Reply on the ``Comment on `Loss-error compensation in quantum- state measurements' ''

The authors of the Comment [G. M. D'Ariano and C. Macchiavello to be published in Phys. Rev. A, quant-ph/9701009] tried to reestablish a 0.5 efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].Comment: LaTex, 2 pages, 1 Figure; to be published in Physical Review

Electronic transport properties of (fluorinated) metal phthalocyanine

The magnetic and transport properties of the metal phthalocyanine (MPc) and F$_{16}$MPc (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn and Ag) families of molecules in contact with S-Au wires are investigated by density functional theory within the local density approximation, including local electronic correlations on the central metal atom. The magnetic moments are found to be considerably modified under fluorination. In addition, they do not depend exclusively on the configuration of the outer electronic shell of the central metal atom (as in isolated MPc and F$_{16}$MPc) but also on the interaction with the leads. Good agreement between the calculated conductance and experimental results is obtained. For M = Ag, a high spin filter efficiency and conductance is observed, giving rise to a potentially high sensitivity for chemical sensor applications.Comment: 8 pages (two-column), 8 figure

Fuzzy clustering with volume prototypes and adaptive cluster merging

Two extensions to the objective function-based fuzzy clustering are proposed. First, the (point) prototypes are extended to hypervolumes, whose size can be fixed or can be determined automatically from the data being clustered. It is shown that clustering with hypervolume prototypes can be formulated as the minimization of an objective function. Second, a heuristic cluster merging step is introduced where the similarity among the clusters is assessed during optimization. Starting with an overestimation of the number of clusters in the data, similar clusters are merged in order to obtain a suitable partitioning. An adaptive threshold for merging is proposed. The extensions proposed are applied to Gustafson–Kessel and fuzzy c-means algorithms, and the resulting extended algorithm is given. The properties of the new algorithm are illustrated by various examples