Generativity of Self-Organizing Processes and Their Correlative Description in Terms of a Formal Language of Meta-Ordinal Generative Nature, in the Light of the Maximum Ordinality Principle and the Explicit Solution to the “Three-Body Problem”

The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be modeled using the Maximum Ordinality Principle and its associated formal language, known as the “Incipient” Differential Calculus (IDC).

Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order

The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this paper.The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance analysis.Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational validity.Then they are capable of having the operational performance of fractional operators and being physical realization.The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.

ARMA–GARCH model with fractional generalized hyperbolic innovations

In this study,a multivariate ARMA–GARCH model with fractional generalized hyperbolic innovations exhibiting fat-tail,volatility clustering,and long-range dependence properties is introduced.To define the fractional generalized hyperbolic process,the non-fractional variant is derived by subordinating time-changed Brownian motion to the generalized inverse Gaussian process,and thereafter,the fractional generalized hyperbolic process is obtained using the Volterra kernel.Based on the ARMA–GARCH model with standard normal innovations,the parameters are estimated for the high-frequency returns of six U.S.stocks.Subsequently,the residuals extracted from the estimated ARMA–GARCH parameters are fitted to the fractional and non-fractional generalized hyperbolic processes.The results show that the fractional generalized hyperbolic process performs better in describing the behavior of the residual process of high-frequency returns than the non-fractional processes considered in this study.

A generalized geometric process based repairable system model with bivariate policy

The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.

New Algorithm Model for Processing GeneralizedDynamic Nonlinear Data Derived from Deformation Monitoring Network

The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years. As a result, many linear methods and nonlinear methods have been developed. But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed. A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.

ON CONVERGENCE OF A GENERALIZED P AL INTERPOLATION PROCESS

Let f∈C[-1,1]and R. (r≥1 ) be the reneralized Pal iner polation polynomials satisf ying the conditions Rn, where{xk} are the roots of n-th Jacobi polynomial Pn and are the roots of In this paper,we prove that Rn holds uniformly on [0,1].

Motor Imagery EEG Fuzzy Fusion of Multiple Classification

Due to the volume conduction,electroencephalogram（EEG） gives a rather blurred image of brain activities. It is a challenge for generating satisfactory performance with EEG. This paper studies the multiple areas fusion of EEG classifiers to improve the motor imagery EEG classification performance. Two feature extraction methods are employed to extract the feature from three different areas of EEG. One is power spectral density（PSD）, and the other is common spatial patterns（CSP）. Classifiers are designed based on the well-known linear discrimination analysis（LDA）. The fusion of the individual classifiers is realized by means of the Choquet fuzzy integral. It is demonstrated that the proposed method comes with better performance compared with the individual classifier.

Generalized Markov interacting branching processes

We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.

Construction of Generalized Diffusion Processes: the Resolvent Approach

In this paper,we define the generalized diffusion operator L=d/dMd/dS for two suitable measures on the line,which includes the generators of the birth-death processes,the one-dimensional diffusion and the gap diffusion among others.Via the standard resolvent approach,the associated generalized diffusion processes are constructed.

Limit Distributions for Generalized Jirina Processes with Immigration

A relationship between continuous state population-size-dependent branching （CSDB） processes with or without immigration and discrete state population-size-dependent branching （DSDB） processes with or without immigration is established via the representation of the former. Based on this relationship, some limiting distributions of CSDB processes with or without immigration are obtained.

Performance Modeling for Data Monitoring Services in Smart Grid: A Network Calculus Based Approach

This paper focuses on solving the modeling issues of monitoring system service performance based on the network calculus theory.First,we formulate the service model of the smart grid monitoring system.Then,we derive the flow arrival curve based on the incremental process related functions.Next,we develop flow arrival curves for the case of the incremental process being a fractional Gaussian process,and then we obtain the generalized Cauchy process.Three technical theorems related to network calculus are presented as our main results.Mathematically,the variance of arrival flow for the continuous time case is derived.Assuming that the incremental process of network flow is a Gaussian stationary process,and given the auto-correlation function of the incremental process with violation probability,the formula of the arrival curve is derived.In addition,the overall flow variance under the discrete time case is explicitly derived.The theoretical results are evaluated in smart grid applications.Simulations indicate that the generalized Cauchy process outperforms the fractional Gaussian process for our considered problem.

Identification of important factors influencing nonlinear counting systems

Identifying factors that exert more influence on system output from data is one of the most challenging tasks in science and engineering.In this work,a sensitivity analysis of the generalized Gaussian process regression(SA-GGPR)model is proposed to identify important factors of the nonlinear counting system.In SA-GGPR,the GGPR model with Poisson likelihood is adopted to describe the nonlinear counting system.The GGPR model with Poisson likelihood inherits the merits of nonparametric kernel learning and Poisson distribution,and can handle complex nonlinear counting systems.Nevertheless,understanding the relationships between model inputs and output in the GGPR model with Poisson likelihood is not readily accessible due to its nonparametric and kernel structure.SA-GGPR addresses this issue by providing a quantitative assessment of how different inputs affect the system output.The application results on a simulated nonlinear counting system and a real steel casting-rolling process have demonstrated that the proposed SA-GGPR method outperforms several state-of-the-art methods in identification accuracy.

Parisian ruin over a finite-time horizon

For a risk process R_u(t) = u + ct- X(t), t≥0, where u≥0 is the initial capital, c > 0 is the premium rate and X(t), t≥0 is an aggregate claim process, we investigate the probability of the Parisian ruin P_S(u, T_u) = P{inf (t∈[0,S]_(s∈[t,t+T_u])) sup R_u(s) < 0}, S, T_u > 0.For X being a general Gaussian process we derive approximations of P_S(u, T_u) as u →∞. As a by-product, we obtain the tail asymptotic behaviour of the infimum of a standard Brownian motion with drift over a finite-time interval.