57,481 research outputs found
Higher order approximation of isochrons
Phase reduction is a commonly used techinque for analyzing stable
oscillators, particularly in studies concerning synchronization and phase lock
of a network of oscillators. In a widely used numerical approach for obtaining
phase reduction of a single oscillator, one needs to obtain the gradient of the
phase function, which essentially provides a linear approximation of isochrons.
In this paper, we extend the method for obtaining partial derivatives of the
phase function to arbitrary order, providing higher order approximations of
isochrons. In particular, our method in order 2 can be applied to the study of
dynamics of a stable oscillator subjected to stochastic perturbations, a topic
that will be discussed in a future paper. We use the Stuart-Landau oscillator
to illustrate the method in order 2
Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics
Stochastic Thermodynamics uses Markovian jump processes to model random
transitions between observable mesoscopic states. Physical currents are
obtained from anti-symmetric jump observables defined on the edges of the graph
representing the network of states. The asymptotic statistics of such currents
are characterized by scaled cumulants. In the present work, we use the
algebraic and topological structure of Markovian models to prove a gauge
invariance of the scaled cumulant-generating function. Exploiting this
invariance yields an efficient algorithm for practical calculations of
asymptotic averages and correlation integrals. We discuss how our approach
generalizes the Schnakenberg decomposition of the average entropy-production
rate, and how it unifies previous work. The application of our results to
concrete models is presented in an accompanying publication.Comment: PACS numbers: 05.40.-a, 05.70.Ln, 02.50.Ga, 02.10.Ox. An accompanying
pre-print "Fluctuating Currents in Stochastic Thermodynamics II. Energy
Conversion and Nonequilibrium Response in Kinesin Models" by the same authors
is available as arXiv:1504.0364
Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks
Because of their superior ability to preserve sequence information over time,
Long Short-Term Memory (LSTM) networks, a type of recurrent neural network with
a more complex computational unit, have obtained strong results on a variety of
sequence modeling tasks. The only underlying LSTM structure that has been
explored so far is a linear chain. However, natural language exhibits syntactic
properties that would naturally combine words to phrases. We introduce the
Tree-LSTM, a generalization of LSTMs to tree-structured network topologies.
Tree-LSTMs outperform all existing systems and strong LSTM baselines on two
tasks: predicting the semantic relatedness of two sentences (SemEval 2014, Task
1) and sentiment classification (Stanford Sentiment Treebank).Comment: Accepted for publication at ACL 201
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