Shape Function Effects in B -> X_c l \nu_l

Owing to the fact that m_c^2 ~ m_b \Lambda_QCD, the endpoint region of the charged lepton energy spectrum in the inclusive decay B -> X_c l \nu_l is affected by the Fermi motion of the initial-state b quark bound in the B meson. This effect is described in QCD by shape functions. Including the mass of the final-state quark, we find that a different set of operators as employed in Ref. hep-ph/0205150 is needed for a consistent matching, when incorporating the subleading contributions in B -> X_q l \nu_l for both q = u and q = c. In addition, we modify the usual twist expansion in such a way that it yields a description of the lepton energy spectrum which is not just valid in the endpoint region, but over the entire phase space.Comment: 8 Pages, LaTeX, 2 figures; a few typos corrected and some clarifications added, final journal versio

The Expected Perimeter in Eden and Related Growth Processes

Following Richardson and using results of Kesten on First-passage percolation, we obtain an upper bound on the expected perimeter in an Eden Growth Process. Using results of the author from a problem in Statistical Mechanics, we show that the average perimeter of the lattice animals resulting from a very natural family of "growth histories" does not obey a similar bound.Comment: 11 page

Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of small points if it is a non-special subvariety. The key of the proof is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of equidistribution theory due to Gubler. This article includes an appendix by Walter Gubler. He shows that the minimal dimension of the components of a canonical measure is equal to the dimension of the abelian part of the subvariety. We can apply this result to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page

General Lower Bounds for b -> d Penguin Processes

For the exploration of flavour physics, b -> d penguin processes are an important aspect, with the prominent example of \bar B^0_d -> K^0 \bar K^0. We recently derived lower bounds for the CP-averaged branching ratio of this channel in the Standard Model; they were found to be very close to the corresponding experimental upper limits, thereby suggesting that \bar B^0_d -> K^0 \bar K^0 should soon be observed. In fact, the BaBar collaboration subsequently announced the first signals of this transition. Here we point out that it is also possible to derive lower bounds for \bar B -> \rho \gamma decays, which are again surprisingly close to the current experimental upper limits. We show that these bounds are realizations of a general bound that holds within the Standard Model for b -> d penguin processes, allowing further applications to decays of the kind B^\pm -> K^{(\ast)\pm} K^{(\ast)} and B^\pm -> \pi^\pm \ell^+ \ell^-, \rho^\pm \ell^+ \ell^-.Comment: Minor changes, to appear as rapid communication in Phys. Rev

Meta-Learning for Phonemic Annotation of Corpora

We apply rule induction, classifier combination and meta-learning (stacked classifiers) to the problem of bootstrapping high accuracy automatic annotation of corpora with pronunciation information. The task we address in this paper consists of generating phonemic representations reflecting the Flemish and Dutch pronunciations of a word on the basis of its orthographic representation (which in turn is based on the actual speech recordings). We compare several possible approaches to achieve the text-to-pronunciation mapping task: memory-based learning, transformation-based learning, rule induction, maximum entropy modeling, combination of classifiers in stacked learning, and stacking of meta-learners. We are interested both in optimal accuracy and in obtaining insight into the linguistic regularities involved. As far as accuracy is concerned, an already high accuracy level (93% for Celex and 86% for Fonilex at word level) for single classifiers is boosted significantly with additional error reductions of 31% and 38% respectively using combination of classifiers, and a further 5% using combination of meta-learners, bringing overall word level accuracy to 96% for the Dutch variant and 92% for the Flemish variant. We also show that the application of machine learning methods indeed leads to increased insight into the linguistic regularities determining the variation between the two pronunciation variants studied.Comment: 8 page

Scaling Laws for Advection Dominated Flows: Applications to Low Luminosity Galactic Nuclei

We present analytical scaling laws for self-similar advection dominated flows. The spectra from these systems range from 10$^{8}$ - 10$^{20}$ Hz, and are determined by considering cooling of electrons through synchrotron, bremsstrahlung, and Compton processes. We show that the spectra can be quite accurately reproduced without detailed numerical calculations, and that there is a strong testable correlation between the radio and X-ray fluxes from these systems. We describe how different regions of the spectrum scale with the mass of the accreting black hole, $M$, the accretion rate of the gas, $\dot{M}$, and the equilibrium temperature of the electrons, $T_e$. We show that the universal radio spectral index of 1/3 observed in most elliptical galaxies (Slee et al. 1994) is a natural consequence of self-absorbed synchrotron radiation from these flows. We also give expressions for the total luminosity of these flows, and the critical accretion rate, $\dot{M}_{crit}$, above which the advection solutions cease to exist. We find that for most cases of interest the equilibrium electron temperature is fairly insensitive to $M$, $\dot{M}$, and parameters in the model. We apply these results to low luminosity black holes in galactic nuclei. We show that the problem posed by Fabian & Canizares (1988) of whether bright elliptical galaxies host dead quasars is resolved, as pointed out recently by Fabian & Rees (1995), by considering advection-dominated flows.Comment: 30 pages, 5 postscript files. Accepted to ApJ. Also available http://cfa-www.harvard.edu/~rohan/publications.htm

Semileptonic B Decays and Determination of |Vub|

Semileptonic decays of the B mesons provide an excellent probe for the weak and strong interactions of the bottom quark. The large data samples collected at the B Factories have pushed the experimental studies of the semileptonic B decays to a new height and stimulated significant theoretical developments. I review recent progresses in this fast-evolving field, with an emphasis on the determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|.Comment: 16 pages, 4 figures, accepted by Mod. Phys. Lett.