Networks Of Dynamical Systems Research Articles

Dual amplification dynamic DNA network system for CRISPR/Cas12a based p53 gene detection

BackgroundIt is estimated that over 50 % of human cancers are caused by mutations in the p53 gene. Early sensitive and accurate detection of the p53 gene is important for diagnosis of cancers in the early stage. However, conventional detection techniques often suffer from strict reaction conditions, or unsatisfied sensitivity, so we need to develop a new strategy for accurate detection of p53 gene with smart designability, multiple signal amplification in mild reaction conditions. ResultsIn this study, CRISPR/Cas system is exploited in entropy-driven catalysis (EDC) and hybridization chain reaction (CHA) dual signal amplification sensing strategies. The products of both reactions can efficiently and separately activate CRISPR/Cas12a which greatly amplifies the fluorescent signal. The method has good linearity in p53 detection with the concentration ranged from 0.1 fM to 0.5 pM with ultra-low detection limit of 0.096 fM. It also showed good performance in serum, offering potentials for early disease detection. SignificanceThe designed dual amplification dynamic DNA network system exhibits an ultra-sensitive fluorescence biosensing for p53 gene identification. The method is simple to operate and requires only one buffer for the experiment, and meanwhile shows smart designability which could be used for a wide range of markers. Thus, we believe the present work will provide a potential tool for the construction and development of sensitive fluorescent biosensors for diseases.

Early Predictor for the Onset of Critical Transitions in Networked Dynamical Systems

Numerous natural and human-made systems exhibit critical transitions whereby slow changes in environmental conditions spark abrupt shifts to a qualitatively distinct state. These shifts very often entail severe consequences; therefore, it is imperative to devise robust and informative approaches for anticipating the onset of critical transitions. Real-world complex systems can comprise hundreds or thousands of interacting entities, and implementing prevention or management strategies for critical transitions requires knowledge of the exact condition in which they will manifest. However, most research so far has focused on low-dimensional systems and small networks containing fewer than ten nodes or has not provided an estimate of the location where the transition will occur. We address these weaknesses by developing a deep-learning framework which can predict the specific location where critical transitions happen in networked systems with size up to hundreds of nodes. These predictions do not rely on the network topology, the edge weights, or the knowledge of system dynamics. We validate the effectiveness of our machine-learning-based framework by considering a diverse selection of systems representing both smooth (second-order) and explosive (first-order) transitions: the synchronization transition in coupled Kuramoto oscillators; the sharp decline in the resource biomass present in an ecosystem; and the abrupt collapse of a Wilson-Cowan neuronal system. We show that our method provides accurate predictions for the onset of critical transitions well in advance of their occurrences, is robust to noise and transient data, and relies only on observations of a small fraction of nodes. Finally, we demonstrate the applicability of our approach to real-world systems by considering empirical vegetated ecosystems in Africa. Published by the American Physical Society 2024

On the higher-order smallest ring-star network of Chialvo neurons under diffusive couplings.

Network dynamical systems with higher-order interactions are a current trending topic, pervasive in many applied fields. However, our focus in this work is neurodynamics. We numerically study the dynamics of the smallest higher-order network of neurons arranged in a ring-star topology. The dynamics of each node in this network is governed by the Chialvo neuron map, and they interact via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through multi-body interactions. We deploy the higher-order coupling strength as the primary bifurcation parameter. We start by analyzing our model using standard tools from dynamical systems theory: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of disparate chaotic attractors. We also observe an interesting route to chaos from a fixed point via period-doubling and the appearance of cyclic quasiperiodic closed invariant curves. Furthermore, we numerically observe the existence of codimension-1 bifurcation points: saddle-node, period-doubling, and Neimark-Sacker. We also qualitatively study the typical phase portraits of the system, and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure, respectively. Finally, we study the synchronization behavior among the neurons using the cross correlation coefficient and the Kuramoto order parameter. We conjecture that unfolding these patterns and behaviors of the network model will help us identify different states of the nervous system, further aiding us in dealing with various neural diseases and nervous disorders.

Percolation-induced explosive synchronization in pinning control

Percolation and synchronization are two paradigmatic examples of phase transitions that can take place in network dynamical systems. In this paper, we show how percolation can induce an explosive, first-order transition to synchronization in pinning control, a classical feedback strategy that exploits the network topology to drive the network dynamics to a desired synchronous solution. When the number of control signals is limited by physical or economical constraints, only a fraction of the network nodes can be effectively synchronized onto the desired trajectory. Determining the sensitivity of this fraction to the number of pinning control signals is then key to decide if it is worth adding additional control signals. We find that when the network graph percolates, that is, it becomes endowed with a giant strongly connected component (GSCC), an explosive transition to synchronization occurs as we increase the fraction of nodes where we can inject the pinning signals. Motivated by this numerical observation, we exploit the probabilistic conditions that ensure the presence of a GSCC to predict the number of pinning signals such that all of its nodes will converge to the desired synchronous trajectory. We test the validity and robustness of our analytical derivations through numerical simulations on both synthetic and real networks, proving the benefit of such analysis in supporting decision-making for control design.

Dynamical Analysis and Synchronization of Complex Network Dynamic Systems under Continuous-Time

In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation.

Distributed Reinforcement Learning for Networked Dynamical Systems

Distributed Reinforcement Learning for Networked Dynamical Systems

Sustainability under Active Inference

In this paper, we explore the known connection among sustainability, resilience, and well-being within the framework of active inference. Initially, we revisit how the notions of well-being and resilience intersect within active inference before defining sustainability. We adopt a holistic concept of sustainability denoting the enduring capacity to meet needs over time without depleting crucial resources. It extends beyond material wealth to encompass community networks, labor, and knowledge. Using the free energy principle, we can emphasize the role of fostering resource renewal, harmonious system–entity exchanges, and practices that encourage self-organization and resilience as pathways to achieving sustainability both as an agent and as a part of a collective. We start by connecting active inference with well-being, building on existing work. We then attempt to link resilience with sustainability, asserting that resilience alone is insufficient for sustainable outcomes. While crucial for absorbing shocks and stresses, resilience must be intrinsically linked with sustainability to ensure that adaptive capacities do not merely perpetuate existing vulnerabilities. Rather, it should facilitate transformative processes that address the root causes of unsustainability. Sustainability, therefore, must manifest across extended timescales and all system strata, from individual components to the broader system, to uphold ecological integrity, economic stability, and social well-being. We explain how sustainability manifests at the level of an agent and then at the level of collectives and systems. To model and quantify the interdependencies between resources and their impact on overall system sustainability, we introduce the application of network theory and dynamical systems theory. We emphasize the optimization of precision or learning rates through the active inference framework, advocating for an approach that fosters the elastic and plastic resilience necessary for long-term sustainability and abundance.

Intellectual Property Law's Confiscatory Losses: Its Application in Dynamic Network Environments

This paper discusses confiscatory losses in the dynamic network enforcement of intellectual property (IP). IP law protects copyrights, patents, and trademarks. Instead, IP enforcement may consequence in "confiscatory damages." This occurs when the defendant's property is apprehended pursuant to a court order. For both individuals and companies, the internet has made sharing and disseminating innovative creations simpler. IP infringement is also increased by this. In these circumstances, IP law enforcement has become more crucial. Penalisations and sanctions for IP infringement in these conditions may be severe and upshot in confiscatory losses. So as to apply confiscatory losses in dynamic network conditions, this paper suggests reviewing IP law enforcement strategies. Hence, IP infringement penalisations and compensation should be proportionate to the harm caused and avoid confiscatory losses. Moreover, IP infringement can also be minimized by education, information, and alternative dispute resolution. IP law enforcement in dynamic network systems must strike a compromise between protecting IP rights and sidestepping confiscatory damages.

Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise

This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates spurious associations across pairs of nodes, rendering the problem much harder. To address the challenge of noise correlation and partial observability, we assign to each pair of nodes a feature vector computed from the time series data of observed nodes. The feature embedding is engineered to yield structural consistency: there exists an affine hyperplane that consistently partitions the set of features, separating the feature vectors corresponding to connected pairs of nodes from those corresponding to disconnected pairs. The causal inference problem is thus addressed via clustering the designed features. We demonstrate with simple baseline supervised methods the competitive performance of the proposed causal inference mechanism under broad connectivity regimes and noise correlation levels, including a real world network. Further, we devise novel technical guarantees of structural consistency for linear NDS under the considered regime.

Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction

Recently, machine learning methods, including reservoir computing (RC), have been tremendously successful in predicting complex dynamics in many fields. However, a present challenge lies in pushing for the limit of prediction accuracy while maintaining the low complexity of the model. Here, we design a data-driven, model-free framework named higher-order Granger reservoir computing (HoGRC), which owns two major missions: The first is to infer the higher-order structures incorporating the idea of Granger causality with the RC, and, simultaneously, the second is to realize multi-step prediction by feeding the time series and the inferred higher-order information into HoGRC. We demonstrate the efficacy and robustness of the HoGRC using several representative systems, including the classical chaotic systems, the network dynamical systems, and the UK power grid system. In the era of machine learning and complex systems, we anticipate a broad application of the HoGRC framework in structure inference and dynamics prediction.

Revealing Higher-Order Interactions in High-Dimensional Complex Systems: A Data-Driven Approach

Natural and manmade complex systems are comprised of different elementary units, being either system components or diverse subsystems as in the case of networked systems. These units interact with each other in a possibly nonlinear way, which results in a complex dynamics that is generally dissipative and nonstationary. One of the challenges in the modeling of such systems is the identification of not only pairwise but, more importantly, higher-order interactions, together with their directions and strengths from measured multivariate time series. Here, we propose a novel data-driven approach for characterizing interactions of different orders. Our approach is based on solving a set of linear equations constructed from Kramers-Moyal coefficients derived from statistical moments of N-dimensional multivariate time series. We demonstrate the substantial potential for applications by a data-driven reconstruction of interactions in various multidimensional and networked dynamical systems. Published by the American Physical Society 2024

Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares.

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equationsto compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

Heteroclinic dynamics in network dynamical systems with higher-order interactions

Abstract Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.

Automatic Proper Orthogonal Block Decomposition method for network dynamical systems with multiple timescales

In this work, we introduce a novel reduced order model technique, based on the Proper Orthogonal Decomposition method, for dynamical systems with multiple timescales. The main ideas are to retain the structure of the original model, which is lost in the original POD procedure, while producing a competitive reduction in the number of equations and computational time, and to determine the best structure for the reduced system automatically, via a data-driven analysis of the original model data. For these novel techniques, we present some numerical tests for various behaviors of three different neural network models with multiple timescales, which support the use of these new methods.

Distributed Management of Fluctuating Energy Resources in Dynamic Networked Systems

Distributed Management of Fluctuating Energy Resources in Dynamic Networked Systems

Practical Cyber Attack Detection With Continuous Temporal Graph in Dynamic Network System

Practical Cyber Attack Detection With Continuous Temporal Graph in Dynamic Network System

Improved zeroing neural models based on two novel activation functions with exponential behavior

A family of zeroing neural networks based on new nonlinear activation functions is proposed for solving various time-varying linear matrix equations (TVLME). The proposed neural network dynamical systems, symbolized as Li-VPZNN1 and Li-VPZNN2, include an exponential parameter in nonlinear activation function (AF) that leads to faster convergence to the theoretical result compared to previous categories of nonlinearly activated neural networks. Theoretical analysis as well as numerical tests in MATLAB's environment confirm the efficiency and accelerated convergence property of the novel dynamics.

TEMPO bacterial cellulose and MXene nanosheets synergistically promote tough hydrogels for intelligent wearable human-machine interaction

Conductive hydrogels have received increasing attention in the field of wearable electronics, but they also face many challenges such as temperature tolerance, biocompatibility, and stability of mechanical properties. In this paper, a double network hydrogel of MXene/TEMPO bacterial cellulose (TOBC) system is proposed. Through solvent replacement, the hydrogel exhibits wide temperature tolerance (−20–60 °C) and stable mechanical properties. A large number of hydrogen bonds, MXene/TOBC dynamic three-dimensional network system, and micellar interactions endow the hydrogel with excellent mechanical properties (elongation at break ~2800 %, strength at break ~420 kPa) and self-healing ability. The introduction of tannic acid prevents the oxidation of MXene and the loss of electrical properties of the hydrogel. In addition, the sensor can also quickly (74 ms) and sensitive (gauge factor = 15.65) wirelessly monitor human motion, and the biocompatibility can well avoid the stimulation when it comes into contact with the human body. This series of research work reveals the fabrication of MXene-like flexible wearable electronic devices based on self-healing, good cell compatibility, high sensitivity, wide temperature tolerance and durability, which can be used in smart wearable, wireless monitoring, human-machine Interaction and other aspects show great application potential.

A hybrid framework of dynamic periodic event-triggered networked control systems subject to time-varying delays

This paper investigates the dynamic output-feedback control for networked control systems (NCSs). The data transmissions in the sensor-to-controller and the controller-to-actuator channels are generated by the dynamic periodic event-triggering mechanism. Due to the existence of time-varying delays in the two channels, the updated data is received after a time delay. To cope with this problem, a hybrid dynamical framework of the NCSs is established. With the help of Lyapunov function-based approach, a new event-triggering condition is designed and sufficient conditions on input-to-state stability are derived. By introducing an auxiliary function, the obtained sufficient conditions are transformed into linear matrix inequalities and the explicit forms of the dynamic output-feedback controller gains are provided. Moreover, the upper bounds on the maximum allowable transfer intervals and the maximum allowable delays are derived. Finally, a numerical example illustrates the feasibility of the proposed method.

On a framework of data assimilation for hyperparameter estimation of spiking neuronal networks

When handling real-world data modeled by a complex network dynamical system, the number of the parameters is often much more than the size of the data. Therefore, in many cases, it is impossible to estimate these parameters and the exact value of each parameter is frequently less interesting than the distribution of the parameters. In this paper, we aim to estimate the distribution of the parameters in the mesoscopic neuronal network model from the macroscopic experimental data, for example, the BOLD (blood oxygen level dependent) signal. Herein, we assume that the parameters of the neurons and synapses are inhomogeneous but independently and identically distributed from certain distributions with unknown hyperparameters. Thus, we estimate these hyperparameters of the distributions of the parameters, instead of estimating the parameters themselves. We formulate this problem under the framework of data assimilation and hierarchical Bayesian method and present an efficient method named Hierarchical Data Assimilation (HDA) to conduct the statistical inference on the neuronal network model with the BOLD signal data simulated by the hemodynamic model. We consider the Leaky Integral-Fire (LIF) neuronal networks with four synapses and show that the proposed algorithm can estimate the BOLD signals and the hyperparameters with high preciseness. In addition, we discuss the influence on the performance of the algorithm configuration and the LIF network model setup.