Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

A method to find unstable periodic orbits for the diamagnetic Kepler problem

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up to length 6, a one to one correspondence between the unstable periodic orbits and their corresponding symbolic sequences is shown under the system symmetry decomposition.

Wavelike patterns in one-dimensional coupled map lattices

We investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two-dimensional mapping. The existence of such wavelike solutions is proved by the implicit function theorem with constraints. We also examine the stabilities of these wave solutions under perturbations of uniform small deformation type. We show that in some specific cases these perturbations are completely general. The technique used in this paper is also applicable to investigate other space-time regular patterns.

Convective coupled map for simulating spatiotemporal chaos in flows

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.

The mechanism of pattern selection in coupled map lattices

The pattern selection of one-dimensional coupled map lattices is studied in this paper. It is shown by spatiotemporal variable separation that there exists a threshold wavelength in pattern selection which possesses wave-like structures in space and periodic chaotic motion in time.

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.

The dynamic evolution of the kepler supernova remnant

been analyzed in detail. The effects ofm icroscopic energy transfer from

Sensitivity map of laser tweezers Raman spectroscopy for single-cell analysis of colorectal cancer

Raman spectroscopy on single, living epithelial cells captured in a laser trap is shown to have diagnostic power over colorectal cancer. This new single-cell technology comprises three major components: primary culture processing of human tissue samples to produce single-cell suspensions, Raman detection on singly trapped cells, and diagnoses of the cells by artificial neural network classifications. it is compared with DNA flow cytometry for similarities and differences. Its advantages over tissue Raman spectroscopy are also discussed. In the actual construction of a diagnostic model for colorectal cancer, real patient data were taken to generate a training set of 320 Raman spectra and, a test set of 80. By incorporating outlier corrections to a conventional binary neural classifier, our network accomplished significantly better predictions than logistic regressions, with sensitivity improved from 77.5% to 86.3% and specificity improved from 81.3% to 86.3% for the training set and moderate improvements for the test set. Most important, the network approach enables a sensitivity map analysis to quantitate the relevance of each Raman band to the normal-to-cancer transform at the cell level. Our technique has direct clinic applications for diagnosing cancers and basic science potential in the study of cell dynamics of carcinogenesis. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Sensitivity map of laser tweezers Raman spectroscopy for single-cell analysis of colorectal cancer

Raman spectroscopy on single, living epithelial cells captured in a laser trap is shown to have diagnostic power over colorectal cancer. This new single-cell technology comprises three major components: primary culture processing of human tissue samples to produce single-cell suspensions, Raman detection on singly trapped cells, and diagnoses of the cells by artificial neural network classifications. it is compared with DNA flow cytometry for similarities and differences. Its advantages over tissue Raman spectroscopy are also discussed. In the actual construction of a diagnostic model for colorectal cancer, real patient data were taken to generate a training set of 320 Raman spectra and, a test set of 80. By incorporating outlier corrections to a conventional binary neural classifier, our network accomplished significantly better predictions than logistic regressions, with sensitivity improved from 77.5% to 86.3% and specificity improved from 81.3% to 86.3% for the training set and moderate improvements for the test set. Most important, the network approach enables a sensitivity map analysis to quantitate the relevance of each Raman band to the normal-to-cancer transform at the cell level. Our technique has direct clinic applications for diagnosing cancers and basic science potential in the study of cell dynamics of carcinogenesis. (C) 2007 Society of Photo-Optical Instrumentation Engineers.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources. (c) 2006 Elsevier GmbH. All rights reserved.