WEIGHTED APPROXIMATION OF RANDOM FUNCTIONS

Let (Ω, A, P) be a probability space, X(t, ω) a random function continuous in probability for t∈[0,+∞) or (-∞,+∞)(ω∈Ω), and F(t) a positive function continuous for t∈[0,+∞) or (-∞, +∞). If X(t, ω) and F(t) verify certain conditions, then there exists a sequence {Qn(t,ω)} of random polynomials such that we have almost surely: for t∈[0,+∞) or (-∞, +∞), lim|X(t, ω)-Qn(t, ω)|/F(t)=0.

Mean-square Almost Periodic Random Functions

In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.

THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS

The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.

QUANTITATIVE THEOREM AND SATURATION THEOREM FOR MULTIVARIATE RANDOMFUNCTIONS

In this paper, we give the quantitative theorem and saturation theorem for random functions with compact convex parameter spaces.

Underwater Image Classification Based on EfficientnetB0 and Two-Hidden-Layer Random Vector Functional Link

The ocean plays an important role in maintaining the equilibrium of Earth’s ecology and providing humans access to a wealth of resources.To obtain a high-precision underwater image classification model,we propose a classification model that combines an EfficientnetB0 neural network and a two-hidden-layer random vector functional link network(EfficientnetB0-TRVFL).The features of underwater images were extracted using the EfficientnetB0 neural network pretrained via ImageNet,and a new fully connected layer was trained on the underwater image dataset using the transfer learning method.Transfer learning ensures the initial performance of the network and helps in the development of a high-precision classification model.Subsequently,a TRVFL was proposed to improve the classification property of the model.Net construction of the two hidden layers exhibited a high accuracy when the same hidden layer nodes were used.The parameters of the second hidden layer were obtained using a novel calculation method,which reduced the outcome error to improve the performance instability caused by the random generation of parameters of RVFL.Finally,the TRVFL classifier was used to classify features and obtain classification results.The proposed EfficientnetB0-TRVFL classification model achieved 87.28%,74.06%,and 99.59%accuracy on the MLC2008,MLC2009,and Fish-gres datasets,respectively.The best convolutional neural networks and existing methods were stacked up through box plots and Kolmogorov-Smirnov tests,respectively.The increases imply improved systematization properties in underwater image classification tasks.The image classification model offers important performance advantages and better stability compared with existing methods.

ON THE DISTRIBUTION OF VALUES AND DEFICIENT FUNCTION OF A GENERAL RANDOM INTEGRAL FUNCTION

Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).

Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment

This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.

ON MULTIPLE WIENER INTEGRAL EXPANSIONS FOR D'-VALUED NONLINEAR RANDOM FUNCTIONALS

In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integral kernels such that the nonlinear functional can be expanded by series of multiple Wiener integrals of the integral kernels with respect to the Wiener D'-process.

AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS

Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.

Robust H_∞ control of piecewise-linear chaotic systems with random data loss

This paper studies the problem of robust H∞ control of piecewise-linear chaotic systems with random data loss. The communication links between the plant and the controller are assumed to be imperfect （that is, data loss occurs intermittently, which appears typically in a network environment）. The data loss is modelled as a random process which obeys a Bernoulli distribution. In the face of random data loss, a piecewise controller is designed to robustly stabilize the networked system in the sense of mean square and also achieve a prescribed H∞ disturbance attenuation performance based on a piecewise-quadratic Lyapunov function. The required H∞ controllers can be designed by solving a set of linear matrix inequalities （LMIs）. Chua＇s system is provided to illustrate the usefulness and applicability of the developed theoretical results.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT(I):MODEL,MARKOV PROPERTY,MOMENTS

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.

RVFLN-based online adaptive semi-supervised learning algorithm with application to product quality estimation of industrial processes

Direct online measurement on product quality of industrial processes is difficult to be realized,which leads to a large number of unlabeled samples in modeling data.Therefore,it needs to employ semi-supervised learning(SSL)method to establish the soft sensor model of product quality.Considering the slow time-varying characteristic of industrial processes,the model parameters should be updated smoothly.According to this characteristic,this paper proposes an online adaptive semi-supervised learning algorithm based on random vector functional link network(RVFLN),denoted as OAS-RVFLN.By introducing a L2-fusion term that can be seen a weight deviation constraint,the proposed algorithm unifies the offline and online learning,and achieves smoothness of model parameter update.Empirical evaluations both on benchmark testing functions and datasets reveal that the proposed OAS-RVFLN can outperform the conventional methods in learning speed and accuracy.Finally,the OAS-RVFLN is applied to the coal dense medium separation process in coal industry to estimate the ash content of coal product,which further verifies its effectiveness and potential of industrial application.

A numerical simulation of seepage structure surface and its feasibility

According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Adaptive Control of Discrete-time Nonlinear Systems Using ITF-ORVFL

Random vector functional ink(RVFL)networks belong to a class of single hidden layer neural networks in which some parameters are randomly selected.Their network structure in which contains the direct links between inputs and outputs is unique,and stability analysis and real-time performance are two difficulties of the control systems based on neural networks.In this paper,combining the advantages of RVFL and the ideas of online sequential extreme learning machine(OS-ELM)and initial-training-free online extreme learning machine(ITFOELM),a novel online learning algorithm which is named as initial-training-free online random vector functional link algo rithm(ITF-ORVFL)is investigated for training RVFL.The link vector of RVFL network can be analytically determined based on sequentially arriving data by ITF-ORVFL with a high learning speed,and the stability for nonlinear systems based on this learning algorithm is analyzed.The experiment results indicate that the proposed ITF-ORVFL is effective in coping with nonparametric uncertainty.

Itopride therapy for functional dyspepsia:A meta-analysis

AIM:To evaluate the therapeutic effects of itopride vs other drugs(placebo,domperidone,mosapride) for functional dyspepsia(FD).METHODS:Randomized controlled trials(RCTs) of itopride for FD were retrieved from databases.Relevant information was extracted and analyzed,using the relative risk(RR) and weighted mean deviation,as appropriate.A random or fixed effect model was used,based on the heterogeneity of the included articles,and visual inspection of funnel plots was used to evaluate publication bias.RESULTS:Nine RCTs enrolling 2620 FD cases were included;1372 cases received itopride treatment and 1248 cases received placebo or other drugs(control groups).Compared with control groups,itopride had superior RR values of 1.11 [95%CI:(1.03,1.19),P = 0.006],1.21 [95%CI:(1.03,1.44),P = 0.02],and1.24 [95%CI:(1.01,1.53),P = 0.04] for global patient assessment,postprandial fullness,and early satiety,respectively.For the Leeds Dyspepsia Questionnaire score,the weighted mean deviation was-1.38 [95%CI:(-1.75,-1.01),P < 0.01].The incidence of adverse effects was similar in the itopride and control groups.The funnel plots for all indicators showed no evidence of publication bias.CONCLUSION:Itopride has good efficacy in terms of global patients assessment,postprandial fullness,and early satiety in the treatment of patients with FD and shows a low rate of adverse reactions.Itopride can greatly improve FD syndromes-score.

The distribution of normalized zero-sets of random meromorphic functions

This paper is concerned with the distribution of normalized zero-sets of random meromorphic functions.The normalization of the zero-set plays the same role as the counting function for a meromorphic function in Nevanlinna theory.The results generalize the theory of Shiffman and Zelditch on the distribution of the zeroes of random holomorphic sections of powers of positive Hermitian holomorphic line bundles.As in a very special case,our paper resembles a form of First Main Theorem in classical Nevanlinna Theory.

A Machine Learning Approach for Artifact Removal from Brain Signal

Electroencephalography(EEG),helps to analyze the neuronal activity of a human brain in the form of electrical signals with high temporal resolution in the millisecond range.To extract clean clinical information from EEG signals,it is essential to remove unwanted artifacts that are due to different causes including at the time of acquisition.In this piece of work,the authors considered the EEG signal contaminated with Electrocardiogram(ECG)artifacts that occurs mostly in cardiac patients.The clean EEG is taken from the openly available Mendeley database whereas the ECG signal is collected from the Physionet database to create artifacts in the EEG signal and verify the proposed algorithm.Being the artifactual signal is non-linear and non-stationary the Random Vector Functional Link Network(RVFLN)model is used in this case.The Machine Learning approach has taken a leading role in every field of current research and RVFLN is one of them.For the proof of adaptive nature,the model is designed with EEG as a reference and artifactual EEG as input.The peaks of ECG signals are evaluated for artifact estimation as the amplitude is higher than the EEG signal.To vary the weight and reduce the error,an exponentially weighted Recursive Least Square(RLS)algorithm is used to design the adaptive filter with the novel RVFLN model.The random vectors are considered in this model with a radial basis function to satisfy the required signal experimentation.It is found that the result is excellent in terms of Mean Square Error(MSE),Normalized Mean Square Error(NMSE),Relative Error(RE),Gain in Signal to Artifact Ratio(GSAR),Signal Noise Ratio(SNR),Information Quantity(IQ),and Improvement in Normalized Power Spectrum(INPS).Also,the proposed method is compared with the earlier methods to show its efficacy.

Physical random function model of ground motions for engineering purposes

A physical random function model of ground motions for engineering purposes is presented with verification of sample level. Firstly,we derive the Fourier spectral transfer form of the solution to the definition problem,which describes the one-dimensional seismic wave field. Then based on the special models of the source,path and local site,the physical random function model of ground motions is obtained whose physical parameters are random variables. The superposition method of narrow-band harmonic wave groups is improved to synthesize ground motion samples. Finally,an application of this model to simulate ground motion records in 1995 Kobe earthquake is described. The resulting accelerograms have the frequencydomain and non-stationary characteristics that are in full agreement with the realistic ground motion records.

Pseudorandomness of Camellia-Like Scheme

Luby and Rackoff idealized DES by replacing each round function with one large random function. In this paper, the author idealizes Camellia by replacing each S-box with one small random function, which is named Camellialike scheme. It is then proved that five-round Camellia-like scheme is pseudorandom and eight-round Camellia-like scheme is super-pseudorandom for adaptive adversaries. Further the paper considers more efficient construction of Camellia-like scheme, and discusses how to construct pseudorandom Camellia-like scheme from less random functions.