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.

Generalized Penalized Least Squares and Its Statistical Characteristics

The solution properties of semiparametric model are analyzed, especially that penalized least squares for semiparametric model will be invalid when the matrix B^TPB is ill-posed or singular. According to the principle of ridge estimate for linear parametric model, generalized penalized least squares for semiparametric model are put forward, and some formulae and statistical properties of estimates are derived. Finally according to simulation examples some helpful conclusions are drawn.

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.

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial States

We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schr?dinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.

Statistical Properties of Multispecies Competition Ecosystems Subjected to Dichotomous Noises

We investigate statistical properties of multispecies competition ecosystems subjected to both symmetric and asymmetric dichotomous noises. The expression of the stationary probability distribution function （SPDF） is analytically derived by means of mean-field approximation, and verified by stochastic simulations. The results indicate that： （i） A noise amplitude （a0）, a noise autocorrelation time （τ0） and a noise symmetry parameter （k） all can affect the SPDF; （ii） There is an optimal τ0, which makes the mean value of population density be maximal, near which a transition takes place, i.e., the stationary mean value of species density （（x）st） suddenly falls to a lower constant, （iii） As k decreases, the maximum of （x）xt and the optimal 70 increase. The parameter planes of TO -- a20 and τ0- k for the transition are plotted.

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.

Statistical Behaviors of Quantum Spectra in Superheavy Nuclei

From the point of view of the interplay between order and chaos, the most regular single-particle motion of neutrons has been found in the superheavy system with and based on the Skyrme–Hartree–Fock model and in the system with and based on the relativistic mean-field model. It has been shown that the statistical analysis of spectra can give valuable information about the stability of suprheavy systems. In addition it may yield deep insight into the single-particle motion in the mean field formed by the superheavy system.

Statistical Properties of the nonlinear SU（1,1） Coherent States

Using non-Hermitian realizations of SU(1,1) Lie algebra in terms of an f-oscillator, we generalize the notion of nonlinear coherent states to the single-mode and two-mode nonlinear SU(1,1) coherent states. Taking the nonlinearity function , their statistical properties are studied.

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.

Efficient and Accurate Simulator for Rayleigh and Rician Fading

With an improved Rayleigh fading model and a zero-mean stochastic sinusoid as the scattering and specular components respectively,a stochastic simulation model is proposed for the generation of Rayleigh and Rician fading waveforms.Compared with the existing stochastic models,the proposed simulator needs only one trial to obtain the desired statistical properties even if the number of samples is not large enough.Moreover,the proposed simulation model can directly generate multiple uncorrelated waveforms for different fading scenarios,such as single-input single-output frequency selective channels and multiple-input multiple-output channels.The performance evaluation and comparison show that the proposed simulator is efficient and accurate.

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.

Deterministic and Stochastic Simulators for Non-Isotropic V2V-MIMO Wideband Channels

In this paper, we consider a novel two-dimensional(2D) geometry-based stochastic model(GBSM) for multiple-input multiple-output(MIMO) vehicle-to-vehicle(V2V) wideband fading channels. The proposed model employs the combination of a two-ring model and a multiple confocal ellipses model, where the signal is sum of the line-of-sight(Lo S) component, single-bounced(SB) rays, and double-bounced(DB) rays. Based on the reference model, we derive some expressions of channel statistical properties, including space-time correlation function(STCF), Doppler spectral power density(DPSD), envelope level crossing rate(LCR) and average fade duration(AFD). In addition, corresponding deterministic and stochastic simulation models are developed based on the reference model. Moreover, we compare the statistical properties of the reference model and the two simulation models in different scenarios and investigate the impact of different vehicular traffic densities(VTDs) on the channel statistical properties of the proposed model. Finally, the great agreement between simulation models and the reference model demonstrates not only the utility of simulation models, but also the correctness of theoretical derivations and simulations.

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.

Quantum Properties of Two-Mode Squeezed Even and Odd Coherent States

Two new types of quantum states are constructed by applying the operator s（ξ） = exp（ξ＊ ab - ξa＋b＋） on the two-mode even and odd coherent states. The mathematical and quantum statistical properties of such states are investigated. Various nonclassical features of these states, such as squeezing properties, the inter-mode photon bunching, and the violation of Cauchy-Schwarz inequality, are discussed. The Wigner function in these states are studied in detail.

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.