The relevant prefixes of coloured Motzkin walks: An average case analysis

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The Tennis Ball Problem

AbstractMallows and Shapiro, (J. Integer Sequences2 (1999)) have recently considered what they dubbed the problem of balls on the lawn. Our object is to explore a natural generalization, the s-tennis ball problem, which reduces to that considered by Mallows and Shapiro in the case s=2. We show how this generalization is connected with s-ary trees, and employ the notion of generating trees to obtain a solution expressed in terms of generating functions

A systematic screen for morphological abnormalities during fission yeast sexual reproduction identifies a mechanism of actin aster formation for cell fusion.

In non-motile fungi, sexual reproduction relies on strong morphogenetic changes in response to pheromone signaling. We report here on a systematic screen for morphological abnormalities of the mating process in fission yeast Schizosaccharomyces pombe. We derived a homothallic (self-fertile) collection of viable deletions, which, upon visual screening, revealed a plethora of phenotypes affecting all stages of the mating process, including cell polarization, cell fusion and sporulation. Cell fusion relies on the formation of the fusion focus, an aster-like F-actin structure that is marked by strong local accumulation of the myosin V Myo52, which concentrates secretion at the fusion site. A secondary screen for fusion-defective mutants identified the myosin V Myo51-associated coiled-coil proteins Rng8 and Rng9 as critical for the coalescence of the fusion focus. Indeed, rng8Δ and rng9Δ mutant cells exhibit multiple stable dots at the cell-cell contact site, instead of the single focus observed in wildtype. Rng8 and Rng9 accumulate on the fusion focus, dependent on Myo51 and tropomyosin Cdc8. A tropomyosin mutant allele, which compromises Rng8/9 localization but not actin binding, similarly leads to multiple stable dots instead of a single focus. By contrast, myo51 deletion does not strongly affect fusion focus coalescence. We propose that focusing of the actin filaments in the fusion aster primarily relies on Rng8/9-dependent cross-linking of tropomyosin-actin filaments

Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.Comment: 14 pages, 9 figures; introduction expanded, references added; published versio

Intramolecular friedel-crafts reaction of indoles with carbonyl groups: a simple synthesis of 3- and 4-substituted \u3b2-carbolin-1-ones

The intramolecular Friedel-Crafts reaction of indole-2-carboxylic acid \u3b2-oxoamides catalyzed by trifluoroacetic acid or InCl3, is a convenient method for the synthesis of 3-aryl-, 4-aryl-, and 4-alkyl-\u3b2-carbolin-1-ones

Infertility and hypergonadotropic hypogonadism as first evidence of hereditary apolipoprotein A-I amyloidosis

Purpose: We report that primary infertility and hypergonadotropic hypogonadism in young patients may be caused by testicular amyloidosis and it is associated with the presence of a mutation in the apoA-I gene, resulting in the replacement of proline for leucine at residue 75 of the protein. Materials and Methods: Ten patients presenting with infertility, gynecomastia, decreased libido, erectile dysfunction or a family history of amyloidosis underwent clinical evaluation, hormone assays, semen analysis, ultrasonographic investigation of the testicles, testicular biopsy and DNA sequencing of the apoA-I gene. Results: All patients showed azoospermia and 9 had increased testicular volume. Massive amyloid deposition was observed in all testicular biopsies and the apoA-I mutation of replacement of proline for leucine at residue 75 of the protein was noted. Five patients showed hypergonadotropic hypogonadism and 5 had normal testosterone values with high gonadotropin levels. Conclusions: Nonobstructive azoospermia and macro-orchidism with or without hypogonadism may be caused by hereditary apoA-I amyloidosis in young patients. Testicular amyloidosis can be the first manifestation of this systemic disease. Specific staining for amyloid deposits and genetic analysis of apoA-I mutations are recommended in young, infertile patients with macro-orchidism. Finally, surveillance in asymptomatic mutation carriers is suggested to evaluate the opportunity to implement sperm retrieval and start androgen replacement therapy when necessary

University Student Progressions and First Year Behaviour

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Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem

The partition function of the Baxter-Wu model is exactly related to the generating function of a site-colouring problem on a hexagonal lattice. We extend the original Bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions. The operator content of these models are studied by solving numerically the Bethe-ansatz equations and by exploring conformal invariance. Since the eigenspectra are calculated for large lattices, the corrections to finite-size scaling are also calculated.Comment: 12 pages, latex, to appear in J. Phys. A: Gen. Mat