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,ther...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.展开更多
In a quantum many-body system,autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium.In this letter,we bring out the connection between the operator compl...In a quantum many-body system,autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium.In this letter,we bring out the connection between the operator complexity and the autocorrelation function.In particular,we focus on a particular kind of operator complexity called the Krylov complexity.We find that a set of Lanczos coefficients{b_(n)}computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations,which are otherwise impossible.When the time axis is scaled by b1,different autocorrelation functions obey a universal function form at short time.We further propose a characteristic parameter deduced from{b_(n)}that can largely determine the behavior of autocorrelations at the intermediate time.This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time.We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations.We emphasize that these universal behaviors are held across different operators and different physical systems.展开更多
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 ...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.展开更多
Network anomalies caused by network attacks can significantly degrade or even terminate network services.A Real-time and reliable detection of anomalies is essential to rapid anomaly diagnosis,anomaly mitigation,and m...Network anomalies caused by network attacks can significantly degrade or even terminate network services.A Real-time and reliable detection of anomalies is essential to rapid anomaly diagnosis,anomaly mitigation,and malfunction recovering.Unlike most detection methods based on the statistical analysis of the packet headers(Such as IP addresses and ports),a new approach only using network traffic volumes is proposed to detect anomalies reliably.Our method is based on autocorrelation function to judge whether anomalies have happened.In details,the correlation coefficients of normal and anomaly data fluctuate slightly respectively,while those of the overlapped data composed of them fluctuate greatly.Experimental results on network traffic volumes transformed from 1999 DARPA intrusion evaluation data set show that this method can effectively detect network anomalies,while avoiding the high false alarms rate.展开更多
In this paper, the Box-Jenkins modelling procedure is used to determine an ARIMA model and go further to forecasting. The mobile cellular subscription data for the study were taken from the administrative data submitt...In this paper, the Box-Jenkins modelling procedure is used to determine an ARIMA model and go further to forecasting. The mobile cellular subscription data for the study were taken from the administrative data submitted to the Zambia Information and Communications Technology Authority (ZICTA) as quarterly returns by all three mobile network operators Airtel Zambia, MTN Zambia and Zamtel. The time series of annual figures for mobile cellular subscription for all mobile network operators is from 2000 to 2014 and has a total of 15 observations. Results show that the ARIMA (1, 2, 1) is an adequate model which best fits the mobile cellular subscription time series and is therefore suitable for forecasting subscription. The model predicts a gradual rise in mobile cellular subscription in the next 5 years, culminating to about 9.0% cumulative increase in 2019.展开更多
A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the proper...A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.展开更多
Rock failure process as a natural response to mining activities is associated with seismic events, which can pose a potential hazard to mine operators, equipment and infrastructures. Mining-induced seismicity has been...Rock failure process as a natural response to mining activities is associated with seismic events, which can pose a potential hazard to mine operators, equipment and infrastructures. Mining-induced seismicity has been found to be internally correlated in both time and space domains as a result of rock fracturing during progressive mining activities. Understanding the spatio-temporal(ST) correlation of mininginduced seismic events is an essential step to use seismic data for further analysis, such as rockburst prediction and caving assessment. However, there are no established methods to perform this critical task. Input parameters used for the prediction of seismic hazards, such as the time window of past data and effective prediction distance, are determined based on site-specific experience without statistical or physical reasons to support. Therefore, the accuracy of current seismic prediction methods is largely constrained, which can only be addressed by quantitively assessing the ST correlations of mininginduced seismicity. In this research, the ST correlation of seismic event energy collected from a study mine is quantitatively analysed using various statistical methods, including autocorrelation function(ACF), semivariogram and Moran’s I analysis. In addition, based on the integrated ST correlation assessment, seismic events are further classified into seven clusters, so as to assess the correlations within individual clusters. The correlation of seismic events is found to be quantitatively assessable, and their correlations may vary throughout the mineral extraction process.展开更多
By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect t...By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect the micro-parameters of the cracks with the macro- mechanical properties, and can be effectively applied to model the real inhomogeneous medium. Numerical example indicates that the random distribution characters could be different for different elastic constants under the same random distribution of number density of cracks. By changing the value of the autocorrelation length pair, it is possible to model the difference of the distribution in the two coordinate directions. Numerical modeling results for seismic wave propagating in rocks with random distributed fractures using a staggered high-order finite-difference (SHOFD) are also presented.展开更多
A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the ne...A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.展开更多
This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite ...This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanica is shown explicitly in the system.展开更多
A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, wh...A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, where the tensors of energy-momentum and angular momentum of an alternating field are considered, for which the type and structure of the Maxwell stress tensor σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> are given and the corresponding angular momentum tensor, using the dynamic equation for the evolution of internal stresses and the correlation between the stresses σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> in the defect core and the elastic stresses σ<sup>el</sup><sub style="margin-left:-9px;">ik</sub> in its environment, obtains elastic displacement and deformation fields identical to these fields from Burgers and Frank vectors of continuous models. The spectral density of the autocorrelation functions of the velocity of photoelectrons Ψ<sup>β</sup><sub style="margin-left:-6px;">⊥</sub>(β) and cations <img src="Edit_e2d8e074-eb94-44dc-8ab6-6644bbf74f9c.bmp" alt="" /> , which transforms into linear spectra as T → 0, is considered reflecting the existence of threshold values of oscillation and rotations currents of photoelectrons and cations at all stages of plastic deformation and fracture. The features of the process of sliding linear defects in metals are disclosed.展开更多
Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometr...Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.展开更多
Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unk...Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criterion (AIC) and Yule-Walker equations are applied to estimate an AR model fit to the data. Numerical results demonstrate that the proposed estimation algorithm is suitable for different data series. Furthermore, the algorithm is used in a clinical study of electroencephalogram (EEG) with satisfactory results, and the ability to deal with real-time data is the most outstanding characteristic of on-line structural breaks estimation algorithm proposed.展开更多
A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They hav...A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They have good pseudo random characteristics demonstrated by the expression of periodic autocorrelation function found out in this paper.展开更多
A new approach was put torward for estimating the polarization mode dispersion(PMD)induced power degradation to do a performance analysis of millimeter-wave(mm-wave)generation systems based on optical self-heterodyne ...A new approach was put torward for estimating the polarization mode dispersion(PMD)induced power degradation to do a performance analysis of millimeter-wave(mm-wave)generation systems based on optical self-heterodyne technique.Unlike those established ones,this new approach was proposed from another perspective.Considering the optical cartier which is distributed over optical fiber as a stochastic process.The autocorrelation function of the stochastic process was calculated,and then the power degradation could be estimated with Parseval's theorem.This approach to estimate PMD-induced power degradation in normal signal mode fiber(SMF)was used.The results of the approach are well approximates to those established ones,which proves that the theoretical approach is correct.At last,schematics of the power degradation of a 60 GHz signal due to PMD with three different fiber lengths were given to provide intuitive assistance for readers.展开更多
The dynamical properties of one-dimensional random transverse Ising model （RTIM） with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, t...The dynamical properties of one-dimensional random transverse Ising model （RTIM） with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function （SAF） and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σg （or OrB） of the exchange couplings Ji （or the random transverse fields Bi） is small, no long-time tail appears in the SAE The spin system undergoes a crossover from a central-peak behavior to a collectivemode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σJ （or σB） is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C（t） ~ t ^-2 for large t. Similar properties are obtained when Ji （or Bi） satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.展开更多
A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the h...A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the height distribution of the generated Gaussian surface and the root-mean-square height of the rough surface are also considered. It is found that the height distribution of the generated surface follows the Gaussian distribution, the deviation of the root-mean-square height of the modeled rough surface from the desired value is smaller than that of Patir's method, and the autocorrelation function of the modeled surface is also in good agreement with the desired autocorrelation function. Compared with Patir's method, the modeled surface generated by the IDFT method is in better agreement with the desired autocorrelation function, especially when the correlation length is relatively large.展开更多
The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various...The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengthswith different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F(l)is described by a power law.Theautocorrelation function C(l),which is used to measure the linear dependence and periodicity,exists a power law ofC(l)-l^(-μ).We also calculate the mean-square distance<R^2(l)>along the DNA chain,and it may be expressed as<R^2(l)>-l^(?)with 2>γ>1.Our investigations can provide some insights into long-range correlations in DNA sequences.展开更多
A simple and mathematically tractable model of a nonstationary process is developed.The process is the sum of waves where the parameters of the waves are random.Explicit expres-sions for the mean and autocorrelation f...A simple and mathematically tractable model of a nonstationary process is developed.The process is the sum of waves where the parameters of the waves are random.Explicit expres-sions for the mean and autocorrelation function at each position as a function of time are obtained.In the case of infinite time,the model evolves into a stationary process.The time-frequency distri-bution at each position is also obtained.An explicit example is given where the initial waves are Gaussian.The case where there is dispersion in the propagation is also discussed.展开更多
With the development of Internet of Things(IoT),the speed estimation technology has attracted significant attention in the field of indoor security,intelligent home and personalized service.Due to the indoor multipath...With the development of Internet of Things(IoT),the speed estimation technology has attracted significant attention in the field of indoor security,intelligent home and personalized service.Due to the indoor multipath propagation,the speed information is implicit in the motion-induced reflected signal.Thus,the wireless signal can be leveraged to measure the speed of moving target.Among existing speed estimation approaches,users need to either carry a specialized device or walk in a predefined route.Wi-Fi based approaches provide an alternative solution in a device-free way.In this paper,we propose a direction independent indoor speed estimation system in terms of Electromagnetic(EM)wave statistical theory.Based on the statistical characteristics of EM waves,we establish the deterministic relationship between the Autocorrelation Function(ACF)of Channel State Information(CSI)and the speed of a moving target.Extensive experiments show that the system achieves a median error of 0.18 m/s for device-free single target walking speed estimation.展开更多
基金supported in part by the national natural science foundation of China (NSFC) under Grant61871193in part by the R&D Program of key science and technology fields in Guangdong province under Grant 2019B090912001in part by the Guangzhou Key Field R&D Program under Grant 202206030005
文摘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.
基金supported by NSFC 12174300(RZ)the National Key R&D Program of China 2018YFA0307601(RZ)+3 种基金Tang Scholar(RZ)Innovation Program for Quantum Science and Technology 2021ZD0302005(HZ),2021ZD0302001(RZ)the Beijing Outstanding Young Scholar Program(HZ)the XPLORER Prize(HZ).
文摘In a quantum many-body system,autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium.In this letter,we bring out the connection between the operator complexity and the autocorrelation function.In particular,we focus on a particular kind of operator complexity called the Krylov complexity.We find that a set of Lanczos coefficients{b_(n)}computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations,which are otherwise impossible.When the time axis is scaled by b1,different autocorrelation functions obey a universal function form at short time.We further propose a characteristic parameter deduced from{b_(n)}that can largely determine the behavior of autocorrelations at the intermediate time.This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time.We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations.We emphasize that these universal behaviors are held across different operators and different physical systems.
文摘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.
基金This work was supported by a grant from the National Natural Science Foundation of China(No.60773192).
文摘Network anomalies caused by network attacks can significantly degrade or even terminate network services.A Real-time and reliable detection of anomalies is essential to rapid anomaly diagnosis,anomaly mitigation,and malfunction recovering.Unlike most detection methods based on the statistical analysis of the packet headers(Such as IP addresses and ports),a new approach only using network traffic volumes is proposed to detect anomalies reliably.Our method is based on autocorrelation function to judge whether anomalies have happened.In details,the correlation coefficients of normal and anomaly data fluctuate slightly respectively,while those of the overlapped data composed of them fluctuate greatly.Experimental results on network traffic volumes transformed from 1999 DARPA intrusion evaluation data set show that this method can effectively detect network anomalies,while avoiding the high false alarms rate.
文摘In this paper, the Box-Jenkins modelling procedure is used to determine an ARIMA model and go further to forecasting. The mobile cellular subscription data for the study were taken from the administrative data submitted to the Zambia Information and Communications Technology Authority (ZICTA) as quarterly returns by all three mobile network operators Airtel Zambia, MTN Zambia and Zamtel. The time series of annual figures for mobile cellular subscription for all mobile network operators is from 2000 to 2014 and has a total of 15 observations. Results show that the ARIMA (1, 2, 1) is an adequate model which best fits the mobile cellular subscription time series and is therefore suitable for forecasting subscription. The model predicts a gradual rise in mobile cellular subscription in the next 5 years, culminating to about 9.0% cumulative increase in 2019.
基金Supported by National Natural Science Foundation of China (69972042),Natural Science Fund of Hebei Provice(599245)and Science Foundation of Yanshan University
文摘A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.
文摘Rock failure process as a natural response to mining activities is associated with seismic events, which can pose a potential hazard to mine operators, equipment and infrastructures. Mining-induced seismicity has been found to be internally correlated in both time and space domains as a result of rock fracturing during progressive mining activities. Understanding the spatio-temporal(ST) correlation of mininginduced seismic events is an essential step to use seismic data for further analysis, such as rockburst prediction and caving assessment. However, there are no established methods to perform this critical task. Input parameters used for the prediction of seismic hazards, such as the time window of past data and effective prediction distance, are determined based on site-specific experience without statistical or physical reasons to support. Therefore, the accuracy of current seismic prediction methods is largely constrained, which can only be addressed by quantitively assessing the ST correlations of mininginduced seismicity. In this research, the ST correlation of seismic event energy collected from a study mine is quantitatively analysed using various statistical methods, including autocorrelation function(ACF), semivariogram and Moran’s I analysis. In addition, based on the integrated ST correlation assessment, seismic events are further classified into seven clusters, so as to assess the correlations within individual clusters. The correlation of seismic events is found to be quantitatively assessable, and their correlations may vary throughout the mineral extraction process.
文摘By using the spectrum expanding theory of random processes and Hudson's crack model,we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect the micro-parameters of the cracks with the macro- mechanical properties, and can be effectively applied to model the real inhomogeneous medium. Numerical example indicates that the random distribution characters could be different for different elastic constants under the same random distribution of number density of cracks. By changing the value of the autocorrelation length pair, it is possible to model the difference of the distribution in the two coordinate directions. Numerical modeling results for seismic wave propagating in rocks with random distributed fractures using a staggered high-order finite-difference (SHOFD) are also presented.
基金Project supported by the National Natural Science Foundation of China (Grant No 60575038)the Natural Science Foundation of Jiangnan University, China (Grant No 20070365)the Program for Innovative Research Team of Jiangnan University, China
文摘A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.
基金Project partially supported by the State Key Development Program of Basic Research of China (Grant No 2007CB310405)
文摘This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanica is shown explicitly in the system.
文摘A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, where the tensors of energy-momentum and angular momentum of an alternating field are considered, for which the type and structure of the Maxwell stress tensor σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> are given and the corresponding angular momentum tensor, using the dynamic equation for the evolution of internal stresses and the correlation between the stresses σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> in the defect core and the elastic stresses σ<sup>el</sup><sub style="margin-left:-9px;">ik</sub> in its environment, obtains elastic displacement and deformation fields identical to these fields from Burgers and Frank vectors of continuous models. The spectral density of the autocorrelation functions of the velocity of photoelectrons Ψ<sup>β</sup><sub style="margin-left:-6px;">⊥</sub>(β) and cations <img src="Edit_e2d8e074-eb94-44dc-8ab6-6644bbf74f9c.bmp" alt="" /> , which transforms into linear spectra as T → 0, is considered reflecting the existence of threshold values of oscillation and rotations currents of photoelectrons and cations at all stages of plastic deformation and fracture. The features of the process of sliding linear defects in metals are disclosed.
基金Project supported by the Natural Science Foundation of Zhejiang Province (No. M603228), Zhejiang Science and Technology Plan Project, and Ningbo Science Foundation for Doctor, China
文摘Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.
基金supported by Fund of National Science & Technology monumental projects under Grants No. 2012ZX03005012, 2011ZX03005-004-03, 2009ZX03003-007
文摘Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criterion (AIC) and Yule-Walker equations are applied to estimate an AR model fit to the data. Numerical results demonstrate that the proposed estimation algorithm is suitable for different data series. Furthermore, the algorithm is used in a clinical study of electroencephalogram (EEG) with satisfactory results, and the ability to deal with real-time data is the most outstanding characteristic of on-line structural breaks estimation algorithm proposed.
文摘A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They have good pseudo random characteristics demonstrated by the expression of periodic autocorrelation function found out in this paper.
文摘A new approach was put torward for estimating the polarization mode dispersion(PMD)induced power degradation to do a performance analysis of millimeter-wave(mm-wave)generation systems based on optical self-heterodyne technique.Unlike those established ones,this new approach was proposed from another perspective.Considering the optical cartier which is distributed over optical fiber as a stochastic process.The autocorrelation function of the stochastic process was calculated,and then the power degradation could be estimated with Parseval's theorem.This approach to estimate PMD-induced power degradation in normal signal mode fiber(SMF)was used.The results of the approach are well approximates to those established ones,which proves that the theoretical approach is correct.At last,schematics of the power degradation of a 60 GHz signal due to PMD with three different fiber lengths were given to provide intuitive assistance for readers.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11302118 and 11275112)the Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2013AQ015 and ZR2011AM018)the Postdoctoral Science Foundation of Qufu Normal University(Grant No.BSQD2012053)
文摘The dynamical properties of one-dimensional random transverse Ising model （RTIM） with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function （SAF） and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σg （or OrB） of the exchange couplings Ji （or the random transverse fields Bi） is small, no long-time tail appears in the SAE The spin system undergoes a crossover from a central-peak behavior to a collectivemode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σJ （or σB） is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C（t） ~ t ^-2 for large t. Similar properties are obtained when Ji （or Bi） satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.
基金Supported by the National Basic Research Program of China("973"Program,No.2013CB632305)
文摘A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the height distribution of the generated Gaussian surface and the root-mean-square height of the rough surface are also considered. It is found that the height distribution of the generated surface follows the Gaussian distribution, the deviation of the root-mean-square height of the modeled rough surface from the desired value is smaller than that of Patir's method, and the autocorrelation function of the modeled surface is also in good agreement with the desired autocorrelation function. Compared with Patir's method, the modeled surface generated by the IDFT method is in better agreement with the desired autocorrelation function, especially when the correlation length is relatively large.
基金This work was financially support by the National Natural Science Foundation of China(Nos.29874012,20174036,20274040)Natural Science Foundation of Zhejiang Province(No.10102).
文摘The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengthswith different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F(l)is described by a power law.Theautocorrelation function C(l),which is used to measure the linear dependence and periodicity,exists a power law ofC(l)-l^(-μ).We also calculate the mean-square distance<R^2(l)>along the DNA chain,and it may be expressed as<R^2(l)>-l^(?)with 2>γ>1.Our investigations can provide some insights into long-range correlations in DNA sequences.
文摘A simple and mathematically tractable model of a nonstationary process is developed.The process is the sum of waves where the parameters of the waves are random.Explicit expres-sions for the mean and autocorrelation function at each position as a function of time are obtained.In the case of infinite time,the model evolves into a stationary process.The time-frequency distri-bution at each position is also obtained.An explicit example is given where the initial waves are Gaussian.The case where there is dispersion in the propagation is also discussed.
基金This work was supported in part by the Science and Technology Research Project of the Chongqing Natural Science Foundation Project under Grant No.CSTC2020jcyj-msxmX0842the National Natural Science Foundation of China under Grant Nos.61771083 and 61771209.
文摘With the development of Internet of Things(IoT),the speed estimation technology has attracted significant attention in the field of indoor security,intelligent home and personalized service.Due to the indoor multipath propagation,the speed information is implicit in the motion-induced reflected signal.Thus,the wireless signal can be leveraged to measure the speed of moving target.Among existing speed estimation approaches,users need to either carry a specialized device or walk in a predefined route.Wi-Fi based approaches provide an alternative solution in a device-free way.In this paper,we propose a direction independent indoor speed estimation system in terms of Electromagnetic(EM)wave statistical theory.Based on the statistical characteristics of EM waves,we establish the deterministic relationship between the Autocorrelation Function(ACF)of Channel State Information(CSI)and the speed of a moving target.Extensive experiments show that the system achieves a median error of 0.18 m/s for device-free single target walking speed estimation.
