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Chaotic Pattern (chaotic + pattern)
Selected AbstractsStatistical behavior of complex cancer karyotypesGENES, CHROMOSOMES AND CANCER, Issue 4 2005Mattias Höglund Epithelial tumors commonly show complex and variable karyotypes that obscure the identification of general patterns of the karyotypic evolution. To overcome some of these problems, we previously systematically analyzed the accumulated cytogenetic data from individual tumor types by using various statistical means. In the present study, we compare previous results obtained for nine tumor types and perform several meta-analyses of data obtained from a number of epithelial tumors, including head and neck, kidney, bladder, breast, colorectal, ovarian, and lung cancer, as well as from malignant melanoma and Wilms tumor, with the specific aim of discovering common patterns of karyotypic evolution. We show that these tumors frequently develop through a hypo- or a hyperdiploid pathway and progress by an increasing number of alternative imbalances through at least two karyotypic phases, Phases I and II, and possibly through a third, Phase III. During Phase I, the karyotypes exhibited a power law distribution of both the number of changes per tumor and the frequency distribution at which bands were involved in breaks. At the transition from Phase I to Phase II/III, the observed power law distributions were lost, indicating a transition from an ordered and highly structured process to a disordered and chaotic pattern. The change in karyotypic orderliness at the transition from Phase I to Phase II/III was also shown by a drastic difference in karyotypic entropy. © 2005 Wiley-Liss, Inc. [source] Comparison of sequential data assimilation methods for the Kuramoto,Sivashinsky equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010M. Jardak Abstract The Kuramoto,Sivashinsky equation plays an important role as a low-dimensional prototype for complicated fluid dynamics systems having been studied due to its chaotic pattern forming behavior. Up to now, efforts to carry out data assimilation with this 1-D model were restricted to variational adjoint methods domain and only Chorin and Krause (Proc. Natl. Acad. Sci. 2004; 101(42):15013,15017) tested it using a sequential Bayesian filter approach. In this work we compare three sequential data assimilation methods namely the Kalman filter approach, the sequential Monte Carlo particle filter approach and the maximum likelihood ensemble filter methods. This comparison is to the best of our knowledge novel. We compare in detail their relative performance for both linear and nonlinear observation operators. The results of these sequential data assimilation tests are discussed and conclusions are drawn as to the suitability of these data assimilation methods in the presence of linear and nonlinear observation operators. Copyright © 2009 John Wiley & Sons, Ltd. [source] Quantum bios and biotic complexity in the distribution of galaxies,COMPLEXITY, Issue 4 2006Hector Sabelli Abstract Bios is a nonstationary chaotic pattern that resembles stochastic noise. New time series analyses identify features of creativity, namely episodic patterns, novelty, increasing variance, and nonrandom complexity. These properties characterize bios and are absent in chaotic attractors. Biotic patterns are found in biological processes. Here we report the demonstration of bios in two fundamental physical processes. Time series generated with the Schrödinger's equation display biotic features. Quantum bios is consistent with evidence for quantum chaos. The distribution of galaxies recorded in two recent surveys show a biotic pattern along the time-space axis. This is consistent with the demonstration of fractal features. Bipolar feedback recursions generate increasingly complex patterns (equilibrium, periods, chaos, bios), thus offering a model for the causal creation of complexity. © 2006 Wiley Periodicals, Inc. Complexity 11: 14,25, 2006 [source] Numerical error patterns for a scheme with hermite interpolation for 1 + 1 linear wave equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2004Zuojin Zhu Abstract Numerical error patterns were presented when the fourth-order scheme based on Hermite interpolation was used to solve the 1 + 1 linear wave equation. Since most non-linear equations for real systems can be converted into linear forms by using proper transformations, this study certainly pertains its practical significance. The analytical solution was obtained under inhomogeneous initial and boundary conditions. It was found that not only the Hurst index of an error train at a given position but also its spatial distribution is dependent on the ratio of temporal to spatial intervals. The solution process with the fourth-order scheme based on Hermite interpolation diverges as the ratio is greater than unity. The results show that regular error pattern and smaller maxima of absolute values of numerical errors can be obtained when the ratio is set as unity; while chaotic phenomena for the numerical error propagation process can appear when the ratio is less than unity. It was found that it is better to choose the ratio as unity for the numerical solution of 1 + 1 linear wave equation with the scheme; while other selections for the ratio in the scheme can bring about chaotic patterns for the numerical errors. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||