A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

A Probing Model of Secret Key Generation Based on Channel Autocorrelation Function

Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.

Measurement of spatiotemporal characteristics of femtosecond laser pulses by a modified single-shot autocorrelation

To overcome the shortcomings of the single-shot autocorrelation SSA where only one pulse width is obtained when the SSA is applied to measure the pulse width of ultrashort laser pulses a modified SSA for measuring the spatiotemporal characteristics of ultrashort laser pulses at different spatial positions is proposed. The spatiotemporal characteristics of femtosecond laser pulses output from the Ti sapphire regenerative amplifier system are experimentally measured by the proposed method. It was found that the complex spatial characteristics are measured accurately.The pulse widths at different spatial positions are various which obey the Gaussian distribution.The pulse width at the same spatial position becomes narrow with the increase in input average power when femtosecond laser pulses pass through a carbon disulfide CS2 nonlinear medium.The experimental results verify that the proposed method is valid for measuring the spatiotemporal characteristics of ultrashort laser pulses at different spatial positions.

Design of a spatial sampling scheme considering the spatial autocorrelation of crop acreage included in the sampling units

Information on crop acreage is important for formulating national food polices and economic planning. Spatial sampling, a combination of traditional sampling methods and remote sensing and geographic information system （GIS） technology, provides an efficient way to estimate crop acreage at the regional scale. Traditional sampling methods require that the sampling units should be independent of each other, but in practice there is often spatial autocorrelation among crop acreage contained in the sampling units. In this study, using Dehui County in Jilin Province, China, as the study area, we used a thematic crop map derived from Systeme Probatoire d＇Observation de la Terre （SPOT-5） imagery, cultivated land plots and digital elevation model data to explore the spatial autocorrelation characteristics among maize and rice acreage included in sampling units of different sizes, and analyzed the effects of different stratification criteria on the level of spatial autocorrelation of the two crop acreages within the sampling units. Moran＇s/, a global spatial autocorrelation index, was used to evaluate the spatial autocorrelation among the two crop acreages in this study. The results showed that although the spatial autocorrelation level among maize and rice acreages within the sampling units generally decreased with increasing sampling unit size, there was still a significant spatial autocorrelation among the two crop acreages included in the sampling units （Moran＇s / varied from 0.49 to 0.89）, irrespective of the sampling unit size. When the sampling unit size was less than 3000 m, the stratification design that used crop planting intensity （CPI） as the stratification criterion, with a stratum number of 5 and a stratum interval of 20% decreased the spatial autocorrelation level to almost zero for the maize and rice area included in sampling units within each stratum. Therefore, the traditional sampling methods can be used to estimate the two crop acreages. Compared with CPI, there was still a strong spatial correlation among the two crop acreages included in the sampling units belonging to each stratum when cultivated land fragmentation and ground slope were used as stratification criterion. As far as the selection of stratification criteria and sampling unit size is concerned, this study provides a basis for formulating a reasonable spatial sampling scheme to estimate crop acreage.

STUDY ON SPATIAL AUTOCORRELATION OF URBAN LAND PRICE DISTRIBUTION IN CHANGZHOU CITY OF JIANGSU PROVINCE

This paper uses a spatial statistics method based on the calculation of spatial autocorrelation as a possible approach for modeling and quantifying the distribution of urban land price in Changzhou City, Jiangsu Province. GIS and spatial statistics provide a useful way for describing the distribution of urban land price both spatially and temporally, and have proved to be useful for understanding land price distribution pattern better. In this paper, we apply the statistical analysis method to 8379 urban land price samples collected from Changzhou Land Market, and it is turned out that the proposed approach can effectively identify the spatial clusters and local point patterns in dataset and forms a general method for conceptualizing the land price structure. The results show that land price structure in Changzhou City is very complex and that even where there is a high spatial autocorrelation, the land price is still relatively heterogeneous. Furthermore, lands for different uses have different degrees of spatial autocorrelation. Spatial autocorrelation of commercial lands is more intense than that of residential and industrial lands in regional central district. This means that treating land price as integration of homogeneous units can limit analysis of pattern, over-simplifying the structure of land price, but the methods, just as the autocorrelation approaches, are useful tools for quantifying the variables of land price.

Spatial Autocorrelation Analysis on Regional Economic Disparity of Northeast Economic Region in China

Popular regional inequality indexes such as variation coefficient and Gini coefficient can only reveal overall inequality, and have limited ability in revealing spatial dependence or spatial agglomeration. Recently some methods of exploratory spatial data analysis such as spatial autocorrelation have provided effective tools to analyze spatial agglomeration and cluster, which can reveal the pattern of regional inequality. This article attempts to use spatial autocorrelation at county level to get refined spatial pattern of regional disparity in Chinese northeast economic region over 2000-2006 (2001 absent). The result indicates that the basic trend of regional economy is an increasing concentration of growth among counties in northeast economic region, and there are two geographical clusters of poorer counties including the counties in western Liaoning Province and adjacent counties in Inner Mongolia, poorer counties of Heihe, Qiqihar and Suihua in Heilongjiang Province. This article also reveals that we can use the methods of exploratory spatial data analysis as the supplementary analysis methods in regional economic analysis.

LPI radar signal detection based on the combination of FFT and segmented autocorrelation plus PAHT

This paper proposes a desirable method to detect different kinds of low probability of intercept (LPI) radar signals, targeted at the main intra-pulse modulation method of LPI radar signals including the signals of linear frequency modulation, phase code, and frequency code. Firstly, it improves the coherent integration of LPI radar signals by adding the periodicity of the ambiguity function. Then, it develops a frequency domain detection method based on fast Fourier transform (FFT) and segmented autocorrelation function to detect signals without features of linear frequency modulation by virtue of the distribution characteristics of noise signals in the frequency domain. Finally, this paper gives a verification of the performance of the method for different signal-to-noise ratios by conducting simulation experiments, and compares the method with existing ones. Additionally, this method is characterized by the straightforward calculation and high real-time performance, which is conducive to better detecting all kinds of LPI radar signals.

An Improved Markov Chain Model Based on Autocorrelation and Entropy Techniques and Its Application to State Prediction of Water Resources

According to the relationships among state transition probability matrixes with different step lengths, an improved Markov chain model based on autocorrelation and entropy techniques was introduced. In the improved Markov chain model, the state transition probability matrixes can be adjusted. The steps of the historical state of the event, which was significantly related to the future state of the event, were determined by the autocorrelation technique, and the impact weights of the event historical state on the event future state were determined by the entropy technique. The presented model was applied to predicting annual precipitation and annual runoff states, showing that the improved model is of higher precision than those existing Markov chain models, and the determination of the state transition probability matrixes and the weights is more reasonable. The physical concepts of the improved model are distinct, and its computation process is simple and direct, thus, the presented model is sufficiently general to be applicable to the prediction problems in hydrology and water resources.

The impact of spatial autocorrelation on CPUE standardization between two different fisheries

Catch per unit of eff ort(CPUE) data can display spatial autocorrelation. However, most of the CPUE standardization methods developed so far assumes independency of observations for the dependent variable, which is often invalid. In this study, we collected data of two fisheries, squid jigging fishery and mackerel trawl fishery. We used standard generalized linear model(GLM) and spatial GLMs to compare the impact of spatial autocorrelation on CPUE standardization for different fisheries. We found that spatialGLMs perform better than standard-GLM for both fisheries. The overestimation of precision of CPUE estimates was observed in both fisheries. Moran's I was used to quantify the level of autocorrelation for the two fisheries. The results show that autocorrelation in mackerel trawl fishery was much stronger than that in squid jigging fishery. According to the results of this paper, we highly recommend to account for spatial autocorrelation when using GLM to standardize CPUE data derived from commercial fisheries.

Spatial Autocorrelation and Localization of Urban Development

A nonlinear analysis of urban evolution is made by using of spatial autocorrelation theory. A first-order nonlinear autoregression model based on Clark’s negative exponential model is proposed to show urban population density. The new method and model are applied to Hangzhou City, China, as an example. The average distance of population activities, the auto-correlation coefficient of urban population density, and the auto-regressive function values all show trends of gradual increase from 1964 to 2000, but there always is a sharp first-order cutoff in the partial auto- correlations. These results indicate that urban development is a process of localization. The discovery of urban locality is significant to improve the cellular-automata-based urban simulation of modeling spatial complexity.

Confocal laser speckle autocorrelation imaging of dynamic flow in microvasculature

Laser speckle imaging has been widely used for in-vivo visualization of blood perfusion in biological tissues.However,existing laser speckle imaging techniques suffer from limited quantification accuracy and spatial resolution.Here we re-port a novel design and implementation of a powerful laser speckle imaging platform to solve the two critical limitations.The core technique of our platform is a combination of line scan confocal microscopy with laser speckle autocorrelation imaging,which is termed Line Scan Laser Speckle Autocorrelation Imaging(LS-LSAI).The technical advantages of LS-LSAI include high spatial resolution(~4.4μm)for visualizing and quantifying blood flow in microvessels,as well as video-rate imaging speed for tracing dynamic flow.

Vertex degree autocorrelation topological index and its application in QSAR study of organic chemicals

Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2  and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.

Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear complexity,minimal polynomial,and autocorrelation are investigated.The results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey attack.Furthermore,the autocorrelation values are close to 0 with a probability of approximately 1?1/r.Therefore,when r is a big prime,the new sequence has a good autocorrelation.

Parallelism of spatial data mining based on autocorrelation decision tree

Define and theory of autocorrelation decision tree （ADT） is introduced. In spatial data mining, spatial parallel query are very expensive operations. A new parallel algorithm in terms of autocorrelation decision tree is presented. And the new method reduces CPU- and I/O-time and improves the query efficiency of spatial data. For dynamic load balancing, there are better control and optimization. Experimental performance comparison shows that the improved algorithm can obtain a optimal accelerator with the same quantities of processors. There are more completely accesses on nodes. And an individual implement of intelligent information retrieval for spatial data mining is presented.

New autocorrelation topological indexes and their application in QSAR study

Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and A(t), B(t), C(t), D(t) were developed on the basis of molecular topology and autocorrelation function in mathematics. The first group were obtained from Van der Waals volume, electronegativity and topological vertex degree;and the second group were obtained from the different combination of topological vertex degree.Corresponding softwares of ATIJP and ATITP have been developed for calculating these two new groups of indexes. Better results have been obtained from the application of these indexes in QSAR study.

Spatial autocorrelation analysis of 13 leading malignant neoplasms in Taiwan: a comparison between the 1995-1998 and 2005-2008 periods

Spatial autocorrelation methodologies, including Global Moran’s I and Local Indicators of Spatial Association statistic (LISA), were used to describe and map spatial clusters of 13 leading malignant neoplasms in Taiwan. A logistic regression fit model was also used to identify similar characteristics over time. Two time periods (1995-1998 and 2005-2008) were compared in an attempt to formulate common spatio-temporal risks. Spatial cluster patterns were identified using local spatial autocorrelation analysis. We found a significant spatio-temporal variation between the leading malignant neoplasms and well-documented spatial risk factors. For instance, in Taiwan, cancer of the oral cavity in males was found to be clustered in locations in central Taiwan, with distinct differences between the two time periods. Stomach cancer morbidity clustered in aboriginal townships, where the prevalence of Helicobacter pylori is high and even quite marked differences between the two time periods were found. A method which combines LISA statistics and logistic regression is an effective tool for the detection of space-time patterns with discontinuous data. Spatio-temporal mapping comparison helps to clarify issues such as the spatial aspects of both two time periods for leading malignant neoplasms. This helps planners to assess spatio-temporal risk factors, and to ascertain what would be the most advantageous types of health care policies for the planning and implementation of health care services. These issues can greatly affect the performance and effectiveness of health care services and also provide a clear outline for helping us to better understand the results in depth.

A Novel Hybrid Method for Measuring the Spatial Autocorrelation of Vehicular Crashes: Combining Moran’s Index and Getis-Ord G_i<sup style='margin-left:-7px;'>*</sup>Statistic

Spatial autocorrelation is a measure of the correlation of an observation with other observations through space. Most statistical analyses are based on the assumption that the values of observations are independent of one another. Spatial autocorrelation violates this assumption, because observations at near-by locations are related to each other, and hence, the consideration of spatial autocorrelations has been gaining attention in crash data modeling in recent years, and research have shown that ignoring this factor may lead to a biased estimation of the modeling parameters. This paper examines two spatial autocorrelation indices: Moran’s Index;and Getis-Ord Gi* statistic to measure the spatial autocorrelation of vehicle crashes occurred in Boone County roads in the state of Missouri, USA for the years 2013-2015. Since each index can identify different clustering patterns of crashes, therefore this paper introduces a new hybrid method to identify the crash clustering patterns by combining both Moran’s Index and Gi*?statistic. Results show that the new method can effectively improve the number, extent, and type of crash clustering along roadways.

Identifying Vehicular Crash High Risk Locations along Highways via Spatial Autocorrelation Indices and Kernel Density Estimation

Identifying vehicular crash high risk locations along highways is important for understanding the causes of vehicle crashes and to determine effective countermeasures based on the analysis. This paper presents a GIS approach to examine the spatial patterns of vehicle crashes and determines if they are spatially clustered, dispersed, or random. Moran’s I and Getis-Ord Gi* statistic are employed to examine spatial patterns, clusters mapping of vehicle crash data, and to generate high risk locations along highways. Kernel Density Estimation (KDE) is used to generate crash concentration maps that show the road density of crashes. The proposed approach is evaluated using the 2013 vehicle crash data in the state of Indiana. Results show that the approach is efficient and reliable in identifying vehicle crash hot spots and unsafe road locations.

Application of Non-Linear Cobb-Douglas Production Function with Autocorrelation Problem to Selected Manufacturing Industries in Bangladesh

In developing counties, efficiency of economic development has been determined by the analysis of industrial production. An examination of the characteristic of industrial sector is an essential aspect of growth studies. The growth of a country can be measured by Gross Domestic Product (GDP). GDP is substantially affected by the industrial output. Industrial gross output is mainly a function of capital and labor input. If the effect of labor and capital input to output is at a satisfactory level in an industry or in a group of industries, then industrial investment will increase. As a result, the number of industries will increase, which will directly affect GDP and also will decrease the unemployment rate. This is why, industrial input-output relationship is so important for any industry as well as for the overall industrial sector of a country. To forecast the production of a firm is necessary to identify the appropriate model. MD. M. Hossain et al. [1] have shown that Cobb-Douglas production function with additive errors was more suitable for some selected manufacturing industries in Bangladesh. The main purpose of this paper is to detect the autocorrelation problem of Cobb-Douglas production model with additive errors. The result shows that autocorrelation is presented in some manufacturing industries. Finally, this paper removes the autocorrelation problem and re-estimates the parameters of the Cobb- Douglas production function with additive errors.

The Partial Autocorrelation Function of an ARMA (1.1) Process

In this paper, we obtain an explicit expression for the partial autocorrelation of an ARMA (1.1) process and discuss its asymptotic behaviour briefly.