Discrete Dynamic Network Research Articles

Discrete Mathematics in Dynamic Network Analysis: Long-Term Efficacy Evaluation of Fotona Laser Therapy for Overactive Bladder Syndrome Using Clustering-Based Patient Subgroup Identification.

Dynamic network analysis, a state-of-the-art application of discrete mathematics, offers unprecedented insight into complex, time-evolving clinical data. This technical report demonstrates the value of evaluating the long-term efficacy of Fotona laser therapy (Fotona d.o.o., Ljubljana, Slovenia) in overactive bladder (OAB) syndrome. We analyzed data from 101 female patients aged ≥60 years who underwent Fotona laser treatment, including Vaginal Erbium Laser (VEL) and Urethral Erbium Laser (UEL), between 2020 and 2022. OAB symptom scores (OABSS) were collected at baseline (T0) and at six, 12, 18, and 24 months post treatment. Network graphs were constructed, representing patients as nodes, and symptom similarities as edges. Clustering techniques identify patient subgroups, whereas principal component analysis reduces dimensionality. The dynamic evolution of patient clusters was visualized through changes in average degree centrality over time. This approach revealed three distinct patient clusters with unique treatment response patterns. The results showed a progressive reduction in OABSS, with the total score decreasing by 2.82 ± 3.03 at 24 months. Our method provides novel visualization and analysis of complex longitudinal clinical data, offering insights into personalized treatment strategies for OAB. This report presents one of the first applications of discrete mathematics and dynamic network analysis to evaluate the long-term outcomes of Fotona laser therapy for OAB and introduces an innovative perspective for clinical decision-making in urogynecology.

Extended dissipative synchronization for discrete complex dynamical networks with random successive coupling delays through PID control

AbstractThis work investigates the synchronization problem for a kind of discrete complex dynamical networks (CDNs) including nonlinearities, exogenous disturbance, and successive time‐varying random coupling delays. Also, the stochastic variable obeying Bernoulli distribution is exploited to describe the randomness of the coupling delays. The main target of this work is to devise a novel PID controller ensuring that the proposed network is asymptotically synchronized in mean‐square and also meets a specified extended dissipative performance. With the aid of Kronecker product properties, Lyapunov stability theory and free weighting matrix technique, less conservative sufficient criteria is obtained in the form of Linear matrix inequalities (LMIs) to affirm the synchronization of the considered network. At last, the efficacy and potency of the designed control protocol are verified through two examples including the Chen system.

Switching clusters’ synchronization for discrete space-time complex dynamical networks via boundary feedback controls

Unlike the existing literatures that consider only discrete-time networks, this paper explores the double effects of both discrete time and discrete spatial diffusions in a switching complex dynamical networks. By means of the knowledge of clusters controls, a clusters synchronous frame of space-time discrete switching complex networks with boundary feedback controller is newly proposed and established. With the helps of some indispensable vector-valued sequence inequalities and Lyapunov function with switching signals and clusters’ information, the boundary feedback controllers are designed to synchronize space-time discrete switching complex networks coupled with nodes’ states or spatial diffusions in the form of clusters. Additionally, a realizable computer algorithm is given to make the derived results of this paper easier to enforce. The current work is pioneering in consideration of discrete spatial diffusions and provides a theoretical and practical basis for future research in this regard.

Synchronization for a class of discrete complex dynamical networks in presence of Markov jump topology and actuator saturation

AbstractThis work addresses the synchronization problem for discrete complex dynamical networks (CDNs) that are associated with Markov jump outer coupling, parameter uncertainties, actuator saturation, and time delay. Especially, the uncertainties which occur in the inner coupling matrix are categorized with the use of the interval matrix approach. The main purpose of this work is to design an appropriate state feedback controller with a saturation effect that guarantees asymptotic synchronization and also satisfy a prescribed level of mixed and passivity performance for the addressed CDNs. Moreover, a new set of adequate criteria are expressed in the form of linear matrix inequalities to synchronize the considered network plant. The above synchronization criteria are retrieved with the support of an appropriate Lyapunov–Krasovskii functional, Kronecker product properties together with Jensen's inequality and Abel lemma. Eventually, the efficiency and superiority of our proposed synchronization criteria are demonstrated through two numerical examples.

Dynamic network link prediction based on learning continuous time events

Dynamic network link prediction is a hot research problem in complex networks. Network representation learning can effectively learn the similarity of nodes and can be used for link prediction. Existing dynamic network representation learning methods mainly discrete window dynamic networks and then model them on static network snapshot graphs, which is difficult to effectively deal with dynamic networks with fine-grained temporal characteristics. In this paper, we propose a link prediction model that can learn complex temporal properties in dynamic networks. The model uses continuous time event sequences to represent dynamic networks, learns continuous temporal information and structural evolution features in the networks, and proposes a temporal attention-based information transfer mechanism to model the diffusion and aggregation of information in the networks. Finally, it transforms link prediction into a classification problem. The experiments are conducted on four real dynamic network datasets and simulated networks, using ap and auc as evaluation metrics. The experimental results of real networks demonstrate that the model can effectively learn the continuity of network evolution and obtain an effective node representation, thus improving the link prediction effect. The experimental results of the simulated network show that the effect of link prediction is related to the network model, but the model in this paper can still obtain better prediction results.

Asymptotic and Finite-Time Semistability for Nonlinear Discrete-Time Systems With Application to Network Consensus

This article focuses on semistability and finite-time semistability analysis and synthesis of discrete-time dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this article, we build on the theories of semistability and finite-time semistability for continuous-time dynamical systems to develop a rigorous framework for discrete semistability and discrete finite-time semistability. Specifically, Lyapunov and converse Lyapunov theorems for semistability and finite-time semistability are developed, and the regularity properties of the Lyapunov function establishing finite-time semistability are shown to be related to the settling time function capturing the finite settling time behavior of the dynamical system. These results are then used to develop a general framework for designing semistable and finite-time semistable consensus protocols for discrete dynamical networks for achieving multiagent coordination tasks asymptotically and in finite time. The proposed controller architectures involve the exchange of generalized energy state information between agents guaranteeing that the closed-loop dynamical network is semistable to an equipartitioned equilibrium representing a state of consensus consistent with basic thermodynamic principles.

DynHEN: A heterogeneous network model for dynamic bipartite graph representation learning

Learning node representations in graphs is a widespread problem in node classification and link prediction. Current research has focused on static heterogeneous, homogeneous networks, and dynamic homogeneous networks. However, many existing graphs, such as citation and social networks, are heterogeneous. Therefore, it is still a great challenge to obtain heterogeneous information in a dynamic heterogeneous graph to assist node representation learning. In this paper, we propose a Dynamic HEterogeneous Network (DynHEN) for user-item bipartite networks. It is a discrete dynamic graph neural network model that can be used directly for node representation learning by utilizing dynamic heterogeneous graphs. Specifically, DynHEN takes a bipartite graph at each time step as input, gets the corresponding embedding by capturing the deep heterogeneous information of the nodes while fusing the temporal information. To illustrate the effectiveness of heterogeneous information for graph representation learning, we compare with the current SOTA methods in the two type experiments of link prediction and node classification, and achieve outstanding results.

Event-Based Pinning Synchronization Control for Time-Delayed Complex Dynamical Networks: The Finite-Time Boundedness

The paper is concerned with the synchronization control issue for a kind of nonlinear discrete time-delayed complex dynamical networks. To improve energy efficiency, a dynamic event-triggering strategy is introduced to regulate the signal transmission from the controller to the actuator. Then, the event-based pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in control process. Subsequently, a new concept of finite-time boundedness in the mean square is put forward to evaluate the synchronization control performance by means of a settling-like time function. Furthermore, by using the Lyapunov stability theory and the stochastic analysis technique, a sufficient condition is provided to ensure that the synchronization error is finite-time bounded in the mean square with a prescribed error upper bound in the presence of both time-delay and external noise disturbances. By solving an optimization problem with some inequality constraints, the desired controller gain matrix is parameterized to minimize the settling-like time. Finally, a numerical simulation example is carried out to illustrate the effectiveness and usefulness of the obtained theoretical results.

H∞ Pinning Control of Complex Dynamical Networks Under Dynamic Quantization Effects: A Coupled Backward Riccati Equation Approach.

In this article, a pinning control strategy is developed for the finite-horizon H∞ synchronization problem for a kind of discrete time-varying nonlinear complex dynamical network in a digital communication circumstance. For the sake of complying with the digitized data exchange, a feedback-type dynamic quantizer is introduced to reflect the transformation from the raw signals into the discrete-valued ones. Then, a quantized pinning control scheme takes place on a small fraction of the network nodes with the hope of cutting down the control expenses while achieving the expected global synchronization objective. Subsequently, by resorting to the completing-the-square technique, a sufficient condition is established to ensure the finite-horizon H∞ index of the synchronization error dynamics against both quantization errors and external noises. Moreover, a controller design algorithm is put forward via an auxiliary H2 -type criterion, and the desired controller gains are acquired in terms of two coupled backward Riccati equations. Finally, the validity of the presented results is verified via a simulation example.

PD-type ℓ2 - ℓ∞ Intermittent Pinning Synchronization Control of Discrete Time-delay Nonlinear Dynamical Networks

In this paper, the PD-type l2 - l∞ synchronization control problem is concerned for a class of discrete time-delayed nonlinear dynamical networks. A PD-type (proportional-derivative-type) pinning control protocol is proposed where only a small fraction of network nodes is controlled in order to achieve the global synchronization performance. Meanwhile, for the sake of decreasing the update frequency of the controller, the periodic intermittent control strategy is developed. The main purpose of the addressed problem is to design a PD-type intermittent pinning feedback controller such that the closed-loop system achieves both the exponential synchronization and the prescribed l2 - l∞ performance index. Subsequently, by means of the Lyapunov-Krasovskii functional method, a sufficient condition is established under which the addressed PD-type controller design problem is recast into a linear convex optimization one that can be easily solved via available software packages. Finally, a simulation example is given to show the applicability of the developed theoretical results.

Simultaneous evacuation and entrance planning in complex building based on dynamic network flows

• This paper presents mathematical models that address the simultaneous evacuation of victims and entrance of responders. • Solutions provide the optimal routes for evacuees and responders within a critical timeframe. • Four types of models are developed according to the three different degrees of the golden time. • A heuristic algorithm is developed by extending the capacity constrained route planner. This paper presents mathematical models and a heuristic algorithm that address a simultaneous evacuation and entrance planning. For the simultaneous evacuation and entrance planning, four types of mathematical models based on the discrete time dynamic network flow model are developed to provide the optimal routes for evacuees and responders within a critical timeframe. The optimal routes obtained by the mathematical models can minimize the densification of evacuees and responders into specific areas. However, the mathematical model has a weakness in terms of long computation time for the large-size problem. To overcome the limitation, we developed a heuristic algorithm. We also analyzed the characteristics of each model and the heuristic algorithm by conducting case studies. This study pioneers area related to evacuation planning by developing and analyzing four types of mathematical models and a heuristic algorithm which take into account simultaneous evacuation and entrance planning.

Application of dynamic evidential networks in reliability analysis of complex systems with epistemic uncertainty and multiple life distributions

With the modernization and intelligent of industrial equipment and systems, the challenges of dynamic characteristics, failure dependency and uncertainties have aroused by the increasing of system complexity. Besides, various types of components may follow different life distributions which bring the multiple life distributions problem in systems. In order to model the impact of time dependency and epistemic uncertainty on the failure behavior of system, this paper combines the flexible dynamic modeling with the uncertainty expression. Its advantages are intuitively graphical representation and reasoning that brought by evidential network (EN). After that, the discrete time dynamic evidential network (DT-DEN) is introduced to analyze the reliability of complex systems, and the network inference mechanism is clearly defined. The evidence theory and original definition and inference mechanism of conventional EN is firstly recommended, and the DT-DEN is further presented. Furthermore, the multiple life distributions are synthesized into the DT-DEN to tackle the epistemic uncertainty and mixed life distribution challenges. Specifically, the dynamic logic gates are converted into equivalent DENs with distinguished conditional mass tables, and then the belief interval of system reliability can be calculated by network forward reasoning. Finally, the availability and efficiency of the proposed method is verified by some numerical examples.

Synchronization Control for A Class of Discrete Time-Delay Complex Dynamical Networks: A Dynamic Event-Triggered Approach.

This paper is concerned with the synchronization control problem for a class of discrete time-delay complex dynamical networks under a dynamic event-triggered mechanism. For the efficiency of energy utilization, we make the first attempt to introduce a dynamic event-triggering strategy into the design of synchronization controllers for complex dynamical networks. A new discrete-time version of the dynamic event-triggering mechanism is proposed in terms of the absolute errors between control input updates. By constructing an appropriate Lyapunov functional, the dynamics of each network node combined with the introduced event-triggering mechanism are first analyzed, and a sufficient condition is then provided under which the synchronization error dynamics is exponentially ultimately bounded. Subsequently, a set of the desired synchronization controllers is designed by solving a matrix inequality. Finally, a simulation example is provided to verify the effectiveness of the proposed dynamic event-triggered synchronization control scheme.

Hybrid function projective synchronization in discrete dynamical networks via adaptive control

Hybrid function projective synchronization in discrete dynamical networks via adaptive control

Hybrid function projective synchronization of uncertain discrete complex dynamical networks

The problem of hybrid function projective synchronization behavior in discrete complex dynamical networks with delay coupling is investigated in this paper. Sufficient conditions are derived to guarantee the realization of the hybrid function projective synchronization with different nodes and different dimension based on Lyapunov stability theory and adaptive control schema. In addition, the adaptive control gains are designed. Furthermore, different cases of topological structure of nodes are considered. Finally, numerical examples demonstrate the effectiveness of the proposed method.

Statistical Clustering of Temporal Networks Through a Dynamic Stochastic Block Model

SummaryStatistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model for its static part with independent Markov chains for the evolution of the nodes groups through time. We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the importance of controlling for label switching issues across the different time steps, focuses on detecting groups characterized by a stable within-group connectivity behaviour. We study identifiability of the model parameters and propose an inference procedure based on a variational expectation–maximization algorithm as well as a model selection criterion to select the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and we compare our procedure with existing procedures on synthetic data sets. We also illustrate our approach on dynamic contact networks: one of encounters between high school students and two others on animal interactions. An implementation of the method is available as an R package called dynsbm.

Event-Based $H_\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises.

In this paper, the event-based finite-horizon H∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

Pinning synchronization of discrete dynamical networks with delay coupling

The purpose of this paper is to investigate the pinning synchronization analysis for nonlinear coupled delayed discrete dynamical networks with the identical or nonidentical topological structure. Based on the Lyapunov stability theory, pinning control method and linear matrix inequalities, several adaptive synchronization criteria via two kinds of pinning control method are obtained. Two examples based on Rulkov chaotic system are included to illustrate the effectiveness and verification of theoretical analysis.

Stochastic Dynamic Traffic Assignment Model under Emergent Incidents

Urban emergent incidents affect transportation operation and result in the rapid spread of traffic congestion in network, so it's necessary to analyze the dynamic changes of traffic flow distribution under emergent incidents. Therefore, model and algorithm for the dynamic traffic assignment problem under emergent incidents have been highly concerned by government and scholars. This paper proposes a stochastic dynamic traffic assignment (SDTA) model based user optimum considering the loss of node capacity and change of network structure under traffic and environment emergencies. The Nested Logit model is used to describe the departure time and path choice. Then, the variational inequality formulation is proposed and discrete dynamic network loading algorithm is designed and validated by a numerical example. The results show that the model and algorithm can be used to express the development trend of actual dynamic network under emergency.

Geometrical Dissipativity‐Based Output Synchronization of Discrete Dynamical Networks with Non‐Identical Nodes

AbstractIn this paper, we investigate the generalized output synchronization problem for discrete dynamic networks with non‐identical nodes. We consider two cases: output synchronization for fixed topology and arbitrary switching topology. For the first case, we establish several criteria for generalized output synchronization using the geometrical dissipativity property. For the other case, we present a LaSalle invariance principle for discrete switched systems, based on which criteria for generalized output synchronization under arbitrary switching topology are given. Finally, an example is provided to illustrate the effectiveness of the main results.