Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

The LHC di-photon excess and Gauge Coupling Unification in Extra Z′Z^\prime Heterotic-String Derived Models

The di-photon excess observed at the LHC can be explained as a Standard Model singlet that is produced and decays by heavy vector-like colour triplets and electroweak doublets in one-loop diagrams. The characteristics of the required spectrum are well motivated in heterotic-string constructions that allow for a light $Z^\prime$. Anomaly cancellation of the $U(1)_{Z^\prime}$ symmetry requires the existence of the Standard Model singlet and vector-like states in the vicinity of the $U(1)_{Z^\prime}$ breaking scale. In this paper we show that the agreement with the gauge coupling data at one-loop is identical to the case of the Minimal Supersymmetric Standard Model, owing to cancellations between the additional states. We further show that effects arising from heavy thresholds may push the supersymmetric spectrum beyond the reach of the LHC, while maintaining the agreement with the gauge coupling data. We show that the string inspired model can indeed account for the observed signal and discuss the feasibility of obtaining viable scalar mass spectrum.Comment: 26 pages. 11 figures. Published versio

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Wilsonian dark matter in string derived Z' model

The dark matter issue is among the most perplexing in contemporary physics. The problem is more enigmatic due to the wide range of possible solutions, ranging from the ultra-light to the super-massive. String theory gives rise to plausible dark matter candidates due to the breaking of the non--Abelian Grand Unified Theory (GUT) symmetries by Wilson lines. The physical spectrum then contains states that do not satisfy the quantisation conditions of the unbroken GUT symmetry. Given that the Standard Model states are identified with broken GUT representations, and provided that any ensuing symmetry breaking is induced by components of GUT states, leaves a remnant discrete symmetry that forbid the decay of the Wilsonian states. A class of such states are obtained in a heterotic-string derived $Z^\prime$ model. The model exploits the spinor-vector duality symmetry, observed in the fermionic $Z_2\times Z_2$ heterotic-string orbifolds, to generate a $Z^\prime\in E_6$ symmetry that may remain unbroken down to low energies. The $E_6$ symmetry is broken at the string level with discrete Wilson lines. The Wilsonian dark matter candidates in the string derived model are $SO(10)$, and hence Standard Model, singlets and possess non-$E_6$ $U(1)_{Z^\prime}$ charges. Depending on the $U(1)_{Z^\prime}$ breaking scale and the reheating temperature they give rise to different scenarios for the relic abundance, and in accordance with the cosmological constraints.Comment: 24 pages. 5 figures. Standard LaTex. Additional comments and clarifications. Published versio

Study of the Bcl-2 Interactome by BiFC reveals differences in the activation mechanism of Bax and Bak

Evasion of apoptosis is one of the hallmarks of cancer cells. Proteins of the Bcl-2 family are key regulators of the intrinsic pathway of apoptosis, and alterations in some of these proteins are frequently found in cancer cells. Permeabilization of the outer mitochondrial membrane, regulated by pro- and antiapoptotic members of the Bcl-2 family of proteins, is essential for the release of apoptogenic factors leading to caspase activation, cell dismantlement, and death. Mitochondrial permeabilization depends on the formation of oligomers of the effector proteins Bax and Bak after an activation event mediated by BH3-only proteins and regulated by antiapoptotic members of the Bcl-2 family. In the present work, we have studied interactions between different members of the Bcl-2 family in living cells via the BiFC technique. Despite the limitations of this technique, present data suggest that native proteins of the Bcl-2 family acting inside living cells establish a complex network of interactions, which would fit nicely into “mixed” models recently proposed by others. Furthermore, our results point to differences in the regulation of Bax and Bak activation by proteins of the antiapoptotic and BH3-only subfamilies. We have also applied the BiFC technique to explore the different molecular models proposed for Bax and Bak oligomerization. Bax and Bak’s mutants lacking the BH3 domain were still able to associate and give BiFC signals, suggesting the existence of alternative surfaces of interaction between two Bax or Bak molecules. These results agree with the widely accepted symmetric model for the dimerization of these proteins and also suggest that other regions, different from the α6 helix, could be involved in the oligomerization of BH3-in groove dimers

A Next-to-Leading-Order Study of Dihadron Production

The production of pairs of hadrons in hadronic collisions is studied using a next-to-leading-order Monte Carlo program based on the phase space slicing technique. Up-to-date fragmentation functions based on fits to LEP data are employed, together with several versions of current parton distribution functions. Good agreement is found with data for the dihadron mass distribution. A comparison is also made with data for the dihadron angular distribution. The scale dependence of the predictions and the dependence on the choices made for the fragmentation and parton distribution functions are also presented. The good agreement between theory and experiment is contrasted to the case for single $\pi^0$ production where significant deviations between theory and experiment have been observed.Comment: 22 pages, 15 figures; 3 references added, one figure modified for clarit

Examination of direct-photon and pion production in proton-nucleon collisions

We present a study of inclusive direct-photon and pion production in hadronic interactions, focusing on a comparison of the ratio of gamma/pi0 yields with expectations from next-to-leading order perturbative QCD (NLO pQCD). We also examine the impact of a phenomenological model involving k_T smearing (which approximates effects of additional soft-gluon emission) on absolute predictions for photon and pion production and their ratio.Comment: 20 pages, 12 figures. Minor changes in wording and in figure