FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.

Numerical Computation of SEIR Model for the Zika Virus Spreading

The purpose of this study is to present the numerical performancesand interpretations of the SEIR nonlinear system based on the Zika virusspreading by using the stochastic neural networks based intelligent computingsolver. The epidemic form of the nonlinear system represents the four dynamicsof the patients, susceptible patients S(y), exposed patients hospitalized inhospital E(y), infected patients I(y), and recovered patients R(y), i.e., SEIRmodel. The computing numerical outcomes and performances of the systemare examined by using the artificial neural networks (ANNs) and the scaledconjugate gradient (SCG) for the training of the networks, i.e., ANNs-SCG.The correctness of the ANNs-SCG scheme is observed by comparing theproposed and reference solutions for three cases of the SEIR model to solvethe nonlinear system based on the Zika virus spreading dynamics throughthe knacks of ANNs-SCG procedure based on exhaustive experimentations.The outcomes of the ANNs-SCG algorithm are found consistently in goodagreement with standard numerical solutions with negligible errors. Moreover,the procedure’s constancy, dependability, and exactness are perceived by usingthe values of state transitions, error histogram measures, correlation, andregression analysis.

Sense Estimation and Instrumental Evaluation of Fabric-Evoked Prickle

In this paper, the mechanism of fabric-evoked prickle is discussed, which indicates that the mechanical stimuli aroused by the fiber ends on the fabric surface to the skin-sensory receptors are responsible for prickle. The factors influencing the intensity of prickle are specialized and anatomized. Several means of sense estimate, including the corresponding statistical measures, are described. A few groping objective methods of evaluating prickle are analyzed, including the testing principles, the advantages and the disadvantages. At last, a new concept is proposed on the objective evaluation of prickle.

A New Approach to Probability Assessment

Using spreadsheets and ranges for pairwise judgments,candidate probability distributions are generated for the decision-maker to consider.This replaces event-by-event determination of probabilities.Basic statistics of the distributions are then used to determine a final distribution for decision purposes as in buy,sell,or hold.

Complexity analyses of multi-wing chaotic systems

The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.

The chaotification of discrete Hopfield neural networks via impulsive control

The chaotification of discrete Hopfield neural networks is studied with impulsive control techniques. No matter whether the original systems are stable or not, chaotilication theorems for discrete Hopfield neural networks are derived, respectively. Finally, the effectiveness of the theoretical results is illustrated by some numerical examples.

Information Feedback Strategies in a Signal Controlled Network with Overlapped Routes

We investigate the effects of four different information feedback strategies on the dynamics of traffic, travelers＇ route choice and the resultant system performance in a signal controlled network with overlapped routes. Simulation results given by the cellular automaton model show that the system purpose-based mean velocity feedback strategy and the congestion coefficient feedback strategy have more advantages in improving network utilization efficiency and reducing travelers＇ travel times. The travel time feedback strategy and the individual purposed-based mean velocity feedback strategy behave slightly better to ensure user equity.

Chaos Control and Synchronization of Cellular Neural Network with Delays Based on OPNCL Control

The problem of chaos control and complete synchronization of cellular neural network with delays is studied. Based on the open plus nonlinear closed loop （OPNCL） method, the control scheme and synchronization scheme are designed. Both the schemes can achieve the chaos control and complete synchronization of chaotic neural network respectively, and their validity is further verified by numerical simulation experiments.

Measure theory of statistical convergence

The question of establishing measure theory for statistical convergence has been moving closer to center stage, since a kind of reasonable theory is not only fundamental for unifying various kinds of statistical convergence, but also a bridge linking the studies of statistical convergence across measure theory, integration theory, probability and statistics. For this reason, this paper, in terms of subdifferential, first shows a representation theorem for all finitely additive probability measures defined on the σ-algebra of all subsets of N, and proves that every such measure can be uniquely decomposed into a convex combination of a countably additive probability measure and a statistical measure (i.e. a finitely additive probability measure μ with μ(k) = 0 for all singletons {k}). This paper also shows that classical statistical measures have many nice properties, such as: The set of all such measures endowed with the topology of point-wise convergence on forms a compact convex Hausdorff space; every classical statistical measure is of continuity type (hence, atomless), and every specific class of statistical measures fits a complementation minimax rule for every subset in N. Finally, this paper shows that every kind of statistical convergence can be unified in convergence of statistical measures.

I.I.D.STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.

Statistical Convergence and Measure Convergence Generated by a Single Statistical Measure

The purpose of this paper is to discuss those kinds of statistical convergence, in terms of F , or ideal Z-convergence, which are equivalent to measure convergence defined by a single statistical measure. We prove a number of characterizations of a single statistical measure μ-convergence by using properties of its corresponding quotient Banach space l∞/l∞ （Iμ）. We also show that the usual sequential convergence is not equivalent to a single measure convergence.

Statistical Measure for Risk-seeking Stochastic Wind Power Offering Strategies in Electricity Markets

This study proposes a statistical measure and a stochastic optimization model for generating risk-seeking wind power offering strategies in electricity markets. Inspired by the value at risk(VaR) to quantify risks in the worst-case scenarios of a profit distribution, a statistical measure is proposed to quantify potential high profits in the best-case scenarios of a profit distribution,which is referred to as value at best(VaB)in the best-case scenarios. Then, a stochastic optimization model based on VaB is developed for a risk-seeking wind power producer, which is formulated as a mixed-integer linear programming problem. By adjusting the parameters in the proposed model, the wind power producer can flexibly manage the potential high profits in the best-case scenarios from the probabilistic perspective. Finally, the proposed statistical measure and riskseeking stochastic optimization model are verified through case studies.

Measurement of Joint Roughness Coefficient by Using Profilograph and Roughness Ruler

Joint roughness coefficient（JRC） is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS（joint wall compressive strength） model.Because JRC has such characteristics as nonuniformity,anisotropy,and unhomogeneity,directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method.However,the directional statistical measurement of JRC is time-consuming.In order to present an ideal measurement method of JRC,new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC.Operation methods of the profilographs and roughness rulers were also introduced.A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC.

A cumulative standard deviation sum based method for high resistance fault identification and classification in power transmission lines

High resistance fault poses an enormous challenge to the existing algorithms of fault detection and fault classification.In this paper,the standard deviation and accumulation method are employed to perform the fault detection and classification.It is primarily built in two stages.Firstly,the standard deviations for the measured current’s signals of the local and remote terminals is computed to extract the fault feature.Secondly,the cumulative approach is used to enlarge the fault feature to perform the high resistance fault.The proposed scheme is known as Standard Deviation Index(SDI),and it is obtained for the three phases and zero sequence.The proposed algorithm has been tested through different fault circumstances such as multiple faults locations,fault resistances,and fault inception time.Moreover,far-end faults with high-resistance,faults happened nearby the terminal,faults considering variable loading angle,sudden load change,different sampling frequency,bad signaling and a fault occurred in the presence of series compensation are also discussed.The results show that the proposed scheme performed remarkably well regarding the fault with resistance up to 1.5kΩand can be detected within a millisecond after the fault inception.Additionally,the computational simplicity that characterizes the processes makes it more efficient and suitable for domain applications.

A Survey of Repetitive Control for Nonlinear Systems

In aerospace engineering and industry, control tasks are often of a periodic nature,while repetitive control is especially suitable for tracking and rejection of periodic exogenous signals.Because of limited research effort on nonlinear systems, we give a survey of repetitive control for nonlinear systems in this paper.First,a brief introduction of repetitive control is presented.Then,after giving a brief overview of repetitive control for linear systems,this paper summarizes design methods and existing problems of repetitive control for nonlinear systems in detail.Lastly,relationships between repetitive control and other control schemes are analyzed to recognize repetitive control from different aspects more insightfully.

A novel multiple-outlier-robust Kalman filter

This paper presents a novel multiple-outlier-robust Kalman filter(MORKF)for linear stochastic discretetime systems.A new multiple statistical similarity measure is first proposed to evaluate the similarity between two random vectors from dimension to dimension.Then,the proposed MORKF is derived via maximizing a multiple statistical similarity measure based cost function.The MORKF guarantees the convergence of iterations in mild conditions,and the boundedness of the approximation errors is analyzed theoretically.The selection strategy for the similarity function and comparisons with existing robust methods are presented.Simulation results show the advantages of the proposed filter.