Hadronic Spectrum in Inclusive Semileptonic B Decays

We evaluate the inclusive semileptonic B decay spectrum as a function of the final-state hadrons energy to second order in the inverse quark mass expansion and tree level in $\alpha_{s}$. We argue that there is an energy interval below the $c$ production threshold that could be used to determine $V_{ub}$.Comment: 10 pages, UCLA/94/TEP/10. (LaTeX file, one uuencoded PostScript figure appended at the end.

Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip

The Bethe Strip of width $m$ is the cartesian product \B\times\{1,...,m\}, where \B is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have "extended states" for small disorder. More precisely, we consider Anderson-like Hamiltonians \;H_\lambda=\frac12 \Delta \otimes 1 + 1 \otimes A + \lambda \Vv on a Bethe strip with connectivity $K \geq 2$, where $A$ is an $m\times m$ symmetric matrix, \Vv is a random matrix potential, and $\lambda$ is the disorder parameter. Given any closed interval $I\subset (-\sqrt{K}+a_{\mathrm{max}},\sqrt{K}+a_{\mathrm{min}})$, where $a_{\mathrm{min}}$ and $a_{\mathrm{max}}$ are the smallest and largest eigenvalues of the matrix $A$, we prove that for $\lambda$ small the random Schr\"odinger operator $\;H_\lambda$ has purely absolutely continuous spectrum in $I$ with probability one and its integrated density of states is continuously differentiable on the interval $I$

Average-case analysis of perfect sorting by reversals (Journal Version)

Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any common interval. B\'erard et al. (2007) make use of strong interval trees to describe an algorithm for sorting signed permutations by reversals. Combinatorial properties of this family of trees are essential to the algorithm analysis. Here, we use the expected value of certain tree parameters to prove that the average run-time of the algorithm is at worst, polynomial, and additionally, for sufficiently long permutations, the sorting algorithm runs in polynomial time with probability one. Furthermore, our analysis of the subclass of commuting scenarios yields precise results on the average length of a reversal, and the average number of reversals.Comment: A preliminary version of this work appeared in the proceedings of Combinatorial Pattern Matching (CPM) 2009. See arXiv:0901.2847; Discrete Mathematics, Algorithms and Applications, vol. 3(3), 201

Effect of a Split Interval on Simple Prefix B+-trees

This study examines the effect a split interval has on a simple pref ix B+-tree. A simple pref ix B+-tree is a cousin of the well-known B - tree indexing organization and a split interval is a proposed method to improve the performance of this organization. The purpose of this paper is to determine the usefulness of a split interval by empirically testing its effect on an experimental implementation of a simple pref ix B+-tree.Computing and Information Science

Forward triplets and topological entropy on trees

We provide a new and very simple criterion of positive topological entropy for tree maps. We prove that a tree map f has positive entropy if and only if some iterate fk has a periodic orbit with three aligned points consecutive in time, that is, a triplet (a,b,c) such that fk(a)=b, fk(b)=c and b belongs to the interior of the unique interval connecting a and c (a forward triplet of fk). We also prove a new criterion of entropy zero for simplicial n-periodic patterns P based on the non existence of forward triplets of fk for any 1≤k<n inside P. Finally, we study the set Xn of all n-periodic patterns P that have a forward triplet inside P. For any n, we define a pattern that attains the minimum entropy in Xn and prove that this entropy is the unique real root in (1,∞) of the polynomial xn−2x−1