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The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is firstly proved that the trajectory field of the stochastic delayed HNNM admits an almost sure continuous version, which is compact for t > τ (where τ is the delay) by a construction based on the random semiflow generated by the diffusion term due to Mohammed (Stoch. Stoch. Rep. 29: 89–131, 1990). Then, this version is shown to generate a random dynamical system (RDS) by a Wong–Zakai approximation, after which the existence of a random absorbing set is obtained via uniform apriori estimate of the solutions. Subsequently, the pullback asymptotic compactness of the RDS generated by the stochastic delayed HNNM is established and hence the existence of random attractors is obtained. Sufficient conditions under which the attractors turn out to be an exponential attracting stationary solution are also given. Finally, some numerical simulations illustrate the results. [ABSTRACT FROM AUTHOR]

This paper discusses the exponential stability of periodic solutions for stochastic neural networks with multiple time-varying delays. For these networks, sufficient conditions in the linear matrix inequality forms are rare in the literature. We constructed an appropriate Lyapunov-Krasovskii functional to eliminate the items with multiple delays and establish some sufficient conditions in linear matrix inequality forms, to ensure exponential stability of the periodic solutions. Several examples are provided to demonstrate that our results are effective and less conservative than previous ones.

A new highly nonlinear hybrid stochastic neural network with variable time delays is formulated, which is usually found to be unstable. In addition, the network coefficients considered in this article grow polynomially rather than linearly as we always considered before. Since original system is unstable, the purpose of this article is to construct a variable-delay feedback control function to make the augmented system stable. Then, four results on the stabilisation of the controlled system are given separately. At last, an example is provided to display the feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

The mean square exponential stability of stochastic time-delay neural networks (STDNNs) with random delayed impulses (RDIs) is addressed in this paper. Focusing on the variable delays in impulses, the notion of average random delay is adopted to consider these delays as a whole, and the stability criterion of STDNNs with RDIs is developed by using stochastic analysis idea and the Lyapunov method. Taking into account the impulsive effect, interference function and stabilization function of delayed impulses are explored independently. The results demonstrate that delayed impulses with random properties take a crucial role in dynamics of STDNNs, not only making stable STDNNs unstable, but also stabilizing unstable STDNNs. Our conclusions, specifically, allow for delays in both impulsive dynamics and continuous subsystems that surpass length of impulsive interval, which alleviates certain severe limitations, such as presence of upper bound for impulsive delays or requirement that impulsive delays can only exist between two impulsive events. Finally, feasibility of the theoretical results is verified through three simulation examples. [ABSTRACT FROM AUTHOR]

Stock market is an example of a stochastic environment in the real world. multilayer perceptron (MLP) is often applied to forecast stock price. However, it is widely used to approximate the input-output mapping deterministically. Hence, this study aims to adapt stochasticity into MLP by introducing the Gaussian process into the sigmoid activation function. In addition, the adapted activation function incorporates Roger-Satchell and Yang-Zhang volatity estimators. Besides, the stochastic activation function was considered as a hyperparameter by applying it either only in training time or in both testing and training time. The stochastic multilayer perceptron (S-MLP) is then applied to forecast one day's highest stock price of eight constituents in FTSE Bursa Malaysia KLCI (FBMKLCI). The result shows that the proposed network is inferior in comparison to MLP except for several constituents. In addition, S-MLP with stochastic activation function during both the training and testing time performs better compared to the presence of stochastic activation function in S-MLP during training time only. [ABSTRACT FROM AUTHOR]

Detecting anomalous edges and/or nodes is a challenging problem for dynamic networks, due to the spatio-temporal (ST) patterns and randomness underneath the time-varying topology and node attributes. Existing methods commonly ignore randomness, and the anomaly detectors would be sensitive, especially in highly variable dynamic networks. In this paper, a new reconstruction method, the multi-scale variational graph recurrent autoencoder (M-VGRAE), is designed to detect anomalies in stochastic dynamic networks. Overall, upon the framework of Learning from Pure Normal (LPN), the M-VGRAE is trained to reconstruct the normal nodes and edges, and is used to detect the anomalies that cannot be reconstructed well by the trained M-VGRAE. To reduce sensitivity against the high variability, the reconstruction of stochastic dynamic networks is performed in a multi-scale manner. Specifically, the randomness is modeled by introducing multiple latent random variables at each node, each of which models the local randomness of attributes and connectivity within the temporal neighborhoods in a specific hop and historical interval. Then, the local randomness is approximated by employing the variational autoencoder (VAE) with a designed multi-scale ST feature extractor based on graph neural networks and recurrent neural networks. By such design, the capture of ST patterns and the modeling of randomness are jointly achieved. To show the effectiveness of the M-VGRAE in detecting anomalous edges and nodes, experiments are conducted on four real-world datasets of dynamic networks. The results demonstrate that the M-VGRAE consistently outperforms the existing baselines in terms of AUC score on anomaly detection. [ABSTRACT FROM AUTHOR]

In this paper, a class of Clifford‐valued stochastic neural network with delays is investigated, by using a direct method, that is, without decomposing the Clifford‐valued system into a real‐valued system. Based on the contraction mapping principle and contradiction, sufficient conditions are derived to ensure the existence and stability of almost automorphic solutions for the stochastic networks under consideration. Finally, two numerical examples are provided to show the feasibility of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays whose coefficients are Clifford numbers except the time delays. Based on the Banach fixed point theorem and inequality techniques, we obtain the existence and global exponential stability of almost periodic solutions in distribution of this class of neural networks. Even if the considered neural networks degenerate into real-valued, complex-valued and quaternion-valued ones, our results are new. Finally, we use a numerical example and its computer simulation to illustrate the validity and feasibility of our theoretical results.

Since multispectral images (MSIs) have much more sufficient spectral information than RGB images (RGBs), reconstructing MS images from RGB images is a severely underconstrained problem. We have to generate colossally different information between the two scopes. Almost all previous approaches are based on static and dependent neural networks, which fail to explain how to supplement the massive lost information. This paper presents a low-cost and high-efficiency approach, “VAE-GAN”, based on stochastic neural networks to directly reconstruct high-quality MSIs from RGBs. Our approach combines the advantages of the Generative Adversarial Network (GAN) and the Variational Autoencoder (VAE). The VAE undertakes the generation of the lost variational MS distributions by reparameterizing the latent space vector with sampling from Gaussian distribution. The GAN is responsible for regulating the generator to produce MSI-like images. In this way, our approach can create huge missed information and make the outputs look real, which also solves the previous problem. Moreover, we use several qualitative and quantitative methods to evaluate our approach and obtain excellent results. In particular, with much less training data than the previous approaches, we obtained comparable results on the CAVE dataset and surpassed state-of-the-art results on the ICVL dataset.

In this paper, a class of stochastic neural networks with time delays is studied. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence of Stepanov-like almost periodic solutions for the stochastic neural networks under consideration. Then, by designing a novel state-feedback controller and constructing a suitable Lyapunov function, the global asymptotic synchronization and exponential stability of the stochastic neural networks are researched. Finally, two numerical examples are provided to show the feasibility of our results. [ABSTRACT FROM AUTHOR]

In this paper, the existence and stability ofWeyl almost automorphic solutions in distribution sense for a class of Clifford-valued stochastic neural networks with time-varying delays are studied by using the direct method. Firstly, the existence and uniqueness of Weyl almost automorphic solutions in distribution sense for this class of neural networks are studied by using the Banach fixed point theorem and the relationship between several different senses of random almost automorphy. Then, the global exponential stability in pth mean of the unique Weyl almost automorphic solution in distribution sense is proved by inequality technique and counter proof method. Even when this class of neural networks we consider is real-valued, our results are new. Meanwhile, the method proposed in this paper can be used to study the existence of Weyl almost automorphic solutions of other types of neural networks including stochastic and deterministic neural networks. Finally, an example is given to illustrate the feasibility of our results. [ABSTRACT FROM AUTHOR]

The competition for talent is always intense, especially in the era of big data, the data analysis‐related talent recruitment plays an important role in promoting the development of enterprises. Regarding resume screening, it is considerably significant during the process of talent recruitment. Consider that Neural Network (NN) has the strong stability on the prediction result and is given a lot of attention, this paper uses Stochastic NN (SNN) to optimize the data analysis‐related talent recruitment. Meanwhile, SNN is used to train resume‐related dataset and make resume screening. In addition, in order to accelerate the training process and decrease the training complexity, this paper uses Locally Linear Embedding (LLE) to do dimension reduction in terms of the extracted data features. Furthermore, in order to guarantee the on‐line resume screening, this paper does resume screening under Content Delivery Network (CDN) scenario, where CDN has two functions, that is, data storage and hot resumes recommendation. The experiments are made based on the collected 7000 resumes, and the result show that this paper has good optimization effect on data analysis‐related talent recruitment. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the problem of the almost surely asymptotic synchronization for a class of stochastic neural networks of neutral type with both Markovian jumping parameters and mixed time delays. Based on the stochastic analysis theory, LaSalle‐type invariance principle, and delayed state‐feedback control technique, some novel delay‐dependent sufficient criteria to guarantee the almost surely asymptotic synchronization are given. These criteria are expressed as the linear matrix inequalities, which can be easily checked by MATLAB LMI Control Toolbox. Finally, four numerical examples and their simulations are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study aims to develop a model that predicts high-frequency response spectra and damage-related ground motion parameters using low-frequency physics-based simulations (PBS) for horizontal and vertical components. The model is a stochastic dropout-based long short-term memory (LSTM) network, which accounts for spectra interdependencies and high-frequency spectra's stochastic nature. Adding anelastic distance as an input term significantly improved the model's performance. Models are developed for different cutoff periods (validity of PBS low-frequency spectra): 0.75 s, 1 s, 1.5 s, and 2 s, using the 2015 Nepal main and aftershocks and combining them with global near-source strong-motion data. The models are validated using near- and far-field predictions and a good agreement with the recorded data is observed. The mean squared error, mean absolute error, and coefficient of determination for the 0.75 s horizontal model is 0.174, 0.3171, and 0.9295, respectively. Additionally, the study generates spectra and time histories for the 2001 M w 7.6 Bhuj earthquake, which had no recordings. The obtained spectral values agree well with global stable-continental region models, and the time histories could capture characteristics such as duration, amplitude, and arrival times. • Developed a stochastic network to predict high-frequency spectra from low-frequency. • LSTM network captures frequency dependencies. • Distance and PSA(T = T ∗ ) terms have high weightage in the prediction. • Developed broadband time histories to the 2001 Bhuj earthquake. [ABSTRACT FROM AUTHOR]

In this paper, the problem of stability condition for mixed delayed stochastic neural networks with neutral delay and leakage delay is investigated. A novel Lyapunov functional is constructed with double and triple integral terms. New sufficient conditions are derived to guarantee the global asymptotic stability of the concerned neural network. This paper is more general than the paper by Zhu et al. [Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms, Neural Process. Lett. 41 (2015), pp. 1-27]. In our paper, we considered both the neutral delay and leakage delay, but the paper by Zhu et al. is not considering the neutral delay. Also we employed triple integrals in the Lyapunov functional which is not used in the paper by Zhu et al. Finally, two numerical examples are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Li, X., Lin, X., and Lin, Y. [(2016). Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion. Journal of Mathematicase Analysis and Applications, 439, 235-255] proposed the sufficient conditions for the exponential instability to stochastic differential equations driven by G-Brownian motion (G-SDEs, in short). A natural question is whether we can design a controller to make G-SDEs be stable. By means of the G-Lyapunov function, we design a state-feedback controller to stabilise the system. In addition, applications to stabilisation and synchronisation of Hopfield neural networks driven by G-Brownian motion (G-HNNs, in short) and examples are proposed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Turbomachinery often suffers various defects such as impeller cracking, resulting in forced outage, increased maintenance costs, and reduced productivity. Condition monitoring and damage prognostics has been widely used as an increasingly important and powerful tool to improve the system availability, reliability, performance, and maintainability, but still very challenging due to multiple sources of data uncertainties and the complexity of analytics modeling. This paper presents an intelligent probabilistic methodology for anomaly prediction of high-fidelity turbomachine, considering multiple data imperfections and multivariate correlation. The proposed method adeptly integrates several advanced state-of-the-art signal processing and artificial intelligence techniques: wavelet multi-resolution decomposition, Bayesian hypothesis testing, probabilistic principal component analysis, and fuzzy stochastic neural network modeling. The advanced signal processing is employed to reduce dimensionality and to address multivariate correlation and data uncertainty for damage prediction. Instead of conventionally using raw time series data, principal components are utilized in the establishment of stochastic neural network model and anomaly prediction. Bayesian interval hypothesis testing metric is then presented to quantitatively compare the predicted and measured data for model validation and anomaly evaluation, thus providing a confidence indicator to judge the model quality and evaluate the equipment status. Bayesian method is developed in this study for denoising the raw data with multiresolution wavelet decomposition, quantifying the model accuracy, and assessing the equipment status. The dynamic stochastic neural network model is established via the nonlinear autoregressive moving average with exogenous inputs approach. It seamlessly integrates the fuzzy clustering and independent Bernoulli random function into radial basis function neural network. A natural gradient method based on Kullback-Leibler distance criterion is employed to maximize the log-likelihood loss function. The effectiveness of the proposed methodology and procedure is demonstrated with the 11-variable time series data and the forced outage event of a real-world centrifugal compressor.

In this paper, the problem of passivity analysis is investigated for a class of stochastic neural networks with Markovian jumping parameters and time delay in the leakage term. The discrete delay is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples are given to show the effectiveness and less conservatism of the proposed criteria. [ABSTRACT FROM AUTHOR]

Random search is a behavioral strategy used by organisms from bacteria to humans to locate food that is randomly distributed and undetectable at a distance. We investigated this behavior in the nematode Caenorhabditis elegans, an organism with a small, well-described nervous system. Here we formulate a mathematical model of random search abstracted from the C. elegans connectome and fit to a large-scale kinematic analysis of C. elegans behavior at submicron resolution. The model predicts behavioral effects of neuronal ablations and genetic perturbations, as well as unexpected aspects of wild type behavior. The predictive success of the model indicates that random search in C. elegans can be understood in terms of a neuronal flip-flop circuit involving reciprocal inhibition between two populations of stochastic neurons. Our findings establish a unified theoretical framework for understanding C. elegans locomotion and a testable neuronal model of random search that can be applied to other organisms.