108,401 research outputs found
Gravitational dynamics in a 2+1+1 decomposed spacetime along nonorthogonal double foliations: Hamiltonian evolution and gauge fixing
Motivated by situations with temporal evolution and spatial symmetries both
singled out, we develop a new 2+1+1 decomposition of spacetime, based on a
nonorthogonal double foliation. Time evolution proceeds along the leaves of the
spatial foliation. We identify the gravitational variables in the velocity
phase-space as the 2-metric (induced on the intersection of
the hypersurfaces of the foliations), the 2+1 components of the spatial shift
vector, together with the extrinsic curvature, normal fundamental form and
normal fundamental scalar of , all constructed with the
normal to the temporal foliation. This work generalizes a previous
decomposition based on orthogonal foliations, a formalism lacking one metric
variable, now reintroduced. The new metric variable is related to (i) the angle
of a Lorentz-rotation between the nonorthogonal bases adapted to the
foliations, and (ii) to the vorticity of these basis vectors. As a first
application of the formalism, we work out the Hamiltonian dynamics of general
relativity in terms of the variables identified as canonical, generalizing
previous work. As a second application we present the unambiguous gauge-fixing
suitable to discuss the even sector scalar-type perturbations of spherically
symmetric and static spacetimes in generic scalar-tensor gravitational
theories, which has been obstructed in the formalism of orthogonal double
foliation.Comment: 16 pages, 4 figures, to appear in Phys. Rev.
The Spectrum of the 4-Generation Dirac-Kaehler Extension of the SM
We compute the mass spectrum of the fermionic sector of the Dirac-Kaehler
extension of the SM (DK-SM) by showing that there exists a Bogoliubov
transformation that transforms the DK-SM into a flavor U(4) extension of the SM
(SM-4) with a particular choice of masses and mixing textures. Mass relations
of the model allow determination of masses of the 4th generation. Tree level
prediction for the mass of the 4th charged lepton is 370 GeV. The model selects
the normal hierarchy for neutrino masses and reproduces naturally the near
tri-bimaximal and quark mixing textures. The electron neutrino and the 4th
neutrino masses are related via a see-saw-like mechanism.Comment: 14 pages. Phys Lett B versio
Invariant-based approach to symmetry class detection
In this paper, the problem of the identification of the symmetry class of a
given tensor is asked. Contrary to classical approaches which are based on the
spectral properties of the linear operator describing the elasticity, our
setting is based on the invariants of the irreducible tensors appearing in the
harmonic decomposition of the elasticity tensor [Forte-Vianello, 1996]. To that
aim we first introduce a geometrical description of the space of elasticity
tensors. This framework is used to derive invariant-based conditions that
characterize symmetry classes. For low order symmetry classes, such conditions
are given on a triplet of quadratic forms extracted from the harmonic
decomposition of the elasticity tensor , meanwhile for higher-order classes
conditions are provided in terms of elements of , the higher irreducible
space in the decomposition of . Proceeding in such a way some well known
conditions appearing in the Mehrabadi-Cowin theorem for the existence of a
symmetry plane are retrieved, and a set of algebraic relations on polynomial
invariants characterizing the orthotropic, trigonal, tetragonal, transverse
isotropic and cubic symmetry classes are provided. Using a genericity
assumption on the elasticity tensor under study, an algorithm to identify the
symmetry class of a large set of tensors is finally provided.Comment: 32 page
Complex Embeddings for Simple Link Prediction
In statistical relational learning, the link prediction problem is key to
automatically understand the structure of large knowledge bases. As in previous
studies, we propose to solve this problem through latent factorization.
However, here we make use of complex valued embeddings. The composition of
complex embeddings can handle a large variety of binary relations, among them
symmetric and antisymmetric relations. Compared to state-of-the-art models such
as Neural Tensor Network and Holographic Embeddings, our approach based on
complex embeddings is arguably simpler, as it only uses the Hermitian dot
product, the complex counterpart of the standard dot product between real
vectors. Our approach is scalable to large datasets as it remains linear in
both space and time, while consistently outperforming alternative approaches on
standard link prediction benchmarks.Comment: 10+2 pages, accepted at ICML 201
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