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.

Spatial and Temporal Distribution of Different Grades of Short-time Precipitation in Xining City

Based on the hourly precipitation data from 4 observation stations of Xining City from June to September during 2005-2011,the temporal and spatial distribution characteristics of short-time precipitation were analyzed.The results show that the precipitation distribution in Xining region exhibited the less-more-less trend from southwest to northeast,while the torrential rain gradually increased from the northwest and southwest to the middle.The hourly general precipitation in Xining region had obviously seasonal characteristics,and its annual distribution showed wavy changes,but the annual variation of short-time heavy precipitation and rainstorm was very obvious.Furthermore,short-time heavy precipitation was concentrated from 18:00 to 24:00,followed by 03:00-07:00 on the following day.The occurrence time of short-time rainstorm accorded with short-time heavy precipitation.It offers a useful reference for the accurate and timely short-term forecast.

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.

Motor Fault Diagnosis Based on Short-time Fourier Transform and Convolutional Neural Network

With the rapid development of mechanical equipment, the mechanical health monitoring field has entered the era of big data. However, the method of manual feature extraction has the disadvantages of low efficiency and poor accuracy, when handling big data. In this study, the research object was the asynchronous motor in the drivetrain diagnostics simulator system. The vibration signals of different fault motors were collected. The raw signal was pretreated using short time Fourier transform （STFT） to obtain the corresponding time-frequency map. Then, the feature of the time-frequency map was adap- tively extracted by using a convolutional neural network （CNN）. The effects of the pretreatment method, and the hyper parameters of network diagnostic accuracy, were investigated experimentally. The experimental results showed that the influence of the preprocessing method is small, and that the batch-size is the main factor affecting accuracy and training efficiency. By investigating feature visualization, it was shown that, in the case of big data, the extracted CNN features can represent complex mapping relationships between signal and health status, and can also overcome the prior knowledge and engineering experience requirement for feature extraction, which is used by tra- ditional diagnosis methods. This paper proposes a new method, based on STFT and CNN, which can complete motor fault diagnosis tasks more intelligently and accurately.

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.

Microstructural evolution in Al–Zn–Mg–Cu–Sc–Zr alloys during short-time homogenization

Abstract： Microstructural evolution in a new kind of aluminum （A1） alloy with the chemical composition of AI-8.82Zn-2.08Mg- 0.80Cu-3.31Sc-0.3Zr was investigated. It is found that the secondary phase MgZn2 is completely dissolved into the matrix during a short homogenization treatment （470℃, 1 h）, while the primary phase A13（Sc,Zr） remains stable. This is due to Sc and Zr additions into the A1 al- loy, high Zn/Mg mass ratio, and low Cu content. The experimental findings fit well with the results calculated by the homogenization diffusion kinetics equation. The alloy shows an excellent mechanical performance after the short homogenization process followed by hot-extrusion and T6 treatment. Consequently, a good combination of low energy consumotion and favorable mechanical properties is obtained.

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.

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.

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.

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.

Characteristics of Radar Echo Parameters and Microphysical Structure Simulation of a Short-Time Heavy Precipitation Supercell

By using the conventional observations, radar data, NCEP/NCAR FNL 1°×1° reanalysis data and numerical simulation data and with the construction and calculation of radar echo parameters, this paper presents the structural characteristics and physical processes of a short-time heavy precipitation supercell that occurred in the squall line process in Shanxi Province on 24 June 2020. The results show that this squall line event occurred in front of a surface cold front,combined with infiltration of low-level cold air and continuous increase of near-surface humidity in the afternoon. The surface mesoscale convergence line and mesoscale dew point front contributed to the development and systemization of the squall line by a large degree. The short-time extremely heavy precipitation in Pingshun County was caused by the development of a supercell from thunderstorm cells on the front side of the squall line. The characteristics of sharp increase in vertical integral liquid water content, persistent increase in reflectivity factor and continuous rise in the echo top height appeared about 23 min earlier than the severe precipitation, which has qualitative indicating significance for the nowcasting of short-time heavy precipitation. A quantitative analysis of the radar echo parameters suggests that the“sudden drop”of FV40was a precursor signal of cells’ coalescence and rapid development to the mature stage. The areal change of the echo core at the 6 km height was highly subject to the merging and developing of cells, the rapid change of hydrometeor particles in clouds and the precipitation intensity. Changes in the cross-sectional area of convective cells at different heights can indirectly reflect the changes of liquid particles and ice particles in clouds, which is indicatively meaningful for predicting the coalescing and developing-to-maturing of cells and heavy precipitation 30-45 min earlier.A comprehensive echo parameter prediction model constructed by the random forest principle can predict the magnitude of short-time heavy precipitation 40-50 min in advance. Numerical simulation reveals that large amounts of water vapor existed in the near-surface atmosphere, and that the cells rapidly obtained moisture from the ambient atmosphere and developed rapidly through maternal feeding. The cold cloud zone was narrow, upright and had a high stretch height. The upward motion in clouds was strong and deep, and very rich in liquid water content. The graupel particles had a large vertical distribution range, the coexistence area of graupel and snow was large, the height of raindrops was close to the surface with a wide horizontal scale, and the precipitation efficiency was high. These may be the important elements responsible for the occurrence of the short-time heavy precipitation that exceeded historical extreme values. On the basis of the above analyses, a comprehensive parameter(CP) prediction model is worked out, which can estimate the developing trend of supercells and the intensity of short-time heavy precipitation about 1 h in advance.

Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy

Traditional short-time fractional Fourier transform(STFrFT)has a single and fixed window function,which can not be adjusted adaptively according to the characteristics of fre-quency and frequency change rate.In order to overcome the shortcomings,the STFrFT method with adaptive window function is proposed.In this method,the window function of STFrFT is ad-aptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion,so as to obtain a time-frequency distribution that better matches the desired signal.This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window func-tion,improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated sig-nals.

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.

Characteristics Analysis on Short-Time Heavy Rainfall during the Flood Season in Shanxi Province, China

In order to provide a reference for the correct forecasting of short-term heavy rainfall and better disaster prevention and mitigation services in Shanxi Province, China, it is very important to carry out systematic research on short-term heavy precipitation events in Shanxi Province. Based on hourly precipitation data during the flood season (May to September) from 109 meteorological stations in Shanxi, China in 1980-2015, the temporal and spatial variation characteristics of short-time heavy rainfall during the flood season are analyzed by using wavelet analysis and Mann-Kendall test. The results show that the short-time heavy rainfall in the flood season in Shanxi Province is mainly at the grade of 20 - 30 mm/h, with an average of 97 stations having short-time heavy rainfall each year, accounting for 89% of the total stations. The short-time heavy rainfall mainly concentrated in July and August, and the maximal rain intensity in history appeared at 23 - 24 on June 17, 1991 in Yongji, Shanxi is 91.7 mm/h. During the flood season, the short-time heavy rainfalls always occur at 16 - 18 pm, and have slightly different concentrated time in different months. The main peaks of June, July and August are at 16, 17 and 18 respectively, postponed for one hour. Short-time heavy rainfall overall has the distribution that the south is more than the north and the east less than the west in Shanxi area. In the last 36 years, short-time heavy rainfall has a slight increasing trend in Shanxi, but not significant. There is a clear 4-year period of oscillation and inter-decadal variation. It has a good correlation between the total precipitation and times of short-time heavy rainfall during the flood season.

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.