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Journal articles on the topic 'Complex dynamical network models'
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1
WANG, XIAO FAN. "COMPLEX NETWORKS: TOPOLOGY, DYNAMICS AND SYNCHRONIZATION." International Journal of Bifurcation and Chaos 12, no. 05 (May 2002): 885–916. http://dx.doi.org/10.1142/s0218127402004802.
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Dramatic advances in the field of complex networks have been witnessed in the past few years. This paper reviews some important results in this direction of rapidly evolving research, with emphasis on the relationship between the dynamics and the topology of complex networks. Basic quantities and typical examples of various complex networks are described; and main network models are introduced, including regular, random, small-world and scale-free models. The robustness of connectivity and the epidemic dynamics in complex networks are also evaluated. To that end, synchronization in various dynamical networks are discussed according to their regular, small-world and scale-free connections.
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Wu, Xu, Guo-Ping Jiang, and Xinwei Wang. "A New Model for Complex Dynamical Networks Considering Random Data Loss." Entropy 21, no. 8 (August 15, 2019): 797. http://dx.doi.org/10.3390/e21080797.
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Model construction is a very fundamental and important issue in the field of complex dynamical networks. With the state-coupling complex dynamical network model proposed, many kinds of complex dynamical network models were introduced by considering various practical situations. In this paper, aiming at the data loss which may take place in the communication between any pair of directly connected nodes in a complex dynamical network, we propose a new discrete-time complex dynamical network model by constructing an auxiliary observer and choosing the observer states to compensate for the lost states in the coupling term. By employing Lyapunov stability theory and stochastic analysis, a sufficient condition is derived to guarantee the compensation values finally equal to the lost values, namely, the influence of data loss is finally eliminated in the proposed model. Moreover, we generalize the modeling method to output-coupling complex dynamical networks. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed model.
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Gupta, Abhinav, and Pierre F. J. Lermusiaux. "Neural closure models for dynamical systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (August 2021): 20201004. http://dx.doi.org/10.1098/rspa.2020.1004.
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Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile and rigorous methodology to learn non-Markovian closure parametrizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new neural closure models augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models and augment the simplification of complex biological and physical–biogeochemical models. We find that using non-Markovian over Markovian closures improves long-term prediction accuracy and requires smaller networks. We derive adjoint equations and network architectures needed to efficiently implement the new discrete and distributed nDDEs, for any time-integration schemes and allowing non-uniformly spaced temporal training data. The performance of discrete over distributed delays in closure models is explained using information theory, and we find an optimal amount of past information for a specified architecture. Finally, we analyse computational complexity and explain the limited additional cost due to neural closure models.
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TADIĆ, BOSILJKA, G. J. RODGERS, and STEFAN THURNER. "TRANSPORT ON COMPLEX NETWORKS: FLOW, JAMMING AND OPTIMIZATION." International Journal of Bifurcation and Chaos 17, no. 07 (July 2007): 2363–85. http://dx.doi.org/10.1142/s0218127407018452.
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Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper, we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics.
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O'Dea, Reuben, Jonathan J. Crofts, and Marcus Kaiser. "Spreading dynamics on spatially constrained complex brain networks." Journal of The Royal Society Interface 10, no. 81 (April 6, 2013): 20130016. http://dx.doi.org/10.1098/rsif.2013.0016.
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The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way.
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House, Thomas, and Matt J. Keeling. "Insights from unifying modern approximations to infections on networks." Journal of The Royal Society Interface 8, no. 54 (June 10, 2010): 67–73. http://dx.doi.org/10.1098/rsif.2010.0179.
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Networks are increasingly central to modern science owing to their ability to conceptualize multiple interacting components of a complex system. As a specific example of this, understanding the implications of contact network structure for the transmission of infectious diseases remains a key issue in epidemiology. Three broad approaches to this problem exist: explicit simulation; derivation of exact results for special networks; and dynamical approximations. This paper focuses on the last of these approaches, and makes two main contributions. Firstly, formal mathematical links are demonstrated between several prima facie unrelated dynamical approximations. And secondly, these links are used to derive two novel dynamical models for network epidemiology, which are compared against explicit stochastic simulation. The success of these new models provides improved understanding about the interaction of network structure and transmission dynamics.
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Uthamacumaran, A. "A Review of Complex Systems Approaches to Cancer Networks." Complex Systems 29, no. 4 (December 15, 2020): 779–835. http://dx.doi.org/10.25088/complexsystems.29.4.779.
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Cancers remain the leading cause of disease-related pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple strange attractors. Machine learning, network science and algorithmic information dynamics are discussed as current tools for cancer network reconstruction. Deep learning architectures and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complex systems and complexity theory.
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HOLME, PETTER. "CONGESTION AND CENTRALITY IN TRAFFIC FLOW ON COMPLEX NETWORKS." Advances in Complex Systems 06, no. 02 (June 2003): 163–76. http://dx.doi.org/10.1142/s0219525903000803.
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The central points of communication network flow have often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the underlying network structure. In this work we investigate the relationship between centrality measures and the density of traffic for some simple particle hopping models on networks with emerging scale-free degree distributions. We also study how the speed of the dynamics are affected by the underlying network structure. Among other conclusions, we find that, even at low traffic densities, the dynamical measure of traffic density (the occupation ratio) has a non-trivial dependence on the static centrality (quantified by "betweenness centrality"), where non-central vertices get a comparatively large portion of the traffic.
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Hanel, Rudolf, Manfred Pöchacker, and Stefan Thurner. "Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1933 (December 28, 2010): 5583–96. http://dx.doi.org/10.1098/rsta.2010.0267.
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Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems , their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network , and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.
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Ma’ayan, Avi. "Colliding Dynamical Complex Network Models: Biological Attractors versus Attractors from Material Physics." Biophysical Journal 103, no. 9 (November 2012): 1816–17. http://dx.doi.org/10.1016/j.bpj.2012.09.019.
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MUEZZINOGLU, MEHMET K., IRMA TRISTAN, RAMON HUERTA, VALENTIN S. AFRAIMOVICH, and MIKHAIL I. RABINOVICH. "TRANSIENTS VERSUS ATTRACTORS IN COMPLEX NETWORKS." International Journal of Bifurcation and Chaos 20, no. 06 (June 2010): 1653–75. http://dx.doi.org/10.1142/s0218127410026745.
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Understanding and predicting the behavior of complex multiagent systems like brain or ecological food net requires new approaches and paradigms. Traditional analyses based on just asymptotic results of behavior as time goes to infinity, or on straightforward mathematical images that can accommodate only fixed points or limit cycles do not tell much about these systems. To obtain sensible dynamical models of natural phenomena, such as the reproducible order observed in ecological, cognitive or behavioral experiments, one cannot afford to neglect the transient dynamics of the underlying complex network. In disclosing such dynamical mechanisms, the focus of interest must be on reproducible or, even, structurally stable transients. In this tutorial, we formulate the Winnerless Competition (WLC) principle that induces robust transient dynamics in open complex networks. The main point of WLC principle is the transformation of the acquired information into ensemble (spatio)-temporal output via intrinsic transient dynamics of the network. Such encoding provides a reproducible transient response, whose geometrical image in phase space is a stable heteroclinic sequence. We compile a diverse list of natural phenomena which can be rigorously modeled by the WLC. Together with the experimental and numerical results of the networks with different levels of complexity, we evaluate the robustness and reproducibility of the WLC dynamics and discuss the advantages of future possible application of the discussed approach.
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Gates, Alexander J., Rion Brattig Correia, Xuan Wang, and Luis M. Rocha. "The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling." Proceedings of the National Academy of Sciences 118, no. 12 (March 18, 2021): e2022598118. http://dx.doi.org/10.1073/pnas.2022598118.
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The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization—the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.
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Tanzi, Matteo, and Lai-Sang Young. "Existence of physical measures in some excitation–inhibition networks*." Nonlinearity 35, no. 2 (December 22, 2021): 889–915. http://dx.doi.org/10.1088/1361-6544/ac3eb6.
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Abstract In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but can be arbitrarily large. They are inspired by real biological networks, and possess features that are idealizations of those in biological systems. Individual components of the network are represented by simple, much studied dynamical systems. Complex dynamical patterns on the network level emerge as a result of the coupling among its constituent subsystems. Appealing to existing techniques in (nonuniform) hyperbolic theory, we study their Lyapunov exponents and entropy, and prove that large time network dynamics are governed by physical measures with the SRB property.
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Arellano-Delgado, A., C. Cruz-Hernández, R. M. López Gutiérrez, and C. Posadas-Castillo. "Outer Synchronization of Simple Firefly Discrete Models in Coupled Networks." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/895379.
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Synchronization is one of the most important emerging collective behaviors in nature, which results from the interaction in groups of organisms. In this paper, network synchronization of discrete-time dynamical systems is studied. In particular, network synchronization with fireflies oscillators like nodes is achieved by using complex systems theory. Different cases of interest on network synchronization are studied, including for a large number of fireflies oscillators; we consider synchronization in small-world networks and outer synchronization among different coupled networks topologies; for all presented cases, we provide appropriate ranges of values for coupling strength and extensive numerical simulations are included. In addition, for illustrative purposes, we show the effectiveness of network synchronization by means of experimental implementation of coupled nine electronics fireflies in different topologies.
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Huo, Liang’an, Fan Ding, Chen Liu, and Yingying Cheng. "Dynamical Analysis of Rumor Spreading Model considering Node Activity in Complex Networks." Complexity 2018 (November 12, 2018): 1–10. http://dx.doi.org/10.1155/2018/1049805.
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The dynamic models are proposed to investigate the influence node activity has on rumor spreading process in both homogeneous and heterogeneous networks. Different from previous studies, we believe that the activity of nodes in complex networks affects the process of rumor spreading. An active node can have contact with all the nodes it directly links to, while an inactive node could only interact with its active neighbors. We explore the joint effort of activity rate, spreading rate and network topology on rumor spreading process by mean-field equations and numerical simulations, which reveals that there exists a critical curve consisting of critical activity rate and spreading rate; meanwhile, activity rate and spreading rate both have influence on the final rumor spreading scale.
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LU, JIANQUAN, DANIEL W. C. HO, and JINDE CAO. "SYNCHRONIZATION IN AN ARRAY OF NONLINEARLY COUPLED CHAOTIC NEURAL NETWORKS WITH DELAY COUPLING." International Journal of Bifurcation and Chaos 18, no. 10 (October 2008): 3101–11. http://dx.doi.org/10.1142/s0218127408022275.
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A general complex dynamical network consisting of N nonlinearly coupled identical chaotic neural networks with coupling delays is firstly formulated. Many studied models with coupling systems are special cases of this model. Synchronization in such dynamical network is considered. Based on the Lyapunov–Krasovskii stability theorem, some simple controllers with updated feedback strength are introduced to make the network synchronized. The update gain γi can be properly chosen to make some important nodes synchronized quicker or slower than the rest. Two examples including nearest-neighbor coupled networks and scale-free network are given to verify the validity and effectiveness of the proposed control scheme.
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Asllani, Malbor, Renaud Lambiotte, and Timoteo Carletti. "Structure and dynamical behavior of non-normal networks." Science Advances 4, no. 12 (December 2018): eaau9403. http://dx.doi.org/10.1126/sciadv.aau9403.
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We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.
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McDermott, Patrick, and Christopher Wikle. "Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data." Entropy 21, no. 2 (February 15, 2019): 184. http://dx.doi.org/10.3390/e21020184.
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Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. Recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications.
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Ramasamy, Mohanasubha, Suresh Kumarasamy, Ashokkumar Srinivasan, Pavithra Subburam, and Karthikeyan Rajagopal. "Dynamical effects of hypergraph links in a network of fractional-order complex systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (December 2022): 123128. http://dx.doi.org/10.1063/5.0103241.
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In recent times, the fractional-order dynamical networks have gained lots of interest across various scientific communities because it admits some important properties like infinite memory, genetic characteristics, and more degrees of freedom than an integer-order system. Because of these potential applications, the study of the collective behaviors of fractional-order complex networks has been investigated in the literature. In this work, we investigate the influence of higher-order interactions in fractional-order complex systems. We consider both two-body and three-body diffusive interactions. To elucidate the role of higher-order interaction, we show how the network of oscillators is synchronized for different values of fractional-order. The stability of synchronization is studied with a master stability function analysis. Our results show that higher-order interactions among complex networks help the earlier synchronization of networks with a lesser value of first-order coupling strengths in fractional-order complex simplices. Besides that, the fractional-order also shows a notable impact on synchronization of complex simplices. For the lower value of fractional-order, the systems get synchronized earlier, with lesser coupling strengths in both two-body and three-body interactions. To show the generality in the outcome, two neuron models, namely, Hindmarsh–Rose and Morris–Leccar, and a nonlinear Rössler oscillator are considered for our analysis.
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Rosell-Tarragó, Gemma, Emanuele Cozzo, and Albert Díaz-Guilera. "A Complex Network Framework to Model Cognition: Unveiling Correlation Structures from Connectivity." Complexity 2018 (July 12, 2018): 1–19. http://dx.doi.org/10.1155/2018/1918753.
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Several approaches to cognition and intelligence research rely on statistics-based model testing, namely, factor analysis. In the present work, we exploit the emerging dynamical system perspective putting the focus on the role of the network topology underlying the relationships between cognitive processes. We go through a couple of models of distinct cognitive phenomena and yet find the conditions for them to be mathematically equivalent. We find a nontrivial attractor of the system that corresponds to the exact definition of a well-known network centrality and hence stresses the interplay between the dynamics and the underlying network connectivity, showing that both of the two are relevant. Correlation matrices evince there must be a meaningful structure underlying real data. Nevertheless, the true architecture regarding the connectivity between cognitive processes is still a burning issue of research. Regardless of the network considered, it is always possible to recover a positive manifold of correlations. Furthermore, we show that different network topologies lead to different plausible statistical models concerning the correlation structure, ranging from one to multiple factor models and richer correlation structures.
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Flechsig, Holger, and Yuichi Togashi. "Designed Elastic Networks: Models of Complex Protein Machinery." International Journal of Molecular Sciences 19, no. 10 (October 13, 2018): 3152. http://dx.doi.org/10.3390/ijms19103152.
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Recently, the design of mechanical networks with protein-inspired responses has become increasingly popular. Here, we review contributions which were motivated by studies of protein dynamics employing coarse-grained elastic network models. First, the concept of evolutionary optimization that we developed to design network structures which execute prescribed tasks is explained. We then review what presumably marks the origin of the idea to design complex functional networks which encode protein-inspired behavior, namely the design of an elastic network structure which emulates the cycles of ATP-powered conformational motion in protein machines. Two recent applications are reviewed. First, the construction of a model molecular motor, whose operation incorporates both the tight coupling power stroke as well as the loose coupling Brownian ratchet mechanism, is discussed. Second, the evolutionary design of network structures which encode optimal long-range communication between remote sites and represent mechanical models of allosteric proteins is presented. We discuss the prospects of designed protein-mimicking elastic networks as model systems to elucidate the design principles and functional signatures underlying the operation of complex protein machinery.
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Knabe, Johannes F., Chrystopher L. Nehaniv, and Maria J. Schilstra. "Genetic Regulatory Network Models of Biological Clocks: Evolutionary History Matters." Artificial Life 14, no. 1 (January 2008): 135–48. http://dx.doi.org/10.1162/artl.2008.14.1.135.
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We study the evolvability and dynamics of artificial genetic regulatory networks (GRNs), as active control systems, realizing simple models of biological clocks that have evolved to respond to periodic environmental stimuli of various kinds with appropriate periodic behaviors. GRN models may differ in the evolvability of expressive regulatory dynamics. A new class of artificial GRNs with an evolvable number of complex cis-regulatory control sites—each involving a finite number of inhibitory and activatory binding factors—is introduced, allowing realization of complex regulatory logic. Previous work on biological clocks in nature has noted the capacity of clocks to oscillate in the absence of environmental stimuli, putting forth several candidate explanations for their observed behavior, related to anticipation of environmental conditions, compartmentation of activities in time, and robustness to perturbations of various kinds or to unselected accidents of neutral selection. Several of these hypotheses are explored by evolving GRNs with and without (Gaussian) noise and blackout periods for environmental stimulation. Robustness to certain types of perturbation appears to account for some, but not all, dynamical properties of the evolved networks. Unselected abilities, also observed for biological clocks, include the capacity to adapt to change in wavelength of environmental stimulus and to clock resetting.
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Nikolic, Sasa S., Dragan S. Antic, Nikola B. Dankovic, Aleksandra A. Milovanovic, Darko B. Mitic, Miroslav B. Milovanovic, and Petar S. Djekic. "Generalized Quasi-Orthogonal Functional Networks Applied in Parameter Sensitivity Analysis of Complex Dynamical Systems." Elektronika ir Elektrotechnika 28, no. 4 (August 24, 2022): 19–26. http://dx.doi.org/10.5755/j02.eie.31110.
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This paper presents one possible application of generalized quasi-orthogonal functional networks in the sensitivity analysis of complex dynamical systems. First, a new type of first order (k = 1) generalized quasi-orthogonal polynomials of Legendre type via classical quasi-orthogonal polynomials was introduced. The short principle to design generalized quasi-orthogonal polynomials and filters was also shown. A generalized quasi-orthogonal functional network represents an extension of classical orthogonal functional networks and neural networks, which deal with general functional models. A sequence of the first order (k = 1) generalized quasi-orthogonal polynomials was used as a new basis in the proposed generalized quasi-orthogonal functional networks. The proposed method for determining the parameter sensitivity of complex dynamical systems is also given, and an example of a complex industrial system in the form of a tower crane was considered. The results obtained have been compared with different methods for parameter sensitivity analysis.
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XING, CHANGMING. "THE TRAPPING PROBLEM OF WEIGHTED (2,2)-FLOWER NETWORKS WITH THE SAME WEIGHT SEQUENCE." Fractals 27, no. 07 (November 2019): 1950112. http://dx.doi.org/10.1142/s0218348x19501123.
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Intuitively, edge weight has an effect on the dynamical processes occurring on the networks. However, the theoretical research on the effects of edge weight on network dynamics is still rare. In this paper, we present two weighted network models by adjusting the matching relationship between weights and edges. Both network models are controlled by the weight factor [Formula: see text]. They have the same connection structure and weight sequence when [Formula: see text] is fixed. Based on their self-similar network structure, we study two types of biased walks with a trap. One is standard weight-dependent walk, while the other is mixed weight-dependent walk including both nearest-neighbor and next-nearest-neighbor jumps. For both weighted scale-free networks, we obtain exact solutions of the average trapping time (ATT) measuring the efficiency of the trapping process in both network models. Analyzing and comparing the obtained solutions, we find that the ATT is related to the walking rule and the spectral dimension of the fractal network, and not all ATT for the weighted networks are affected by the weight factor [Formula: see text]. In other words, not all weight adjustments can change the trapping efficiency in the network. We hope that the present findings could help us get deeper understanding about the influence factor of biased walk in complex systems.
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Rozum, Jordan C., Jorge Gómez Tejeda Zañudo, Xiao Gan, Dávid Deritei, and Réka Albert. "Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks." Science Advances 7, no. 29 (July 2021): eabf8124. http://dx.doi.org/10.1126/sciadv.abf8124.
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We present new applications of parity inversion and time reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal construction efficiently reveal discrete analogs of stable and unstable manifolds. We demonstrate their predictive power by studying decision-making in systems biology and statistical physics models. These applications underpin a novel attractor identification algorithm implemented for Boolean networks under stochastic dynamics. Its speed enables resolving a long-standing open question of how attractor count in critical random Boolean networks scales with network size and whether the scaling matches biological observations. Via 80-fold improvement in probed network size (N = 16,384), we find the unexpectedly low scaling exponent of 0.12 ± 0.05, approximately one-tenth the analytical upper bound. We demonstrate a general principle: A system’s relationship to its time reversal and state-space inversion constrains its repertoire of emergent behaviors.
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Cheng, Shin-Ming, Vasileios Karyotis, Pin-Yu Chen, Kwang-Cheng Chen, and Symeon Papavassiliou. "Diffusion Models for Information Dissemination Dynamics in Wireless Complex Communication Networks." Journal of Complex Systems 2013 (September 4, 2013): 1–13. http://dx.doi.org/10.1155/2013/972352.
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Information dissemination has become one of the most important services of communication networks. Modeling the diffusion of information through such networks is crucial for our modern information societies. In this work, novel models, segregating between useful and malicious types of information, are introduced, in order to better study Information Dissemination Dynamics (IDD) in wireless complex communication networks, and eventually allow taking into account special network features in IDD. According to the proposed models, and inspired from epidemiology, we investigate the IDD in various complex network types through the use of the Susceptible-Infected (SI) paradigm for useful information dissemination and the Susceptible-Infected-Susceptible (SIS) paradigm for malicious information spreading. We provide analysis and simulation results for both types of diffused information, in order to identify performance and robustness potentials for each dissemination process with respect to the characteristics of the underlying complex networking infrastructures. We demonstrate that the proposed approach can generically characterize IDD in wireless complex networks and reveal salient features of dissemination dynamics in each network type, which could eventually aid in the design of more advanced, robust, and efficient networks and services.
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Wang, Qi, Yinhe Wang, and Zilin Gao. "Initial State Causes the Structural Balance of Complex Networks With Dynamical Models." IEEE Access 8 (2020): 35245–52. http://dx.doi.org/10.1109/access.2020.2975047.
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Peng, Xiaoyi, Michael Small, Yi Zhao, and Jack Murdoch Moore. "Detecting and Predicting Tipping Points." International Journal of Bifurcation and Chaos 29, no. 08 (July 2019): 1930022. http://dx.doi.org/10.1142/s0218127419300222.
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Tipping points are sudden, and sometimes irreversible and catastrophic, changes in a system’s dynamical regime. Complex networks are now widely used in the analysis of time series from a complex system. In this paper, we investigate the scope of network methods to indicate tipping points. In particular, we verify that the permutation entropy of transition networks constructed from time series observations of the logistic map can distinguish periodic and chaotic regimes and indicate bifurcations. The permutation entropy of transition networks, the mean edge betweenness of visibility graphs and the number of code words in compression networks, are each shown to indicate the onset of transition of a pitchfork bifurcation system. Our study shows that network methods are effective in detecting transitions. Network-based forecasts can be applied to models of real systems, as we illustrate by considering a lake eutrophication model.
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Yin, Yuan, Vincent Le Guen, Jérémie Dona, Emmanuel de Bézenac, Ibrahim Ayed, Nicolas Thome, and Patrick Gallinari. "Augmenting physical models with deep networks for complex dynamics forecasting*." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 12 (December 1, 2021): 124012. http://dx.doi.org/10.1088/1742-5468/ac3ae5.
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Abstract Forecasting complex dynamical phenomena in settings where only partial knowledge of their dynamics is available is a prevalent problem across various scientific fields. While purely data-driven approaches are arguably insufficient in this context, standard physical modeling-based approaches tend to be over-simplistic, inducing non-negligible errors. In this work, we introduce the APHYNITY framework, a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models. It consists of decomposing the dynamics into two components: a physical component accounting for the dynamics for which we have some prior knowledge, and a data-driven component accounting for errors of the physical model. The learning problem is carefully formulated such that the physical model explains as much of the data as possible, while the data-driven component only describes information that cannot be captured by the physical model; no more, no less. This not only provides the existence and uniqueness for this decomposition, but also ensures interpretability and benefit generalization. Experiments made on three important use cases, each representative of a different family of phenomena, i.e. reaction–diffusion equations, wave equations and the non-linear damped pendulum, show that APHYNITY can efficiently leverage approximate physical models to accurately forecast the evolution of the system and correctly identify relevant physical parameters. The code is available at https://github.com/yuan-yin/APHYNITY.
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Wong, Wee, Ewan Chee, Jiali Li, and Xiaonan Wang. "Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing." Mathematics 6, no. 11 (November 7, 2018): 242. http://dx.doi.org/10.3390/math6110242.
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The pharmaceutical industry has witnessed exponential growth in transforming operations towards continuous manufacturing to increase profitability, reduce waste and extend product ranges. Model predictive control (MPC) can be applied to enable this vision by providing superior regulation of critical quality attributes (CQAs). For MPC, obtaining a workable system model is of fundamental importance, especially if complex process dynamics and reaction kinetics are present. Whilst physics-based models are desirable, obtaining models that are effective and fit-for-purpose may not always be practical, and industries have often relied on data-driven approaches for system identification instead. In this work, we demonstrate the applicability of recurrent neural networks (RNNs) in MPC applications in continuous pharmaceutical manufacturing. RNNs were shown to be especially well-suited for modelling dynamical systems due to their mathematical structure, and their use in system identification has enabled satisfactory closed-loop performance for MPC of a complex reaction in a single continuous-stirred tank reactor (CSTR) for pharmaceutical manufacturing.
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Kompothrekas, Aristotelis, Basilis Boutsinas, and Konstantinos Kollias. "TOPOLOGICAL AND DYNAMICAL PROPERTIES OF THE NETWORK OF SHAREHOLDERS IN S&P 500 COMPANIES BASED ON GRAPH DATABASES." JOURNAL OF INTERNATIONAL MONEY, BANKING AND FINANCE 3, no. 1 (2022): 1–12. http://dx.doi.org/10.47509/jimbf.2022.v03i01.01.
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The interesting properties of scale-free and small-world networks recently observed have triggered the attention of the research community to the study of real growing complex networks. In scale-free networks, most vertices are sparsely connected, while a few vertices are intensively connected to many others, indicating a “preferential linking” during growing. In small-world networks, the average length of the shortest path between two randomly chosen nodes is small. In this paper, we study the topological and dynamical properties of the network of shareholders (NOS) in 11593 different companies. Based on Graph Databases, we calculate all the well-known in the literature topological and dynamical properties of a network along with centrality measures of nodes of NOS, which quantify the role that a node plays in the overall structure of NOS. We prove that NOS is both a scale-free and smallworld network. An understanding of NOS helps in predicting the emergence of important new phenomena affecting portfolio management in general. Also, this work reveals the fact that graph databases could serve as an efficient tool for analyzing such network models for stock markets. To the best of the authors’ knowledge, this is the first study calculating all the well-known in the literature topological and dynamical properties for Market Investments Networks, that is based on graph databases.
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Plaster, Benjamin, and Gautam Kumar. "Data-Driven Predictive Modeling of Neuronal Dynamics Using Long Short-Term Memory." Algorithms 12, no. 10 (September 24, 2019): 203. http://dx.doi.org/10.3390/a12100203.
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Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions have been of interest to engineers, mathematicians and physicists over the last several decades. With the motivation of developing computationally efficient models of brain dynamics to use in designing control-theoretic neurostimulation strategies, we have developed a novel data-driven approach in a long short-term memory (LSTM) neural network architecture to predict the temporal dynamics of complex systems over an extended long time-horizon in future. In contrast to recent LSTM-based dynamical modeling approaches that make use of multi-layer perceptrons or linear combination layers as output layers, our architecture uses a single fully connected output layer and reversed-order sequence-to-sequence mapping to improve short time-horizon prediction accuracy and to make multi-timestep predictions of dynamical behaviors. We demonstrate the efficacy of our approach in reconstructing the regular spiking to bursting dynamics exhibited by an experimentally-validated 9-dimensional Hodgkin-Huxley model of hippocampal CA1 pyramidal neurons. Through simulations, we show that our LSTM neural network can predict the multi-time scale temporal dynamics underlying various spiking patterns with reasonable accuracy. Moreover, our results show that the predictions improve with increasing predictive time-horizon in the multi-timestep deep LSTM neural network.
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S Neves, Fabio, and Marc Timme. "Bio-inspired computing by nonlinear network dynamics—a brief introduction." Journal of Physics: Complexity 2, no. 4 (December 1, 2021): 045019. http://dx.doi.org/10.1088/2632-072x/ac3ad4.
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Abstract The field of bio-inspired computing has established a new Frontier for conceptualizing information processing, aggregating knowledge from disciplines as different as neuroscience, physics, computer science and dynamical systems theory. The study of the animal brain has shown that no single neuron or neural circuit motif is responsible for intelligence or other higher-order capabilities. Instead, complex functions are created through a broad variety of circuits, each exhibiting an equally varied repertoire of emergent dynamics. How collective dynamics may contribute to computations still is not fully understood to date, even on the most elementary level. Here we provide a concise introduction to bio-inspired computing via nonlinear dynamical systems. We first provide a coarse overview of how the study of biological systems has catalyzed the development of artificial systems in several broad directions. Second, we discuss how understanding the collective dynamics of spiking neural circuits and model classes thereof, may contribute to and inspire new forms of ‘bio-inspired’ computational paradigms. Finally, as a specific set of examples, we analyze in more detail bio-inspired approaches to computing discrete decisions based on multi-dimensional analogue input signals, via k-winners-take-all functions. This article may thus serve as a brief introduction to the qualitative variety and richness of dynamical bio-inspired computing models, starting broadly and focusing on a general example of computation from current research. We believe that understanding basic aspects of the variety of bio-inspired approaches to computation on the coarse level of first principles (instead of details about specific simulation models) and how they relate to each other, may provide an important step toward catalyzing novel approaches to autonomous and computing machines in general.
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Perc, Matjaž, Jesús Gómez-Gardeñes, Attila Szolnoki, Luis M. Floría, and Yamir Moreno. "Evolutionary dynamics of group interactions on structured populations: a review." Journal of The Royal Society Interface 10, no. 80 (March 6, 2013): 20120997. http://dx.doi.org/10.1098/rsif.2012.0997.
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Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.
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Manjunath, G. "Evolving Network Model That Almost Regenerates Epileptic Data." Neural Computation 29, no. 4 (April 2017): 937–67. http://dx.doi.org/10.1162/neco_a_00941.
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In many realistic networks, the edges representing the interactions between nodes are time varying. Evidence is growing that the complex network that models the dynamics of the human brain has time-varying interconnections, that is, the network is evolving. Based on this evidence, we construct a patient- and data-specific evolving network model (comprising discrete-time dynamical systems) in which epileptic seizures or their terminations in the brain are also determined by the nature of the time-varying interconnections between the nodes. A novel and unique feature of our methodology is that the evolving network model remembers the data from which it was conceived from, in the sense that it evolves to almost regenerate the patient data even on presenting an arbitrary initial condition to it. We illustrate a potential utility of our methodology by constructing an evolving network from clinical data that aids in identifying an approximate seizure focus; nodes in such a theoretically determined seizure focus are outgoing hubs that apparently act as spreaders of seizures. We also point out the efficacy of removal of such spreaders in limiting seizures.
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Mohan, T. R. Krishna. "Bifurcations and Chaos in a Model Biochemical Reaction Pathway." International Journal of Bifurcation and Chaos 08, no. 02 (February 1998): 381–94. http://dx.doi.org/10.1142/s0218127498000231.
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Control mechanisms in the form of positive and negative feedback loops are responsible for the sensitivity and stability in the coherent behavior of the spatio-temporal organization in living cells. Models of these networks involving such feedback mechanisms have been shown to exhibit a rich spectrum of dynamical behaviors. A network involving both positive and negative feedbacks was earlier investigated by Sinha and Ramaswamy [1987]. We obtain a phase diagram of the possible dynamical behaviors for this model. Further, we investigate the origin and properties of the complex oscillations in the model. A simpler system is derived and shown to possess similar dynamical behaviors. Avenues for further investigation of the system with respect to relevant variations in some of the parameter values are suggested.
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Abrevaya, Germán, Guillaume Dumas, Aleksandr Y. Aravkin, Peng Zheng, Jean-Christophe Gagnon-Audet, James Kozloski, Pablo Polosecki, et al. "Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks." Neural Computation 33, no. 8 (July 26, 2021): 2087–127. http://dx.doi.org/10.1162/neco_a_01401.
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Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.
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KINOUCHI, OSAME, and MARCELO H. R. TRAGTENBERG. "MODELING NEURONS BY SIMPLE MAPS." International Journal of Bifurcation and Chaos 06, no. 12a (December 1996): 2343–60. http://dx.doi.org/10.1142/s0218127496001508.
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We introduce a simple generalization of graded response formal neurons which presents very complex behavior. Phase diagrams in full parameter space are given, showing regions with fixed points, periodic, quasiperiodic and chaotic behavior. These diagrams also represent the possible time series learnable by the simplest feed-forward network, a two input single-layer perceptron. This simple formal neuron (‘dynamical perceptron’) behaves as an excitable ele ment with characteristics very similar to those appearing in more complicated neuron models like FitzHugh-Nagumo and Hodgkin-Huxley systems: natural threshold for action potentials, dampened subthreshold oscillations, rebound response, repetitive firing under constant input, nerve blocking effect etc. We also introduce an ‘adaptive dynamical perceptron’ as a simple model of a bursting neuron of Rose-Hindmarsh type. We show that networks of such elements are interesting models which lie at the interface of neural networks, coupled map lattices, excitable media and self-organized criticality studies.
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Bauer, Roman, and Marcus Kaiser. "Nonlinear growth: an origin of hub organization in complex networks." Royal Society Open Science 4, no. 3 (March 2017): 160691. http://dx.doi.org/10.1098/rsos.160691.
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Many real-world networks contain highly connected nodes called hubs. Hubs are often crucial for network function and spreading dynamics. However, classical models of how hubs originate during network development unrealistically assume that new nodes attain information about the connectivity (for example the degree) of existing nodes. Here, we introduce hub formation through nonlinear growth where the number of nodes generated at each stage increases over time and new nodes form connections independent of target node features. Our model reproduces variation in number of connections, hub occurrence time, and rich-club organization of networks ranging from protein–protein, neuronal and fibre tract brain networks to airline networks. Moreover, nonlinear growth gives a more generic representation of these networks compared with previous preferential attachment or duplication–divergence models. Overall, hub creation through nonlinear network expansion can serve as a benchmark model for studying the development of many real-world networks.
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Wang, Hong Yu, Bing Yao, Chao Yang, Si Hua Yang, and Xiang En Chen. "Labelling Properties of Models Related with Complex Networks Based on Constructible Structures." Advanced Materials Research 765-767 (September 2013): 1118–23. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.1118.
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Network structure is irregular, complex and dynamically evolving in time. In the Internet of Things, we are Things. Labelled graphs are used in researching areas of many networks, cryptography, computer science, biology, information etc. For simulating real networks we construct compound split-graphs and compound split-trees having particular labellings almost in arbitrary manners by our methods. We have several algorithms in polynomial time.
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Shappell, Heather, Yorghos Tripodis, Ronald J. Killiany, and Eric D. Kolaczyk. "A paradigm for longitudinal complex network analysis over patient cohorts in neuroscience." Network Science 7, no. 2 (June 2019): 196–214. http://dx.doi.org/10.1017/nws.2019.9.
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AbstractThe study of complex brain networks, where structural or functional connections are evaluated to create an interconnected representation of the brain, has grown tremendously over the past decade. Many of the statistical network science tools for analyzing brain networks have been developed for cross-sectional studies and for the analysis of static networks. However, with both an increase in longitudinal study designs and an increased interest in the neurological network changes that occur during the progression of a disease, sophisticated methods for longitudinal brain network analysis are needed. We propose a paradigm for longitudinal brain network analysis over patient cohorts, with the key challenge being the adaptation of Stochastic Actor-Oriented Models to the neuroscience setting. Stochastic Actor-Oriented Models are designed to capture network dynamics representing a variety of influences on network change in a continuous-time Markov chain framework. Network dynamics are characterized through both endogenous (i.e. network related) and exogenous effects, where the latter include mechanisms conjectured in the literature. We outline an application to the resting-state functional magnetic resonance imaging setting with data from the Alzheimer’s Disease Neuroimaging Initiative study. We draw illustrative conclusions at the subject level and make a comparison between elderly controls and individuals with Alzheimer’s disease.
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Kumagai, Tohru, Mitsuo Wada, Sadayoshi Mikami, and Ryoichi Hashimoto. "Learning Control Method for Robotic Dynamical System." Journal of Robotics and Mechatronics 9, no. 1 (February 20, 1997): 57–64. http://dx.doi.org/10.20965/jrm.1997.p0057.
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We present a new learning control method to control a single input multi output system. In conventional learning controllers using a neural network, it is difficult to treat a multi-output system because of the difficulty in designing reference models. Hence, we propose to divide a complex plant into sub-plants and to use a learning controller for each one. We use our method to the regulation problem of the inverted pendulum that is a oneinput, two-output system. In the simulation and the experimental system, we regulate the inverted pendulum and show the effectiveness of this method. We also show that our learning control system can regulate a system that has a time lag between the input and the output signals. Moreover, we show that a reference model of order lower than the plant order is available.
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Yang, Si Hua, Bing Yao, Ming Yao, Wan Jia Zhang, and Xiang En Chen. "On Felicitous Properties of Series Sun-Graphs." Applied Mechanics and Materials 644-650 (September 2014): 2502–5. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.2502.
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Network structure is irregular, complex and dynamically evolving in time. Labelled graphs are used in researching areas of many networks, cryptography, computer science, biology, information etc. For simulating real networks we construct several classes of sun-like network models, and show that sun-like network models have can be strictly distinguished by felicitous labellings. We have several algorithms in polynomial time..
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Whiteaker, Brian, and Peter Gerstoft. "Reducing echo state network size with controllability matrices." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073116. http://dx.doi.org/10.1063/5.0071926.
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Echo state networks are a fast training variant of recurrent neural networks excelling at approximating nonlinear dynamical systems and time series prediction. These machine learning models act as nonlinear fading memory filters. While these models benefit from quick training and low complexity, computation demands from a large reservoir matrix are a bottleneck. Using control theory, a reduced size replacement reservoir matrix is found. Starting from a large, task-effective reservoir matrix, we form a controllability matrix whose rank indicates the active sub-manifold and candidate replacement reservoir size. Resulting time speed-ups and reduced memory usage come with minimal error increase to chaotic climate reconstruction or short term prediction. Experiments are performed on simple time series signals and the Lorenz-1963 and Mackey–Glass complex chaotic signals. Observing low error models shows variation of active rank and memory along a sequence of predictions.
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Herbert, Elizabeth, and Srdjan Ostojic. "The impact of sparsity in low-rank recurrent neural networks." PLOS Computational Biology 18, no. 8 (August 9, 2022): e1010426. http://dx.doi.org/10.1371/journal.pcbi.1010426.
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Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces. How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics. This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are known to be highly sparse. Here we investigate the dynamics of low-rank recurrent networks in which the connections are randomly sparsified, which makes the network connectivity formally full-rank. We first analyse the impact of sparsity on the eigenvalue spectrum of low-rank connectivity matrices, and use this to examine the implications for the dynamics. We find that in the presence of sparsity, the eigenspectra in the complex plane consist of a continuous bulk and isolated outliers, a form analogous to the eigenspectra of connectivity matrices composed of a low-rank and a full-rank random component. This analogy allows us to characterise distinct dynamical regimes of the sparsified low-rank network as a function of key network parameters. Altogether, we find that the low-dimensional dynamics induced by low-rank connectivity structure are preserved even at high levels of sparsity, and can therefore support rich and robust computations even in networks sparsified to a biologically-realistic extent.
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Lieblappen, Ross M., Deip D. Kumar, Scott D. Pauls, and Rachel W. Obbard. "A network model for characterizing brine channels in sea ice." Cryosphere 12, no. 3 (March 22, 2018): 1013–26. http://dx.doi.org/10.5194/tc-12-1013-2018.
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Abstract. The brine pore space in sea ice can form complex connected structures whose geometry is critical in the governance of important physical transport processes between the ocean, sea ice, and surface. Recent advances in three-dimensional imaging using X-ray micro-computed tomography have enabled the visualization and quantification of the brine network morphology and variability. Using imaging of first-year sea ice samples at in situ temperatures, we create a new mathematical network model to characterize the topology and connectivity of the brine channels. This model provides a statistical framework where we can characterize the pore networks via two parameters, depth and temperature, for use in dynamical sea ice models. Our approach advances the quantification of brine connectivity in sea ice, which can help investigations of bulk physical properties, such as fluid permeability, that are key in both global and regional sea ice models.
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Seifter, Jared, and James A. Reggia. "Lambda and the Edge of Chaos in Recurrent Neural Networks." Artificial Life 21, no. 1 (February 2015): 55–71. http://dx.doi.org/10.1162/artl_a_00152.
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The idea that there is an edge of chaos, a region in the space of dynamical systems having special meaning for complex living entities, has a long history in artificial life. The significance of this region was first emphasized in cellular automata models when a single simple measure, λCA, identified it as a transitional region between order and chaos. Here we introduce a parameter λNN that is inspired by λCA but is defined for recurrent neural networks. We show through a series of systematic computational experiments that λNN generally orders the dynamical behaviors of randomly connected/weighted recurrent neural networks in the same way that λCA does for cellular automata. By extending this ordering to larger values of λNN than has typically been done with λCA and cellular automata, we find that a second edge-of-chaos region exists on the opposite side of the chaotic region. These basic results are found to hold under different assumptions about network connectivity, but vary substantially in their details. The results show that the basic concept underlying the lambda parameter can usefully be extended to other types of complex dynamical systems than just cellular automata.
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Bansal, Kanika, Javier O. Garcia, Steven H. Tompson, Timothy Verstynen, Jean M. Vettel, and Sarah F. Muldoon. "Cognitive chimera states in human brain networks." Science Advances 5, no. 4 (April 2019): eaau8535. http://dx.doi.org/10.1126/sciadv.aau8535.
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The human brain is a complex dynamical system, and how cognition emerges from spatiotemporal patterns of regional brain activity remains an open question. As different regions dynamically interact to perform cognitive tasks, variable patterns of partial synchrony can be observed, forming chimera states. We propose that the spatial patterning of these states plays a fundamental role in the cognitive organization of the brain and present a cognitively informed, chimera-based framework to explore how large-scale brain architecture affects brain dynamics and function. Using personalized brain network models, we systematically study how regional brain stimulation produces different patterns of synchronization across predefined cognitive systems. We analyze these emergent patterns within our framework to understand the impact of subject-specific and region-specific structural variability on brain dynamics. Our results suggest a classification of cognitive systems into four groups with differing levels of subject and regional variability that reflect their different functional roles.
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Boonsatit, N., R. Sugumar, D. Ajay, G. Rajchakit, C. P. Lim, P. Hammachukiattikul, M. Usha, and P. Agarwal. "Mixed ℋ -Infinity and Passive Synchronization of Markovian Jumping Neutral-Type Complex Dynamical Networks with Randomly Occurring Distributed Coupling Time-Varying Delays and Actuator Faults." Complexity 2021 (May 3, 2021): 1–19. http://dx.doi.org/10.1155/2021/5553884.
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This article examines mixed ℋ -infinity and passivity synchronization of Markovian jumping neutral-type complex dynamical network (MJNTCDN) models with randomly occurring coupling delays and actuator faults. The randomly occurring coupling delays are considered to design the complex dynamical networks in practice. These delays complied with certain Bernoulli distributed white noise sequences. The relevant data including limits of actuator faults, bounds of the nonlinear terms, and external disturbances are available for designing the controller structure. Novel Lyapunov–Krasovskii functional (LKF) is constructed to verify the stability of the error model and performance level. Jensen’s inequality and a new integral inequality are applied to derive the outcomes. Sufficient conditions for the synchronization error system (SES) are given in terms of linear matrix inequalities (LMIs), which can be analyzed easily by utilizing general numerical programming. Numerical illustrations are given to exhibit the usefulness of the obtained results.
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Wang, Shuo, and Lijun Pei. "Complex Dynamics and Periodic Oscillation Mechanism in Two Novel Gene Expression Models with State-Dependent Delays." International Journal of Bifurcation and Chaos 31, no. 01 (January 2021): 2150002. http://dx.doi.org/10.1142/s0218127421500024.
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The reaction time delay in the transcription process depends on the concentration of the protein because the transportation of mRNA from the nucleus to the cytoplasm becomes saturated. Thus the gene regulatory network is a state-dependent delayed model. This study aims to provide some mathematical explanations for the dynamics of the system, such as the linear stability and periodic oscillation, using mathematical techniques, such as formal linearization, linear stability analysis, the method of multiple scale (MMS), and the normal form. First, Hopf bifurcation of the state-dependent delayed gene regulatory networks model in the gene expression is analyzed by the method of multiple scales (MMS). Mechanism of periodic oscillations is obtained by Hopf bifurcation. The findings show that when degradation effects of the mRNA and protein are very strong, the oscillatory gene expression disappears. Then, a more realistic version of the aforementioned model with both constant and state-dependent time delays is established due to the existence of the constant time delay in the protein degradation process. Its nonresonant double Hopf bifurcation is found and analyzed using MMS. Interesting complex dynamic phenomena, such as periodic, quasi-periodic, and global period-[Formula: see text] solutions, are also discovered. These observations indicate that both state-dependent delay and constant delay could induce richer dynamics of the system, and the modified model may potentially describe the real dynamical mechanism (both the transcription process and the degradation process) more accurately in the gene expression. The findings may provide important guidance or hints to understand the real dynamic mechanism of the gene expression process.