Nonlinear Network Research Articles

Downside and upside risk spillovers between financial industry and real economy based on linear and nonlinear networks

The spillover effects between financial sectors and real economy in different risk levels are of concern for investors and regulatory authorities. Firstly, based on the sector returns of China, the VaRs at different quantiles are estimated by MVMQ-CAViaR model. Then, we construct linear and nonlinear risk spillover networks in downside, normal and upside cases by employing DY and nonlinear Granger causality methods. Finally, we analyze topological characteristics of linear and nonlinear risk spillover networks at the system and sector levels. The results show that linear and nonlinear risk spillover networks in different risk levels exhibit various topology properties, they are unevenly spread over each risk level. At the system-level, we observe that there is a significant difference between linear and nonlinear risk spillover networks in uniqueness and overlapping. At the sector-level, the financial sectors (such as DF and RE sectors) can form a certain spillover effect on sectors of real economy across quantiles, but the net spillover effects of the financial sectors are smaller than that of some real economy sectors. Finally, the crisis shocks have impact on risk spillover effects between financial sectors and real economy. In downside and upside cases, the spillover effects between sectors during crisis period is higher than that during pre-crisis period.

Performance of short-terms prediction methods of vertical total electron content using nonlinear autoregressive neuronal network and stochastic autoregressive model

In this contribution the performance of global short-term predictions methods of vertical total electron content (vTEC) is analyzed during high solar activity. Two kind of predicted global vTEC maps value every 1 h, one-day-ahead, are used. They are C1PG, produced by the Center for Orbit Determination in Europe (CODE), based on the extrapolation of Spherical Harmonic coefficient using Least-squares collocation and the M1PG, proposed in this work, based on multi-step Nonlinear Autoregressive Neural Network (NAR-NN).Global vTEC maps from CODE (CODG) along the year 2015, are used as reference data. The results are obtained for quiet and disturbed conditions, based on geomagnetic and ionospheric planetary indexes.The performance of the forecasting approach is extensively tested under different geospatial conditions. The testing results are very similar in terms of RMSE, as it has been found to range between 1.7 and 7 TECu. RMSE depend on the latitude sectors and geomagnetic conditions, in terms of Mean Forecast Error (MFE) the C1PG shows a clear systematic behavior being negative at Southern Hemisphere and positive at Northern Hemisphere. According to the Mean Absolute Percentage Error (MAPE) values, the relative behavior of vTEC prediction is better for M1PG than for C1PG specially during quiet days and at mid-high latitudes. In general, both models are less accuracy in the equatorial ionization anomaly region and the Southern Hemisphere.Other important contribution of this manuscript is the definition of a planetary ionospheric disturbance index, Wd, based on W-index. This parameter is useful to more complete definition in quiet and disturbed days selection, and it is shown that the dependence of the RMSE according to the latitudinal bands, it is strongly related with the respective value of Wd.

Pipeline visualization based on RIR-RepVGG network

Electrical Capacitance Tomography (ECT) is a process tomography technology based on capacitance-sensitive field, which is of vital importance to accelerate the development of industrial intelligence by measuring the required capacitance data through sensors to achieve the flow pattern detection of filled pipes and thus meet the controllability of pipe flow patterns. The traditional ECT flow pattern recognition method has low recognition rate and more complicated operation. In this paper, the detection method of filling pipeline is studied based on electrical capacitance tomography (ECT) technology. Aiming at the low imaging accuracy of traditional ECT reconstruction algorithms, an ECT image reconstruction method based on improved residual neural network was proposed. The RIR-RepVGG residual network structure is proposed and a nonlinear mapping network is designed. The improved residual network is used to establish the mapping relationship between the capacitance vector and the two-phase flow image. Through the static study by filling pipeline simulation experiments and static experiments, it is proved that the ECT image reconstruction method proposed in this paper can reduce the artifacts and deformation of the reconstructed image, improve the reconstruction accuracy, and has a better reconstruction effect for complex flow patterns. Application is of great significance.

Nonlinear active distribution network optimization for improving the renewable energy power quality and economic efficiency: a multi-objective bald eagle search algorithm

Nonlinear active distribution network optimization for improving the renewable energy power quality and economic efficiency: a multi-objective bald eagle search algorithm

A New Method for Erosion Prediction of 90° Elbow Based on Non-Axisymmetric Ultrasonic-Guided Wave and the PSO-LSSVM Algorithm.

The non-axisymmetric exciting guided wave can detect the thinning section of the elbow, and the time domain energy value of the signal collected at the outer arch position of the receiving end displays a downward trend as the remaining thickness of the erosion area decreases. To address the difficulty in detecting the erosion degree of the elbow with high accuracy, this paper uses the linear frequency modulation (LFM) signal to excite a non-axisymmetric guided wave that propagates in the 90° elbow and collects signals through four PZT receivers. To predict the erosion degree, the corresponding relationship between the energy value of the four signals after fractional Fourier filtering and the degree of elbow erosion is established through the particle swarm optimization (PSO)-least squares support vector machine (LSSVM) algorithm. The results show that the method proposed has an average accuracy rate of 98.1864%, 94.7167%, 99.119%, and 99.9593% for predicting the erosion degree of four elbow samples, and 94.0039%. and 81.2976% for two new erosion degrees, which are higher than the nonlinear regression model, LSSVM algorithm, and BP neural network algorithm. This study has guiding significance for real-time monitoring of elbow erosion.

Retraction Note: A new prediction approach of the COVID-19 virus pandemic behavior with a hybrid ensemble modular nonlinear autoregressive neural network

Retraction Note: A new prediction approach of the COVID-19 virus pandemic behavior with a hybrid ensemble modular nonlinear autoregressive neural network

Disturbance rejection‐based cluster synchronization of nonlinear complex dynamical networks with hybrid‐driven mechanism

AbstractThe issue of cluster synchronization and disturbance rejection of multi‐weighted complex dynamical networks subject to nonlinearities and external disturbances are studied in this article. In particular, a hybrid‐triggering control scheme is implemented to mitigate the burden of the network transmission according to the prespecified triggering condition, under which each node will transmit its signal independently to the controller. To be more specific, a Bernoulli distributed stochastic variable is introduced to describe the switching law of the communication scheme. Also, the disturbance rejection performance is carried out with the aid of an improved equivalent input disturbance estimator approach. The sufficient criterion in the form of linear matrix inequalities is derived by constructing a suitable Lyapunov–Krasovskii functional and employing stochastic theory. Based on these settings, the feedback gain matrices and the trigger parameters affirming the desired cluster synchronization performance of the considered networks are established. Eventually, two illustrative examples including Lur'e networks with simulations are presented, which evidently proves the effectiveness of the obtained results.

Intrinsic neural diversity quenches the dynamic volatility of neural networks

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.

Simple and Rapid Discrimination of Methicillin-Resistant Staphylococcus aureus Based on Gram Staining and Machine Vision.

Methicillin-resistant Staphylococcus aureus (MRSA) is a clinical threat with high morbidity and mortality. Here, we describe a new simple, rapid identification method for MRSA using oxacillin sodium salt, a cell wall synthesis inhibitor, combined with Gram staining and machine vision (MV) analysis. Gram staining classifies bacteria as positive (purple) or negative (pink) according to the cell wall structure and chemical composition. In the presence of oxacillin, the integrity of the cell wall for methicillin-susceptible S. aureus (MSSA) was destroyed immediately and appeared Gram negative. In contrast, MRSA was relatively stable and appeared Gram positive. This color change can be detected by MV. The feasibility of this method was demonstrated in 150 images of the staining results for 50 clinical S. aureus strains. Based on effective feature extraction and machine learning, the accuracies of the linear linear discriminant analysis (LDA) model and nonlinear artificial neural network (ANN) model for MRSA identification were 96.7% and 97.3%, respectively. Combined with MV analysis, this simple strategy improved the detection efficiency and significantly shortened the time needed to detect antibiotic resistance. The whole process can be completed within 1 h. Unlike the traditional antibiotic susceptibility test, overnight incubation is avoided. This new strategy could be used for other bacteria and represents a new rapid method for detection of clinical antibiotic resistance. IMPORTANCE Oxacillin sodium salt destroys the integrity of the cell wall of MSSA immediately, appearing Gram negative, whereas MRSA is relatively stable and still appears Gram positive. This color change can be detected by microscopic examination and MV analysis. This new strategy has significantly reduced the time to detect resistance. The results show that using oxacillin sodium salt combined with Gram staining and MV analysis is a new, simple and rapid method for identification of MRSA.

Active vibration control using nonlinear auto-regressive neural network to identify secondary channel

The power unit on board the ship generates periodic low-frequency vibration that affects the normal operation of the equipment on board, and the adaptive feedforward control algorithm can effectively suppress such harmful vibration noise. But the adaptive feedforward control algorithm needs to obtain the identification model of the secondary channels, and the frequency domain least squares method based on the linear Extended auto-regressive model (ARX) is difficult to obtain the identification model with nonlinear characteristics. The nonlinear auto-regressive model (NARX) adds nonlinear mapping layers to the topology of the ARX model to enhance the identification capability of the NARX model for complex systems. In this paper, a block diagram of the Fx-LMS feedforward control algorithm based on the NARX model is proposed, then the initial parameters of the NARX neural network are optimized using the Quantum Particle Swarm Optimization (QPSO) algorithm and the secondary channel is identified, and the identification results show that the accuracy of identifying the secondary channel using the NARX neural network is higher than that of the ARX model. The simulation and experimental results show that the vibration damping effect of the proposed method is better than the traditional Fx-LMS method for both single-line spectrum and multi-line spectrum periodic low-frequency disturbances, which provides a new method for the suppression of periodic low-frequency disturbances.

Individual modelling of haematotoxicity with NARX neural networks: A knowledge transfer approach

Cytotoxic cancer therapy often results in dose-limiting haematotoxic side effects. Predicting an individual's risk is a major objective in precision medicine of cancer treatment. In this regard, patient heterogeneity presents a significant challenge. In this paper, we explore the use of hypothesis-free machine learning models based on recurrent nonlinear auto-regressive networks with exogenous inputs (NARX) as an approach to achieve this goal. Also, we propose a knowledge transfer approach to ameliorate the issue of sparse individual data, which typically hampers learning of individual networks. We demonstrate the feasibility of our approach based on a virtual patient population generated using a semi-mechanistic model of haematopoiesis and imposing different cytotoxic therapy scenarios on it. Employing different techniques of model optimisation, we derive robust and parsimonious individual networks with good generalisation performances. Moreover, we analyse in detail possible factors influencing the generalisation performance. Results suggest that our transfer learning approach using NARX networks can provide robust predictions of individual patient's response to treatment. As a practical perspective, we apply our approach to individual time series data of two patients with non-Hodgkin's lymphoma.

Exploring nonlinear dynamics and network structures in Kuramoto systems using machine learning approaches.

Recent advances in machine learning (ML) have facilitated its application to a wide range of systems, from complex to quantum. Reservoir computing algorithms have proven particularly effective for studying nonlinear dynamical systems that exhibit collective behaviors, such as synchronizations and chaotic phenomena, some of which still remain unclear. Here, we apply ML approaches to the Kuramoto model to address several intriguing problems, including identifying the transition point and criticality of a hybrid synchronization transition, predicting future chaotic behaviors, and understanding network structures from chaotic patterns. Our proposed method also has further implications, such as inferring the structure of neural networks from electroencephalogram signals. This study, finally, highlights the potential of ML approaches for advancing our understanding of complex systems.

Intercellular mechanical signalling in a 3D nonlinear fibrous network model

The extracellular matrix (ECM) consists of a network of polymeric fibres in which cells are embedded and interact with each other. The nonlinear elasticity of the ECM aids in directing the transmission of cell-induced mechanical loads over long distances, thereby facilitating mechanical communication between cells that are not in direct contact. Previous computational models have established the role of compression-buckling of the ECM fibres in increasing the propagation range of mechanical loads and fibre remodelling, however, most of them are two-dimensional (2D). Here, we generate a more realistic, 3D finite-element simulation of two cells contracting within the ECM by means of two contractile spheres embedded within a network of beam elements. We explore the effects of the mechanical behaviour of the fibres (linear-elastic, compression-bucklable), network connectivity (3.7, 8, 12) and intercellular distance (1–5 cell radii) on the structural remodelling and mechanical loads occurring on the cell surface and within the intercellular region of the ECM. When cells were embedded in a matrix of bucklable rather than linear-elastic fibres, contraction-induced loads were more directed towards the neighbouring cell, and the fibre rearrangement in the intercellular ECM was more eminent up to an intercellular distance of ∼2.5–5 cell radii. Our 3D discrete model highlights the role of the ECM nonlinear elasticity in the efficient transfer of mechanical signals between cells, a mechanism governing numerous multicellular processes such as tissue morphogenesis, wound healing, angiogenesis and cancer metastasis. The findings reemphasise the importance of using nonlinear elastic gels in in vitro cellular models.

Estimation of Discriminative Multimodal Brain Network Connectivity Using Message-Passing-Based Nonlinear Network Fusion.

Effective estimation of brain network connectivity enables better unraveling of the extraordinary complexity interactions of brain regions and helps in auxiliary diagnosis of psychiatric disorders. Considering different modalities can provide comprehensive characterizations of brain connectivity, we propose the message-passing-based nonlinear network fusion (MP-NNF) algorithm to estimate multimodal brain network connectivity. In the proposed method, the initial functional and structural networks were computed from fMRI and DTI separately. Then, we update every unimodal network iteratively, making it more similar to the others in every iteration, and finally converge to one unified network. The estimated brain connectivities integrate complementary information from multiple modalities while preserving their original structure, by adding the strong connectivities present in unimodal brain networks and eliminating the weak connectivities. The effectiveness of the method was evaluated by applying the learned brain connectivity for the classification of major depressive disorder (MDD). Specifically, 82.18% classification accuracy was achieved even with the simple feature selection and classification pipeline, which significantly outperforms the competing methods. Exploration of brain connectivity contributed to MDD identification suggests that the proposed method not only improves the classification performance but also was sensitive to critical disease-related neuroimaging biomarkers.

An artificial neural network based method for company valuation

Purpose - Company value is a crucial issue for everyone operating in financial markets. Both firm managers and investors should calculate the value of a firm, and there are many methods available to do so. Calculating valuation methods is challenging due to the multiple parameters and stages that are involved. Due to these reasons, it's possible for managers, owners, investors, and other stakeholders to estimate a company's value inaccurately or with difficulty. The main objective of this essay is to demonstrate how to evaluate a company's value using the NARX model as an alternative to other models. Methodology – It is estimated that the firm value using an artificial neural network nonlinear external input autoregressive network model for 50 companies operating in the consumer products and industrial products and services sectors in the Euro Stoxx 50 index. The dataset covers the period from 2000 to 2021, and 20 financial ratios were included as input to the model, with FCFF as the output. Findings- The NARX model with a 20-6-6-1 or 20-10-10-1 network structure provided the best value for both R and MSE at two-time delays. However, the 20-12-12-1 network structure of the NARX model with a time delay of three has a lower error rate after training and the best R value. The model's prediction success rate is 90.82% using the 20-12-12-1 network structure with a time delay of three. Conclusion- As a result, this model can be used by investors and business managers to value a company. By using this method, businesses may gain access to more precise and unbiased appraisals that can guide resource allocation and strategic decision-making. By including macroeconomic factors that have an impact on the sector and employing a longer time frame, the study could be improved. Keywords: Company value, company valuation, cash flow to firm, artificial neural networks, nonlinear external input autoregressive network JEL Codes: C45, C80, G12

Improved generalization of NARX neural networks for enhanced metamodeling of nonlinear dynamic systems under stochastic excitations

Nonlinear autoregressive networks with exogenous inputs (NARX) are popular in data-driven metamodeling of complex dynamic systems. One practical challenge is the insufficient generalization due to excitation stochasticity. To improve the generalization, three novel schemes are proposed. They are: (1) Advanced NARX (A-NARX), where k-fold cross validation-based ensemble with early stopping is implemented over intact time series samples under concurrent training via data reconstruction; (2) Experienced NARX (E-NARX), built on A-NARX and gaining experience about the underneath dynamic system by series–parallel training before entering the parallel training; and (3) Gaussian Experienced NARX (GE-NARX), which introduces the pseudo-parallel training for network precondition to the Gaussian noise contained in the output feedback of the subsequent real parallel training. The proposed schemes are applied with the plain NARX for reference to simulated data corresponding to a nonlinear simple system and a complex offshore floating system, using wave elevation as the input for predicting structural responses. It is found that both the network capability and the training stability are strengthened by proposed schemes. Hence, improved generalization is achieved with increased complexity in the dynamic system and stochastic excitations. GE-NARX consistently demonstrates superior performance over other schemes.

A method to improve the computational performance of nonlinear all—optical diffractive deep neural network model

To further improve the computational performance of the diffractive deep neural network (D2NN) model, we use the ReLU function to limit the phase parameters, which effectively solves the problem of vanishing gradient that occurs in the mitigation model. We add various commonly used nonlinear activation functions to the hidden layer of the model and establish the ReLU phase-limit nonlinear diffractive deep neural network (ReLU phase-limit N-D2NN) model. We evaluate the model by comparing the performance of various nonlinear activation functions, where confusion matrix and accuracy are used as evaluation methods. The numerical simulation results show that the model achieves better classification performance on the MNIST and Fashion-MNIST datasets, respectively. In particular, the highest classification performance is obtained by the ReLU phase-limit N-D2NN model, in which the hidden layer uses PReLU, with 98.38% and 90.14%, respectively. This paper provides a theoretical basis for applying the nonlinear D2NN systems in natural scenes.

Understanding Representation Learnability of Nonlinear Self-Supervised Learning

Self-supervised learning (SSL) has empirically shown its data representation learnability in many downstream tasks. There are only a few theoretical works on data representation learnability, and many of those focus on final data representation, treating the nonlinear neural network as a ``black box". However, the accurate learning results of neural networks are crucial for describing the data distribution features learned by SSL models. Our paper is the first to analyze the learning results of the nonlinear SSL model accurately. We consider a toy data distribution that contains two features: the label-related feature and the hidden feature. Unlike previous linear setting work that depends on closed-form solutions, we use the gradient descent algorithm to train a 1-layer nonlinear SSL model with a certain initialization region and prove that the model converges to a local minimum. Furthermore, different from the complex iterative analysis, we propose a new analysis process which uses the exact version of Inverse Function Theorem to accurately describe the features learned by the local minimum. With this local minimum, we prove that the nonlinear SSL model can capture the label-related feature and hidden feature at the same time. In contrast, the nonlinear supervised learning (SL) model can only learn the label-related feature. We also present the learning processes and results of the nonlinear SSL and SL model via simulation experiments.

Predicting global energy demand for the next decade: A time-series model using nonlinear autoregressive neural networks

Energy demand forecasting has been an indispensable research target for academics, which has led to creative solutions for energy utilities in terms of power system design, control, and planning. The usefulness of energy demand forecasting is confined to the power engineering industry but globally exceeds such outcomes to contribute to the environment and health sectors. Despite the large number of research projects published on this topic, the challenge of energy demand forecasting still exists, especially with the developments in modeling concepts via artificial intelligence, which motivates more attractive solutions for the variables involved in energy demand forecasting. Mathematical correlation or extrapolation-like methods cannot be effective in all situations; however, when a time series neural network is presented, most statistical, empirical, and theoretical problems can be easily handled. This paper presents a simple and easy-to-understand method for the next decade of energy demand forecasting based on a nonlinear autoregressive (NAR) neural network. From its time series past values, NAR structurally is an optimal predictor for a future variable. A publicly available data set for global energy consumption has been used to construct the network model with sufficiently accurate results. The evidence has appeared in precisely following the exponential trend of energy consumption as well as the regressions for training, testing, and validation, which ensures the model's robustness and avoids getting involved in overfitting. The proposed model concepts and results can be easily used in undergraduate engineering education, training graduates, and future research.

Nonlinear Activation-Free Contextual Attention Network for Polyp Segmentation

The accurate segmentation of colorectal polyps is of great significance for the diagnosis and treatment of colorectal cancer. However, the segmentation of colorectal polyps faces complex problems such as low contrast in the peripheral region of salient images, blurred borders, and diverse shapes. In addition, the number of traditional UNet network parameters is large and the segmentation effect is average. To overcome these problems, an innovative nonlinear activation-free uncertainty contextual attention network is proposed in this paper. Based on the UNet network, an encoder and a decoder are added to predict the saliency map of each module in the bottom-up flow and pass it to the next module. We use Res2Net as the backbone network to extract image features, enhance image features through simple parallel axial channel attention, and obtain high-level features with global semantics and low-level features with edge details. At the same time, a nonlinear n on-activation network is introduced, which can reduce the complexity between blocks, thereby further enhancing image feature extraction. This work conducted experiments on five commonly used polyp segmentation datasets, and the experimental evaluation metrics from the mean intersection over union, mean Dice coefficient, and mean absolute error were all improved, which can show that our method has certain advantages over existing methods in terms of segmentation performance and generalization performance.