Condensed Matter Theory

Abstract:

Alagille syndrome is an autosomal dominant disorder comprising cholestasis (associated with intrahepatic bile duct paucity), characteristic facial appearance, and cardiac, ocular and skeletal defects. Multiple patients have been reported with deletions or translocation involving 20p11.23-p12, providing evidence for the localization of the disease gene to this region. Fifty-six Alagille syndrome patients have been studied by cytogenetic and/or molecular analysis to determine the frequency of detectable abnormalities of 20p12. Two of fifty-six patients studied by cytogenetic analysis had abnormalities: an interstitial deletion in one patient and a translocation in another. Of forty-five patients studied by molecular analysis, three were found to have deletions of 20p, including the two patients identified with cytogenetic abnormalities. Molecular and molecular cytogenetic (FISH) analysis of the translocation (46,XX,t(2;20)(q21.3p12)) demonstrated a deletion at the translocation breakpoint. The deletions identified in the three patients are overlapping, contributing to the delineation of an Alagille syndrome critical region within 20p12. This region lies between markers D20S41 and D20S162. The frequency of detectable cytogenetic abnormalities of 20p12 in this group of Alagille patients is 2/56 (3.6%), and the frequency of molecular deletions is 3/45 (6.7%). This is considerably lower than the frequency of deletions observed in contiguous gene deletion syndromes suggesting that Alagille syndrome may be caused by the alteration of a single gene.

Abstract:

We study spectral properties of the Fokker-Planck operator that describes particles diffusing in a quenched random velocity field. This random operator is non-Hermitian and has eigenvalues occupying a finite area in the complex plane. We calculate the eigenvalue density and averaged one-particle Green's function, for weak disorder and dimension d>2. We relate our results to the time-evolution of particle density, and compare them with numerical simulations.