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.

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.

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 EXTENSION THEOREM OF LINEAR RANDOM FUNCTIONALS AND ITS APPLICATIONS

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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.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

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.

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.

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).

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.

Almost sure central limit theorems for random functions

Let {Xn,-∞＜ n ＜∞} be a sequence of independent identically distributed be a random function such that Tn = ASn+ Rn,where supnE|Rn|＜∞ and Rn = o(√n)a.s.,or Rn = O(n1/2-2γ) a.s.,0 ＜γ＜ 1/8.In this paper,we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn.As a consequence,it can be shown that ASCLT and FASCLT also hold for U-statistics,Von-Mises statistics,linear processes,moving average processes,error variance estimates in linear models,power sums,product-limit estimators of a continuous distribution,product-limit estimators of a quantile function,etc.

Random testing for system-level functional verification of system-on-chip

In order to deal with the limitations during the register transfer level verification, a new functional verification method based on the random testing for the system-level of system-on-chip is proposed.The validity of this method is proven theoretically.Specifically, testcases are generated according to many approaches of randomization.Moreover, the testbench for the system-level verification according to the proposed method is designed by using advanced modeling language.Therefore, under the circumstances that the testbench generates testcases quickly, the hardware/software co-simulation and co-verification can be implemented and the hardware/software partitioning planning can be evaluated easily.The comparison method is put to use in the evaluation approach of the testing validity.The evaluation result indicates that the efficiency of the partition testing is better than that of the random testing only when one or more subdomains are covered over with the area of errors, although the efficiency of the random testing is generally better than that of the partition testing.The experimental result indicates that this method has a good performance in the functional coverage and the cost of testing and can discover the functional errors as soon as possible.

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.

RANDOM APPROXIMATION OF AN ADDITIVE FUNCTIONAL EQUATION OF m-APPOLLONIUS TYPE

In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原

Stability of a cubic functional equation in intuitionistic random normed spaces

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.

Memory Function and Fractional Intergral Associated to the Random Self-similar Fractal

For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.

Structure-function Relationships in Human Hypoxanthine-guanine Phosphoribosyltransferase(HGPRT) by Random Mutagenesis

Hypoxanthine-guanine phosphoribosyltransferase （ HGPRT, EC 2.4.2.8） is a key enzyme of the purine salvage pathway, which allows recycling of purine bases into DNA and RNA. It is widely distributed in nature and has been studied both in prokaryotes and eukaryotes. In humans, a complete lack of HGPRT activity causes the Lesch-Nyhan syndrome, which is characterized by hyperuricaemia and neural disorders,

Randomized Objective Function Linear Programming in Risk Management

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.

Exceptional Functions of Random Series

We study the random Taylor series whose random variable sequence in |z|＜1 belongs to a class of non equal distributions which are general enough, and proved that they have not almost surely exceptioinal fu nction.