Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor improvements. 44 pages, 14 figure

On the Potts model partition function in an external field

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial

CMS physics technical design report : Addendum on high density QCD with heavy ions

Peer reviewe

Karyotypic variation of Glanidium ribeiroi Haseman, 1911 (Siluriformes, Auchenipteridae) along the Iguazu river basin

Abstract The Iguazu river is a tributary of the left margin of the Paraná river, isolated from this basin about 22 million years ago with the appearance of the Iguazu Falls. The Iguazu river is characterized by high endemism due to two factors: its rugged topography and the old isolation caused by formation of the Iguazu Falls. This study analyzed cytogenetically a population of Glanidium ribeiroi collected in a region at the final stretch of this basin, by Giemsa staining, C-banding, impregnation by silver nitrate, and FISH with probes of 5S rDNA, 18S rDNA, telomeric sequence [TTAGGG]n, and [GATA]n repeats. The diploid number was equal to 58 chromosomes. The heterochromatin was present in the terminal region of almost all chromosomes. The Ag-NORs were simple and presented interstitially on the short arm of the submetacentric pair 14, which was confirmed by FISH with 18S rDNA probe. The 5S rDNA-FISH marked only the submetacentric pair 16 on the long arm in interstitial position. The FISH with [TTAGGG]n probe presented all telomeres labeled as expected, with an absence of Interstitial Telomeric Sequence (ITS). The repetitive [GATA]n sequence was dispersed throughout the genome, with preferential location in the terminal region of all chromosomes. The data obtained are discussed herein with other species of Auchenipteridae, and other previously analyzed populations of G. ribeiroi from the Iguazu river, verifying differences among these populations, which should be mainly related to the rugged topography of this basin