Nonresonant Contributions in B->rho pi Decay

We consider nonresonant contributions in the Dalitz plot analysis of B->rho pi->pi^+ pi^- pi^0 decay and their potential impact on the extraction of the CKM parameter alpha. In particular, we examine the role of the heavy mesons B^* and B_0, via the process B->pi (B^*, B_0)->pi^+ pi^- pi^0, and their interference with resonant contributions in the rho-mass region. We discuss the inherent uncertainties and suggest that the effects may be substantially smaller than previously indicated.Comment: 15 pages, 3 figures; minor changes, version to appear in Phys. Rev.

Equation of State of Oscillating Brans-Dicke Scalar and Extra Dimensions

We consider a Brans-Dicke scalar field stabilized by a general power law potential with power index $n$ at a finite equilibrium value. Redshifting matter induces oscillations of the scalar field around its equilibrium due to the scalar field coupling to the trace of the energy momentum tensor. If the stabilizing potential is sufficiently steep these high frequency oscillations are consistent with observational and experimental constraints for arbitrary value of the Brans-Dicke parameter $\omega$. We study analytically and numerically the equation of state of these high frequency oscillations in terms of the parameters $\omega$ and $n$ and find the corresponding evolution of the universe scale factor. We find that the equation of state parameter can be negative and less than -1 but it is not related to the evolution of the scale factor in the usual way. Nevertheless, accelerating expansion is found for a certain parameter range. Our analysis applies also to oscillations of the size of extra dimensions (the radion field) around an equilibrium value. This duality between self-coupled Brans-Dicke and radion dynamics is applicable for $\omega= -1 + 1/D$ where D is the number of extra dimensions.Comment: 10 two-column pages, RevTex4, 8 figures. Added clarifying discussions, new references. Accepted in Phys. Rev. D (to appear

Multifractality and percolation in the coupling space of perceptrons

The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(\alpha)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in Phys. Rev.