2,482 research outputs found
On the expected number of perfect matchings in cubic planar graphs
A well-known conjecture by Lov\'asz and Plummer from the 1970s asserted that
a bridgeless cubic graph has exponentially many perfect matchings. It was
solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other
hand, Chudnovsky and Seymour (Combinatorica 2012) proved the conjecture in the
special case of cubic planar graphs. In our work we consider random bridgeless
cubic planar graphs with the uniform distribution on graphs with vertices.
Under this model we show that the expected number of perfect matchings in
labeled bridgeless cubic planar graphs is asymptotically , where
and is an explicit algebraic number. We also
compute the expected number of perfect matchings in (non necessarily
bridgeless) cubic planar graphs and provide lower bounds for unlabeled graphs.
Our starting point is a correspondence between counting perfect matchings in
rooted cubic planar maps and the partition function of the Ising model in
rooted triangulations.Comment: 19 pages, 4 figure
Enumeration of labelled 4-regular planar graphs
We present the first combinatorial scheme for counting labelled 4-regular
planar graphs through a complete recursive decomposition. More precisely, we
show that the exponential generating function of labelled 4-regular planar
graphs can be computed effectively as the solution of a system of equations,
from which the coefficients can be extracted. As a byproduct, we also enumerate
labelled 3-connected 4-regular planar graphs, and simple 4-regular rooted maps
Memoization for Unary Logic Programming: Characterizing PTIME
We give a characterization of deterministic polynomial time computation based
on an algebraic structure called the resolution semiring, whose elements can be
understood as logic programs or sets of rewriting rules over first-order terms.
More precisely, we study the restriction of this framework to terms (and logic
programs, rewriting rules) using only unary symbols. We prove it is complete
for polynomial time computation, using an encoding of pushdown automata. We
then introduce an algebraic counterpart of the memoization technique in order
to show its PTIME soundness. We finally relate our approach and complexity
results to complexity of logic programming. As an application of our
techniques, we show a PTIME-completeness result for a class of logic
programming queries which use only unary function symbols.Comment: Soumis {\`a} LICS 201
Structural health monitoring of high voltage electrical switch ceramic insulators in seismic areas
High voltage electrical switches are crucial components to restart rapidly the electrical network right after an earthquake. But there currently exists no automatic procedure to check if these ceramic insulators have suffered after an earthquake, and there exists no method to recertify a given switch. To deploy a vibration-based structural health monitoring method on ceramic insulators a large shake table able to generate accelerations up to 3 g was used. The idea underlying the SHM procedure proposed here is to monitor the apparition of cracks in the ceramic insulators at their early stage through the change of the resonant frequency of the first mode of the structure and the non-linearity that they generate in its dynamic response. The Exponential Sine Sweep Method is used to estimate a nonlinear model of the structure under test from only one dynamic measurement. A classic linear damage index (DI) based on the variation of the frequency of the first mode is compared to an original nonlinear one using the ratio of the amplitudes of the third harmonic and the fundamental frequency. Results show that both DIs increase monotonically with the number of solicitations, thus validating the use of the nonlinear DI. It is also shown that the nonlinear DI presented here seems more sensitive than the linear one
Density estimation on an unknown submanifold
We investigate density estimation from a -sample in the Euclidean space , when the data is supported by an unknown submanifold of possibly unknown dimension under a reach condition. We study nonparametric kernel methods for pointwise and integrated loss, with data-driven bandwidths that incorporate some learning of the geometry via a local dimension estimator. When has H\"older smoothness and has regularity in a sense to be defined, our estimator achieves the rate and does not depend on the ambient dimension and is asymptotically minimax for . Following Lepski's principle, a bandwidth selection rule is shown to achieve smoothness adaptation. We also investigate the case : by estimating in some sense the underlying geometry of , we establish in dimension that the minimax rate is proving in particular that it does not depend on the regularity of . Finally, a numerical implementation is conducted on some case studies in order to confirm the practical feasibility of our estimators
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and Nlogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is rooted in proof
theory and more specifically linear logic and geometry of interaction. We show
how to build a model of computation in the unification algebra and then, by
means of a syntactic representation of finite permutations in the algebra, we
prove that whether an observation (the algebraic counterpart of a program)
accepts a word can be decided within logarithmic space. Finally, we show that
the construction naturally corresponds to pointer machines, a convenient way of
understanding logarithmic space computation.Comment: arXiv admin note: text overlap with arXiv:1402.432
Unification and Logarithmic Space: Journal Version
Soumis au numéro spécial de LMCS pour RTA/TLCA 2014 ( http://www.lmcs-online.org/ojs/specialIssues.php?id=67 )We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, an convenient way of understanding logarithmic space computation
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