Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets

Three heavy jet events at hadron colliders as a sensitive probe of the Higgs sector

Assuming that a non-standard neutral Higgs with an enhanced Yukawa coupling to a bottom quark is observed at future hadron experiments, we propose a method for a better understanding of the Higgs sector. Our procedure is based on "counting" the number of events with heavy jets (where "heavy" stands for a c or b jet) versus b jets, in the final state of processes in which the Higgs is produced in association with a single high p_T c or b jet. We show that an observed signal of the type proposed, at either the Tevatron or the LHC, will rule out the popular two Higgs doublet model of type II as well as its supersymmetric version - the Minimal Supersymmetric Standard Model (MSSM), and may provide new evidence in favor of some more exotic multi Higgs scenarios. As an example, we show that in a version of a two Higgs doublet model which naturally accounts for the large mass of the top quark, our signal can be easily detected at the LHC within that framework. We also find that such a signal may be observable at the upgraded Tevatron RunIII, if the neutral Higgs in this model has a mass around 100 GeV and \tan\beta > 50 and if the efficiency for distinguishing a c jet from a light jet will reach the level of 50%.Comment: Revtex, 11 pages, 4 figures embedded in the text. Main changes with respect to Version 1: Numerical results re-calculated using the CTEQ5L pdf, improved discussion on the experimental consequences, new references added. Conclusions remain unchanged. As will appear in Phys. Rev.

Coherent Neutrino Interactions in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_F\rho)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.Comment: 28 pages, 6 figures, Latex; minor changes, one reference added; version to appear in Phys. Rev.

Remarks upon the mass oscillation formulas

The standard formula for mass oscillations is often based upon the approximation $t \approx L$ and the hypotheses that neutrinos have been produced with a definite momentum $p$ or, alternatively, with definite energy $E$. This represents an inconsistent scenario and gives an unjustified reduction by a factor of two in the mass oscillation formulas. Such an ambiguity has been a matter of speculations and mistakes in discussing flavour oscillations. We present a series of results and show how the problem of the factor two in the oscillation length is not a consequence of gedanken experiments, i.e. oscillations in time. The common velocity scenario yields the maximum simplicity.Comment: 9 pages, AMS-Te

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

Addendum to Finite-size effects on multibody neutrino exchange

The interaction energy of the neutrons due to massless neutrino exchange in a neutron star has recently been proved, using an effective theory, to be extremely small and infrared-safe. Our comment here is of conceptual order: two approaches to compute the total interaction energy density have recently been proposed. Here, we study the connection between these two approaches. From CP invariance, we argue that the resulting interaction energy has to be even in the parameter $b=-G_F n_n /\sqrt{2}$, which expresses the static neutrino potential created by a neutron medium of density $n_n$.Comment: Latex file (Revtex), 9 pages, 1 figure, one reference change

Towards a unique formula for neutrino oscillations in vacuum

We show that all correct results obtained by applying quantum field theory to neutrino oscillations can be understood in terms of a single oscillation formula. In particular, the model proposed by Grimus and Stockinger is shown to be a subcase of the model proposed by Giunti, Kim and Lee, while the new oscillation formulas proposed by Ioannisian and Pilaftsis and by Shtanov are disproved. We derive an oscillation formula without making any relativistic assumption and taking into account the dispersion, so that the result is valid for both neutrinos and mesons. This unification gives a stronger phenomenological basis to the neutrino oscillation formula. We also prove that the coherence length can be increased without bound by more accurate energy measurements. Finally, we insist on the wave packet interpretation of the quantum field treatments of oscillations.Comment: 30 pages, 1 figure; the proof that plane wave oscillations do no exist is extended to stationary models; the influence of dispersion is explained in more detail

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

Dirac and Majorana neutrinos in matter

We consider the matter effects on neutrinos moving in background on the basis of the corresponding quantum wave equations. Both Dirac and Majorana neutrino cases are discussed. The effects for Dirac neutrino reflection and trapping as well as neutrino-antineutrino annihilation and $\nu\overline{\nu}$ pair creation in matter at the interface between two media with different densities are considered. The spin light of neutrino in matter is also discussed.Comment: 11 pages, 2 figures, in: Proceedings of the 5th International Conference on Non-Accelerator New Physics (Dubna, Russia, June 20-25, 2005). V2: typos correcte