4,598 research outputs found
ATLsc with partial observation
Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful
formalism for expressing properties of multi-agent systems: it extends CTL with
strategy quantifiers, offering a convenient way of expressing both
collaboration and antagonism between several agents. Incomplete observation of
the state space is a desirable feature in such a framework, but it quickly
leads to undecidable verification problems. In this paper, we prove that
uniform incomplete observation (where all players have the same observation)
preserves decidability of the model-checking problem, even for very expressive
logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Dimensional contraction via Markov transportation distance
It is now well known that curvature conditions \`a la Bakry-Emery are
equivalent to contraction properties of the heat semigroup with respect to the
classical quadratic Wasserstein distance. However, this curvature condition may
include a dimensional correction which up to now had not induced any
strenghtening of this contraction. We first consider the simplest example of
the Euclidean heat semigroup, and prove that indeed it is so. To consider the
case of a general Markov semigroup, we introduce a new distance between
probability measures, based on the semigroup, and adapted to it. We prove that
this Markov transportation distance satisfies the same properties for a general
Markov semigroup as the Wasserstein distance does in the specific case of the
Euclidean heat semigroup, namely dimensional contraction properties and
Evolutional variational inequalities
Annotation of Tribolium nuclear receptors reveals an evolutionary overacceleration of a network controlling the ecdysone cascade
The Tribolium genome contains 21 nuclear receptors, representing all of the
six known subfamilies. When compared to other species, this first complete set
for a Coleoptera reveals a strong conservation of the number and identity of
nuclear receptors in holometabolous insects. Two novelties are observed: the
atypical NR0 gene knirps is present only in brachyceran flies, while the NR2E6
gene is found only in Tribolium and in Apis. Using a quantitative analysis of
the evolutionary rate, we discovered that nuclear receptors could be divided
into two groups. In one group of 13 proteins, the rates follow the trend of the
Mecopterida genome-wide acceleration. In a second group of five nuclear
receptors, all acting together at the top of the ecdysone cascade, we observed
an overacceleration of the evolutionary rate during the early divergence of
Mecopterida. We thus extended our analysis to the twelve classic ecdysone
transcriptional regulators and found that six of them (ECR, USP, HR3, E75, HR4
and Kr-h1) underwent an overacceleration at the base of the Mecopterida
lineage. By contrast, E74, E93, BR, HR39, FTZ-F1 and E78 do not show this
divergence. We suggest that coevolution occurred within a network of regulators
that control the ecdysone cascade. The advent of Tribolium as a powerful model
should allow a better understanding of this evolution
Non ultracontractive heat kernel bounds by Lyapunov conditions
Nash and Sobolev inequalities are known to be equivalent to ultracontractive
properties of heat-like Markov semigroups, hence to uniform on-diagonal bounds
on their kernel densities. In non ultracontractive settings, such bounds can
not hold, and (necessarily weaker, non uniform) bounds on the semigroups can be
derived by means of weighted Nash (or super-Poincar\'e) inequalities. The
purpose of this note is to show how to check these weighted Nash inequalities
in concrete examples, in a very simple and general manner. We also deduce
off-diagonal bounds for the Markov kernels of the semigroups, refining E. B.
Davies' original argument
On the Linear Extension Complexity of Regular n-gons
In this paper, we propose new lower and upper bounds on the linear extension
complexity of regular -gons. Our bounds are based on the equivalence between
the computation of (i) an extended formulation of size of a polytope ,
and (ii) a rank- nonnegative factorization of a slack matrix of the polytope
. The lower bound is based on an improved bound for the rectangle covering
number (also known as the boolean rank) of the slack matrix of the -gons.
The upper bound is a slight improvement of the result of Fiorini, Rothvoss and
Tiwary [Extended Formulations for Polygons, Discrete Comput. Geom. 48(3), pp.
658-668, 2012]. The difference with their result is twofold: (i) our proof uses
a purely algebraic argument while Fiorini et al. used a geometric argument, and
(ii) we improve the base case allowing us to reduce their upper bound by one when for some integer . We conjecture that this new upper bound
is tight, which is suggested by numerical experiments for small . Moreover,
this improved upper bound allows us to close the gap with the best known lower
bound for certain regular -gons (namely, and ) hence allowing for the first time to determine their extension
complexity.Comment: 20 pages, 3 figures. New contribution: improved lower bound for the
boolean rank of the slack matrices of n-gon
Algorithms for Positive Semidefinite Factorization
This paper considers the problem of positive semidefinite factorization (PSD
factorization), a generalization of exact nonnegative matrix factorization.
Given an -by- nonnegative matrix and an integer , the PSD
factorization problem consists in finding, if possible, symmetric -by-
positive semidefinite matrices and such
that for , and . PSD
factorization is NP-hard. In this work, we introduce several local optimization
schemes to tackle this problem: a fast projected gradient method and two
algorithms based on the coordinate descent framework. The main application of
PSD factorization is the computation of semidefinite extensions, that is, the
representations of polyhedrons as projections of spectrahedra, for which the
matrix to be factorized is the slack matrix of the polyhedron. We compare the
performance of our algorithms on this class of problems. In particular, we
compute the PSD extensions of size for the
regular -gons when , and . We also show how to generalize our
algorithms to compute the square root rank (which is the size of the factors in
a PSD factorization where all factor matrices and have rank one)
and completely PSD factorizations (which is the special case where the input
matrix is symmetric and equality is required for all ).Comment: 21 pages, 3 figures, 3 table
Sparsity-Promoting Bayesian Dynamic Linear Models
Sparsity-promoting priors have become increasingly popular over recent years
due to an increased number of regression and classification applications
involving a large number of predictors. In time series applications where
observations are collected over time, it is often unrealistic to assume that
the underlying sparsity pattern is fixed. We propose here an original class of
flexible Bayesian linear models for dynamic sparsity modelling. The proposed
class of models expands upon the existing Bayesian literature on sparse
regression using generalized multivariate hyperbolic distributions. The
properties of the models are explored through both analytic results and
simulation studies. We demonstrate the model on a financial application where
it is shown that it accurately represents the patterns seen in the analysis of
stock and derivative data, and is able to detect major events by filtering an
artificial portfolio of assets
Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful
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