STATISTICAL PROPERTY OF THRESHOLD-CROSSING FOR ZERO-MEAN-VALUED, NARROW-BANDED GAUSSIAN PROCESSES

Based on a comprehensive discussion of the calculation method for the threshold-crossing statistics of zero mean valued, narrow banded Gaussian processes of various practical engineering problems, including the threshold-crossing probability, average number of crossing events per unit time, mean threshold-crossing duration and amplitude, a new Simple numerical procedure is proposed for the efficient evaluation of mean threshold-crossing duration. A new dimensionless parameter, called the threshold-crossing intensity, is defined as a measure of the threshold-crossing severity, which is equal to the ratio of the product of average number of crossing events per unit time and mean threshold-crossing duration and amplitude over the threshold. It is found, by the calculation results for various combinations of stochastic processes and different thresholds, that the threshold-crossing intensity, irrelevant of the threshold and spectral density of the process, is dependent only on the threshold-crossing probability.

Novel Sum-of-Sinusoids Simulation Channel Modeling for 6G Multiple-Input Multiple-Output Vehicle-to-Everything Communications

In this paper,a statistical cluster-based simulation channel model with a finite number of sinusoids is proposed for depicting the multiple-input multiple-output(MIMO)communications in vehicleto-everything(V2X)environments.In the proposed sum-of-sinusoids(SoS)channel model,the waves that emerge from the transmitter undergo line-of-sight(LoS)and non-line-of-sight(NLoS)propagation to the receiver,which makes the model suitable for describing numerous V2X wireless communication scenarios for sixth-generation(6G).We derive expressions for the real and imaginary parts of the complex channel impulse response(CIR),which characterize the physical propagation characteristics of V2X wireless channels.The statistical properties of the real and imaginary parts of the complex CIRs,i.e.,autocorrelation functions(ACFs),Doppler power spectral densities(PSDs),cross-correlation functions(CCFs),and variances of ACFs and CCFs,are derived and discussed.Simulation results are generated and match those predicted by the underlying theory,demonstrating the accuracy of our derivation and analysis.The proposed framework and underlying theory arise as an efficient tool to investigate the statistical properties of 6G MIMO V2X communication systems.

Statistical Tensile Strength for High Strain Rate of Aramid and UHMWPE Fibers

Dynamic tensile impact properties of aramid (Technora) and UHMWPE (DC851) fiber bundles were studied at two high strain rates by means of reflecting type Split Hopkinson Bar, and stress-strain curves of fiber yarns at different strain rates were obtained. Experimental results show that the initial elastic modulus, failure strength and unstable strain of aramid fiber yarns are strain rate insensitive, whereas the initial elastic modulus and unstable strain of UHMWPE fiber yarns are strain rate sensitive. A fiber-bundle statistical constitutive equation was used to describe the tensile behavior of aramid and UHMWPE fiber bundles at high strain rates. The good consistency between the simulated results and experimental data indicates that the modified double Weibull function can represent the tensile strength distribution of aramid and UHMWPE fibers and the method of extracting Weibull parameters from fiber bundles stress-strain data is valid.

Statistical Modeling with a Hidden Markov Tree and High-resolution Interpolation for Spaceborne Radar Reflectivity in the Wavelet Domain

With the increasing availability of precipitation radar data from space,enhancement of the resolution of spaceborne precipitation observations is important,particularly for hazard prediction and climate modeling at local scales relevant to extreme precipitation intensities and gradients.In this paper,the statistical characteristics of radar precipitation reflectivity data are studied and modeled using a hidden Markov tree(HMT)in the wavelet domain.Then,a high-resolution interpolation algorithm is proposed for spaceborne radar reflectivity using the HMT model as prior information.Owing to the small and transient storm elements embedded in the larger and slowly varying elements,the radar precipitation data exhibit distinct multiscale statistical properties,including a non-Gaussian structure and scale-to-scale dependency.An HMT model can capture well the statistical properties of radar precipitation,where the wavelet coefficients in each sub-band are characterized as a Gaussian mixture model(GMM),and the wavelet coefficients from the coarse scale to fine scale are described using a multiscale Markov process.The state probabilities of the GMM are determined using the expectation maximization method,and other parameters,for instance,the variance decay parameters in the HMT model are learned and estimated from high-resolution ground radar reflectivity images.Using the prior model,the wavelet coefficients at finer scales are estimated using local Wiener filtering.The interpolation algorithm is validated using data from the precipitation radar onboard the Tropical Rainfall Measurement Mission satellite,and the reconstructed results are found to be able to enhance the spatial resolution while optimally reproducing the local extremes and gradients.

Photon statistical properties of photon-added two-mode squeezed coherent states

We investigate photon statistical properties of the multiple-photon-added two-mode squeezed coherent states （PA- TMSCS）. We find that the photon statistical properties are sensitive to the compound phase involved in the TMSCS. Our numerical analyses show that the photon addition can enhance the cross-correlation and anti-bunching effects of the PA- TMSCS. Compared with that of the TMSCS, the photon number distribution of the PA-TMSCS is modulated by a factor that is a monotonically increasing function of the numbers of adding photons to each mode; further, that the photon addition essentially shifts the photon number distribution.

Statistical properties of the photoelectron energy spectrum generated by an intense laser pulse and a continuous X-ray

This study shows that the photoelectron energy spectrum generated by an intense laser pulse in the presence of a continuous X-ray has interesting and useful statistical properties. The total photoionization production is linearly propor- tional to the time duration of the laser pulse and the square of the beam size. The spectral double energy-integration is an intrinsic value of the laser-assisted X-ray photoionization, which linearly depends on the laser intensity and which quantita- tively reflects the strengths of the laser-field modulation and the quantum interference between photoelectrons. The spectral energy width also linearly depends on the laser intensity. These linear relationships suggest new methods for the in-situ measurement of laser intensity and pulse duration with high precision.

Far-zone behaviors of scattering-induced statistical properties of partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam

In this study, we explore the far-zero behaviors of a scattered partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam irradiating on a deterministic medium. The analytical formula for the cross-spectral density matrix elements of this beam in the spherical coordinate system is derived. Within the framework of the first-order Born approximation, the effects of the scattering angle θ, the source parameters (i.e., the pulse duration T0 and the temporal coherence length Tcxx), and the scatterer parameter (i.e., the effective width of the medium σR) on the spectral density, the spectral shift, the spectral degree of polarization, and the degree of spectral coherence of the scattered source in the far-zero field are studied numerically and comparatively. Our work improves the scattering theory of stochastic electromagnetic beams and it may be useful for the applications involving the interaction between incident light waves and scattering media.

Photon Statistical Properties of Single Terrylene Molecules in P-Terphenyl Crystals

We consider the photon emission statistical properties of a single molecule under pump-probe field driving, using the generating function method. The first- and second-order moments of statistical quantities are presented. Derived from the first-order moment, the line shapes are in good agreement with the experimental results. Derived from the second-order moment, Mandel＇s Q parameters show an obvious quantum effect of photon statistical distribution, i.e., the anti-bunching effect.

MAXIMUM TEST FOR A SEQUENCE OF QUADRATIC FORM STATISTICS ABOUT SCORE TEST IN LOGISTIC REGRESSION MODEL

This article proposes the maximum test for a sequence of quadratic form statistics about score test in logistic regression model which can be applied to genetic and medicine fields.Theoretical properties about the maximum test are derived.Extensive simulation studies are conducted to testify powers robustness of the maximum test compared to other two existed test.We also apply the maximum test to a real dataset about multiple gene variables association analysis.

Statistic properties of Fermi gas in a strong magnetic field

Based on the thermodynamic potential function of Fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of Fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.

Maximal entanglement from photon-added nonlinear coherent states via unitary beam splitters

In this paper, we construct photon-added f-deformed coherent states （PAf-DCSs） for nonlinear bosonic fields by discussing Klauder＇s minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m. Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PAf-DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.

Effects of postselected von Neumann measurement on the properties of single-mode radiation fields

Postselected von Neumann measurement characterized by postselection and weak value has been found to possess potential applications in quantum metrology and solved plenty of fundamental problems in quantum theory. As an application of this new measurement technique in quantum optics and quantum information processing, its effects on the features of single-mode radiation fields such as coherent state, squeezed vacuum state and Schrödinger cat sate are investigated by considering full-order effects of unitary evolution. The results show that the conditional probabilities of finding photons, second-order correlation functions, Qm-factors and squeezing effects of those states after the postselected measurement is significantly changed are comparable with the corresponding initial pointer states.

Noise composed of multiplication of two dichotomous noises

In this paper, we introduce a noise which is composed of multiplication of two dichotomous noises, and derive the probability density and the statistical properties of this noise. The obtained results can help study the resonant activation phenomenon, the phenomenon of stochastic resonance, the transport of particles, and the nonequilibrium （phase） transition for the systems driven by this noise.

Reliability analysis of extended generalized inverted exponential distribution with applications

A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.

Uncertainties of critical temperatures based on higher-order fluctuations of the largest fragment charge

The new signature of liquid-gas phase transition has been well indicated by the higher-order fluctuations of the largest fragment charge,but the uncertainties of critical temperatures based on this signature have not been revealed.This study extracts the critical temperatures of liquid-gas phase transition in nuclear reactions and investigates their uncertainties.Utilizing the isospin-dependent quantum molecular dynamics model in conjunction with the statistical model GEMINI enables us to describe the dynamical path from the initial to the final state.An isotope thermometer and a quantum fluctuation thermometer are employed to extract the nuclear temperature.The higher-order fluctuations of the largest fragment charge and critical temperatures are studied in^(124)Sn+^(120)Sn collisions ranging from 400 to 1000 MeV/nucleon and^(124)Sn+AZ collisions at 600 MeV/nucleon.Observations revealed that the pseudo-critical point is robustly indicated by the higher-order fluctuations of the largest fragment charge.The critical temperatures extracted by the isotope thermometer are relatively consistent,with an uncertainty of 15%,while those obtained by the quantum fluctuation thermometer are heavily influenced by the incident energy and mass number of target nuclei.The excitation energy E∗and bound charge Zbound are used for event-sorting.These two ensembles represent the statistical properties of the initial and final states of the system,respectively.The initial-final correlations of statistical properties might lead to two phenomena.First,the size distribution of the largest fragment at the pseudo-critical point based on the Zbound ensemble is wide,while that based on E∗ensemble exhibits bimodality,which is a typical characteristic in the liquid-gas coexistence of a finite system.Second,the temperature at the pseudo-critical point based on the Zbound ensemble is higher than that based on the E∗ensemble.Furthermore,the projectile-like system exhibits a significant dynamical effect in its evolution path from the initial to final state,closely associated with the fluctuation of critical temperature.

A new method of studying the statistical properties of speckle phase

A new theoretical method with generality is proposed to study the statistical properties of the speckle phase. The general expression of the standard deviation of the speckle phase about the first-order statistics is derived according to the relation between the phase and the complex speckle amplitude. The statistical properties of the speckle phase have been studied in the diffraction fields with this new theoretical method.

A Unified Theoretical Treatment on Statistical Properties of the Semi-batch Self-condensing Vinyl Polymerization System

We present a novel generating function(GF)method for the self-condensing vinyl polymerization(SCVP)system with any initial distribution of preexisted polymers.Such a method was proven to be especially useful to investigate the semi-batch SCVP system allowing a sequence of feeding operations during the polymerization.Consequently,the number-,weight-,and z-average molecular weights as well as dispersity index of hyperbranched polymers can be explicitly given,which are determined by predetermined feeding details and conversions in each polymerization step.These analytical results are further confirmed by the corresponding Monte Carlo simulations.Therefore,the present GF method has provided a unified treatment to the semi-batch SCVP system.Accordingly,hyperbranched polymers with desired properties can be prepared by designing feeding details and presetting conversions at each step based on the present GF method.

Statistical properties of ultrasound speckles reflected from an interface

The first- and second-order statistical properties of ultrasound -speckles reflected from an interface are studied theoretically and experimentally. A theoretical model for predicting statistical properties of ultrasound speckles is constructed based on the Fresnel-Huygens principle and three basic assumptions. Distributions of amplitude and phase of ultrasound speckles in a scattering space are studied. And the study shows that they are in the form of Rayleigh and uniform distribution respectively. Using the proposed model, the average transverse size of the speckles within a scattering domain which are received by a focus probe is investigated. The average transverse size is found to be dependent on the characteristics of the measuring system only, and does not vary with the position in the domain. To verify the applicability of the theoretical model, a special experimental set-up was designed and the corresponding experiments were conducted for measuring the sound pressure of the ultrasound speckles reflected from an interface between water and Aluminium alloy. The numerical results are compared with the experimental ones. The comparison demonstrates that the theoretical model and the three related assumptions are suitable for analysing statistical properties of ultrasound speckles reflected from an interface.

A review of surface roughness measurements based on laser speckle method

Surface roughness is commonly used to characterize material microstructure during processing,and accurate measurement of surface roughness is the premise and foundation of machining.Therefore,online non-destructive measurement of surface roughness based on the laser speckle method has become a hot issue in recent research.The improvements in surface roughness measurements based on the laser speckle method are systematically reviewed.Theory of speckle formation is introduced.The statistical properties of the speckle patterns including first-order statistical properties and second-order statistical properties are directly related to surface roughness.Surface roughness measurements based on the laser speckle method are roughly divided into the speckle contrast method,speckle correlation method,and fractal method.The three methods are described in detail,and an extensive comparison among all the methods is presented.The recent progresses and application of surface roughness measurements are reviewed.Finally,surface roughness measurements based on the laser speckle method are prospected and summarized.

DESI Legacy Imaging Surveys Data Release 9:Cosmological constraints from galaxy clustering and weak lensing using the minimal bias model

We present a tentative constraint on cosmological parameters Ω_(m) and σ_(8) from a joint analysis of galaxy clustering and galaxygalaxy lensing from DESI Legacy Imaging Surveys Data Release 9(DR9),covering approximately 10000 square degrees and spanning the redshift range of 0.1 to 0.9.To study the dependence of cosmological parameters on lens redshift,we divide lens galaxies into seven approximately volume-limited samples,each with an equal width in photometric redshift.To retrieve the intrinsic projected correlation function w_(p)(r_(p))from the lens samples,we employ a novel method to account for redshift uncertainties.Additionally,we measured the galaxy-galaxy lensing signal ΔΣ(r_(p))for each lens sample,using source galaxies selected from the shear catalog by applying our Fourier Quad pipeline to DR9 images.We model these observables within the flatΛCDM framework,employing the minimal bias model.To ensure the reliability of the minimal bias model,we apply conservative scale cuts:r_(p)>8 and 12 h^(-1)Mpc,for w_(p)(r_(p))and ΔΣ(r_(p)),respectively.Our findings suggest a mild tendency that S_(8)=σ_(8)√Ω_(m)/0.3increases with lens redshift,although this trend is only marginally significant.When we combine low redshift samples,the value of S8is determined to be 0.84±0.02,consistent with the Planck results but significantly higher than the 3×2 pt analysis by 2-5σ.Despite the fact that further refinements in measurements and modeling could improve the accuracy of our results,the consistency with standard values demonstrates the potential of our method for more precise and accurate cosmology in the future.