Candecomp/Parafac with zero constraints at arbitrary positions in a loading matrix

When one interprets Candecomp/Parafac (CP) solutions for analyzing three-way data, small loadings are often ignored, that is, considered to be zero. Rather than just considering them zero, it seems better to actually model such values as zero. This can be done by successive modeling approaches as well as by a simultaneous modeling approach. This paper offers algorithms for three such approaches, and compares them on the basis of empirical data and a simulation study. The conclusion of the latter was that, under realistic circumstances, all approaches recovered the underlying structure well, when the number of values to constrain to zero was given. Whereas the simultaneous modeling approach seemed to perform slightly better, differences were very small and not substantial. Given that the simultaneous approach is far more time consuming than the successive approaches, the present study suggests that for practical purposes successive approaches for modeling zeros in the CP model seem to be indicated

Adaptation and enslavement in endosymbiont-host associations

The evolutionary persistence of symbiotic associations is a puzzle. Adaptation should eliminate cooperative traits if it is possible to enjoy the advantages of cooperation without reciprocating - a facet of cooperation known in game theory as the Prisoner's Dilemma. Despite this barrier, symbioses are widespread, and may have been necessary for the evolution of complex life. The discovery of strategies such as tit-for-tat has been presented as a general solution to the problem of cooperation. However, this only holds for within-species cooperation, where a single strategy will come to dominate the population. In a symbiotic association each species may have a different strategy, and the theoretical analysis of the single species problem is no guide to the outcome. We present basic analysis of two-species cooperation and show that a species with a fast adaptation rate is enslaved by a slowly evolving one. Paradoxically, the rapidly evolving species becomes highly cooperative, whereas the slowly evolving one gives little in return. This helps understand the occurrence of endosymbioses where the host benefits, but the symbionts appear to gain little from the association.Comment: v2: Correction made to equations 5 & 6 v3: Revised version accepted in Phys. Rev. E; New figure adde

Direct CP violation in radiative b decays in and beyond the Standard Model

We consider the partial rate asymmetry in the inclusive decay modes b to s gamma and b to d gamma, concentrating on non-standard models with new charged Higgs interactions. We find that the charged Higgs contribution to the asymmetry for b to s gamma is small in such models due to a universal cancellation mechanism. The asymmetry is therefore difficult to distinguish experimentally from the Standard Model (SM) value, which is also small. The cancellation mechanism is found to be rendered inoperative in supersymmetry due to the presence of chargino loops. Unlike b to s gamma, the rate asymmetry for b to d gamma in Higgs models can be quite different from its SM value, generally ranging from -20% to +20%. Specific model calculations are performed for the Three-Higgs Doublet Model and the ``Top'' Two-Higgs Doublet Model to serve as illustrations. We also offer some suggestions that may be helpful to experimentalists in the detection of the inclusive mode b to d gamma.Comment: RevTex, 24 pages, 6 figures, minor changes, version to appear in PR

Direct CP-asymmetry in Inclusive Rare B-decays in 2HDM

The direct CP-asymmetry in the inclusive $B \to X_d \gamma$ and $B \to X_d e^+ e^ -$ decays is investigated in the two-Higgs doublet extension of the Standard Model (2HDM). The investigation is performed in the lowest non-vanishing order of the perturbation theory using the existing restrictions on the 2HDM parameters space. It is shown that the direct CP-asymmetry in the $B \to X_d \gamma$ decay can deviate significantly from the Standard Model predictions. In the presence of only one source of CP-violation (the CKM matrix weak phase) $a_{CP}(B \to X_d \gamma)$ can have the sign opposite to that in the SM. The new source of CP-violation can make $|a_{CP}(B \to X_d \gamma)|$ arbitrary small (unlike the SM case) and hence unmeasurable. Quantitatively, the obtained results suffer from the uncertainty of the choice of renormalization scale. As for the $B \to X_d e^+ e^ -$ rate asymmetry, its renormalization scale dependence in the lowest non-vanishing order does not allow to conclude if this quantity is efficient for testing New Physics beyond the Standard Model.Comment: 16 pages including 2 figure

Finite-size effects on multibody neutrino exchange

The effect of multibody massless neutrino exchanges between neutrons inside a finite-size neutron star is studied. We use an effective Lagrangian, which incorporates the effect of the neutrons on the neutrinos. Following Schwinger, it is shown that the total interaction energy density is computed by comparing the zero point energy of the neutrino sea with and without the star. It has already been shown that in an infinite-size star the total energy due to neutrino exchange vanishes exactly. The opposite claim that massless neutrino exchange would produce a huge energy is due to an improper summation of an infrared-divergent quantity. The same vanishing of the total energy has been proved exactly in the case of a finite star in a one-dimensional toy model. Here we study the three-dimensional case. We first consider the effect of a sharp star border, assumed to be a plane. We find that there is a non- vanishing of the zero point energy density difference between the inside and the outside due to the refraction index at the border and the consequent non-penetrating waves. An analytical and numerical calculation for the case of a spherical star with a sharp border confirms that the preceding border effect is the dominant one. The total result is shown to be infrared-safe, thus confirming that there is no need to assume a neutrino mass. The ultraviolet cut-offs, which correspond in some sense to the matching of the effective theory with the exact one, are discussed. Finally the energy due to long distance neutrino exchange is of the order of $10^{-8} -- 10^{-13} GeV per neutron$, i.e. negligible with respect to the neutron mass density.Comment: Latex file (Revtex), 34 pages, 8 postscripted figure

Neutrino ground state in a dense star

It has recently been argued that long range forces due to the exchange of massless neutrinos give rise to a very large self-energy in a dense, finite-ranged, weakly-charged medium. Such an effect, if real, would destabilize a neutron star. To address this issue we have studied the related problem of a massless neutrino field in the presence of an external, static electroweak potential of finite range. To be precise, we have computed to one loop the exact vacuum energy for the case of a spherical square well potential of depth alpha and radius R. For small wells, the vacuum energy is reliably determined by a perturbative expansion in the external potential. For large wells, however, the perturbative expansion breaks down. A manifestation of this breakdown is that the vacuum carries a non-zero neutrino charge. The energy and neutrino charge of the ground state are, to a good approximation for large wells, those of a neutrino condensate with chemical potential mu=alpha. Our results demonstrate explicitly that long-range forces due to the exchange of massless neutrinos do not threaten the stability of neutron stars.Comment: 27 pages, 7 figures, revtex; several typos corrected; a few references added; title changed slightly; includes a "note added in proof"; version to appear in Phys. Rev.

Scattering From a Two Dimensional Array of Flux Tubes: A Study of The Validity of Mean Field Theory

Mean Field Theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximation by considering the Quantum Mechanical scattering of a charged particle from a two dimensional array of magnetic flux tubes. The flux tubes are arranged on a regular lattice which is infinitely long in the ``$y$'' direction but which has a (small) finite number of columns in the ``$x$'' direction. Their physical size is assumed to be infinitesimally small. We develop a method for computing the scattering angle as well as the reflection and transmission coefficients to lowest order in the Aharonov--Bohm interaction. The results of our calculation are compared to the scattering of the same particle from a region of constant magnetic field whose magnitude is equal to the mean field of all the flux tubes. For an incident plane wave, the Mean Field approximation is shown to be valid provided the flux in each tube is much less than a single flux quantum. This is precisely the regime in which Mean Field Theory for anyons is expected to be valid. When the flux per tube becomes of order 1, Mean Field Theory is no longer valid.Comment: 23 pages, University of British Columbia Preprint UBCTP93-01

Generalized messengers of supersymmetry breaking and the sparticle mass spectrum

We investigate the sparticle spectrum in models of gauge-mediated supersymmetry breaking. In these models, supersymmetry is spontaneously broken at an energy scale only a few orders of magnitude above the electroweak scale. The breakdown of supersymmetry is communicated to the standard model particles and their superpartners by "messenger" fields through their ordinary gauge interactions. We study the effects of a messenger sector in which the supersymmetry-violating F-term contributions to messenger scalar masses are comparable to the supersymmetry-preserving ones. We also argue that it is not particularly natural to restrict attention to models in which the messenger fields lie in complete SU(5) GUT multiplets, and we identify a much larger class of viable models. Remarkably, however, we find that the superpartner mass parameters in these models are still subject to many significant contraints.Comment: 24 pages, LaTeX, uses epsf.sty, 4 figures. Assumptions clarified, numerical bounds tweaked, typos correcte

Strong CP and Mu Problems in Theories with Gauge Mediated Supersymmetry Breaking

We provide a simple solution to the $\mu$ and strong CP problems in the context of gauge mediated supersymmetry breaking. The generic appearance of R symmetry in dynamical supersymmetry breaking is used to implement Peccei-Quinn symmetry. Acceptable $\mu$ and $B$ terms as well as the large symmetry breaking scale are induced in the presence of nonrenormalizable interactions. Cosmological consequences of this scheme turn out to yield constraints on the PQ symmetry breaking scale and the number of the messenger/heavy quarks. Complexity in introducing non-R Peccei-Quinn symmetry is contrasted with the case of R symmetry.Comment: 10 pages, Revtex. Significantly modified version to apear in Phys. Rev.

A One-Scale Model of Dynamical Supersymmetry Breaking

A model of gauge-mediated supersymmetry breaking is constructed in which the low-energy physics depends on a single dynamical scale. Strong coupling dynamics of gauge theories plays an important role, in particular through its effects on beta functions and through confinement. The model does not have distinct messenger and supersymmetry-breaking sectors. The scale of supersymmetry breaking is of order 10-100 \TeV, implying that the decay of the next-to-lightest superpartner into the gravitino is prompt. Superoblique corrections are enhanced. A Dirac fermion and one complex scalar, in a 10 or \bar{10} of (global) SU(5), are predicted to be relatively light and to satisfy certain mass relations with the standard model squarks and sleptons.Comment: 28 pages, uses revtex, h-physrev.bs