Architecture of optimal transport networks

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape of channels in such optimal networks and show that they must be straight with uniform cross-sectional areas. Then, we establish a relation between the cross-sectional areas of adjoining channels at each junction. Indeed, this relation is a generalization of Murray's law, originally established in the context of local optimization. Moreover, we establish a relation between angles and cross-sectional areas of adjoining channels at each junction, which can be represented as a vectorial force balance equation, where the force weight depends on the channel cross-sectional area. A scaling law between the minimal resistance value and the total volume or surface area value is also derived from the analysis. Furthermore, we show that no more than three or four channels meet in one junction of optimal bi-dimensional networks, depending on the flow profile (e.g.: Poiseuille-like or plug-like) and the considered constraint (fixed volume or surface area). In particular, we show that sources are directly connected to wells, without intermediate junctions, for minimal resistance networks preserving the total channel volume in case of plug flow regime. Finally, all these results are illustrated with a simple example, and compared with the structure of natural networks

Continuity and variability in the parental involvement and advocacy beliefs of Latino families of young children

Parental involvement is an important component of children’s school success. Although the literature on parental involvement among Latino families is growing and moving from deficit-based perspectives, very few studies have examined the parental involvement beliefs and practices of Latino families who vary across demographic and sociocultural lines within the same school community. This qualitative study explored Latino parents’ beliefs about children’s education, their involvement and advocacy beliefs and practices, and their perceptions of feeling welcome at their children’s school. In-depth interviews were conducted with 12 parents of preschool and kindergarten children who attended a bilingual school. Qualitative descriptive analyses revealed that the majority of parents espoused the cultural value of educación, engaged in learning activities at home, and viewed themselves as living models of behavior for children, regardless of their education or immigrant status. Only first generation immigrant parents made explicit reference to children’s futures. All parents attributed supportive relationships with school personnel and a bilingual climate as the most important sources of feeling welcome at school. However, parents with more education valued what they perceived as an “open door policy” and were more vocal in critiquing policies. Findings have implications for the development of multicultural competence among teachers and for ways diverse Latino families might develop a shared voice within the school sector.Published versio

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge