On neutrino and charged lepton masses and mixings: A view from the electroweak-scale right-handed neutrino model

We present a model of neutrino masses within the framework of the EW-$\nu_R$ model in which the experimentally desired form of the PMNS matrix is obtained by applying an $A_4$ symmetry to the \emph{Higgs singlet sector} responsible for the neutrino Dirac mass matrix. This mechanism naturally avoids potential conflict with the LHC data which severely constrains the Higgs sector, in particular the Higgs doublets. Moreover, by making a simple $ans\ddot{a}tz$ we extract $\mathcal{M}_l {\mathcal{M}_l}^\dagger$ for the charged lepton sector. A similar $ans\ddot{a}tz$ is proposed for the quark sector. The sources of masses for the neutrinos are entirely different from those for the charged leptons and for the quarks and this might explain why $U_{PMNS}$ is {\em very different} from $V_{CKM}$.Comment: 19 pages. Two figure

Lepton Flavor Violating Radiative Decays in EW-Scale νR\nu_R Model: An Update

We perform an updated analysis for the one-loop induced lepton flavor violating radiative decays $l_i \to l_j \gamma$ in an extended mirror model. Mixing effects of the neutrinos and charged leptons constructed with a horizontal $A_4$ symmetry are also taken into account. Current experimental limit and projected sensitivity on the branching ratio of $\mu \to e \gamma$ are used to constrain the parameter space of the model. Calculations of two related observables, the electric and magnetic dipole moments of the leptons, are included. Implications concerning the possible detection of mirror leptons at the LHC and the ILC are also discussed.Comment: 9 figures, 36 single-side pages. Updated email addresses and referenc

Two applications of elementary knot theory to Lie algebras and Vassiliev invariants

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis, Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan, January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give, respectively, the exact Kontsevich integral of the unknot and a map intertwining two natural products on a space of diagrams. It turns out that the Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on a wire), and its intertwining property is analogous to the computation of 1+1=2 on an abacus. The Wheels conjecture is proved from the fact that the k-fold connected cover of the unknot is the unknot for all k. Along the way, we find a formula for the invariant of the general (k,l) cable of a knot. Our results can also be interpreted as a new proof of the multiplicativity of the Duflo-Kirillov map S(g)-->U(g) for metrized Lie (super-)algebras g.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper1.abs.htm

Weak local rules for planar octagonal tilings

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure

On the resource allocation for D2D underlaying uplink cellular networks

Device-to-Device (D2D) communications has attracted research interests as an emerging technology towards 5G and beyond cellular networks. In this paper, we investigate the power allocation in D2D underlaying cellular networks with uplink channel reuse. We first develop an optimization problem to minimize the total power consumption subject to per- user Quality-of-Service (QoS) constraints. A distributed power allocation algorithm is proposed to allocate the power for both D2D and cellular users by exploiting the property of strictly non-negative inverse of a Z-matrix. It is shown that the power allocated for users can be considerably saved for low QoS requirements, especially with a large number of D2D users. The proposed algorithm is validated through simulation to realize the impacts of noise power, distance between D2D users and the number of D2D pairs in the network

An optimal power allocation for D2D communications over multi-user cellular uplink channels

Device-to-Device (D2D) communications has emerged as a promising technology for optimizing spectral efficiency, reducing latency, improving data rate and increasing system capacity in cellular networks. Power allocation in D2D communication to maintain Quality-of-Service (QoS) remains as a challenging task. In this paper, we investigate the power allocation in D2D underlaying cellular networks with multi-user cellular uplink channel reuse. Specifically, this paper aims at minimizing the total transmit power of D2D users and cellular users (CUs) sub- ject to QoS requirement at each user in terms of the required signal-to- interference-plus-noise ratio (SINR) at D2D users and base station (BS) over uplink channel as well as their limited transmit power. We first derive expressions of SINR at the D2D users and BS based on which an optimization framework for power allocation is developed. We then propose an optimal power allocation algorithm for all D2D users and CUs by taking into account the property of non-negative inverse of a Z- matrix. The proposed algorithm is validated through simulation results which show the impacts of noise power, distance between D2D users, the number of D2D pairs and the number of CUs on the power allocation in the D2D underlaying cellular networks

Fundamental Limits of Low-Density Spreading NOMA with Fading

Spectral efficiency of low-density spreading non-orthogonal multiple access channels in the presence of fading is derived for linear detection with independent decoding as well as optimum decoding. The large system limit, where both the number of users and number of signal dimensions grow with fixed ratio, called load, is considered. In the case of optimum decoding, it is found that low-density spreading underperforms dense spreading for all loads. Conversely, linear detection is characterized by different behaviors in the underloaded vs. overloaded regimes. In particular, it is shown that spectral efficiency changes smoothly as load increases. However, in the overloaded regime, the spectral efficiency of low- density spreading is higher than that of dense spreading

Kontsevich integral for knots and Vassiliev invariants

We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal gauge considerations which lead to representation of Vassiliev invariants in terms of arrow diagrams. Explicit examples and computational results are presented.Comment: 25 pages, 17 figure