On the Viability of Solutions to Conformable Stochastic Differential Equations

The viability of the conformable stochastic differential equations is studied.Some necessary and sufficient conditions in terms of the distance function to K are given.In addition,when the boundary of K is sufficiently smooth,our necessary and sufficient conditions can reduce to two relations just on the boundary of K.Lastly,an example is given to illustrate our main results.

The Fuzzy Modeling Algorithm for Complex Systems Based on Stochastic Neural Network

A fuzzy modeling method for complex systems is studied. The notation of general stochastic neural network (GSNN) is presented and a new modeling method is given based on the combination of the modified Takagi and Sugeno's (MTS) fuzzy model and one-order GSNN. Using expectation-maximization(EM) algorithm, parameter estimation and model selection procedures are given. It avoids the shortcomings brought by other methods such as BP algorithm, when the number of parameters is large, BP algorithm is still difficult to apply directly without fine tuning and subjective tinkering. Finally, the simulated example demonstrates the effectiveness.

BACKWARD STOCHASTIC VIABILITY AND RELATED PROPERTIES ON Z FOR BSDES WITH APPLICATIONS

This paper investigates some important properties of Z, the martingale integrant of the backward stochastic differential equations, which is the second process of the solution. These include the backward stochastic viability property, bounded property and the comparison theorem. To explain the theoretical results, the authors apply them to study a financial contingent claim pricing problem. The replication portfolio process can be characterized clearly.

Shuffled complex evolution coupled with stochastic ranking for reservoir scheduling problems

This paper introduces an optimization method(SCE-SR)that combines shuffled complex evolution(SCE)and stochastic ranking(SR)to solve constrained reservoir scheduling problems,ranking individuals with both objectives and constrains considered.A specialized strategy is used in the evolution process to ensure that the optimal results are feasible individuals.This method is suitable for handling multiple conflicting constraints,and is easy to implement,requiring little parameter tuning.The search properties of the method are ensured through the combination of deterministic and probabilistic approaches.The proposed SCE-SR was tested against hydropower scheduling problems of a single reservoir and a multi-reservoir system,and its performance is compared with that of two classical methods(the dynamic programming and genetic algorithm).The results show that the SCE-SR method is an effective and efficient method for optimizing hydropower generation and locating feasible regions quickly,with sufficient global convergence properties and robustness.The operation schedules obtained satisfy the basic scheduling requirements of reservoirs.

Global synchronization of general delayed complex networks with stochastic disturbances

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.

Synchronization of stochastic complex networks with time-delayed coupling

Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.

A Complex Algorithm for Solving a Kind of Stochastic Programming

Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm.

Scale, Complexity, and Cybersecurity Risk Management

Elementary information theory is used to model cybersecurity complexity, where the model assumes that security risk management is a binomial stochastic process. Complexity is shown to increase exponentially with the number of vulnerabilities in combination with security risk management entropy. However, vulnerabilities can be either local or non-local, where the former is confined to networked elements and the latter results from interactions between elements. Furthermore, interactions involve multiple methods of communication, where each method can contain vulnerabilities specific to that method. Importantly, the number of possible interactions scales quadratically with the number of elements in standard network topologies. Minimizing these interactions can significantly reduce the number of vulnerabilities and the accompanying complexity. Two network configurations that yield sub-quadratic and linear scaling relations are presented.

Analysis on MAV/UAV cooperative combat based on complex network

A formation model of manned/unmanned aerial vehicle(MAV/UAV) collaborative combat can qualitatively and quantitatively analyze the synergistic effects.However,there is currently no effective and appropriate model construction method or theory,and research in the field of collaborative capability evaluation is basically nonexistent.According to the actual conditions of cooperative operations,a new MAV/UAV collaborative combat network model construction method based on a complex network is presented.By analyzing the characteristic parameters of the abstract network,the index system and complex network are combined.Then,a method for evaluating the synergistic effect of the cooperative combat network is developed.This method provides assistance for the verification and evaluation of MAV/UAV collaborative combat.

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper, the pinning synchronization problem of stochastic delayed complex network （SDCN） is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller, where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller, some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.

Wavelet packet-based identification of complex oscillation in biological signals

Owing to the intrinsic nonlinearities of the system,a contracting mechanism,such as myogenic response,may induce different oscillatory patterns.Many specialists discussed the relations of oscillatory patterns with intrinsic control system or some pathological condition,but there is no single,well-defined criterion to achieve the identification of regular,stochastic,and chaotic activities.In this paper,we focus on the Mallat algorithm of wavelet packet and use it in the identification of the regular periodic,stochastic,and chaotic fluctuations.According to the specific frequency configuration of the chaos activity,we select proper layers of decomposition of wavelet packet and did fine segments to the frequency of signals.The frequency band of energy convergence could be recognized.The signal of periodic,stochastic,and chaotic could be distinguished depending on it.Numerical experiment is given to show its efficiency.Experiments on 12 babies' lung data have been done.This identification by means of wavelet packet could support the cardiologist or cerebral specialist to do more observation and deeper analysis to physic signals.

A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS

A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.

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.

A New Formula for Partitions in a Set of Entities into Empty and Nonempty Subsets, and Its Application to Stochastic and Agent-Based Computational Models

In combinatorics, a Stirling number of the second kind S (n,k)? is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its “share” Pi =0?. Accordingly, a new equation for partitions P (N, m)? in a set of entities into both empty and nonempty subsets was derived. The indistinguishableness of particles (N identical atoms or molecules) makes only sense within a cluster (subset) with the size?0≤ni ≥N. The first-order phase transition is indeed the case of transitions, for example in the simplest interpretation, from completely liquid state?typeL = {n1 =N, n2 = 0} to the completely crystalline state??typeC= {n1 =0, n2 = N }. These partitions are well distinguished from the physical point of view, so they are ‘typed’ differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of super-cooled liquids and glasses, are discussed by using such stochastic cluster-based models.

The Origin of Population Diversity: Stochastic Interactions between a Modifier Variant and the Individual Genetic Background

Stochastic epistasis that is one of the characteristics of epistatic gene modules can have an important role in the maintenance of intraspecific population diversity. The effect of an epistatic modifier variant can vary in size and direction among the modifier careers on the basis of stochastic genetic individuality and the entire module effect can be also individually stochastic. This stochastic genetic contribution under a genetic background may be conditional upon the presence of a monomorphic switch locus in the gene module. The genetic background includes multiple modifier variants and the gene module is composed of the switch and the modifiers. The bell-shaped distribution of quantitative traits can be well simulated by the involvement of multiple stochastic epistatic modules. The phenotypic stochasticity makes the presence of switch and modifiers cryptic or missing in the research field and this cryptic gene networks can maintain and innovate in the phenotypic diversity under selection as a process of the evolution of complexity.

Representation theorem and viability property for multidimensional BSDEs and their applications

The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study,we present a positive answer to the long-standing open question of whether the representation theorem still holds in the L^(2)-sense under the standard assumptions of square integrability and Lipschitzian continuity on the generators of BSDEs.In the process,the multidimensional case is considered.Subsequently,based on the representation theorem,we obtain a necessary and sufficient condition for the viability property of the BSDEs under standard conditions on the generators.This removes the requirement for the generator to possess the properties of stronger integrability and continuity with respect to time variables.As an application of these results,we conduct various types of comparisons and converse comparisons for the solutions of multidimensional BSDEs,and several properties of the multidimensional g-expectation are obtained.

Rectification of RF Fields in Load Dependent Coupled Systems: Application to Non-Invasive Electroceuticals

Electroceuticals are medical devices that employ electric signals to alter the activity of specific nerve fibers to achieve therapeutic effects. The rapid growth of RF microelectronics has resulted in the development of very small, portable, and inexpensive shortwave and microwave radio frequency (RF) amplifiers, raising the possibility of utilizing these new RF technologies to develop non-contact electroceutical devices. However, the bio-electromagnetics literature suggests that beyond 10 MHz, RF fields cannot influence biological tissue, beyond simple heating, because effective demodulation mechanisms at these frequencies do not exist in the body. However, RF amplifiers operating at or near saturation have non-linear interactions with complex loads, and if body tissue creates a complex loading condition, the opportunity exists for the coupled system to produce non-linear effects, that is, the equivalent of demodulation may occur. Correspondingly, exposure of tissue to pulsed RF energy could result in the creation of low frequency demodulation components capable of influencing tissue activity. Here, we develop a one-dimen- sional, numerical simulation to investigate the complex loading conditions under which such demodulation could arise. Applying these results in a physical prototype device, we show that up to7.5% demodulation can be obtained for a 40 MHz RF field pulsed at 1 KHz. Implications for this research include the possibility of developing wearable, electromagnetic electroceutical de- vices.

一个单参数随机拟牛顿算法

本文设计一个单参数随机拟牛顿算法,证明该算法的收敛性并分析了复杂性,对非凸经验风险最小化问题进行数值实验,验证了算法的有效性和竞争性。

隧道涌水量预测计算方法综述

预测隧道涌水量对于保障隧道施工安全、进度、洞室稳定和人身安全问题至关重要。国内外学者已提出多种预测方法,但是存在不同适用条件,根据隧道的水文地质条件选取恰当的方法能有效提高预测精度。对解析公式法、经验公式法、数值法、随机性数学模型预测法等多种涌水量预测方法进行了系统梳理和分析,通过对这些方法的基本原理及适用条件进行综合分析,讨论了当前涌水量预测方法存在的不足之处,并提出改进方向。结果表明:解析公式法应用简单,但结果偏差较大;经验公式法源于工程案例总结,适用于相似条件下隧道涌水量预测;数值法通过数学模型模拟,可以解决复杂水文地质条件下的涌水量预测,但对勘察设计阶段获取的水文地质参数提出更高的要求;随机性数学模型方法需要大量数据来保证结果的准确性;其他方法主要依赖于地理信息系统(GIS)技术、同位素分析法等手段,通过科学分析来识别并判断地下水量及其流动通道的地质特征,需要充分的数据支持和详尽的地下勘探结果作为依据。研究成果可为实际工程中选择合适的涌水量预测方法提供参考。

求解一类随机变分不等式问题的带方差缩减的近端镜像滑动算法

考虑了一类具有特殊结构的随机单调变分不等式(Stochastic Monotone Variational Inequalities,SMVI)问题的求解算法.所考虑的SMVI问题涉及到一个梯度算子与单调算子的和,其中梯度算子的精确信息是可知的,而单调算子的信息通过随机样本估计得到,这使得求解问题的算法具有不确定性.随机近端镜像滑动(Stochastic Mirror-Prox Sliding,SMPS)算法是求解SMVI问题的一种有效算法,但SMPS使用随机信息引入的扰动破坏了单调算子的最优计算复杂度.该文在SMPS的基础上对随机单调算子使用方差缩减技术,提出了带有方差缩减的随机近端镜像滑动(Vraiance Reduced Stochastic Mirror-Prox Sliding,VRSMPS)算法.并且,在一般性的方差可控假设下证明与SMPS相比,使用VRSMPS求解SMVI,获得梯度算子最优计算复杂度O(√L/ε)的同时,把H的计算复杂度从O(√L/ε+M/ε+σ^(2)/ε^(2))降低到O(√L/ε+√(α+M^(2))^(2)/Lε^(3)).