Comparison of detrending methods for fluctuation analysis

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA performs the same as DFA in long data with weak trends and is slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.     

Scaling properties of fluctuation results from the PHENIX experiment at RHIC

The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) has made measurements of event-by-event fluctuations in the charged-particle multiplicity as a function of collision energy, centrality, collision species, and transverse momentum in several heavy-ion collision systems. It is observed that the fluctuations in terms of σ ²/μ ² exhibit a universal power law scaling as a function of N_participants that is independent of the transverse momentum range of the measurement.     

Statistical analysis of human visual impressions on morphological image manipulation of gray scale textures

A method of evaluating human visual impressions of gray scale textures using morphological manipulation is proposed. To study the effects of textural features on human Kansei, we introduced a texture analysis method based on mathematical morphology. Kansei is a Japanese word for sensibility or emotion. Kansei engineering is an approach to connect human sensibility with engineering applications. The proposed method allows us to manipulate global and local properties of a texture separately. Variations of textures were generated by repetitively modifying arranged objects and configurations of the arrangements of original textures. The manipulated textures were presented to human respondents and the similarity of those textures based on human impressions was evaluated. Hierarchical clustering was applied to the similarity matrix generated from respondents’ observations. The results of the human evaluation were compared with that of the objective similarity evaluation adopting six global textural features. The global features such as density, regularity, and directionality of the point configurations were shown to have significant effects on human visual impressions and identification of textures. In the case of a texture without significant characteristics in its point configuration, local features such as grain shape have an effect on visual impressions.     

Scaling theory of relaxation and fluctuation near the instability point

The idea of generalized scale transformation of time is introduced to evaluate asymptotically the relaxation and fluctuation in non-equilibrium systems. This scaling theory is demonstrated to be very powerful in discussing the relaxation just from the instability point.     

Scaling properties of randomly triangulated planar random surfaces: A numerical study

Results of Monte Carlo simulations of a model of random surfaces based on planar random triangulations with gaussian embedding in D-dimensional euclidean space are presented, for various positive and negative values of D and various forms for the action. Estimates are given for the fractal dimension (Hausdorff dimension of the embedding) and the spreading dimension (intrinsic Hausdorff dimension). The scaling properties appear to depend on the short-distance properties of the triangulations and seem to be nonuniversal, at least for positive D.     

Scaling theory of fluctuation in superradiance relaxation from the complete inversion

The general scaling theory of transient phenomena near the instability point, which has been proposed by the author, is applied to investigate the fluctuation and relaxation of superradiance from the complete inversion. This study gives a foundation or justification of the treatment of Glauber and Haake.     

A space-time approach in digital image correlation: Movie-DIC

A new method is proposed to estimate arbitrary velocity fields from a time series of images acquired by a single camera. This approach, here focused on a single spatial plus a time dimension, is specialized to the decomposition of the velocity field over rectangular shaped (finite-element) bilinear shape functions. It is therefore assumed that the velocity field is essentially aligned along one direction. The use of a time sequence over which the velocity is assumed to have a smooth temporal change allows one to use elements whose spatial extension is much smaller than in traditional digital image correlation based on successive image pairs. This method is first qualified by using synthetic numerical test cases, and then applied to a dynamic tensile test performed on a tantalum specimen. Improvements with respect to classical digital image correlation techniques are observed in terms of spatial resolution.     

Scaling properties of switching pulses

We investigate analytically the switching process of a bistable system which is described near each limit point by a single ordinary nonlinear differential equation. For a holding beam near the limit point and a rectangular switching pulse, we prove that the requirement of switching imposes a constraint on the pulse area. This results hold for bistability in general and is applied to purely dispersive optical bistability.     

Energy landscape paving as a perfect optimization approach under detrended fluctuation analysis

Global optimization (GO) is one of the key numerical tools in computational physics. Among the GO algorithms the ones originating in statistical physics are particularly powerful. Recently an adaptive scheme was developed to increase the efficiency of one of these algorithms (stochastic tunneling). This scheme is based on the time-series of minima tested and the respective detrended fluctuation analysis (DFA). We here present a study on another GO methodology (energy landscape paving), which in itself is adaptive, and show that its performance is optimal under the DFA analysis. We give arguments to explain this fact.     

Scaling properties of universal tetramers

We evidence the existence of a universal correlation between the binding energies of successive four-boson bound states (tetramers), for large two-body scattering lengths (a), related to an additional scale not constrained by three-body Efimov physics. Relevant to ultracold atom experiments, the atom-trimer relaxation peaks for |a|→∞ when the ratio between the tetramer and trimer energies is ?4.6 and a new tetramer is formed. The new scale is also revealed for a < 0 by the prediction of a correlation between the positions of two successive peaks in the four-atom recombination process.     

Scaling properties of geometric parallelization

We present a universal scaling law for all geometrically parallelized computer simulation algorithms. For algorithms with local interaction laws we calculate the scaling exponents for zero and infinite lattice size. The scaling is tested on local (cellular automata, Metropolis Ising) as well as cluster (Swendsen-Wang) algorithms. The practical aspects of the scaling properties lead to a simple recipe for finding the optimum number of processors to be used for the parallel simulation of a particular system.     

一种新的数字图像加密算法

利用混沌原理,提出了一种新的二维可逆混沌映射,通过对图像的拉伸和折叠处理,实现了图像的混沌加密。首先按照扫描与插入原则将原始图像拉伸为一条直线,然后按照原始图像的大小,将直线折叠为一个新的图像。映射包括左映射和右映射两个子映射,将密钥设计为二维混沌映射的左映射和右映射的组合。仿真结果表明,图像在加密与解密前后没有信息缺失,且具有较好的安全性。