29,641 research outputs found
Modeling meander morphodynamics over self-formed heterogeneous floodplains
This work addresses the signatures embedded in the planform geometry of meandering rivers consequent to the formation of floodplain heterogeneities as the river bends migrate. Two geomorphic features are specifically considered: scroll bars produced by lateral accretion of point bars at convex banks and oxbow lake fills consequent to neck cutoffs. The sedimentary architecture of these geomorphic units depends on the type and amount of sediment, and controls bank erodibility as the river impinges on them, favoring or contrasting the river migration. The geometry of numerically generated planforms obtained for different scenarios of floodplain heterogeneity is compared to that of natural meandering paths. Half meander metrics and spatial distribution of channel curvatures are used to disclose the complexity embedded in meandering geometry. Fourier Analysis, Principal Component Analysis, Singular Spectrum Analysis and Multivariate Singular Spectrum Analysis are used to emphasize the subtle but crucial differences which may emerge between apparently similar configurations. A closer similarity between observed and simulated planforms is attained when fully coupling flow and sediment dynamics (fully-coupled models) and when considering self-formed heterogeneities that are less erodible than the surrounding floodplain
The approach for complexity analysis of multivariate time series
This paper proposes to estimate the complexity of a multivariate time series by the spatio-temporal entropy based on multivariate singular spectrum analysis (M-SSA). In order to account for both within- and cross-component dependencies in multiple data channels the high dimensional block Toeplitz covariance matrix is decomposed as a Kronecker product of a spatial and a temporal covariance matrix and the multivariate spatio-temporal entropy is defined in terms of modulus and angle of the complex quantity constructed from the spatial and temporal components of the multivariate entropy. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate deterministic and stochastic processes
Spectral quantification of nonlinear behaviour of the nearshore seabed and correlations with potential forcings at Duck, N.C., U.S.A
Local bathymetric quasi-periodic patterns of oscillation are identified from
monthly profile surveys taken at two shore-perpendicular transects at the USACE
field research facility in Duck, North Carolina, USA, spanning 24.5 years and
covering the swash and surf zones. The chosen transects are the two furthest
(north and south) from the pier located at the study site. Research at Duck has
traditionally focused on one or more of these transects as the effects of the
pier are least at these locations. The patterns are identified using singular
spectrum analysis (SSA). Possible correlations with potential forcing
mechanisms are discussed by 1) doing an SSA with same parameter settings to
independently identify the quasi-periodic cycles embedded within three
potentially linked sequences: monthly wave heights (MWH), monthly mean water
levels (MWL) and the large scale atmospheric index known as the North Atlantic
Oscillation (NAO) and 2) comparing the patterns within MWH, MWL and NAO to the
local bathymetric patterns. The results agree well with previous patterns
identified using wavelets and confirm the highly nonstationary behaviour of
beach levels at Duck; the discussion of potential correlations with
hydrodynamic and atmospheric phenomena is a new contribution. The study is then
extended to all measured bathymetric profiles, covering an area of 1100m
(alongshore) by 440m (cross-shore), to 1) analyse linear correlations between
the bathymetry and the potential forcings using multivariate empirical
orthogonal functions (MEOF) and linear correlation analysis and 2) identify
which collective quasi-periodic bathymetric patterns are correlated with those
within MWH, MWL or NAO, based on a (nonlinear) multichannel singular spectrum
analysis (MSSA). (...continued in submitted paper)Comment: 50 pages, 3 tables, 8 figure
Detecting phase synchronization in coupled oscillators by combining multivariate singular spectrum analysis and fast factorization of structured matrices
It is shown that a fast reliable block Fourier algorithm for the factorization of structured matrices improves computational efficiency of known method for detecting phase synchronization in a large system of coupled oscillators, based on multivariate singular spectrum analysis. In this paper, a novel algorithm for the detection of cluster synchronization in a system of coupled oscillators is proposed. The block Toeplitz covariance matrix of the total trajectory matrix is efficiently block-diagonalized by means of the Fast Fourier Transform by embedding it first into a block circulant matrix. The synchronization structure of the underlying multivariate data set is defined based on the 2D spatiotemporal eigenvalue spectrum. The benefits of the proposed method are illustrated by simulations of the phase synchronization effects in a chain of coupled chaotic Rössler oscillators and using multichannel electroencephalogram (EEG) recordings from epilepsy patients
A non-linear analysis of Gibson's paradox in the Netherlands, 1800-2012
This paper adopts a multivariate, non-linear framework to analyse Gibson’s paradox in the Netherlands over the period 1800-2012. Specifically, SSA (singular spectrum) and MSSA (multichannel singular spectrum) techniques are used. It is shown that changes in monetary policy regimes or volatility in the price of gold by themselves cannot account for the behaviour of government bond yields and prices in the Netherlands over the last 200 years. However, the inclusion of changes in the real rate of return on capital, M1, primary credit rate, expected inflation, and money purchasing power enables a nonlinear model to account for a sizeable percentage of the total variance of Dutch bond yields
Analysis of Dynamic Brain Imaging Data
Modern imaging techniques for probing brain function, including functional
Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging,
and magnetoencephalography, generate large data sets with complex content. In
this paper we develop appropriate techniques of analysis and visualization of
such imaging data, in order to separate the signal from the noise, as well as
to characterize the signal. The techniques developed fall into the general
category of multivariate time series analysis, and in particular we extensively
use the multitaper framework of spectral analysis. We develop specific
protocols for the analysis of fMRI, optical imaging and MEG data, and
illustrate the techniques by applications to real data sets generated by these
imaging modalities. In general, the analysis protocols involve two distinct
stages: `noise' characterization and suppression, and `signal' characterization
and visualization. An important general conclusion of our study is the utility
of a frequency-based representation, with short, moving analysis windows to
account for non-stationarity in the data. Of particular note are (a) the
development of a decomposition technique (`space-frequency singular value
decomposition') that is shown to be a useful means of characterizing the image
data, and (b) the development of an algorithm, based on multitaper methods, for
the removal of approximately periodic physiological artifacts arising from
cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9804003
Observability and Synchronization of Neuron Models
Observability is the property that enables to distinguish two different
locations in -dimensional state space from a reduced number of measured
variables, usually just one. In high-dimensional systems it is therefore
important to make sure that the variable recorded to perform the analysis
conveys good observability of the system dynamics. In the case of networks
composed of neuron models, the observability of the network depends
nontrivially on the observability of the node dynamics and on the topology of
the network. The aim of this paper is twofold. First, a study of observability
is conducted using four well-known neuron models by computing three different
observability coefficients. This not only clarifies observability properties of
the models but also shows the limitations of applicability of each type of
coefficients in the context of such models. Second, a multivariate singular
spectrum analysis (M-SSA) is performed to detect phase synchronization in
networks composed by neuron models. This tool, to the best of the authors'
knowledge has not been used in the context of networks of neuron models. It is
shown that it is possible to detect phase synchronization i)~without having to
measure all the state variables, but only one from each node, and ii)~without
having to estimate the phase
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