Moved Score Confidence Intervals for Means of Discrete Distributions

Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means;for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.

LOCALIZED RADON-WIGNER TRANSFORM AND GENERALIZED-MARGINAL TIME-FREQUENCY DISTRIBUTIONS

This paper introduces the localized Radon transform (LRT) into time-frequency distributions and presents the localized Radon-Wigner transform (LRWT). The definition of LRWT and a fast algorithm is derived, the properties of LRWT and its relationship with Radon-Wigner transform, Wigner distribution (WD), ambiguity function (AF), and generalized-marginal time-frequency distributions are analyzed.

A NEW QUADRATIC TIME-FREQUENCY DISTRIBUTIONAND A COMPARATIVE STUDY OF SEVERAL POPULARQUADRATIC TIME-FREQUENCY DISTRIBUTIONS

A new quadratic time-frequency distribution (TFD) with a compound kernel is proposed and a comparative study of several popular quadratic TFD is carried out. It is shown that the new TFD with compound kernel has stronger ability than the exponential distribution (ED) and the cone-shaped kernel distribution (CKD) in reducing cross terms, meanwhile almost not decreasing the time-frequency resolution of ED or CKD.

Mathematical simulation of burden distribution in COREX 3000 shaft by discrete element method

The distribution of reducing gas in a shaft furnace dominates the temperature profile,gas utilization ratio,metallization degree and is the overwhelming factor for stable,high productivities and low-energy-consumption operation.At the same time,the distribution of gas flow is mainly determined by the position of gas inlet,the packed bed porosity distribution as well as its change due to the difference on the mode of top charge and bottom discharge.When injecting position of the process is fixed,the charge mode is the only means for regulating the gas flow distribution.In this paper,a numerical simulation model of burden distribution in the shaft furnace of COREX 3000 has been developed to analyze the porosity distribution under the different charge modes by means of Discrete Element Method(DEM).The effects of the particle size and its distribution under conditions of different charge batches,chute angle,stoke line on the burden surface shape and burden bed particle size distribution and segregation were investigated,and then the porosity distribution in the shaft of corresponding charging pattern was quantitatively accessed.Therefore,the results can be used to optimize the charge patterns base on required gas distribution.

Transitioning from Discrete to Continuous Distribution Mathematica vs. Excel —An Example

Frequencies of the repeated integers of the first n digits of e.g. π utilizing commercial software are listed. The discrete distribution is utilized to evaluate its statistical moments. The distribution is fitted with a polynomial generating a continuous replica of the former. Its statistical moments are evaluated and compared to the former. The procedure clarifies the mechanism transiting from discrete to a continuous domain. Applying Mathematica the fitted polynomial is replaced with an interpolated function with controlled smoothing factor refining the quality of the fit and its corresponding moments. Knowledge learned assists in the understanding of the standard procedure calculating moments of e.g. Maxwell-Boltzmann continuous distribution in kinetic Theory of gases.

Application of a Discrete Phase-Randomized Coherent State Source in Round-Robin Differential Phase-Shift Quantum Key Distribution

Recently, a novel kind of quantum key distribution called the round-robin differential phase-shift （RRDPS） protocol was proposed, which bounds the amount of leakage without monitoring signal disturbance. The protocol can be implemented by a weak coherent source. The security of this protocol with a simply characterized source has been proved. The application of a common phase shift can improve the secret key rate of the protocol. In practice, the randomized phase is discrete and the secret key rate is deviated from the continuous case. In this study, we analyze security of the RRDPS protocol with discrete-phase-randomized coherent state source and bound the secret key rate. We fix the length of each packet at 32 and 64, then simulate the secret key rates of the RRDPS protocol with discrete-phase randomization and continuous-phase randomization. Our simulation results show that the performance of the discrete-phase randomization case is close to the continuous counterpart with only a small number of discrete phases. The research is practically valuable for experimental implementation.

Adaptive Time-Frequency Distribution Based on Time-Varying Autoregressive and Its Application to Machine Fault Diagnosis

The time-varying autoregressive （TVAR） modeling of a non-stationary signal is studied. In the proposed method, time-varying parametric identification of a non-stationary signal can be translated into a linear time-invariant problem by introducing a set of basic functions. Then, the parameters are estimated by using a recursive least square algorithm with a forgetting factor and an adaptive time-frequency distribution is achieved. The simulation results show that the proposed approach is superior to the short-time Fourier transform and Wigner distribution. And finally, the proposed method is applied to the fault diagnosis of a bearing , and the experiment result shows that the proposed method is effective in feature extraction.

The W transform and its improved methods for time-frequency analysis of seismic data

The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.

Particle size spatial distribution in landslide dams

The particle composition and spatial distribution of landslide-induced dam bodies are critical geotechnical parameters for studying the hazards of dam-break floods.However,current research often neglects the influence of the initial particle composition and spatial distribution of the landslide on the particle composition and spatial distribution of the landslide dam.This study investigated the impact of initial particle size distribution,volume,and sliding length on the energy and velocity changes of characteristic particles during the sliding process and the spatial distribution of particle sizes in the landslide dam body.Numerical simulations and physical models were employed to examine the effects of sequential gradient arrangements(where particle sizes decrease from top to bottom)and four other different initial particle arrangements on the energy and velocity changes of particles and the spatial distribution of particle sizes in the dam body.The study reveals the characteristics of translational and rotational energy of different particles and the laws of mechanical energy conversion,obtaining the spatial distribution patterns of particle sizes in landslide-induced dams.The results show that under the sequential gradient arrangement,the energy dissipation of the landslide movement is lower,with larger particles mainly distributed at the distal end and smaller particles at the proximal end of the landslide dam.In contrast,under the reverse gradient arrangement,the energy dissipation of the landslide movement is higher,and the distribution pattern of the dam particles is opposite to that of the sequential gradient arrangement.For the other arrangement modes,the spatial distribution of dam particles falls between the aforementioned two.There is a positive correlation between particle size and translational kinetic energy within the particle flow during the landslide process,and rotational motion increases energy dissipation.Under constant slope conditions,sliding length does not affect the movement pattern of the particle flow or the spatial distribution of particles in the dam body.The findings of this study provide a scientific basis for the accurate simulation and prediction of dam-break flood processes.

Global exponential stability of mixed discrete and distributively delayed cellular neural network

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.

A descriptor system approach to robust stabilityof uncertain degenerate systems with discreteand distribute delays

The robust stability of uncertain linear degenerate systems with discrete and distributed delays is studied in this paper. The uncertainties under consideration are norm bounded, and possibly time varying. A novel robust stability criterion of the system is derived by constructing Lyapunov functions. The degenerate systems are transformed to a descriptor system and the stability criteria are formulated in the form of a linear matrix inequality （LMI）. Therefore, it is easy to check the robust stability of the degenerate systems by using this method. Numerical examples are also worked out to illustrate the obtained results.

Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

Stability of stochastic switched epidemic systems with discrete or distributed time delay

Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

The Lotka-Volterra Competition System with Discrete and Distributed Time Delays

In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

Agent-Based Synthesis of Distributed Controllers for Discrete Manufacturing Systems

A method for designing real-time distributed controllers of discrete manufacturing systems is presented. The approach held is agent based;the controller strategy is distributed into several interacting agents that operate each one on a part of the manufacturing process;these agents may be distributed into several interconnected processors. The proposed method consists of a modelling methodology and software development framework that provides a generic agent architecture and communication facilities supporting the interaction among agents.

Implementation of Hierarchical and Distributed Control for Discrete Event Robotic Manufacturing Systems

The large scale and complex manufacturing systems have a hierarchical structure where a system is composed several lines with some stations and each station also have several machines and so on. In such a hierarchical structure, the controllers are geographically distributed according to their physical structure. So it is desirable to realize the hierarchical and distributed control. In this paper, a methodology is presented using Petri nets for hierarchical and distributed control. The Petri net representation of discrete event manufacturing processes is decomposed and distributed into the machine controllers, which are coordinated through communication between the coordinator and machine controllers so that the decomposed transitions fire at the same time. Implementation of a hierarchical and distributed control system is described for an example robotic manufacturing system. The demonstrations show that the proposed system can be used as an effective tool for consistent modeling and control of large and complex manufacturing systems.

Distributed Fault Detection for Consensus in Second-Order Discrete-Time Multiagent Systems with Adversary

This paper is concerned with distributed fault detection of second-order discrete-time multi-agent systems with adversary,where the adversary is regarded as a slowly time-varying signal.Firstly,a novel intrusion detection scheme based on the theory of unknown input observability( UIO) is proposed. By constructing a bank of UIO,the states of the malicious agents can be directly estimated. Secondly,the faulty-node-removal algorithm is provided.Simulations are also provided to demonstrate the effectiveness of the theoretical results.

TVAR Time-frequency Analysis for Non-stationary Vibration Signals of Spacecraft

Predicting the time-varying auto-spectral density of a spacecraft in high-altitude orbits requires an accurate model for the non-stationary random vibration signals with densely spaced modal frequency. The traditional time-varying algorithm limits prediction accuracy, thus affecting a number of operational decisions. To solve this problem, a time-varying auto regressive （TVAR） model based on the process neural network （PNN） and the empirical mode decomposition （EMD） is proposed. The time-varying system is tracked on-line by establishing a time-varying parameter model, and then the relevant parameter spectrum is obtained. Firstly, the EMD method is utilized to decompose the signal into several intrinsic mode functions （IMFs）. Then for each IMF, the PNN is established and the time-varying auto-spectral density is obtained. Finally, the time-frequency distribution of the signals can be reconstructed by linear superposition. The simulation and the analytical results from an example demonstrate that this approach possesses simplicity, effectiveness, and feasibility, as well as higher frequency resolution.

Wigner-Ville distribution and its application in seismic attenuation estimation

The attenuation of seismic signals is often characterized in the frequency domain using statistical measures of the power spectrum. However, the conventional Fourier transform-based power spectrum estimation methods suffer from time-frequency resolution problems. Wigner-Ville distribution, which is a member of Cohen class time-frequency distributions, possesses many appealing properties, such as time-frequency marginal distribution, time-frequency localization, etc. Therefore, Wigner-Ville distribution offers a new way for estimating the attenuation of seismic signals. This paper initially gives a brief introduction to Wigner-Ville distribution and the smoothed Wigner-Ville distribution that is effective in reducing the cross-term effect, and then presents a method for seismic attenuation estimation based on the instantaneous energy spectrum of the Wigner-Ville distribution. A real data example from central Tarim Basin in western China is presented to illustrate the effectiveness of the proposed method. The results show that the Wigner-Ville distribution-based seismic attenuation estimation method can effectively detect the difference between reef, shoal and lagoon facies by their attenuation properties, indicating that the estimated seismic attenuation can be used for reef and shoal carbonate reservoir characterization.