Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.Comment: 31 pages, 1 figure. Minor changes from previous version. To appear in Advances in Mathematic

The use of polymorphic Alu insertions in human DNA fingerprinting

We have characterized several Human Specific (HS) Alu insertions as either dimorphic (TPA25, PV92, APO), slightly dimorphic (C2N4 and C4N4) or monomorphic (C3N1, C4N6, C4N2, C4N5, C4N8) based on studies of Caucasian, Asian, American Black and African Black populations. Our approach is based upon: 1) PCR amplification using primers complementary to the unique DNA sequences that flank the site of insertion of the different Alu elements studied; 2) gel electrophoresis and scoring according to the presence or absence of an Alu insertion in one or both homologous chromosomes; 3) allele frequencies determined by gene counting and compared to Hardy-Weinberg expectations. Our DNA fingerprinting procedure using PCR amplification of diallelic polymorphic (dimorphic) Human Specific Alu insertions, may be used as a tool for genetic mapping, to characterize populations, study human migrational patterns, and track the inheritance of human genetic disorders