9,464 research outputs found
Bifurcations and singularities for coupled oscillators with inertia and frustration
We prove that any non zero inertia, however small, is able to change the
nature of the synchronization transition in Kuramoto-like models, either from
continuous to discontinuous, or from discontinuous to continuous. This result
is obtained through an unstable manifold expansion in the spirit of J.D.
Crawford, which features singularities in the vicinity of the bifurcation. Far
from being unwanted artifacts, these singularities actually control the
qualitative behavior of the system. Our numerical tests fully support this
picture.Comment: 10 pages, 2 figure
Stratified Static Analysis Based on Variable Dependencies
In static analysis by abstract interpretation, one often uses widening
operators in order to enforce convergence within finite time to an inductive
invariant. Certain widening operators, including the classical one over finite
polyhedra, exhibit an unintuitive behavior: analyzing the program over a subset
of its variables may lead a more precise result than analyzing the original
program! In this article, we present simple workarounds for such behavior
Random-bit optimal uniform sampling for rooted planar trees with given sequence of degrees and Applications
In this paper, we redesign and simplify an algorithm due to Remy et al. for
the generation of rooted planar trees that satisfies a given partition of
degrees. This new version is now optimal in terms of random bit complexity, up
to a multiplicative constant. We then apply a natural process
"simulate-guess-and-proof" to analyze the height of a random Motzkin in
function of its frequency of unary nodes. When the number of unary nodes
dominates, we prove some unconventional height phenomenon (i.e. outside the
universal square root behaviour.)Comment: 19 page
Weakly-Supervised Temporal Localization via Occurrence Count Learning
We propose a novel model for temporal detection and localization which allows
the training of deep neural networks using only counts of event occurrences as
training labels. This powerful weakly-supervised framework alleviates the
burden of the imprecise and time-consuming process of annotating event
locations in temporal data. Unlike existing methods, in which localization is
explicitly achieved by design, our model learns localization implicitly as a
byproduct of learning to count instances. This unique feature is a direct
consequence of the model's theoretical properties. We validate the
effectiveness of our approach in a number of experiments (drum hit and piano
onset detection in audio, digit detection in images) and demonstrate
performance comparable to that of fully-supervised state-of-the-art methods,
despite much weaker training requirements.Comment: Accepted at ICML 201
A Bounded Domain Property for an Expressive Fragment of First-Order Linear Temporal Logic
First-Order Linear Temporal Logic (FOLTL) is well-suited to specify infinite-state systems. However, FOLTL satisfiability is not even semi-decidable, thus preventing automated verification. To address this, a possible track is to constrain specifications to a decidable fragment of FOLTL, but known fragments are too restricted to be usable in practice. In this paper, we exhibit various fragments of increasing scope that provide a pertinent basis for abstract specification of infinite-state systems. We show that these fragments enjoy the Bounded Domain Property (any satisfiable FOLTL formula has a model with a finite, bounded FO domain), which provides a basis for complete, automated verification by reduction to LTL satisfiability. Finally, we present a simple case study illustrating the applicability and limitations of our results
Towards an Updatable Strategy Logic
This article is about temporal multi-agent logics. Several of these
formalisms have been already presented (ATL-ATL*, ATLsc, SL). They enable to
express the capacities of agents in a system to ensure the satisfaction of
temporal properties. Particularly, SL and ATLsc enable several agents to
interact in a context mixing the different strategies they play in a semantical
game. We generalize this possibility by proposing a new formalism, Updating
Strategy Logic (USL). In USL, an agent can also refine its own strategy. The
gain in expressive power rises the notion of "sustainable capacities" for
agents.
USL is built from SL. It mainly brings to SL the two following modifications:
semantically, the successor of a given state is not uniquely determined by the
data of one choice from each agent. Syntactically, we introduce in the language
an operator, called an "unbinder", which explicitely deletes the binding of a
strategy to an agent. We show that USL is strictly more expressive than SL.Comment: In Proceedings SR 2013, arXiv:1303.007
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