2,859 research outputs found
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
We investigate a generalised version of the recently proposed ordinal
partition time series to network transformation algorithm. Firstly we introduce
a fixed time lag for the elements of each partition that is selected using
techniques from traditional time delay embedding. The resulting partitions
define regions in the embedding phase space that are mapped to nodes in the
network space. Edges are allocated between nodes based on temporal succession
thus creating a Markov chain representation of the time series. We then apply
this new transformation algorithm to time series generated by the R\"ossler
system and find that periodic dynamics translate to ring structures whereas
chaotic time series translate to band or tube-like structures -- thereby
indicating that our algorithm generates networks whose structure is sensitive
to system dynamics. Furthermore we demonstrate that simple network measures
including the mean out degree and variance of out degrees can track changes in
the dynamical behaviour in a manner comparable to the largest Lyapunov
exponent. We also apply the same analysis to experimental time series generated
by a diode resonator circuit and show that the network size, mean shortest path
length and network diameter are highly sensitive to the interior crisis
captured in this particular data set
Time-Domain Isolated Phoneme Classification Using Reconstructed Phase Spaces
This paper introduces a novel time-domain approach to modeling and classifying speech phoneme waveforms. The approach is based on statistical models of reconstructed phase spaces, which offer significant theoretical benefits as representations that are known to be topologically equivalent to the state dynamics of the underlying production system. The lag and dimension parameters of the reconstruction process for speech are examined in detail, comparing common estimation heuristics for these parameters with corresponding maximum likelihood recognition accuracy over the TIMIT data set. Overall accuracies are compared with a Mel-frequency cepstral baseline system across five different phonetic classes within TIMIT, and a composite classifier using both cepstral and phase space features is developed. Results indicate that although the accuracy of the phase space approach by itself is still currently below that of baseline cepstral methods, a combined approach is capable of increasing speaker independent phoneme accuracy
Models and analysis of vocal emissions for biomedical applications
This book of Proceedings collects the papers presented at the 3rd International Workshop on Models and Analysis of Vocal Emissions for Biomedical Applications, MAVEBA 2003, held 10-12 December 2003, Firenze, Italy. The workshop is organised every two years, and aims to stimulate contacts between specialists active in research and industrial developments, in the area of voice analysis for biomedical applications. The scope of the Workshop includes all aspects of voice modelling and analysis, ranging from fundamental research to all kinds of biomedical applications and related established and advanced technologies
Shared inputs, entrainment, and desynchrony in elliptic bursters: from slow passage to discontinuous circle maps
What input signals will lead to synchrony vs. desynchrony in a group of
biological oscillators? This question connects with both classical dynamical
systems analyses of entrainment and phase locking and with emerging studies of
stimulation patterns for controlling neural network activity. Here, we focus on
the response of a population of uncoupled, elliptically bursting neurons to a
common pulsatile input. We extend a phase reduction from the literature to
capture inputs of varied strength, leading to a circle map with discontinuities
of various orders. In a combined analytical and numerical approach, we apply
our results to both a normal form model for elliptic bursting and to a
biophysically-based neuron model from the basal ganglia. We find that,
depending on the period and amplitude of inputs, the response can either appear
chaotic (with provably positive Lyaponov exponent for the associated circle
maps), or periodic with a broad range of phase-locked periods. Throughout, we
discuss the critical underlying mechanisms, including slow-passage effects
through Hopf bifurcation, the role and origin of discontinuities, and the
impact of noiseComment: 17 figures, 40 page
Classification and Verification of Online Handwritten Signatures with Time Causal Information Theory Quantifiers
We present a new approach for online handwritten signature classification and
verification based on descriptors stemming from Information Theory. The
proposal uses the Shannon Entropy, the Statistical Complexity, and the Fisher
Information evaluated over the Bandt and Pompe symbolization of the horizontal
and vertical coordinates of signatures. These six features are easy and fast to
compute, and they are the input to an One-Class Support Vector Machine
classifier. The results produced surpass state-of-the-art techniques that
employ higher-dimensional feature spaces which often require specialized
software and hardware. We assess the consistency of our proposal with respect
to the size of the training sample, and we also use it to classify the
signatures into meaningful groups.Comment: Submitted to PLOS On
Moving forward in circles: challenges and opportunities in modelling population cycles
Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research
Permutation entropy and its main biomedical and econophysics applications: a review
Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.Facultad de IngenierÃ
- …