Finite Unified Models

We present phenomenologically viable $SU(5)$ unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV.Comment: 13 pages, latex fil

Weighted Multiplex Networks

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topology of complex multiplex networks. To this end, we study two weighted multiplex co-authorship and citation networks involving the authors included in the American Physical Society. We show that in these networks weights are strongly correlated with multiplex structure, and provide empirical evidence in favor of the advantage of studying weighted measures of multiplex networks, such as multistrength and the inverse multiparticipation ratio. Finally, we introduce a theoretical framework based on the entropy of multiplex ensembles to quantify the information stored in multiplex networks that would remain undetected if the single layers were analyzed in isolation.Comment: (22 pages, 10 figures

Yukawa terms in noncommutative SO(10) and E6 GUTs

We propose a method for constructing Yukawa terms for noncommutative SO(10) and E6 GUTs, when these GUTs are formulated within the enveloping-algebra formalism. The most general noncommutative Yukawa term that we propose contains, at first order in thetamunu, the most general BRS invariant Yukawa contribution whose only dimensionful parameter is the noncommutativity parameter. This noncommutative Yukawa interaction is thus renormalisable at first order in thetamunu.Comment: 14 pages, no figure

Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.Comment: 23 pages, 7 figure

The high-lying 6^6Li levels at excitation energy around 21 MeV

The $^3$H+$^3$He cluster structure in $^6$Li was investigated by the $^3$H($\alpha$,$^3$H $^3$He)n kinematically complete experiment at the incident energy $E_\alpha$ = 67.2 MeV. We have observed two resonances at $E_x^*$ = 21.30 and 21.90 MeV which are consistent with the $^3$He($^3$H, $\gamma$)$^6$Li analysis in the Ajzenberg-Selove compilation. Our data are compared with the previous experimental data and the RGM and CSRGM calculations.Comment: 12 pages, 6 figures. Accepted for publication in J. Phys. Soc. Jp