Intersection form, laminations and currents on free groups

Let $F_N$ be a free group of rank $N\ge 2$, let $\mu$ be a geodesic current on $F_N$ and let $T$ be an $\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $$ is equal to zero if and only if the support of $\mu$ is contained in the dual algebraic lamination $L^2(T)$ of $T$. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a \emph{filling} element in $F_N$ and prove that filling elements are "nearly generic" in $F_N$. We also apply our results to the notion of \emph{bounded translation equivalence} in free groups.Comment: revised version, to appear in GAF

The use of local orbitals in multireference calculations

CAS-SCF-type algorithms based on molecular orbitals that preserve their physical nature during the iterative process have been proposed recently by our groups. Our approach is based on the iterative partial diagonalization of the one-body reduced density matrix. If localized guess orbitals are used, the locality property is kept by the final orbitals. The use of local orbitals in multiference calculations has several advantages. It can be used to reduce the number of active orbitals in CAS-SCF calculations on large systems, and in general to have a better control on the physical nature of the active space. The reduction from a complete to a selected reference space is also possible in the case of configuration interaction calculations. The technique is illustrated through applications to the description of bond breaking and n->pi* excited states in conjugated systems. The efficiency of selection of local excitations is shown on a magnetic complex

Developing Cultural Self-Awareness: The First Step in Values Clarification for Early Interventionists

This article presents a discussion of the need for early interventionists to develop awareness of certain cultural assumptions underlying their practice. A wide range of literature on cultural differences is used to identify five areas of potential dissonance between professionals and families from culturally diverse backgrounds: interpretations of the meaning of disability; concepts of family structure and identity; goals of education; parent-child interaction, and communication style. It is argued that awareness of one's own cultural beliefs in these areas is an essential first step in developing effective collaboration with culturally different families