1,887 research outputs found
On the solution of the initial value constraints for general relativity coupled to matter in terms of Ashtekar's variables
The method of solution of the initial value constraints for pure canonical
gravity in terms of Ashtekar's new canonical variables due to CDJ is further
developed in the present paper. There are 2 new main results : 1) We extend the
method of CDJ to arbitrary matter-coupling again for non-degenerate metrics :
the new feature is that the 'CDJ-matrix' adopts a nontrivial antisymmetric part
when solving the vector constraint and that the Klein-Gordon-field is used,
instead of the symmetric part of the CDJ-matrix, in order to satisfy the scalar
constraint. 2) The 2nd result is that one can solve the general initial value
constraints for arbitrary matter coupling by a method which is completely
independent of that of CDJ. It is shown how the Yang-Mills and gravitational
Gauss constraints can be solved explicitely for the corresponding electric
fields. The rest of the constraints can then be satisfied by using either
scalar or spinor field momenta. This new trick might be of interest also for
Yang-Mills theories on curved backgrounds.Comment: Latex, 15 pages, PITHA93-1, January 9
Learning SO(3) Equivariant Representations with Spherical CNNs
We address the problem of 3D rotation equivariance in convolutional neural
networks. 3D rotations have been a challenging nuisance in 3D classification
tasks requiring higher capacity and extended data augmentation in order to
tackle it. We model 3D data with multi-valued spherical functions and we
propose a novel spherical convolutional network that implements exact
convolutions on the sphere by realizing them in the spherical harmonic domain.
Resulting filters have local symmetry and are localized by enforcing smooth
spectra. We apply a novel pooling on the spectral domain and our operations are
independent of the underlying spherical resolution throughout the network. We
show that networks with much lower capacity and without requiring data
augmentation can exhibit performance comparable to the state of the art in
standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio
Mass varying dark matter in effective GCG scenarios
A unified treatment of mass varying dark matter coupled to cosmon-{\em like}
dark energy is shown to result in {\em effective} generalized Chaplygin gas
(GCG) scenarios. The mass varying mechanism is treated as a cosmon field
inherent effect. Coupling dark matter with dark energy allows for reproducing
the conditions for the present cosmic acceleration and for recovering the
stability resulted from a positive squared speed of sound c_{s}^{\2}, as in
the GCG scenario. The scalar field mediates the nontrivial coupling between the
dark matter sector and the sector responsible for the accelerated expansion of
the universe. The equation of state of perturbations is the same as that of the
background cosmology so that all the effective results from the GCG paradigm
are maintained. Our results suggest the mass varying mechanism, when obtained
from an exactly soluble field theory, as the right responsible for the
stability issue and for the cosmic acceleration of the universe.Comment: 17 pages, 3 figure
Constructive factorization of LPDO in two variables
We study conditions under which a partial differential operator of arbitrary
order in two variables or ordinary linear differential operator admits a
factorization with a first-order factor on the left. The factorization process
consists of solving, recursively, systems of linear equations, subject to
certain differential compatibility conditions. In the generic case of partial
differential operators one does not have to solve a differential equation. In
special degenerate cases, such as ordinary differential, the problem is finally
reduced to the solution of some Riccati equation(s). The conditions of
factorization are given explicitly for second- and, and an outline is given for
the higher-order case.Comment: 16 pages, to be published in Journal "Theor. Math. Phys." (2005
Towards Loop Quantization of Plane Gravitational Waves
The polarized Gowdy model in terms of Ashtekar-Barbero variables is further
reduced by including the Killing equations for plane-fronted parallel
gravitational waves with parallel rays. The resulting constraint algebra,
including one constraint derived from the Killing equations in addition to the
standard ones of General Relativity, are shown to form a set of first-class
constraints. Using earlier work by Banerjee and Date the constraints are
expressed in terms of classical quantities that have an operator equivalent in
Loop Quantum Gravity, making space-times with pp-waves accessible to loop
quantization techniques.Comment: 14 page
Comparing persistence diagrams through complex vectors
The natural pseudo-distance of spaces endowed with filtering functions is
precious for shape classification and retrieval; its optimal estimate coming
from persistence diagrams is the bottleneck distance, which unfortunately
suffers from combinatorial explosion. A possible algebraic representation of
persistence diagrams is offered by complex polynomials; since far polynomials
represent far persistence diagrams, a fast comparison of the coefficient
vectors can reduce the size of the database to be classified by the bottleneck
distance. This article explores experimentally three transformations from
diagrams to polynomials and three distances between the complex vectors of
coefficients.Comment: 11 pages, 4 figures, 2 table
Renormalization of heavy-light currents in moving NRQCD
Heavy-light decays such as , and can be used to constrain the parameters of the Standard
Model and in indirect searches for new physics. While the precision of
experimental results has improved over the last years this has still to be
matched by equally precise theoretical predictions. The calculation of
heavy-light form factors is currently carried out in lattice QCD. Due to its
small Compton wavelength we discretize the heavy quark in an effective
non-relativistic theory. By formulating the theory in a moving frame of
reference discretization errors in the final state are reduced at large recoil.
Over the last years the formalism has been improved and tested extensively.
Systematic uncertainties are reduced by renormalizing the m(oving)NRQCD action
and heavy-light decay operators. The theory differs from QCD only for large
loop momenta at the order of the lattice cutoff and the calculation can be
carried out in perturbation theory as an expansion in the strong coupling
constant. In this paper we calculate the one loop corrections to the
heavy-light vector and tensor operator. Due to the complexity of the action the
generation of lattice Feynman rules is automated and loop integrals are solved
by the adaptive Monte Carlo integrator VEGAS. We discuss the infrared and
ultraviolet divergences in the loop integrals both in the continuum and on the
lattice. The light quarks are discretized in the ASQTad and highly improved
staggered quark (HISQ) action; the formalism is easily extended to other quark
actions.Comment: 24 pages, 11 figures. Published in Phys. Rev. D. Corrected a typo in
eqn. (51
Neurogenic to Gliogenic Fate Transition Perturbed by Loss of HMGB2
Mouse cortical development relies heavily on a delicate balance between neurogenesis and gliogenesis. The lateral ventricular zone produces different classes of excitatory pyramidal cells until just before birth, when the production of astroglia begins to prevail. Epigenetic control of this fate shift is of critical importance and chromatin regulatory elements driving neuronal or astroglial development play an vital role. Different classes of chromatin binding proteins orchestrate the transcriptional repression of neuronal-specific genes, while allowing for the activation of astrocyte-specific genes. Through proteomic analysis of embryonic neural progenitor cells (NPCs) our group had previously identified high mobility group B2 (HMGB2), a chromatin protein dynamically expressed throughout embryonic development. In the current study using cultures of perinatal NPCs from HMGB2+/+ and HMGB2-/- mice we discovered that vital elements of the polycomb group (PcG) epigenetic complexes polycomb repressive complexes 1 and 2 (PRC1/2) were downregulated during the differentiation process of HMGB2-null NPCs. These epigenetic changes led to downstream changes in specific histone modification levels, specifically the trimethylation of H3K27, and a subsequent shift in the perinatal neurogenesis to gliogenesis fate transition. Collectively these results demonstrate that chromatin binding proteins, such as HMGB2, can have significant effects on the epigenetic landscape of perinatal neural stem/progenitor cells
Differentiable Graph Module (DGM) for Graph Convolutional Networks
Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. One of the limitations of the majority of current graph neural network architectures is that they are often restricted to the transductive setting and rely on the assumption that the underlying graph is known and fixed. Often, this assumption is not true since the graph may be noisy, or partially and even completely unknown. In such cases, it would be helpful to infer the graph directly from the data, especially in inductive settings where some nodes were not present in the graph at training time. Furthermore, learning a graph may become an end in itself, as the inferred structure may provide complementary insights next to the downstream task. In this paper, we introduce Differentiable Graph Module (DGM), a learnable function that predicts edge probabilities in the graph which are optimal for the downstream task. DGM can be combined with convolutional graph neural network layers and trained in an end-to-end fashion. We provide an extensive evaluation on applications in healthcare, brain imaging, computer graphics, and computer vision showing a significant improvement over baselines both in transductive and inductive settings
Interacting dark energy in gravity
The field equations in gravity derived from the Palatini variational
principle and formulated in the Einstein conformal frame yield a cosmological
term which varies with time. Moreover, they break the conservation of the
energy--momentum tensor for matter, generating the interaction between matter
and dark energy. Unlike phenomenological models of interacting dark energy,
gravity derives such an interaction from a covariant Lagrangian which is
a function of a relativistically invariant quantity (the curvature scalar ).
We derive the expressions for the quantities describing this interaction in
terms of an arbitrary function , and examine how the simplest
phenomenological models of a variable cosmological constant are related to
gravity. Particularly, we show that for a flat,
homogeneous and isotropic, pressureless universe. For the Lagrangian of form
, which is the simplest way of introducing current cosmic acceleration
in gravity, the predicted matter--dark energy interaction rate changes
significantly in time, and its current value is relatively weak (on the order
of 1% of ), in agreement with astronomical observations.Comment: 8 pages; published versio
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