21,160 research outputs found
Approximating the partition function of the ferromagnetic Potts model
We provide evidence that it is computationally difficult to approximate the
partition function of the ferromagnetic q-state Potts model when q>2.
Specifically we show that the partition function is hard for the complexity
class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard
to approximate the partition function as it is to find approximate solutions to
a wide range of counting problems, including that of determining the number of
independent sets in a bipartite graph. Our proof exploits the first order phase
transition of the "random cluster" model, which is a probability distribution
on graphs that is closely related to the q-state Potts model.Comment: Minor correction
Spinors, Jets, and the Einstein Equations
Many important features of a field theory, {\it e.g.}, conserved currents,
symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors
locally constructed from the fields and their derivatives. Such tensors are
naturally defined as geometric objects on the jet space of solutions to the
field equations. Modern results from the calculus on jet bundles can be
combined with a powerful spinor parametrization of the jet space of Einstein
metrics to unravel basic features of the Einstein equations. These techniques
have been applied to computation of generalized symmetries and ``characteristic
cohomology'' of the Einstein equations, and lead to results such as a proof of
non-existence of ``local observables'' for vacuum spacetimes and a uniqueness
theorem for the gravitational symplectic structure.Comment: to appear in the proceedings of the Sixth Canadian Conference on
General Relativity and Relativistic Astrophysics, 13 pages, uses AMSTeX and
AMSppt.st
Productive Corecursion in Logic Programming
Logic Programming is a Turing complete language. As a consequence, designing
algorithms that decide termination and non-termination of programs or decide
inductive/coinductive soundness of formulae is a challenging task. For example,
the existing state-of-the-art algorithms can only semi-decide coinductive
soundness of queries in logic programming for regular formulae. Another, less
famous, but equally fundamental and important undecidable property is
productivity. If a derivation is infinite and coinductively sound, we may ask
whether the computed answer it determines actually computes an infinite
formula. If it does, the infinite computation is productive. This intuition was
first expressed under the name of computations at infinity in the 80s. In
modern days of the Internet and stream processing, its importance lies in
connection to infinite data structure processing.
Recently, an algorithm was presented that semi-decides a weaker property --
of productivity of logic programs. A logic program is productive if it can give
rise to productive derivations. In this paper we strengthen these recent
results. We propose a method that semi-decides productivity of individual
derivations for regular formulae. Thus we at last give an algorithmic
counterpart to the notion of productivity of derivations in logic programming.
This is the first algorithmic solution to the problem since it was raised more
than 30 years ago. We also present an implementation of this algorithm.Comment: Paper presented at the 33nd International Conference on Logic
Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017
16 pages, LaTeX, no figure
The competitive environment of the European electricity sector in the post-Kyoto scenarios
This paper shows how the uncertainty associated to the absence of a post-Kyoto regime regarding Greenhouse Gas mitigation is affecting investments in mitigation activities in the EU electricity sector and, thus, future emissions levels. Based on a wide survey of EU power companies, the paper identifies the most likely post-Kyoto scenarios considered by these firms and how they are coping with such uncertainty in their current investment decisions. The major conclusion is that the non-existence of a post-Kyoto regime is having a negative effect on current business investment decisions in mitigation activities, increasing risk premiums and financing costs. All in all, the companies surveyed foresee post-Kyoto compliance regimes with emissions trading systems that would guarantee the continuity of the value of the reductions made beforehand, although they differ in their perceptions of the form that a post-Kyoto regime could take.Post-Kyoto scenarios; EU electricity sector; investment decisions
Quantization of Midisuperspace Models
We give a comprehensive review of the quantization of midisuperspace models.
Though the main focus of the paper is on quantum aspects, we also provide an
introduction to several classical points related to the definition of these
models. We cover some important issues, in particular, the use of the principle
of symmetric criticality as a very useful tool to obtain the required
Hamiltonian formulations. Two main types of reductions are discussed: those
involving metrics with two Killing vector fields and spherically symmetric
models. We also review the more general models obtained by coupling matter
fields to these systems. Throughout the paper we give separate discussions for
standard quantizations using geometrodynamical variables and those relying on
loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit
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