Dominant partition method

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails

On the informativeness of dominant and co-dominant genetic markers for Bayesian supervised clustering

We study the accuracy of Bayesian supervised method used to cluster individuals into genetically homogeneous groups on the basis of dominant or codominant molecular markers. We provide a formula relating an error criterion the number of loci used and the number of clusters. This formula is exact and holds for arbitrary number of clusters and markers. Our work suggests that dominant markers studies can achieve an accuracy similar to that of codominant markers studies if the number of markers used in the former is about 1.7 times larger than in the latter

Counting and testing dominant polynomials

In this paper, we concentrate on counting and testing dominant polynomials with integer coefficients. A polynomial is called dominant if it has a simple root whose modulus is strictly greater than the moduli of its remaining roots. In particular, our results imply that the probability that the dominant root assumption holds for a random monic polynomial with integer coefficients tends to 1 in some setting. However, for arbitrary integer polynomials it does not tend to 1. For instance, the proportion of dominant quadratic integer polynomials of height $H$ among all quadratic integer polynomials tends to $(41+6 \log 2)/72$ as $H \to \infty$. Finally, we will design some algorithms to test whether a given polynomial with integer coefficients is dominant or not without finding the polynomial roots

Supersymmetric Scenarios with Dominant Radiative Neutralino Decay

The radiative decay of the next-to-lightest neutralino into a lightest neutralino and a photon is analyzed in the MSSM. We find that significant regions of the supersymmetric parameter space with large radiative BR's (up to about 100%) do exist. The radiative channel turns out to be enhanced when the neutralino tree-level decays are suppressed either "kinematically" or "dynamically". In general, in the regions allowed by LEP data and not characterized by asymptotic values of the SuSy parameters, the radiative enhancement requires tan beta ~= 1 and/or M_1 ~= M_2, and negative values of \mu. We present typical specific scenarios where these "necessary" conditions are fulfilled, relaxing the usual relation M_1=(5/3)*tan^2(th_W)*M_2. The influence of varying the stop masses and mixing angle when the radiative decay is enhanced is also considered. Some phenomenological consequences of the above picture are discussed.Comment: 32 pages, LaTeX file + 23 figures embedded with epsf.sty. In this revised version, Eq.(3) plus some related notations and text passages have been changed. Minor error corrected in Fig.12(a). The numerical analysis and the conclusions of the paper are not affected. (Includes the erratum to appear in Phys. Rev. D.) Source and ps files are also available at ftp://hpteo.roma1.infn.it/pub/preprints/ambr-mele/Rome1-1148/ or at http://feynman.physics.lsa.umich.edu/~ambros/Physics.html#1

Phenomenological implications of moduli-dominant SUSY breaking

We study moduli-dominated SUSY breaking within the framework of string models. This type of SUSY breaking in general leads to non-universal soft masses, i.e. soft scalar masses and gaugino masses. Further gauginos are lighter than sfermions. This non-universality has phenomenologically important implications. We investigate radiative electroweak symmetry breaking in the mass spectrum derived from moduli-dominated SUSY breaking, where the lightest chargino and neutralino are almost gauginos. Moreover, constraints from the branching ratio of $b \to s \gamma$ and the relic abundance of the LSP are also considered. The mass spectrum of moduli-dominated SUSY breaking is favorable to the experimental bound of the $b \to s \gamma$ decay decreasing its branching ratio. We obtain an upper bound for the gravitino mass from the cosmological constraint.Comment: Version to be appeared in Nucl. Phys.