15,553 research outputs found
Accumulating regions of winding periodic orbits in optically driven lasers
We investigate the route to locking in class B lasers subject to optically injected light for injection strengths and detunings near a codimension-two saddle-node Hopf point. This is the parameter region where the Adler approximation is not valid and where Yeung and Strogatz recently reported a self-similar cascade of periodic orbits in the case of a solid-state laser. We explain this cascade as an accumulation of large regions bounded by saddle-node bifurcations of periodic orbits, but also containing further bifurcations, such as period-doubling, torus bifurcations and small pockets of chaos. In the vicinity of the simultaneous saddle-node and Hopf bifurcations, successive periodic orbits wind more and more near the point in phase space where the saddle-node bifurcation is about to occur. This leads to a self-similar period-adding cascade. By varying the linewidth enhancement parameter α from zero, the case of a solid-state or C
Structured Dropout for Weak Label and Multi-Instance Learning and Its Application to Score-Informed Source Separation
Many success stories involving deep neural networks are instances of
supervised learning, where available labels power gradient-based learning
methods. Creating such labels, however, can be expensive and thus there is
increasing interest in weak labels which only provide coarse information, with
uncertainty regarding time, location or value. Using such labels often leads to
considerable challenges for the learning process. Current methods for
weak-label training often employ standard supervised approaches that
additionally reassign or prune labels during the learning process. The
information gain, however, is often limited as only the importance of labels
where the network already yields reasonable results is boosted. We propose
treating weak-label training as an unsupervised problem and use the labels to
guide the representation learning to induce structure. To this end, we propose
two autoencoder extensions: class activity penalties and structured dropout. We
demonstrate the capabilities of our approach in the context of score-informed
source separation of music
Comment on "Scaling feature of magnetic field induced Kondo-peak splittings"
In a recent work Zhang and coworkers (PRB 82, 075111 (2010)) studied the
Zeeman splitting of the Kondo resonance for the single impurity Anderson model
in a finite magnetic field with the numerical renormalization group (NRG)
method. There, it was found that with increasing magnetic field the
position of the Kondo resonance in the total spectral function \textit{does
not} approach its position in the spin resolved spectral function.
Additionally, the position of the Kondo maximum exceeded the Zeeman energy for
, where is the low energy Kondo scale of the model
(, ). In this comment we argue that both these findings
are produced by an improper choice of NRG parameter values. However, we
reproduce the crossover in the splitting from Kondo-like behavior to a
non-universal splitting larger than the Zeeman energy, but this crossover
occurs at much larger fields of the order of the charge scale.Comment: Minor revisions; same version as publishe
Learning curves for Soft Margin Classifiers
Typical learning curves for Soft Margin Classifiers (SMCs) learning both
realizable and unrealizable tasks are determined using the tools of Statistical
Mechanics. We derive the analytical behaviour of the learning curves in the
regimes of small and large training sets. The generalization errors present
different decay laws towards the asymptotic values as a function of the
training set size, depending on general geometrical characteristics of the rule
to be learned. Optimal generalization curves are deduced through a fine tuning
of the hyperparameter controlling the trade-off between the error and the
regularization terms in the cost function. Even if the task is realizable, the
optimal performance of the SMC is better than that of a hard margin Support
Vector Machine (SVM) learning the same rule, and is very close to that of the
Bayesian classifier.Comment: 26 pages, 10 figure
Unnested islands of period-doublings in an injected semiconductor laser
We present a theoretical study of unnested period-doubling islands in three-dimensional rate equations modeling a semiconductor laser subject to external optical injection. In this phenomenon successive curves of period doublings are not arranged in nicely nested islands, but intersect each other. This overall structure is globally organized by several codimension-2 bifurcations. As a consequence, the chaotic region existing inside an unnested island of period doublings can be entered not only via a period-doubling cascade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaotic transitions we reveal underlying global bifurcations and we show how they are connected to codimension-2 bifurcation points. Unnested islands of period doublings appear to be generic and hence must be expected in a large class of dynamical systems
Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium
We numerically study the geometry of a driven elastic string at its
sample-dependent depinning threshold in random-periodic media. We find that the
anisotropic finite-size scaling of the average square width and of
its associated probability distribution are both controlled by the ratio
, where is the
random-manifold depinning roughness exponent, is the longitudinal size of
the string and the transverse periodicity of the random medium. The
rescaled average square width displays a
non-trivial single minimum for a finite value of . We show that the initial
decrease for small reflects the crossover at from the
random-periodic to the random-manifold roughness. The increase for very large
implies that the increasingly rare critical configurations, accompanying
the crossover to Gumbel critical-force statistics, display anomalous roughness
properties: a transverse-periodicity scaling in spite that ,
and subleading corrections to the standard random-manifold longitudinal-size
scaling. Our results are relevant to understanding the dimensional crossover
from interface to particle depinning.Comment: 11 pages, 7 figures, Commentary from the reviewer available in Papers
in Physic
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