41,636 research outputs found
The impact of adjacent-dependencies and staged-input on the learnability of center-embedded hierarchical structures
A theoretical debate in artificial grammar learning (AGL) regards the learnability of hierarchical structures. Recent studies using an AnBn grammar draw conflicting conclusions (Bahlmann and Friederici, 2006, De Vries et al., 2008). We argue that 2 conditions crucially affect learning AnBn structures: sufficient exposure to zero-level-of-embedding (0-LoE) exemplars and a staged-input. In 2 AGL experiments, learning was observed only when the training set was staged and contained 0-LoE exemplars. Our results might help understanding how natural complex structures are learned from exemplars
Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems
We consider an exit-time minimum problem with a running cost, and
unbounded controls. The occurrence of points where can be regarded as a
transversality loss. Furthermore, since controls range over unbounded sets, the
family of admissible trajectories may lack important compactness properties. In
the first part of the paper we show that the existence of a -minimum
restraint function provides not only global asymptotic controllability (despite
non-transversality) but also a state-dependent upper bound for the value
function (provided ). This extends to unbounded dynamics a former result
which heavily relied on the compactness of the control set.
In the second part of the paper we apply the general result to the case when
the system is polynomial in the control variable. Some elementary, algebraic,
properties of the convex hull of vector-valued polynomials' ranges allow some
simplifications of the main result, in terms of either near-affine-control
systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344
Strange nonchaotic attractors in noise driven systems
Strange nonchaotic attractors (SNAs) in noise driven systems are
investigated. Before the transition to chaos, due to the effect of noise, a
typical trajectory will wander between the periodic attractor and its nearby
chaotic saddle in an intermittent way, forms a strange attractor gradually. The
existence of SNAs is confirmed by simulation results of various critera both in
map and continuous systems. Dimension transition is found and intermittent
behavior is studied by peoperties of local Lyapunov exponent. The universality
and generalization of this kind of SNAs are discussed and common features are
concluded
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