scholarly journals Autoregressive models as a tool to discriminate chaos from randomness in geoelectrical time series: an application to earthquake prediction

1997 ◽  
Vol 40 (2) ◽  
Author(s):  
V. Cuomo ◽  
V. Lapenna ◽  
M. Macchiato ◽  
C. Serio
Keyword(s):  
Time Series ◽  
Degrees Of Freedom ◽  
Broad Class ◽  
Scaling Law ◽  
Power Spectra ◽  
Time Dynamics ◽  
Predictive Skill ◽  
Data Points ◽  
Typical Behaviour ◽  
Low Dimensional

The time dynamics of geoelectrical precursory time series has been investigated and a method to discriminate chaotic behaviour in geoelectrical precursory time series is proposed. It allows us to detect low-dimensional chaos when the only information about the time series comes from the time series themselves. The short-term predictability of these time series is evaluated using two possible forecasting approaches: global autoregressive approximation and local autoregressive approximation. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a test to discriminate between low-dimensional chaos and random dynamics. The analyzed time series are geoelectrical measurements recorded by an automatic station located in Tito (Southern Italy) in one of the most seismic areas of the Mediterranean region. Our findings are that the global (linear) approach is superior to the local one and the physical system governing the phenomena of electrical nature is characterized by a large number of degrees of freedom. Power spectra of the filtered time series follow a P(f) = F-a scaling law: they exhibit the typical behaviour of a broad class of fractal stochastic processes and they are a signature of the self-organized systems.

Dynamical Degrees of Freedom of DNA Sequences by Local and Global Short-Range Prediction

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 1-10
Author(s):  
M. Ragosta ◽  
C. Serio ◽  
M. T. Lanfredi ◽  
M. Macchiato
Keyword(s):  
Dna Sequences ◽  
Degrees Of Freedom ◽  
Nonlinear Process ◽  
Short Term ◽  
Chaotic Motions ◽  
Deterministic Systems ◽  
Predictive Skill ◽  
Low Dimensional ◽  
Dynamical Degrees ◽  
Insight Into

The dynamical properties of DNA sequence samples have been analyzed on the basis of a procedure able to distinguish chaos from randomness. The procedure relies on the concept of short-term (range) predictability of low-dimensional chaotic motions and can distinguish merely linear stochastic processes, e.g. fractional Brownian motion, from truly nonlinear deterministic systems. The method consists in obtaining forecasts on the basis of past events in the sequence. Two forecasting strategies are used. The local strategy views the sequence as the outcome of a nonlinear process, whereas the global approach considers the series as the outcome of a linear stochastic process. For both approaches, the predictive skill is computed and their inter-comparison allows us to get insight into and an understanding of the structure of DNA sequences. Nucleotidic sequences belonging to different taxonomic and functional groups have been analyzed. Different behaviors have been detected according to the existence of finite correlation dimension for specific groups of sequences.

AN ALGORITHMIC COMPUTATION OF CORRELATION DIMENSION FROM TIME SERIES

2007 ◽  
Vol 21 (02n03) ◽  
pp. 129-138 ◽  
Author(s):  
K. P. HARIKRISHNAN ◽  
G. AMBIKA ◽  
R. MISRA
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Correlation Dimension ◽  
Visual Inspection ◽  
Chaotic Systems ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Points ◽  
Scaling Region ◽  
Low Dimensional

We present an algorithmic scheme to compute the correlation dimension D2 of a time series, without requiring the visual inspection of the scaling region in the correlation sum. It is based on the standard Grassberger–Proccacia [GP] algorithm for computing D2. The scheme is tested using synthetic data sets from several standard chaotic systems as well as by adding noise to low-dimensional chaotic data. We show that the scheme is efficient with a few thousand data points and is most suitable when a nonsubjective comparison of D2 values of two time series is required, such as, in hypothesis testing.

NONLINEAR TIME-SERIES ANALYSIS OF THE GREEK EXCHANGE-RATE MARKET

2000 ◽  
Vol 10 (07) ◽  
pp. 1729-1758 ◽  
Author(s):  
A. S. ANDREOU ◽  
G. PAVLIDES ◽  
A. KARYTINOS
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical Systems ◽  
Deterministic Chaos ◽  
Data Series ◽  
Nonlinear Dynamical ◽  
Series Analysis ◽  
Low Dimensional ◽  
Bds Test

Using concepts from the theory of chaos and nonlinear dynamical systems, a time-series analysis is performed on four major currencies against the Greek Drachma. The R/S analysis provided evidence for fractality due to noisy chaos in only two of the data series, while the BDS test showed that all four systems exhibit nonlinearity. Correlation dimension and related tests, as well as Lyapunov exponents, gave consistent results, which did not rule out the possibility of deterministic chaos for the two possibly fractal series, rejecting though the occurrence of a simple low-dimensional attractor, while the other two series seemed to have followed a behavior close to that of a random signal. SVD analysis, used to filter away noise, strongly supported the above findings and provided reliable evidence for the existence of an underlying system with a limited number of degrees-of-freedom only for those series found to exhibit fractality, while it revealed a noise domination over the remaining two. These results were further confirmed through a forecasting attempt using artificial neural networks.

scholarly journals A preliminary nonlinear analysis of the earth's chandler wobble

2000 ◽  
Vol 4 (1) ◽  
pp. 39-53 ◽  
Author(s):  
V. Frede ◽  
P. Mazzega
Keyword(s):  
Time Series ◽  
Nonlinear Analysis ◽  
Polar Motion ◽  
Chandler Wobble ◽  
Deterministic Process ◽  
Motion Data ◽  
Predictive Skill ◽  
Lyapunov Spectra ◽  
Global Statistics ◽  
Low Dimensional

The Chandler wobble (CW) is a resonant response of the Earth rotational pole wandering around its figure axis whose excitation mechanism is still uncertain. It appears as polar motion oscillations with an average period of about 433 days and a slowly varying amplitude in the range (0–300) milliarcsec (mas). We here perform a nonlinear analysis of the CW via a time-delay coordinate embedding of its measuredXandYcomponents and show that the CW can be interpreted as a low dimensional unstable deterministic process.In a first step the trend, annual wobble and CW are separated from the raw polar motion data time series spanning the period 1846–1997. The optimal delays as deduced from the average mutual information function are 105 and 115 days for theXandYcomponents respectively. Then from the global statistics of the false neighbours, the embedding dimensionDE=4is estimated for both series. The local dimensionDLcan also be extracted from the time series by testing the predictive skill of local mappings fitted to the embedded data vectors. The resultDL=3is quite robust and corroborate the idea that the CW behaves like a dissipative oscillator driven by a deterministic process. Indeed the orbit reconstructions in pseudo-phase space both draw the figure of a perturbated 1-torus.The computation of the Lyapunov spectra further shows that this torus-like figure is an attractor with a 1D unstable manifold. The theoretical horizons of prediction deduced from the (positive) principal exponents are about 367 and 276 days for theXandYChandler components respectively. Moreover the local Lyapunov exponents exhibit significant variations with maxima (and corresponding losses of predictibility) in the decades 1860–1870 and 1940–1950.

Bifurcations of the respiratory pattern associated with reduced lung volume in the rat

1993 ◽  
Vol 75 (2) ◽  
pp. 887-901 ◽  
Author(s):  
M. Sammon ◽  
J. R. Romaniuk ◽  
E. N. Bruce
Keyword(s):  
Degrees Of Freedom ◽  
Power Spectra ◽  
Phase Portraits ◽  
Respiratory Pattern ◽  
Phase Switching ◽  
Correlation Integral ◽  
Switching Dynamics ◽  
Tracheal Pressure ◽  
Lung Deflation ◽  
Low Dimensional

Rats with intact vagal reflexes exhibit patterns of breathing that contain greater degrees of freedom than those seen after vagotomy. To determine how alterations in end-expiratory volume modify the respiratory pattern, continuous positive (CPAP) and negative (CNAP) airway pressure was applied to tracheal openings of nine urethan-anesthetized vagi-intact rats (+3 to -9 cmH2O). Phase portraits (e.g., volume vs. flow curves), power spectra, correlation integral curves, and inspiratory-to-expiratory duration (TI/TE) ratios are used to interpret the vagal-dependent responses to changes in mean tracheal pressure (Ptr). With CPAP, respiratory oscillation was highly periodic and one dimensional, with TI/TE near 1.0. As Ptr was reduced in a stepwise manner, transient bursts of inspiratory airflow developed local to the expiratory-inspiratory transition, with amplitude increasing proportionally with the level of CNAP. These oscillatory "expiratory interrupts" (doubling TI/TE in five of nine cases) produced highly variable and asymmetric respiratory patterns. Progressive increases in correlation dimension (maximum = 1.8–3.0) and tendencies toward broadband power spectra were seen as Ptr was lowered. The irregular phase-switching dynamics seen with CNAP (which disappeared after vagotomy) are consistent with onset of low-dimensional chaos, probably correlated with activation of feedback mechanisms responsive to lung deflation.

scholarly journals The halo model as a versatile tool to predict intrinsic alignments

2020 ◽  
Author(s):  
Maria Cristina Fortuna ◽  
Henk Hoekstra ◽  
Benjamin Joachimi ◽  
Harry Johnston ◽  
Nora Elisa Chisari ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Power Spectra ◽  
Stage Iv ◽  
Stage Iii ◽  
Radial Dependence ◽  
Additional Parameter ◽  
Small Scales ◽  
Cosmic Shear ◽  
Galaxy Populations ◽  
The Impact

Abstract Intrinsic alignments (IAs) of galaxies are an important contaminant for cosmic shear studies, but the modelling is complicated by the dependence of the signal on the source galaxy sample. In this paper, we use the halo model formalism to capture this diversity and examine its implications for Stage-III and Stage-IV cosmic shear surveys. We account for the different IA signatures at large and small scales, as well for the different contributions from central/satellite and red/blue galaxies, and we use realistic mocks to account for the characteristics of the galaxy populations as a function of redshift. We inform our model using the most recent observational findings: we include a luminosity dependence at both large and small scales and a radial dependence of the signal within the halo. We predict the impact of the total IA signal on the lensing angular power spectra, including the current uncertainties from the IA best-fits to illustrate the range of possible impact on the lensing signal: the lack of constraints for fainter galaxies is the main source of uncertainty for our predictions of the IA signal. We investigate how well effective models with limited degrees of freedom can account for the complexity of the IA signal. Although these lead to negligible biases for Stage-III surveys, we find that, for Stage-IV surveys, it is essential to at least include an additional parameter to capture the redshift dependence.

scholarly journals A chiral switchable photovoltaic ferroelectric 1D perovskite

2020 ◽  
Vol 6 (9) ◽  
pp. eaay4213 ◽  
Author(s):  
Yang Hu ◽  
Fred Florio ◽  
Zhizhong Chen ◽  
W. Adam Phelan ◽  
Maxime A. Siegler ◽  
...  
Keyword(s):  
Electric Fields ◽  
Mirror Symmetry ◽  
Degrees Of Freedom ◽  
Electrical Measurements ◽  
Temperature Dependent ◽  
Paraelectric Phase Transition ◽  
Strongly Coupled ◽  
Yield Phenomena ◽  
Hybrid Perovskite ◽  
Low Dimensional

Spin and valley degrees of freedom in materials without inversion symmetry promise previously unknown device functionalities, such as spin-valleytronics. Control of material symmetry with electric fields (ferroelectricity), while breaking additional symmetries, including mirror symmetry, could yield phenomena where chirality, spin, valley, and crystal potential are strongly coupled. Here we report the synthesis of a halide perovskite semiconductor that is simultaneously photoferroelectricity switchable and chiral. Spectroscopic and structural analysis, and first-principles calculations, determine the material to be a previously unknown low-dimensional hybrid perovskite (R)-(−)-1-cyclohexylethylammonium/(S)-(+)-1 cyclohexylethylammonium) PbI3. Optical and electrical measurements characterize its semiconducting, ferroelectric, switchable pyroelectricity and switchable photoferroelectric properties. Temperature dependent structural, dielectric and transport measurements reveal a ferroelectric-paraelectric phase transition. Circular dichroism spectroscopy confirms its chirality. The development of a material with such a combination of these properties will facilitate the exploration of phenomena such as electric field and chiral enantiomer–dependent Rashba-Dresselhaus splitting and circular photogalvanic effects.

An Experimental Study of the Forced Response of Pre- and Post-Critical Plates

1995 ◽  
Author(s):  
Kevin D. Murphy ◽  
Lawrence N. Virgin ◽  
Stephen A. Rizzi
Keyword(s):  
Experimental Study ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Small Amplitude ◽  
Narrow Band ◽  
Power Spectra ◽  
Forced Response ◽  
Acoustic Excitation ◽  
Rectangular Plates ◽  
Auto Correlation

Abstract Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-correlation functions, small amplitude vibrations are considered about both the pre- and post-critical states. These techniques are then employed to investigate the snap-through response. The results for snap-through suggest that the motion is temporally complex and a Lyapunov exponent calculation confirms that the motion is chaotic. Finally, a snap-through boundary is mapped in the (ω, SPL) parameter space separating the regions of snap-through and no snap-through.

scholarly journals LSTM-Guided Coaching Assistant for Table Tennis Practice

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4112 ◽  
Author(s):  
Se-Min Lim ◽  
Hyeong-Cheol Oh ◽  
Jaein Kim ◽  
Juwon Lee ◽  
Jooyoung Park
Keyword(s):  
Time Series ◽  
State Space ◽  
Time Series Data ◽  
State Space Model ◽  
Skill Assessment ◽  
Series Data ◽  
High Dimensional ◽  
Table Tennis ◽  
Space Model ◽  
Low Dimensional

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.

scholarly journals Optimizing the structure and movement of a robotic bat with biological kinematic synergies

2018 ◽  
Vol 37 (10) ◽  
pp. 1233-1252 ◽  
Author(s):  
Jonathan Hoff ◽  
Alireza Ramezani ◽  
Soon-Jo Chung ◽  
Seth Hutchinson
Keyword(s):  
Principal Component Analysis ◽  
Topological Structure ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Principal Component ◽  
Biologically Inspired ◽  
Wing Kinematics ◽  
Wing Motion ◽  
Kinematic Synergies ◽  
Low Dimensional

In this article, we present methods to optimize the design and flight characteristics of a biologically inspired bat-like robot. In previous, work we have designed the topological structure for the wing kinematics of this robot; here we present methods to optimize the geometry of this structure, and to compute actuator trajectories such that its wingbeat pattern closely matches biological counterparts. Our approach is motivated by recent studies on biological bat flight that have shown that the salient aspects of wing motion can be accurately represented in a low-dimensional space. Although bats have over 40 degrees of freedom (DoFs), our robot possesses several biologically meaningful morphing specializations. We use principal component analysis (PCA) to characterize the two most dominant modes of biological bat flight kinematics, and we optimize our robot’s parametric kinematics to mimic these. The method yields a robot that is reduced from five degrees of actuation (DoAs) to just three, and that actively folds its wings within a wingbeat period. As a result of mimicking synergies, the robot produces an average net lift improvesment of 89% over the same robot when its wings cannot fold.

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