A GALLERY OF CHUA ATTRACTORS PART V

2007 ◽  
Vol 17 (05) ◽  
pp. 1383-1511 ◽  
Author(s):  
ELEONORA BILOTTA ◽  
GIANPIERO DI BLASI ◽  
FAUSTO STRANGES ◽  
PIETRO PANTANO
Keyword(s):  
Experimental Data ◽  
Time Series ◽  
Characteristic Function ◽  
Parameter Space ◽  
Three Dimensional ◽  
Special Kind ◽  
Cubic Equation ◽  
Different Shapes ◽  
Chua Oscillator ◽  
The Universe

Chua Oscillator and its generalizations display a variety of chaotic behaviors, whose most startling manifestation is the presence of strange attractors. These come in many different shapes and sizes yet share a special kind of beauty. In the work reported in this paper, we explored the universe of these attractors — much of which is still virgin territory. We then recorded the most interesting and significant in a "Gallery of Chua attractors". In papers, published in previous issues of this journal, we showed how different versions of the Oscillator follow different "routes to chaos". Parts II–IV of the Gallery describe the attractors generated by the dimensional and dimensionless forms of the Oscillator as well as attractors generated by circuits with a cubic equation for the characteristic function of the Chua diode. Here, we provide a detailed discussion of single scroll Chua systems and present 248 attractors generated by such systems. For each attractor, we provide a three-dimensional image, time series and FFTs. We go on to describe the techniques used to create the Gallery and the main characteristics of the attractors it includes. We use techniques such as PCA to represent the gallery in parameter space. The same techniques allow us to manipulate the shape of the attractors by enlarging them along their main axes of development. We use Hausdorff distances to compare shapes, and exploit the results to create landscapes in parameter space. Finally, we present experimental data from a single scroll attractor, using inertial ellipsoids and Hausdorff distances to show how the shape of the attractor evolves.

scholarly journals TREND OF COLORS IN LIFE

2014 ◽  
Vol 2 (3SE) ◽  
pp. 1-2
Author(s):  
Sadhana Vyas
Keyword(s):  
Special Kind ◽  
Human Beings ◽  
Light Waves ◽  
Different Shapes ◽  
The Brain ◽  
The Universe

Many beautiful things affect the life of human beings in the universe, colors have a prominent place among them. Colors contribute uniquely in making the environment attractive. Also, fill the life of a person with happiness, enthusiasm, enthusiasm and consciousness. Being a beautiful world of colors, they have their own importance. The variety of different colors attracts the attention of any person. Colors also show the expression of a person's emotions and emotions.According to Modern Sanctuary en Cyclopedia, "Color is one of the properties of light that the eye sees and different shapes are also formed by light waves." That is, the lack of special kind of stimulation on the retina by the brain is called color. Light is the source of colors. The feeling of color is related to the quality of reflecting or governing the light of each object. सृष्टि में कई सुंदर वस्तुएँ मनुष्य के जीवन को प्रभावित करती हैं, उनमें रंगों का प्रमुख स्थान है। रंग वातावरण को आकर्षक बनाने में अनूठा योगदान देते है। साथ ही व्यक्ति के जीवन को खुषी, उमंग, उत्साह एवं चेतना से भर देते है। रंगों की हसीन दुनिया होने के कारण इनका अपना अलग ही महत्व है। विविध रंगो की छटा किसी भी व्यक्ति का ध्यान बरबसही अपनी ओर खींच लेती है। रंग व्यक्ति के मनोभावों एवं संवेगों की अभिव्यक्ति भी प्रदर्षित करते है।मार्डन संेचुरी एन साइक्लोपीडिया के अनुसार ’’रंग प्रकाष का ही एक गुण है जिन्हें आंखे देखती है और जो विभिन्न आकार भी प्रकाष लहरों से बनते है।’’ अर्थात् मस्तिष्क द्वारा दृष्टिपटल पर विषेष प्रकार की उत्तेजना के अभाव को ही रंग कहते है। प्रकाष रंगों का स्रोत है। रंग की अनुभूति प्रत्येक वस्तु के प्रकाष को परावर्तित अथवा संचालित करने के गुण से संबंधित है।

Correlation in the heart rate data

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Heart Rate ◽  
Time Series ◽  
Cardiovascular Function ◽  
Statistical Properties ◽  
Rate Data ◽  
Heart Rate Data ◽  
Dynamical Nature ◽  
Analysis Of Time Series

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.

The experience of employment of the mathematical cartography methods in cosmology

2017 ◽  
Vol 923 (5) ◽  
pp. 7-16
Author(s):  
A.V. Kavrayskiy
Keyword(s):  
Background Radiation ◽  
Three Dimensional ◽  
Spherical Coordinates ◽  
Linear Element ◽  
Microwave Background ◽  
Euclidian Space ◽  
Microwave Background Radiation ◽  
Rectangular Coordinates ◽  
The Universe ◽  
Length Distortion

The experience of mathematical modeling of the 3D-sphere in the 4D-space and projecting it by mathematical cartography methods in the 3D-Euclidian space is presented. The problem is solved by introduction of spherical coordinates for the 3D-sphere and their transformation into the rectangular coordinates, using the mathematical cartography methods. The mathematical relationship for calculating the length distortion mp(s) of the ds linear element when projecting the 3D-sphere from the 4-dimensional Euclidian space into three-dimensional Euclidian space is derived. Numerical examples, containing the modeling of the ds small linear element by spherical coordinates of 3D-sphere, projecting this sphere into the 3D-Euclidian space and length of ds calculating by means of its projection dL and size of distortion mp(s) are solved. Based on the model of the Universe known in cosmology as the 3D-sphere, the hypothesis of connection between distortion mp(s) and the known observed effects Redshift and Microwave Background Radiation is considered.

scholarly journals Development of a time-series shotgun metagenomics database for monitoring microbial communities at the Pacific coast of Japan

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kazutoshi Yoshitake ◽  
Gaku Kimura ◽  
Tomoko Sakami ◽  
Tsuyoshi Watanabe ◽  
Yukiko Taniuchi ◽  
...  
Keyword(s):  
Time Series ◽  
Microbial Communities ◽  
Pacific Coast ◽  
Three Dimensional ◽  
Amplicon Sequencing ◽  
Metagenomic Data ◽  
Shotgun Metagenomics ◽  
Functional Features ◽  
Pacific Coast Of Japan ◽  
Marine Microbial Communities

AbstractAlthough numerous metagenome, amplicon sequencing-based studies have been conducted to date to characterize marine microbial communities, relatively few have employed full metagenome shotgun sequencing to obtain a broader picture of the functional features of these marine microbial communities. Moreover, most of these studies only performed sporadic sampling, which is insufficient to understand an ecosystem comprehensively. In this study, we regularly conducted seawater sampling along the northeastern Pacific coast of Japan between March 2012 and May 2016. We collected 213 seawater samples and prepared size-based fractions to generate 454 subsets of samples for shotgun metagenome sequencing and analysis. We also determined the sequences of 16S rRNA (n = 111) and 18S rRNA (n = 47) gene amplicons from smaller sample subsets. We thereafter developed the Ocean Monitoring Database for time-series metagenomic data (http://marine-meta.healthscience.sci.waseda.ac.jp/omd/), which provides a three-dimensional bird’s-eye view of the data. This database includes results of digital DNA chip analysis, a novel method for estimating ocean characteristics such as water temperature from metagenomic data. Furthermore, we developed a novel classification method that includes more information about viruses than that acquired using BLAST. We further report the discovery of a large number of previously overlooked (TAG)n repeat sequences in the genomes of marine microbes. We predict that the availability of this time-series database will lead to major discoveries in marine microbiome research.

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

Three-dimensional asymmetric maximum weight lifting prediction considering dynamic joint strength

2021 ◽  
pp. 095441192098703
Author(s):  
Rahid Zaman ◽  
Yujiang Xiang ◽  
Jazmin Cruz ◽  
James Yang
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Three Dimensional ◽  
Optimization Method ◽  
Weight Lifting ◽  
Joint Torque ◽  
Maximum Weight ◽  
Angular Velocities ◽  
Asymmetric Lifting

In this study, the three-dimensional (3D) asymmetric maximum weight lifting is predicted using an inverse-dynamics-based optimization method considering dynamic joint torque limits. The dynamic joint torque limits are functions of joint angles and angular velocities, and imposed on the hip, knee, ankle, wrist, elbow, shoulder, and lumbar spine joints. The 3D model has 40 degrees of freedom (DOFs) including 34 physical revolute joints and 6 global joints. A multi-objective optimization (MOO) problem is solved by simultaneously maximizing box weight and minimizing the sum of joint torque squares. A total of 12 male subjects were recruited to conduct maximum weight box lifting using squat-lifting strategy. Finally, the predicted lifting motion, ground reaction forces, and maximum lifting weight are validated with the experimental data. The prediction results agree well with the experimental data and the model’s predictive capability is demonstrated. This is the first study that uses MOO to predict maximum lifting weight and 3D asymmetric lifting motion while considering dynamic joint torque limits. The proposed method has the potential to prevent individuals’ risk of injury for lifting.

scholarly journals Nucleation is more than critical: A case study of the electroweak phase transition in the NMSSM

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Sebastian Baum ◽  
Marcela Carena ◽  
Nausheen R. Shah ◽  
Carlos E. M. Wagner ◽  
Yikun Wang
Keyword(s):  
Phase Transition ◽  
Parameter Space ◽  
Local Minima ◽  
Critical Temperatures ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Vacuum Structure ◽  
The Universe ◽  
Scalar Sector

Abstract Electroweak baryogenesis is an attractive mechanism to generate the baryon asymmetry of the Universe via a strong first order electroweak phase transition. We compare the phase transition patterns suggested by the vacuum structure at the critical temperatures, at which local minima are degenerate, with those obtained from computing the probability for nucleation via tunneling through the barrier separating local minima. Heuristically, nucleation becomes difficult if the barrier between the local minima is too high, or if the distance (in field space) between the minima is too large. As an example of a model exhibiting such behavior, we study the Next-to-Minimal Supersymmetric Standard Model, whose scalar sector contains two SU(2) doublets and one gauge singlet. We find that the calculation of the nucleation probabilities prefers different regions of parameter space for a strong first order electroweak phase transition than the calculation based solely on the critical temperatures. Our results demonstrate that analyzing only the vacuum structure via the critical temperatures can provide a misleading picture of the phase transition patterns, and, in turn, of the parameter space suitable for electroweak baryogenesis.

Study of Rehabilitation of Injured Knee Joint Applying Chaotic Theory in Human Body Motion

2007 ◽  
Vol 342-343 ◽  
pp. 581-584
Author(s):  
Byung Young Moon ◽  
Kwon Son ◽  
Jung Hong Park
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Gait Pattern ◽  
Body Motion ◽  
Largest Lyapunov Exponent ◽  
Chaos Analysis ◽  
Nonlinear Technique ◽  
Injured Knee

Gait analysis is essential to identify accurate cause and knee condition from patients who display abnormal walking. Traditional linear tools can, however, mask the true structure of motor variability, since biomechanical data from a few strides during the gait have limitation to understanding the system. Therefore, it is necessary to propose a more precise dynamic method. The chaos analysis, a nonlinear technique, focuses on understanding how variations in the gait pattern change over time. Healthy eight subjects walked on a treadmill for 100 seconds at 60 Hz. Three dimensional walking kinematic data were obtained using two cameras and KWON3D motion analyzer. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. This study quantified the variability present in time series generated from gait parameter via chaos analysis. Gait pattern is found to be chaotic. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

scholarly journals Three-Dimensional Structures of Carbohydrates and Where to Find Them

2020 ◽  
Vol 21 (20) ◽  
pp. 7702 ◽  
Author(s):  
Sofya I. Scherbinina ◽  
Philip V. Toukach
Keyword(s):  
Experimental Data ◽  
Molecular Modeling ◽  
Computational Methods ◽  
Three Dimensional ◽  
Structural Diversity ◽  
Structural Data ◽  
Structural Features ◽  
Data Validation ◽  
Data Generation ◽  
Efficient Treatment

Analysis and systematization of accumulated data on carbohydrate structural diversity is a subject of great interest for structural glycobiology. Despite being a challenging task, development of computational methods for efficient treatment and management of spatial (3D) structural features of carbohydrates breaks new ground in modern glycoscience. This review is dedicated to approaches of chemo- and glyco-informatics towards 3D structural data generation, deposition and processing in regard to carbohydrates and their derivatives. Databases, molecular modeling and experimental data validation services, and structure visualization facilities developed for last five years are reviewed.

scholarly journals Three-dimensional deformation time series of glacier motion from multiple-aperture DInSAR observation

2019 ◽  
Vol 93 (12) ◽  
pp. 2651-2660 ◽  
Author(s):  
Sergey Samsonov
Keyword(s):  
Time Series ◽  
Surface Deformation ◽  
Ground Deformation ◽  
Three Dimensional ◽  
Data Sets ◽  
Ice Flow ◽  
The North ◽  
Glacier Ice ◽  
Deformation Component ◽  
3D Deformation

AbstractThe previously presented Multidimensional Small Baseline Subset (MSBAS-2D) technique computes two-dimensional (2D), east and vertical, ground deformation time series from two or more ascending and descending Differential Interferometric Synthetic Aperture Radar (DInSAR) data sets by assuming that the contribution of the north deformation component is negligible. DInSAR data sets can be acquired with different temporal and spatial resolutions, viewing geometries and wavelengths. The MSBAS-2D technique has previously been used for mapping deformation due to mining, urban development, carbon sequestration, permafrost aggradation and pingo growth, and volcanic activities. In the case of glacier ice flow, the north deformation component is often too large to be negligible. Historically, the surface-parallel flow (SPF) constraint was used to compute the static three-dimensional (3D) velocity field at various glaciers. A novel MSBAS-3D technique has been developed for computing 3D deformation time series where the SPF constraint is utilized. This technique is used for mapping 3D deformation at the Barnes Ice Cap, Baffin Island, Nunavut, Canada, during January–March 2015, and the MSBAS-2D and MSBAS-3D solutions are compared. The MSBAS-3D technique can be used for studying glacier ice flow at other glaciers and other surface deformation processes with large north deformation component, such as landslides. The software implementation of MSBAS-3D technique can be downloaded from http://insar.ca/.

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