters of the bis- and tris(pyrazol-1-yl)borate and arene ligands, and to estimate, for the first time, the values of the Lever E-L ligand parameter for BpBr3, TpBr3, and Tp(iPr,4Br). Theoretical calculations at the DFT level indicated that both oxidation and reduction of the Ru complexes under study are mostly metal-centered with some involvement of the chloride ligand in the former case, and also demonstrated that the experimental isolation of the (3)-binuclear complex 5 (instead of the mononuclear 5) is accounted for by the low thermodynamic stability of the latter species due to steric reasons.

Probabilistic consensus clustering using evidence accumulation

Clustering ensemble methods produce a consensus partition of a set of data points by combining the results of a collection of base clustering algorithms. In the evidence accumulation clustering (EAC) paradigm, the clustering ensemble is transformed into a pairwise co-association matrix, thus avoiding the label correspondence problem, which is intrinsic to other clustering ensemble schemes. In this paper, we propose a consensus clustering approach based on the EAC paradigm, which is not limited to crisp partitions and fully exploits the nature of the co-association matrix. Our solution determines probabilistic assignments of data points to clusters by minimizing a Bregman divergence between the observed co-association frequencies and the corresponding co-occurrence probabilities expressed as functions of the unknown assignments. We additionally propose an optimization algorithm to find a solution under any double-convex Bregman divergence. Experiments on both synthetic and real benchmark data show the effectiveness of the proposed approach.

A MAP approach to evidence accumulation clustering

The Evidence Accumulation Clustering (EAC) paradigm is a clustering ensemble method which derives a consensus partition from a collection of base clusterings obtained using different algorithms. It collects from the partitions in the ensemble a set of pairwise observations about the co-occurrence of objects in a same cluster and it uses these co-occurrence statistics to derive a similarity matrix, referred to as co-association matrix. The Probabilistic Evidence Accumulation for Clustering Ensembles (PEACE) algorithm is a principled approach for the extraction of a consensus clustering from the observations encoded in the co-association matrix based on a probabilistic model for the co-association matrix parameterized by the unknown assignments of objects to clusters. In this paper we extend the PEACE algorithm by deriving a consensus solution according to a MAP approach with Dirichlet priors defined for the unknown probabilistic cluster assignments. In particular, we study the positive regularization effect of Dirichlet priors on the final consensus solution with both synthetic and real benchmark data.