91,426 research outputs found
Causality, Analyticity and an IR Obstruction to UV Completion
We argue that certain apparently consistent low-energy effective field
theories described by local, Lorentz-invariant Lagrangians, secretly exhibit
macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix
satisfies canonical analyticity constraints. The obstruction involves the signs
of a set of leading irrelevant operators, which must be strictly positive to
ensure UV analyticity. An IR manifestation of this restriction is that the
"wrong" signs lead to superluminal fluctuations around non-trivial backgrounds,
making it impossible to define local, causal evolution, and implying a
surprising IR breakdown of the effective theory. Such effective theories can
not arise in quantum field theories or weakly coupled string theories, whose
S-matrices satisfy the usual analyticity properties. This conclusion applies to
the DGP brane-world model modifying gravity in the IR, giving a simple
explanation for the difficulty of embedding this model into controlled stringy
backgrounds, and to models of electroweak symmetry breaking that predict
negative anomalous quartic couplings for the W and Z. Conversely, any
experimental support for the DGP model, or measured negative signs for
anomalous quartic gauge boson couplings at future accelerators, would
constitute direct evidence for the existence of superluminality and macroscopic
non-locality unlike anything previously seen in physics, and almost
incidentally falsify both local quantum field theory and perturbative string
theory.Comment: 34 pages, 10 figures; v2: analyticity arguments improved, discussion
on non-commutative theories and minor clarifications adde
Reweighted belief propagation and quiet planting for random K-SAT
We study the random K-satisfiability problem using a partition function where
each solution is reweighted according to the number of variables that satisfy
every clause. We apply belief propagation and the related cavity method to the
reweighted partition function. This allows us to obtain several new results on
the properties of random K-satisfiability problem. In particular the
reweighting allows to introduce a planted ensemble that generates instances
that are, in some region of parameters, equivalent to random instances. We are
hence able to generate at the same time a typical random SAT instance and one
of its solutions. We study the relation between clustering and belief
propagation fixed points and we give a direct evidence for the existence of
purely entropic (rather than energetic) barriers between clusters in some
region of parameters in the random K-satisfiability problem. We exhibit, in
some large planted instances, solutions with a non-trivial whitening core; such
solutions were known to exist but were so far never found on very large
instances. Finally, we discuss algorithmic hardness of such planted instances
and we determine a region of parameters in which planting leads to satisfiable
benchmarks that, up to our knowledge, are the hardest known.Comment: 23 pages, 4 figures, revised for readability, stability expression
correcte
Scale-Invariant Gravity: Geometrodynamics
We present a scale-invariant theory, conformal gravity, which closely
resembles the geometrodynamical formulation of general relativity (GR). While
previous attempts to create scale-invariant theories of gravity have been based
on Weyl's idea of a compensating field, our direct approach dispenses with this
and is built by extension of the method of best matching w.r.t scaling
developed in the parallel particle dynamics paper by one of the authors. In
spatially-compact GR, there is an infinity of degrees of freedom that describe
the shape of 3-space which interact with a single volume degree of freedom. In
conformal gravity, the shape degrees of freedom remain, but the volume is no
longer a dynamical variable. Further theories and formulations related to GR
and conformal gravity are presented.
Conformal gravity is successfully coupled to scalars and the gauge fields of
nature. It should describe the solar system observations as well as GR does,
but its cosmology and quantization will be completely different.Comment: 33 pages. Published version (has very minor style changes due to
changes in companion paper
Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
The Conformal Einstein equations and the representation of spatial infinity
as a cylinder introduced by Friedrich are used to analyse the behaviour of the
gravitational field near null and spatial infinity for the development of data
which are asymptotically Euclidean, conformally flat and time asymmetric. Our
analysis allows for initial data whose second fundamental form is more general
than the one given by the standard Bowen-York Ansatz. The Conformal Einstein
equations imply upon evaluation on the cylinder at spatial infinity a hierarchy
of transport equations which can be used to calculate in a recursive way
asymptotic expansions for the gravitational field. It is found that the the
solutions to these transport equations develop logarithmic divergences at
certain critical sets where null infinity meets spatial infinity. Associated to
these, there is a series of quantities expressible in terms of the initial data
(obstructions), which if zero, preclude the appearance of some of the
logarithmic divergences. The obstructions are, in general, time asymmetric.
That is, the obstructions at the intersection of future null infinity with
spatial infinity are different, and do not generically imply those obtained at
the intersection of past null infinity with spatial infinity. The latter allows
for the possibility of having spacetimes where future and past null infinity
have different degrees of smoothness. Finally, it is shown that if both sets of
obstructions vanish up to a certain order, then the initial data has to be
asymptotically Schwarzschildean to some degree.Comment: 32 pages. First part of a series of 2 papers. Typos correcte
Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
The consistency of the constraint with the evolution equations for spatially
inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands
that the former are preserved along the timelike congruence represented by the
velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This
fact has been used to conjecture that the resulting models correspond to the
spatially homogeneous (SH) models of Bianchi type I, at least for the case
where the cosmological constant vanish. By exploiting the full set of the
constraint equations as expressed in the 1+3 covariant formalism and using
elements from the theory of the spacelike congruences, we provide a direct and
simple proof of this conjecture for vacuum and dust fluid models, which shows
that the Szekeres family of solutions represents the most general class of SIIS
models. The suggested procedure also shows that, the uniqueness of the SIIS of
the Petrov type D is not, in general, affected by the presence of a non-zero
pressure fluid. Therefore, in order to allow a broader class of Petrov type I
solutions apart from the SH models of Bianchi type I, one should consider more
general ``silent'' configurations by relaxing the vanishing of the vorticity
and the magnetic part of the Weyl tensor but maintaining their ``silence''
properties i.e. the vanishing of the curls of and the pressure
.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an
appendix are added; (v3) minor changes to match published versio
A stability result for purely radiative spacetimes
An existence and stability result for a class of purely radiative vacuum
spacetimes arising from hyperboloidal data is given. This result generalises
semiglobal existence results for Minkowski-like spacetimes to the case where
the reference solution contains gravitational radiation. The analysis makes use
of the extended conformal field equations and a gauge based on conformal
geodesics so that the location and structure of the conformal boundary of the
perturbed solutions is known a priori.Comment: 25 pages, 4 figure
Robust Processing of Natural Language
Previous approaches to robustness in natural language processing usually
treat deviant input by relaxing grammatical constraints whenever a successful
analysis cannot be provided by ``normal'' means. This schema implies, that
error detection always comes prior to error handling, a behaviour which hardly
can compete with its human model, where many erroneous situations are treated
without even noticing them.
The paper analyses the necessary preconditions for achieving a higher degree
of robustness in natural language processing and suggests a quite different
approach based on a procedure for structural disambiguation. It not only offers
the possibility to cope with robustness issues in a more natural way but
eventually might be suited to accommodate quite different aspects of robust
behaviour within a single framework.Comment: 16 pages, LaTeX, uses pstricks.sty, pstricks.tex, pstricks.pro,
pst-node.sty, pst-node.tex, pst-node.pro. To appear in: Proc. KI-95, 19th
German Conference on Artificial Intelligence, Bielefeld (Germany), Lecture
Notes in Computer Science, Springer 199
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