Perfect Simulation of a Coupling Achieving the (d)over-bar-distance Between Ordered Pairs of Binary Chains of Infinite Order

We explicitly construct a stationary coupling attaining Ornstein`s (d) over bar -distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of i.i.d. sequences of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.

Sequence and function of lysosomal and digestive cathepsin D-like proteinases of Musca domestica midgut

Musca domestica larvae display in anterior and middle midgut contents, a proteolytic activity with pH optimum of 3.0-3.5 and kinetic properties like cathepsin D. Three cDNAs coding for preprocathepsin D-like proteinases (ppCAD 1, ppCAD 2, ppCAD 3) were cloned from a M. domestica midgut cDNA library. The coded protein sequences included the signal peptide, propeptide and mature enzyme that has all conserved catalytic and substrate binding residues found in bovine lysosomal cathepsin D. Nevertheless, ppCAD 2 and ppCAD 3 lack the characteristic proline loop and glycosylation sites. A comparison among the sequences of cathepsin D-like enzymes from some vertebrates and those found in M. domestica and in the genomes of Aedes aegypti, Drosophila melanogaster, Tribolium castaneum, and Bombyx mori showed that only flies have enzymes lacking the proline loop (as defined by the motif: DxPxPx(G/A)P), thus resembling vertebrate pepsin. ppCAD 3 should correspond to the digestive cathepsin D-like proteinase (CAD) found in enzyme assays because: (1) it seems to be the most expressed CAD, based on the frequency of ESTs found. (2) The mRNA for CAD 3 is expressed only in the anterior and proximal middle midgut. (3) Recombinant procathepsin D-like proteinase (pCAD 3), after auto-activation has a pH optimum of 2.5-3.0 that is close to the luminal pH of M. domestica midgut. (4) Immunoblots of proteins from different tissues revealed with anti-pCAD 3 serum were positive only in samples of anterior and middle midgut tissue and contents. (5) CAD 3 is localized with immunogold inside secretory vesicles and around microvilli in anterior and middle midguit cells. The data support the view that on adapting to deal with a bacteria-rich food in an acid midgut region, M. domestica digestive CAD resulted from the same archetypical gene as the intracellular cathepsin D, paralleling what happened with vertebrates. The lack of the proline loop may be somehow associated with the extracellular role of both pepsin and digestive CAD 3. (C) 2009 Elsevier Ltd. All rights reserved.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.