Research on a Diagnosis Method Based on a Correlation Integral

For the first time, the diagnosis idea based on a correlation integral isproposed, which regard's the correlation integral as a feature set. The correlation dimension iscontained in the double-log curve of the correlation integral to scale, so extracting featuresdirectly from the correlation integral can avoid the bottleneck problem of determining the range ofnon-scale length. Several features extracted from the correlation integral are better than thesingle feature of the correlation dimension when describing the signal. It is obvious that thismethod utilizes more information of the signal than does the correlation dimension. The diagnosisexamples verify that this method is more accurate and more effective.

Application of Scan-to-Scan Integration-Correlation to Detection of Small Fast-Moving Target on Sea Surface

Conventional scan-to-scan integration correlation （SIC） algorithms can detect small and stationary targets. However, they are ineffective in detecting small and fast-moving targets. This paper presents an improved SIC algorithm together with clutter suppression measures that remove or decrease sea clutter. The algorithm divides the scan-to-scan integration （SI） into two branches, one provides optimum clutter attenuation by means of SI weighting while the other ensures that targets are detected even if they are fast-moving. Sea clutter suppression can lower detection thre-sholds and, at the same time, increase signal-to-clutter ratio. Simulation results show that the proposed approach greatly improves the detection capability for warship radar.

Gorkha earthquake (MW7.8) and aftershock sequence: A fractal approach

On April 25, 2015, Nepal was struck by the MW7.8 Gorkha earthquake followed by an intense aftershock sequence. It was one of the most destructive earthquakes in the Himalayan arc, causing more than 8900 fatalities. In this study, we analyzed the dataset (429 events, magnitude of completeness (Mc) ≥ 4.2 local magnitude) of the first 45 days after the Gorkha earthquake to estimate the seismicity parameters b-value, D-value, and p-value. We used the maximum likelihood method to estimate the b-value and Omori-Utsu parameters, whereas the correlation integral method was applied to estimate the fractal dimension (D-value). The analysis was carried out using running and sliding window techniques. The lowest b-value (0.57 ± 0.04) and the highest D-value (1.65 ± 0.02) were computed at the time of the Gorkha earthquake, after which the b-value significantly increased to a maximum of 1.57. It again dropped to 0.93 at the time of the major aftershock on May 12, 2015. The D-value showed an initial quick drop and then decreased in a wavy pattern until the end of the study period, indicating the clustering and scattering of earthquakes in a fault region. The b-value contour map identified the eastern part of the study area as a high stress region (b = ~0.8), implying that the stress shifted to that region. The D-value contour map reveals that the seismogenic structure shifted from linear to planar in the region. The rate of aftershock decay (p = 0.86 ± 0.04) for a short period reflects that the level of stress decreased rapidly. This study helps to understand the level of stress and seismicity pattern of a region, which could be useful for aftershock studies.

Selection of Optimal Embedding Parameters Applied to Short and Noisy Time Series from Rossler System

Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.

Correlative Analysis between Contents of Nutrients and Secondary Substances in Damaged Pinus massoniana Needles and Population Parameters of Dendrolimus kikuchii(Lepidoptera:Lasiocampidae)

In order to explore the effects of chemical substances changes in damaged masson pine （Pinus massoniana） needles on population dynamics of Dendroli- mus kikuchii, D. kikuchii larvae were reat~ with P. massoniana needles with different damage degrees （mild, moderate and severe）, and its population parame- ters and contents of nutrients and secondary substances in damaged P. massoniana needles were measured, and the integrated correlation coefficient was adopted for data analysis. The results showed that with the damage degree aggravating, flavones in needles increased accordingly, while contents of soluble sugars, polysaeeha- rides and proteins decreased. The average developmental duration and mortality of D. kikuchii larvae increased with the damage degree increasing. No significant correlation was found between the changes in contents of tannins or total phenols and the developmental duration or mortality of each instar larvae. There were signif- icant direct and integrated correlations between contents of nutrients and secondary substances of P. massoniana needles and the developmental duration or mortality of each instar larvae except the 6＇h instar larvae. With the damage degree increasing, all parameters of D. kikuchii population including body weight of the 7~ instar larvae, average feeding capacity of larvae, pupal weight, pupation rate, female ratio and fecundity decreased. No significant correlation was found between the changes in contents of tannins or total phenols and population parameters of D. kikuchii larvae. The results suggest that the contents of nutrients and secondary sub- stances in P. ,mssoniana needles dramatically influenced the population parameters of D. kikuchii, and the importance from high to low successively was soluble sugars 〉 proteins 〉 polysaccharides 〉 flavones. Contents of tannins and total phenols seemed to have little influence.

3D image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging

We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays （PDFAs） with elemental images in computational integral imaging. The multiple PDFAs, whose spatial periods correspond to object＇s depths with the elemental image array （EIA）, can generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method. To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects and present the results.

Revised BDS test

In this paper,we focus on the BDS test,which is a nonparametric test of independence.Specifically,the null hypothesis H0 of it is that {u_(t)} is i.i.d.(independent and identically distributed),where {u_(t)} is a random sequence.The BDS test is widely used in economics and finance,but it has a weakness that cannot be ignored:over-rejecting H0 even if the length T of {u_(t)} is as large as(100;2000).To improve the over-rejection problem of BDS test,considering that the correlation integral is the foundation of this test,we not only accurately describe the expectation of the correlation integral under H_(0),but also calculate all terms of the asymptotic variance of the correlation integral whose order is O(T^(-1))and O(T^(-2)),which is essential to improve the finite sample performance of BDS test.Based on this,we propose a revised BDS(RBDS)test and prove its asymptotic normality under H0.The RBDS test not only inherits all the advantages of BDS test,but also effectively corrects the over-rejection problem of it,which can be fully confirmed by the simulation results we presented.Moreover,based on the simulation results,we find that similar to BDS test,RBDS test would also be affected by the parameter estimations of the ARCH-type model,resulting in size distortion,but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model.Besides,through some actual datasets that have been demonstrated to fit well with ARCH-type models,we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem,and the results reflect that,under the same condition,the performance of the RBDS test is more encouraging.