Arrhythmia Detection by Using Chaos Theory with Machine Learning Algorithms

Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.

Characterization of the Atmospheric Dynamics in Riobamba City Using the Chaos Theory

Chaos studies all that is messy, disorganized and incoherent;mathematically the chaos is a dynamic system governed by nonlinear differential equations. Chaos has an unpredictable behavior;its dynamical is very sensitive to the initial conditions. Atypical chaotic system is the atmosphere;this limits the knowledge about its behavior;but with the advance in the computers, the results that are obtained with the chaos theory improved significantly;the description of atmosphera and its results have extended to other fields of the science, as the economy, health and others. The object of this work was to determine the atmospheric dynamics in the Riobamba city using the theory of chaos, with meteorological data of the meteorological station of the ESPOCH of one year (2010) of data that were processed with model TISEAN. The results determine a hyperchaotic system, according to the coefficients of Lyapunov.

Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings

Based on the evolution of geological dynamics and spatial chaos theory, we proposed the advanced prediction an advanced prediction method of a gas desorption index of drill cuttings to predict coal and gas outbursts. We investigated and verified the prediction method by a spatial series data of a gas desorption index of drill cuttings obtained from the 113112 coal roadway at the Shitai Mine. Our experimental results show that the spatial distribution of the gas desorption index of drill cuttings has some chaotic charac- teristics, which implies that the risk of coal and gas outbursts can be predicted by spatial chaos theory. We also found that a proper amount of sample data needs to be chosen in order to ensure the accuracy and practical maneuverability of prediction. The relative prediction error is small when the prediction pace is chosen carefully. In our experiments, it turned out that the optimum number of sample points is 80 and the optimum prediction pace 30. The corresponding advanced prediction pace basically meets the requirements of engineering applications.

Application of periodic orbit theory in chaos-based security analysis

Chaos-based encryption schemes have been studied extensively, while the security analysis methods for them are still problems to be resolved. Based on the periodic orbit theory, this paper proposes a novel security analysis method. The periodic orbits theory indicates that the fundamental frequency of the spiraling orbits is the natural frequency of associated linearized system, which is decided by the parameters of the chaotic system. Thus, it is possible to recover the plaintext of secure communication systems based on chaotic shift keying by getting the average time on the spiraling orbits. Analysis and simulation results show that the security analysis method can break chaos shift keying secure communication systems, which use the parameters as keys.

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlin- ear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester （MOA） is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifur- cations such as period doubling bifurcation （PDB）, saddle node bifurcation （SNB）, Hopf bifurcation （HB）, and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are il- lustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.

Urban Growth Prediction Modelling Using Fractals and Theory of Chaos

Urban growth prediction has acquired an important consideration in urban sustainability. An effective approach of urban prediction can be a valuable tool in urban decision making and planning. A large urban development has been occurred during last decade in the touristic village of Pogonia Etoloakarnanias, Greece, where an urban growth of 57.5% has been recorded from 2003 to 2011. The prediction of new urban settlements was achieved using fractals and theory of chaos. More specifically, it was found that the urban growth is taken place within a Sierpinski carpet. Several shapes of Sierpinski carpets were tested in order to find the most appropriate, which produced an accuracy percentage of 70.6% for training set and 81.8% for validation set. This prediction method can be effectively applied in urban growth modelling, once cities are fractals and urban complexity can be successfully described through a Sierpinski tessellation.

Suppression and synchronization of chaos in uncertain time-delay physical system

The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Improved PSO algorithm based on chaos theory and its application to design flood hydrograph

The deficiencies of basic particle swarm optimization （bPSO） are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO （COSPSO） algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles＇ initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles＇ path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.

A New Version of Unified Field Theory—Stochastic Quantum Space Theory on Particle Physics and Cosmology

Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.

An improvement on measure methods of the complexity theory and its applications

A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henon map are studied and the results are satisfactory.

COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS

This paper discusses the dynamic behavior of the Kelvin-Stuart cat's eye flow under periodic perturbations. By means of the Melnikov method the conditions to have bifurcations to subharmonics of even order for the oscillating orbits and to have bifurcations to subharmonics of any order for the rotating orbits are given, and further, the coexistence phenomena of the chaotic motions and periodic solutions are presented.

Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy

Euclidean embedding of the 11-dimensional M-theory turned out to require a very large space leaving lavish amounts of 242 dimensional pseudo truly empty “regions” devoid of space and time and consequently of anything resembling ordinary physical energy density. It is shown here using Nash embedding that the ratio of “solid” M-theory spacetime to its required embedding “non-spacetime” is 1/22 for a classical theory and 1/22.18033989 for an analogous fractal theory. This then leads to a maximal ordinary energy density equation equal to that of Einstein’s famous formula E=mc2 but multiplied with in full agreement with previous results obtained using relatively more conventional methods including running the electromagnetic fine structure constant in the exact solution of the hydrogen atom. Consequently, the new equation corresponds to a quantum relativity theory which unlike Einstein’s original equation gives quantitative predictions which agree perfectly with the cosmological measurements of WMAP and the analysis of certain supernova events. Never the less in our view dark energy also exists being the energy of the quantum wave amounting to 95.5 present of the total Einstein theoretical energy which is blind to any distinction between ordinary energy of the quantum particle and the dark energy of the quantum wave. However, since measurement leads to the collapse of the Hawking-Hartle quantum wave, dark energy being a quantum wave non-ordinary energy could not possibly be measured in the usual way unless highly refined quantum wave non-demolition technology is developed if possible. It is a further reason that dark energy having a different sign to ordinary energy is the cause behind the anti gravity force which is pushing the universe apart and accelerating cosmic expansion. Consequently it can be seen as the result of anticlastic Cartan-like curvature caused by extra compactified dimensions of spacetime. A simple toy model demonstration of the effect of curvature in a “material” space is briefly discussed.

Research on Stream Cipher Model Based on Chaos Theory

Chaos is a similar and random process which is very sensitive to initial value in deterministic system. It is a performance of nonlinear dynamical system with built-in randomness. Combined with the advantages and disadvantages of the present chaos encryption model, the paper proposes a chaotic stream cipher model based on chaos theory, which not only overcomes finite precision effect, but also improves the randomness of chaotic system and output sequence. The Sequence cycle theory generated by the algorithm can reach more than 10600 at least, which completely satisfies the actual application requirements of stream cipher system.

Research on General Permutation Encryption Module Based on Chaos Theory

Replacement and substitution encryption are two basic types of encryption historically. The classical encryption algorithm has been compromised now, but they still can play special role for modem cryptnlogy. For example, in digital image encryption system, substitution can disrupt the original order of the images and eliminate the correlation of image information which not only can realize security of images, but also can resist intentional attack and destruction of clipping and noise. And transposition transformation is introduced into the design of block ciphers. The substitution has the feature of high efficiency and resistance, which makes it meet the specific requirements of encryption. So substitution cypher can be applied to modern encryption system.

The chaotic property in the autoionization of Rydberg lithium atom

This paper presents theoretical computations of the ionization rate of Rydberg lithium atom above the classical ionization threshold using semiclassical approximation. The yielded random pulse trains of the escape electrons are recorded as a function of emission time such that they can be related to the terms of the recurrence periods of the photoabsorption. This fact illustrates that it is ionic core scattering processes which give rise to chaos in autoionization dynamics and this is verified by comparison of our results with the hydrogen atom situation. In order to reveal the chaotic properties in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed for different scaled energies. This approach provides a simple explanation for the chaotic character in autoionization decay of Rydberg alkali-metal atoms.

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system, we chose a billiard with a 60° sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size,and position. The spectral properties of generic quantum systems of which the classical counterpart is either integrable or chaotic are universal and well understood. If, however, the classical dynamics is pseudo-integrable or almost-integrable,they exhibit a non-universal intermediate statistics, for which analytical results are known only in a few cases, e.g., if it corresponds to semi-Poisson statistics. Since the latter is, above all, clearly distinguishable from those of integrable and chaotic systems, our aim was to design a billiard with these features which indeed is achievable by adding just one scatterer of appropriate size and position to the sector billiard. We demonstrated that, while the spectral properties of almostintegrable billiards are sensitive to the classical dynamics, this is not the case for the distribution of the wavefunction components, which was analyzed in terms of the strength distribution, and the fluctuation properties of the scattering matrix which coincide with those of typical, fully chaotic systems.

Kinematic Analysis of the Neck and Upper Extremities During Walking in Healthy Young Adults

The objective of this paper is to quantify the local stabilities of the neck and upper extremities （right/left shoulders and right/left elbows）, and investigate differences between linear and nonlinear measurements of the associated joint motions and differences in the local stability between the upper and lower extremities. This attempt involves the calculation of a nonlinear parameter, Lyapunov Exponent （LE）, and a linear parameter, Range of Motion （ROM）, during treadmill walking in conj unction with a large population of healthy subjects. Joint motions of subjects were captured using a three-dimensional motion-capture system. Then mathematical chaos theory and the Rosenstein algorithm were employed to calculate LE of joints as the extent of logarithmic divergence between the neighboring state-space trajectories of flexion-extension angles. LEs computed over twenty males and twenty females were 0.037~0.023 for the neck, 0.043＋0.021 for the right shoulder, 0.045i0.030 for the left shoulder, 0.032i0.021 for the right elbow, and 0.034~0.026 for the left elbow. Although statistically significant difference in the ROM was observed between all pairs of the neck and upper extremity joints, differences in the LE between all pairs of the joints as well as between males and females were not statistically significant. Between the upper and lower extremities, LEs of the neck, shoulder, and elbow were significantly smaller than those of the hip （-0.064） and the knee （-0,062）. These results indicate that a statistical difference in the local stability between the upper extremity joints is not significant. However, the different result between the ROM and LE gives a strong rationale for applying both linear and nonlinear tools together to the evaluation of joint movement. The LEs of the joints calculated from a large population of healthy subjects could provide normative values for the associated joints and can be used to evaluate the recovery progress of patients with joint related diseases.

A study of the logical model of capital market complexity theories

Analyzes the shortcomings of the classic capital market theories based on EMH and discloses the complexity essence of the capital market. Considering the capital market a complicated, interactive and adaptable dynamic system, with complexity science as the method for researching the operation law of the capital market, this paper constructs a nonlinear logical model to analyze the applied realm, focal point and interrelationship of such theories as dissipative structure theory, chaos theory, fractal theory, synergetics theory, catastrophe theory and scale theory, and summarizes and discusses the achievements and problems of each theory. Based on the research, the paper foretells the developing direction of eomplexity science in a capital market.