A new diabatization scheme for direct quantum dynamics : procrustes diabatization

We present a new scheme for diabatizing electronic potential energy surfaces, for use within the recently implemented direct-dynamics grid-based (DD-GB) class of computational nuclear quantum dynamics methods (DD-SM and DD-MCTDH), called Procrustes diabatization. Calculations on the well-studied molecular systems LiF and the butatriene cation, using both Procrustes diabatization and the previously implemented propagation and projection diabatization schemes, have allowed detailed comparisons to be made which indicate that the new method combines the best features of the older approaches; it generates smooth surfaces which cross at the correct molecular geometries, reproduces interstate couplings accurately and hence allows the correct modelling of non-adiabatic dynamics

Rotated canonical correlation analysis for multilingual corpora

This paper aims at proposing the joint use of Canonical Correlation Analysis and Procrustes Rotations (RCA), when we deal with a text and its translation into another language. The basic idea is representing words in the two different natural languages on a common reference space. The main characteristic of this space is to be lan-guage independent, although Procrustes Rotation is performed transforming the lexical table derived from trans-lation by minimizing its distance from the lexical table belonging to the original corpus, while the subsequent Canonical Correlation Analysis treats symmetrically the two word sets. The most interesting RCA feature is building a unique reference space for representing the correlation structure in the data, inducing the two systems of canonical factors to lie on the same space. These graphical representations enables us to read distances be-tween corresponding points in terms of different way of translating the same word in relation with the general context defined by the canonical variates. Trying to understand the distances between matched points could rep-resent an useful tool for enriching lexical resources in a translation procedure. In this paper we propose the com-parison of the most frequent content bearing words in the two languages, analyzing one year (2003) of Le Monde Diplomatique and its Italian edition