Localization-delocalization transition for drift diffusion in a random environment

We investigate the localization-delocalization transition for the drift-diffusion equation on a regular tree with quenched random drift velocities on its branches. The inverse of the steady-state amplitude at the origin is expressed in terms of a random geometric series whose convergence or otherwise determines the critical phase boundary. We establish exact criteria for localization valid for an arbitrary distribution of the drift velocities. The phase transition is shown to be first order except in the percolation limit

Classical localization and percolation in random environments on trees

We consider a simple model of transport on a regular tree, whereby species evolve according to the drift-diffusion equation, and the drift velocity on each branch of the tree is a quenched random variable. The inverse of the steady-state amplitude at the origin is expressed in terms of a random geometric series whose convergence or otherwise determines whether the system is localized or delocalized. In a recent paper [P. C. Bressloff et al., Phys. Rev. Lett. 77, 5075 (1996)], exact criteria were presented that enable one to determine the critical phase boundary for the transition, valid for any distribution of the drift velocities. In this paper we present a detailed derivation of these criteria, consider a number of examples of interest, and establish a connection with conventional percolation theory. The latter suggests a wider application of the results to other models of statistical processes occurring on treelike structures. Generalizations to the case where the underlying tree is irregular in nature are also considered

The polycystic kidney disease 1 gene encodes a 14 kb transcript and lies within a duplicated region on chromosome 16

Autosomal dominant polycystic kidney disease (ADPKD) is a common genetic disorder that frequently results in renal fallure due to progressive cyst development. The major locus, PKD1, maps to 16p13.3. We identified a chromosome translocation associated with ADPKD that disrupts a gene (PBP) encoding a 14 kb transcript in the PKD1 candidate region. Further mutations of the PBP gene were found in PKD1 patients, two deletions (one a de novo event) and a splicing defect, confirming that PBP is the PKD1 gene. This gene is located adjacent to the TSC2 locus in a genomic region that is reiterated more proximally on 16p. The duplicate area encodes three transcripts substantially homologous to the PKD1 transcript. Partial sequence analysis of the PKD1 transcript shows that it encodes a novel protein whose function is at present unknown

Pesticide Chemistry : Human Welfare and The Environment

viii,429 hal.;ill.;30 cm

DNA sequences of chromosome 21-specific YAC detect the t(8;21) breakpoint of acute myelogenous leukemia

The t(8;21)(q22;q22) is a nonrandom translocation specifically marking blasts of acute myelogenous leukemia (AML) with undifferentiated phenotype. The breakpoint on chromosome 21 involved by this rearrangement has been precisely localized relative to cloned DNA markers by physical and genetic linkage analysis enabling the use of positional cloning for its isolation. Yeast artificial chromosome (YAC) clones for loci proximal (D21S65) and distal (ERG) to the (21q22) breakpoint have been developed and their chromosome 21 origin and location relative to the breakpoint has been established. By using in situ hybridization analysis, a 240 kb YAC clone for the D21S65 locus clearly identified both derivative chromosomes of the (8;21) translocation in metaphase spreads of leukemia blasts with the rearrangement. The characterization of the DNA sequences contained in this 240 kb YAC can reveal the functional consequences of their derangement in leukemia with abnormalities of the (21q22) region