Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A Haldane-Shastry spin chain of BC_N type in a constant magnetic field

We compute the spectrum of the trigonometric Sutherland spin model of BC_N type in the presence of a constant magnetic field. Using Polychronakos's freezing trick, we derive an exact formula for the partition function of its associated Haldane-Shastry spin chain.Comment: LaTeX, 13 page

On the level density of spin chains of Haldane--Shastry type

We provide a rigorous proof of the fact that the level density of all su(m) spin chains of Haldane-Shastry type associated with the A_{N-1} root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the dispersion relation.Comment: 6 pages, revte

Genome-Wide Footprints of Pig Domestication and Selection Revealed through Massive Parallel Sequencing of Pooled DNA

Background Artificial selection has caused rapid evolution in domesticated species. The identification of selection footprints across domesticated genomes can contribute to uncover the genetic basis of phenotypic diversity. Methodology/Main Findings Genome wide footprints of pig domestication and selection were identified using massive parallel sequencing of pooled reduced representation libraries (RRL) representing ~2% of the genome from wild boar and four domestic pig breeds (Large White, Landrace, Duroc and Pietrain) which have been under strong selection for muscle development, growth, behavior and coat color. Using specifically developed statistical methods that account for DNA pooling, low mean sequencing depth, and sequencing errors, we provide genome-wide estimates of nucleotide diversity and genetic differentiation in pig. Widespread signals suggestive of positive and balancing selection were found and the strongest signals were observed in Pietrain, one of the breeds most intensively selected for muscle development. Most signals were population-specific but affected genomic regions which harbored genes for common biological categories including coat color, brain development, muscle development, growth, metabolism, olfaction and immunity. Genetic differentiation in regions harboring genes related to muscle development and growth was higher between breeds than between a given breed and the wild boar. Conclusions/Significance These results, suggest that although domesticated breeds have experienced similar selective pressures, selection has acted upon different genes. This might reflect the multiple domestication events of European breeds or could be the result of subsequent introgression of Asian alleles. Overall, it was estimated that approximately 7% of the porcine genome has been affected by selection events. This study illustrates that the massive parallel sequencing of genomic pools is a cost-effective approach to identify footprints of selection

Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds

We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.Comment: 20 pages; to appear in Annales Henri Poincar