10,735 research outputs found
Resurrecting Minimal Yukawa Sector of SUSY SO(10)
Supersymmetric models with Yukawa coupling matrices involving only a
and a of Higgs fields can lead to a predictive and
consistent scenario for fermion masses and mixings, including the neutrino
sector. However, when coupled minimally to a symmetry breaking sector that
includes a and a , these models lead either to an unacceptably
small neutrino mass scale, or to non-perturbative values of the gauge
couplings. Here we show that with the addition of a to the symmetry
breaking sector, the successful predictions of these models for fermion masses
and mixings can be maintained. The enables a reduction of the
symmetry breaking scale to an intermediate value of order GeV,
consistent with the observed neutrino mass spectrum, while preserving
perturbative gauge coupling unification. We obtain an excellent fit to all
fermion masses and mixings in this framework. We analyze carefully the
prediction of the model for CP violation in neutrino oscillations. Consistency
with proton lifetime, however, requires a mini-split SUSY spectrum with the
squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale
gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation,
which would predict the partial lifetime for the decay to be an order of magnitude above the current experimental
limit.Comment: 29 pages, 3 figures, replacement to match the published versio
Numerical simulation of Faraday waves
We simulate numerically the full dynamics of Faraday waves in three
dimensions for two incompressible and immiscible viscous fluids. The
Navier-Stokes equations are solved using a finite-difference projection method
coupled with a front-tracking method for the interface between the two fluids.
The domain of calculation is periodic in the horizontal directions and bounded
in the vertical direction by two rigid horizontal plates. The critical
accelerations and wavenumbers, as well as the temporal behaviour at onset are
compared with the results of the linear Floquet analysis of Kumar and Tuckerman
[J. Fluid Mech. 279, 49-68 (1994)]. The finite amplitude results are compared
with the experiments of Kityk et al. [Phys. Rev. E 72, 036209 (2005)]. In
particular we reproduce the detailed spatiotemporal spectrum of both square and
hexagonal patterns within experimental uncertainty
On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units - Steepest Gradient Descent and Natural Gradient Descent -
The permutation symmetry of the hidden units in multilayer perceptrons causes
the saddle structure and plateaus of the learning dynamics in gradient learning
methods. The correlation of the weight vectors of hidden units in a teacher
network is thought to affect this saddle structure, resulting in a prolonged
learning time, but this mechanism is still unclear. In this paper, we discuss
it with regard to soft committee machines and on-line learning using
statistical mechanics. Conventional gradient descent needs more time to break
the symmetry as the correlation of the teacher weight vectors rises. On the
other hand, no plateaus occur with natural gradient descent regardless of the
correlation for the limit of a low learning rate. Analytical results support
these dynamics around the saddle point.Comment: 7 pages, 6 figure
On the Shapley-like Payoff Mechanisms in Peer-Assisted Services with Multiple Content Providers
This paper studies an incentive structure for cooperation and its stability
in peer-assisted services when there exist multiple content providers, using a
coalition game theoretic approach. We first consider a generalized coalition
structure consisting of multiple providers with many assisting peers, where
peers assist providers to reduce the operational cost in content distribution.
To distribute the profit from cost reduction to players (i.e., providers and
peers), we then establish a generalized formula for individual payoffs when a
"Shapley-like" payoff mechanism is adopted. We show that the grand coalition is
unstable, even when the operational cost functions are concave, which is in
sharp contrast to the recently studied case of a single provider where the
grand coalition is stable. We also show that irrespective of stability of the
grand coalition, there always exist coalition structures which are not
convergent to the grand coalition. Our results give us an important insight
that a provider does not tend to cooperate with other providers in
peer-assisted services, and be separated from them. To further study the case
of the separated providers, three examples are presented; (i) underpaid peers,
(ii) service monopoly, and (iii) oscillatory coalition structure. Our study
opens many new questions such as realistic and efficient incentive structures
and the tradeoffs between fairness and individual providers' competition in
peer-assisted services.Comment: 13 pages, 4 figures, an extended version of the paper to be presented
in ICST GameNets 2011, Shanghai, China, April 201
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