Discrete Network Research Articles

Dual optimization approach in discrete Hopfield neural network

Having effective learning and retrieval phases of satisfiability logic in Discrete Hopfield Neural Network models ensures optimal synaptic weight management, which consequently leads to the production of optimal final neuron states. However, the problem with this model is that different initial states can affect the biasedness of the retrieval phase since the model memorizes final states without generating new ones and produces suboptimal final neuron states. To date, there is no recent research that solves this issue by improving both phases in the Discrete Hopfield Neural Network that involves first-order satisfiability logic. Therefore, this research contributes to the improvement of the learning and retrieval phases by integrating the Hybrid Differential Evolution Algorithm and Swarm Mutation respectively. This research utilizes Y-Type Random 2 Satisfiability, which combines first and second-order clauses to expand the storage capacity of DHNN models, facilitating the retrieval of optimal final neuron states. To evaluate the effectiveness of the Hybrid Differential Evolution Algorithm and Swarm Mutation in the learning and retrieval phases, several performance metrics are employed in terms of synaptic weight management, learning errors, testing errors, energy profiles, solution variations, and similarity for 10 different cases. Quantitative evaluations show that the proposed model successfully enhances the optimization of both phases, ranking first compared to 10 recent algorithms for all metrics. In terms of convergence analysis, the proposed model progressed fast towards the optimal solution with only one iteration for all cases. Additionally, the proposed model can generate a 100 % global minima ratio when dealing with a high number of neurons for Case 5.

Parameter optimization of hot dry rock heat extraction based on discrete element crack network model

Hot-dry-rock (HDR) has long been considered a potential exploitable energy source due to its high energy content, cleanliness, and abundant reserves. However, HDR typically resides in ultra-deep strata with high temperatures and pressures, which makes its extraction a highly complex thermal-hydrological-mechanical (THM) coupling. In this paper, the THM coupling relationship in the geothermal extraction is clarified. It establishes a dynamic porosity and permeability model and creates a pair-well geothermal extraction model. The investigation focuses on understanding the influence of the pressure difference between pair-wells, number of cracks, and injection temperature on the heat extraction temperature, permeability ratio, geothermal reservoir reduction rate, and heat extraction temperature. The research findings indicate the following: (1) Increasing the inter-well pressure difference from 2 to 10 MPa reduces the extraction temperature from 155 to 138 °C. However, the thermal reservoir permeability ratio increases from 1.07 to 1.35. Consequently, the extraction efficiency rises from 6.2 to 12.4 MW. (2) The number of cracks from 200 to 400 led to a decrease in extraction temperature from 160 to 115 °C. However, the thermal reservoir permeability ratio increases from 1.12 to 1.35. In the first 8 years of extraction, the thermal pumping power of 400 cracks exceeded 200 cracks, but later this trend reversed. (3) Elevating the injection temperature from 20 to 60 °C increases the extraction temperature from 142 to 158 °C while reducing the permeability ratio from 1.28 to 1.20. Consequently, the extraction power decreases from 8 to 6 MW. (4) The inter-well pressure difference has the greatest impact on the decrease in extraction temperature, whereas the number of cracks has the greatest impact on the increase in permeability ratio. Injection temperature has the most significant impact on extraction power. This study reveals that increasing the pressure difference between wells, increasing the number of cracks, and lowering the injection fluid temperature will enhance geothermal extraction power. These findings provide valuable insights for geothermal development.

Stretch-induced damage in endothelial monolayers

Endothelial cells are constantly exposed to mechanical stimuli, of which mechanical stretch has shown various beneficial or deleterious effects depending on whether loads are within physiological or pathological levels, respectively. Vascular properties change with age, and on a cell-scale, senescence elicits changes in endothelial cell mechanical properties that together can impair its response to stretch. Here, high-rate uniaxial stretch experiments were performed to quantify and compare the stretch-induced damage of monolayers consisting of young, senescent, and aged endothelial populations. The aged and senescent phenotypes were more fragile to stretch-induced damage. Prominent damage was detected by immunofluorescence and scanning electron microscopy as intercellular and intracellular void formation. Damage increased proportionally to the applied level of deformation and, for the aged and senescent phenotype, induced significant detachment of cells at lower levels of stretch compared to the young counterpart. Based on the phenotypic difference in cell-substrate adhesion of senescent cells indicating more mature focal adhesions, a discrete network model of endothelial cells being stretched was developed. The model showed that the more affine deformation of senescent cells increased their intracellular energy, thus enhancing the tendency for cellular damage and impending detachment. Next to quantifying for the first-time critical levels of endothelial stretch, the present results indicate that young cells are more resilient to deformation and that the fragility of senescent cells may be associated with their stronger adhesion to the substrate.

A Forward Learning Algorithm for Neural Memory Ordinary Differential Equations.

The deep neural network, based on the backpropagation learning algorithm, has achieved tremendous success. However, the backpropagation algorithm is consistently considered biologically implausible. Many efforts have recently been made to address these biological implausibility issues, nevertheless, these methods are tailored to discrete neural network structures. Continuous neural networks are crucial for investigating novel neural network models with more biologically dynamic characteristics and for interpretability of large language models. The neural memory ordinary differential equation (nmODE) is a recently proposed continuous neural network model that exhibits several intriguing properties. In this study, we present a forward-learning algorithm, called nmForwardLA, for nmODE. This algorithm boasts lower computational dimensions and greater efficiency. Compared with the other learning algorithms, experimental results on MNIST, CIFAR10, and CIFAR100 demonstrate its potency.

Integrated numerical simulation of hydraulic fracturing and production in shale gas well considering gas-water two-phase flow

Based on the displacement discontinuity method and the discrete fracture unified pipe network model, a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water. The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation, allowing for a more accurate fracturing-production integrated simulation. The results show that the reservoir physical properties have great impacts on fracture propagation, and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells. Compared with the conventional method, the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation. The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells. The simulation results are in good agreement with the practical production data, thus verifying the accuracy of the model.

Quake-DFN: A Software for Simulating Sequences of Induced Earthquakes in a Discrete Fault Network

ABSTRACT We present an earthquake simulator, Quake-DFN, which allows simulating sequences of earthquakes in a 3D discrete fault network governed by rate and state friction. The simulator is quasi-dynamic, with inertial effects being approximated by radiation damping and a lumped mass. The lumped mass term allows for accounting for inertial overshoot and, in addition, makes the computation more effective. Quake-DFN is compared against three publicly available simulation results: (1) the rupture of a planar fault with uniform prestress (SEAS BP5-QD), (2) the propagation of a rupture across a stepover separating two parallel planar faults (RSQSim and FaultMod), and (3) a branch fault system with a secondary fault splaying from a main fault (FaultMod). Examples of injection-induced earthquake simulations are shown for three different fault geometries: (1) a planar fault with a wide range of initial stresses, (2) a branching fault system with varying fault angles and principal stress orientations, and (3) a fault network similar to the one that was activated during the 2011 Prague, Oklahoma, earthquake sequence. The simulations produce realistic earthquake sequences. The time and magnitude of the induced earthquakes observed in these simulations depend on the difference between the initial friction and the residual friction μi−μf, the value of which quantifies the potential for runaway ruptures (ruptures that can extend beyond the zone of stress perturbation due to the injection). The discrete fault simulations show that our simulator correctly accounts for the effect of fault geometry and regional stress tensor orientation and shape. These examples show that Quake-DFN can be used to simulate earthquake sequences and, most importantly, magnitudes, possibly induced or triggered by a fluid injection near a known fault system.

Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization

Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization

Anomaly Detection in Dynamic Graphs: A Comprehensive Survey

This survey paper presents a comprehensive and conceptual overview of anomaly detection using dynamic graphs. We focus on existing graph-based anomaly detection (AD) techniques and their applications to dynamic networks. The contributions of this survey paper include the following: i) a comparative study of existing surveys on anomaly detection; ii) a D ynamic G raph-based A nomaly D etection ( DGAD ) review framework in which approaches for detecting anomalies in dynamic graphs are grouped based on traditional machine-learning models, matrix transformations, probabilistic approaches, and deep-learning approaches; iii) a discussion of graphically representing both discrete and dynamic networks; and iv) a discussion of the advantages of graph-based techniques for capturing the relational structure and complex interactions in dynamic graph data. Finally, this work identifies the potential challenges and future directions for detecting anomalies in dynamic networks. This DGAD survey approach aims to provide a valuable resource for researchers and practitioners by summarizing the strengths and limitations of each approach, highlighting current research trends, and identifying open challenges. In doing so, it can guide future research efforts and promote advancements in anomaly detection in dynamic graphs.

Health Risk Prediction of Operational Subsea Tunnel Structure Based on Bayesian Network

Recently, subsea tunnel construction has developed rapidly in China. The traffic volume of subsea metro tunnels is large. Once a safety accident occurs, economic losses and social impacts will be extremely serious. To eliminate accidents in operational subsea metro tunnel structures, a health risk prediction method is proposed based on a discrete Bayesian network. Detecting and monitoring data of the tunnel structures in operation were used to evaluate the health risk by employing the proposed method. This method establishes a Bayesian network model for the health risk prediction of the shield tunnel structure through the dependency relationship between the health risk of the operational tunnel structure and 13 risk factors in five aspects: the mechanical condition, material performance, integrity state, environmental state, and deformation state. By utilizing actual detection and monitoring data of various risk factors for the health risk of the operational subsea metro shield tunnel structure, this method reflects the actual state of the tunnel structure and improves the accuracy of health risk predictions. The validity of the proposed method is verified through expert knowledge and the subsea shield tunnel structure of the Dalian Subway Line 5. The results demonstrate that the health risk prediction outcomes effectively reflect the actual service state of the shield tunnel structure, thus providing decision support for the control of health risks in the subsea metro shield tunnel.

Industrial technology network security measurement in international trade under discrete hopfield neural network

As global economic integration continues to advance, international trade has become increasingly vital for the economic development and growth of nations. This research aims to assess the trends in industrial technology security within China’s international trade and provide practical guidance for policy-making, corporate strategies, and international cooperation. The significance of the rising trend in security within China’s international trade industry lies in its establishment of a robust foundation for the long-term development of China’s international trade, contributing to its cooperation and competitiveness with other countries. In addressing the limitations of traditional measurement methods and providing a more comprehensive and accurate assessment of industrial technology security, this research presents an approach based on a discrete Hopfield Neural Network (HNN) for evaluating industrial technology security in international trade. This method integrates multiple indicators, including technology gap rates, to construct the Superior Quality Engineering (SQE) comprehensive evaluation model. The research employs a combination model of “entropy-grey relational-Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS)-discrete HNN” to assess industrial technology security. This research evaluates international trade industry technology security using patent data from 2015 to 2022 as samples. The results indicate an overall upward trend in security in China’s international trade industry. Within this trend, the research observes a stepwise increase in scale components, leading to continuous improvement in security. In terms of quality components, although security develops relatively slowly overall, it exhibits a trend of initial gradual decline followed by rapid growth. Regarding efficiency components, there is overall slow growth with periodic fluctuations. This research outcome provides substantial support for the research of industrial technology in international trade. The proposed method can assist businesses in evaluating their technological security in international trade and offer robust support for international trade decision-making.

Dynamic Analysis, Image Encryption Application and FPGA Implementation of a Discrete Memristor-Coupled Neural Network

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

Research on resilience assessment method of train control on-board system

To address the problem of difficult performance assessment of train control on-board system after recovery from failures, we have proposed a resilience assessment methodology that uses reliability as an indicator of system resilience. Since the system failures are time-dependent, we adopted the Discrete Time Bayesian Network method to obtain the system's reliability before and after failure. Subsequently, we used an exponential recovery model to quantify the system's performance curve during the recovery phase, and finally utilized the resilient triangle area method to quantify its resilience size. Analyzing the CTCS3-300T train control on-board system, we found that the resilience of the system with cold standby redundancy design and hot standby redundancy design were 89.44 % and 87.34 %, respectively, indicating a slight decrease in system performance after recovery from failures compared to pre-failure levels. At that time, it was necessary to adjust operational plans based on actual conditions to avoid greater impact on the railway network. This paper realizes performance resilience of train control on-board system after failure recovery, which can be applied to similar systems and provide theoretical references for realizing intelligent maintenance of the high-speed train.

Mean-squared exponential stability of distributed almost periodic sequence for nonlocal space-time discrete shunting inhibitory cellular neural networks with Brownian motions

The discrete-time and discrete-space model for stochastic nonlocal shunting inhibitory cellular neural networks with reaction diffusions are modelled in the first time. Owing to the consideration of spatial variables, the discrete model derived in this article is more complex than the traditional ordinary difference model. In accordance with the constant-variation-formula for discrete-time and discrete-space model, Banach contracting mapping principle, the method of proof by contradiction and stochastic calculus, we also obtain the existence of a unique bounded almost periodic sequence for the discrete model, which is exponentially stable in the mean-square sense. Noting that it is the first time to consider the dynamics of almost periodicity in distribution of time-space discrete neural network models. The practicability of the present results is demonstrated by means of an illustration.

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

Impulsive Control Discrete Fractional Neural Networks in Product Form Design: Practical Mittag-Leffler Stability Criteria

The planning, regulation and effectiveness of the product design process depend on various characteristics. Recently, bio-inspired collective intelligence approaches have been applied in this process in order to create more appealing product forms and optimize the design process. In fact, the use of neural network models in product form design analysis is a complex process, in which the type of network has to be determined, as well as the structure of the network layers and the neurons in them; the connection coefficients, inputs and outputs have to be explored; and the data have to be collected. In this paper, an impulsive discrete fractional neural network modeling approach is introduced for product design analysis. The proposed model extends and complements several existing integer-order neural network models to the generalized impulsive discrete fractional-order setting, which is a more flexible mechanism to study product form design. Since control and stability methods are fundamental in the construction and practical significance of a neural network model, appropriate impulsive controllers are designed, and practical Mittag-Leffler stability criteria are proposed. The Lyapunov function strategy is applied in providing the stability criteria and their efficiency is demonstrated via examples and a discussion. The established examples also illustrate the role of impulsive controllers in stabilizing the behavior of the neuronal states. The proposed modeling approach and the stability results are applicable to numerous industrial design tasks in which multi-agent systems are implemented.

Knowledge-based self-tuning of PID control gains for continuum soft robots

In recent years, a class of soft (deformable) robots has attracted the attention of researchers due to their continuum features being advantageous over rigid robots for dexterous and safe compliant motions. These distinct advantages are obtained from the elastomer hyperelastic material properties because continuum robots are manufactured and actuated through embedded pneumatic energy fields. In this way, the continuum deformation raises novel problems in modeling and control due to its highly nonlinear behavior. That is, the deformable shape of its components varies continuously, unlike rigid robots, suggesting that the controller should compensate for its varying continuum model. Motivated by the deformable soft robot subject to parametric uncertainties and unmodeled dynamics, this paper proposes an adaptive, instead of constant, tuning of feedback gains of a model-free controller. The tuning mechanism is based on a knowledge-based scheme using a discrete wavelet neural network (DWN) by an efficient input–output identification updating its parameters and weights online, with a gradient descent algorithm driven by the identification error. At the same time, the control feedback gains are self-tuned, minimizing a convex cost function of tracking errors. Dynamic simulations show the performance of the proposed approach considering the parameters of a real soft robot mimicking a gelatin-like behavior. Finally, some discussions on the proposed scheme’s computational cost, feasibility, and viability are briefly addressed.

J-type random 2,3 satisfiability: a higher-order logical rule in discrete hopfield neural network

J-type random 2,3 satisfiability: a higher-order logical rule in discrete hopfield neural network

Dynamic research of hidden attractors in discrete memristive neural network with trigonometric functions and FPGA implementation

Dynamic research of hidden attractors in discrete memristive neural network with trigonometric functions and FPGA implementation

Cholinergic Neuromodulation of Prefrontal Attractor Dynamics Controls Performance in Spatial Working Memory.

The behavioral and neural effects of the endogenous release of acetylcholine following stimulation of the nucleus basalis (NB) of Meynert have been recently examined in two male monkeys (Qi et al., 2021). Counterintuitively, NB stimulation enhanced behavioral performance while broadening neural tuning in the prefrontal cortex (PFC). The mechanism by which a weaker mnemonic neural code could lead to better performance remains unclear. Here, we show that increased neural excitability in a simple continuous bump attractor model can induce broader neural tuning and decrease bump diffusion, provided neural rates are saturated. Increased memory precision in the model overrides memory accuracy, improving overall task performance. Moreover, we show that bump attractor dynamics can account for the nonuniform impact of neuromodulation on distractibility, depending on distractor distance from the target. Finally, we delve into the conditions under which bump attractor tuning and diffusion balance in biologically plausible heterogeneous network models. In these discrete bump attractor networks, we show that reducing spatial correlations or enhancing excitatory transmission can improve memory precision. Altogether, we provide a mechanistic understanding of how cholinergic neuromodulation controls spatial working memory through perturbed attractor dynamics in the PFC.

From Streamline to Pathline: Visualizing Particle Trajectories Under Changing Velocity Fields

Summary Monitoring of subsurface fluid motion is critical for optimizing hydrocarbon production and CO2 sequestration. Streamlines are frequently used to visualize fluid flow; however, they provide only an instantaneous snapshot of the velocity field and do not offer an exact representation of fluid movement under varying field conditions. In contrast, pathlines are constructed by tracking individual particles within the fluid, enabling us to trace the movement of these particles as they traverse through changing velocity fields. Pathline is the trajectory that an individual fluid particle follows in the reservoir. It can be thought of as “recording” the path of a fluid element in the flow field for a given time interval. Pathlines are distinct from streamlines which represent a snapshot of the velocity field at a given instant. The direction the path takes is determined by the streamlines at a specific instant. To start with, streamlines are traced based on the grid face fluxes of finite-difference simulation. Streamline tracing continues till the time of flight equals the current time. The endpoints of the current streamlines become the starting points for the next tracing period. Thus, our formulation incorporates changing flow fields, and the process is repeated for each time interval until the end. The proposed injection monitoring method is tested using a 3D field-scale model with complex geologic features to demonstrate its power and utility. The pathlines were compared with streamlines, as well as the water saturation distribution. Three scenarios are tested: a constant well schedule, a changing well schedule with partial shut-in, and a changing well schedule with a whole field cessation. Results indicate that the pathline provides a more accurate swept volume, consistent with saturation distribution. The robustness of our algorithm and implementation is demonstrated with a complex embedded discrete fracture model (EDFM) to visualize flow patterns in discrete facture network. Pathlines display the fluid flow across fractures and are subsequently used to explore the sweep efficiency and the well connectivity.