‡We describe the use of singular value decomposition in transforming genome-wide expression data from genes 3 arrays space to reduced diagonalized ‘‘eigengenes’’ 3 ‘‘eigenarrays’’ space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

Since the early 1980s, short-term traffic forecasting has been an integral part of most Intelligent Transportation Systems (ITS) research and applications; most effort has gone into developing methodologies that can be used to model traffic characteristics and produce anticipated traffic conditions. Existing literature is voluminous, and has largely used single point data from motorways and has employed univariate mathematical models to predict traffic volumes or travel times. Recent developments in technology and the widespread use of powerful computers and mathematical models allow researchers an unprecedented opportunity to expand horizons and direct work in 10 challenging, yet relatively under researched, directions. It is these existing challenges that we review in this paper and offer suggestions for future work.

Short-term traffic forecasting: Where we are and where we’re going

Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES

/pdf/analysis-of-observed-chaotic-data-3spe9uweeb.pdf

Analysis of observed chaotic data

Weighted multifractal cross-correlation analysis based on Shannon entropy

Permutation and weighted-permutation entropy analysis for the complexity of nonlinear time series

Empirical mode decomposition (EMD) is a data-driven signal analysis method for nonlinear and nonstationary data. Since it is intuitive, direct, posterior and adaptive, EMD is widely applied to various fields of study. In this paper, EMD and ensemble empirical mode decomposition (EEMD), a modified method of EMD, are applied to financial time series. Through analyzing the intrinsic mode functions (IMFs) of EMD and EEMD, we find EEMD method performs better on the orthogonality of IMFs than EMD. With clustering the ordered frequencies of IMFs, the IMFs obtained from EEMD method are grouped into high-, medium-, and low-frequency components, representing the short-, medium-, and long-term volatilities of the index sequences, respectively. With the cross-correlation analysis of DCCA cross-correlation coefficient, our findings allow us to gain further and detailed insight into the cross-correlations of stock markets.

Cross-correlation analysis of stock markets using EMD and EEMD

We use multiscale detrended fluctuation analysis (MSDFA) and multiscale detrended cross-correlation analysis (MSDCCA) to investigate auto-correlation (AC) and cross-correlation (CC) in the US and Chinese stock markets during 1997–2012. The results show that US and Chinese stock indices differ in terms of their multiscale AC structures. Stock indices in the same region also differ with regard to their multiscale AC structures. We analyze AC and CC behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly. We choose S&P500, NQCI, HSI, and the Shanghai Composite Index as representative samples for simplicity. MSDFA and MSDCCA results and average MSDFA spectra for local scaling exponents (LSEs) for individual series are presented. We find that the MSDCCA spectrum for LSE CC between two time series generally tends to be greater than the average MSDFA LSE spectrum for individual series. We obtain detailed multiscale structures and relations for CC between the four representatives. MSDFA and MSDCCA with secant rolling windows of different sizes are then applied to reanalyze the AC and CC. Vertical and horizontal comparisons of different window sizes are made. The MSDFA and MSDCCA results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained.

Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets

The purpose of the present study is to investigate the presence of fractal behaviors in the sediment transport phenomenon to consider the possibility of using a fractal approach for suspended sediment characterization. Suspended sediment concentration data collected from the Yellow River basin at Tongguan, Shanxi, China are studied. The power spectrum, the empirical probability distribution function, the statistical moment scaling function and the autocorrelation function are used as indicators to investigate the presence of fractal. The results from the fractal identification methods indicate that the sediment data exhibit fractal behavior.

Pengjian Shang

Papers

Weighted multifractal cross-correlation analysis based on Shannon entropy

Permutation and weighted-permutation entropy analysis for the complexity of nonlinear time series

Cross-correlation analysis of stock markets using EMD and EEMD

Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets

Fractal nature of time series in the sediment transport phenomenon