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CHIU, CHINCHUAN, and MICHAEL A. SHANBLATT. "HUMAN-LIKE DYNAMIC PROGRAMMING NEURAL NETWORKS FOR DYNAMIC TIME WARPING SPEECH RECOGNITION." International Journal of Neural Systems 06, no. 01 (March 1995): 79–89. http://dx.doi.org/10.1142/s012906579500007x.
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This paper presents a human-like dynamic programming neural network method for speech recognition using dynamic time warping. The networks are configured, much like human’s, such that the minimum states of the network’s energy function represent the near-best correlation between test and reference patterns. The dynamics and properties of the neural networks are analytically explained. Simulations for classifying speaker-dependent isolated words, consisting of 0 to 9 and A to Z, show that the method is better than conventional methods. The hardware implementation of this method is also presented.
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Sun, Zejun, Jinfang Sheng, Bin Wang, Aman Ullah, and FaizaRiaz Khawaja. "Identifying Communities in Dynamic Networks Using Information Dynamics." Entropy 22, no. 4 (April 9, 2020): 425. http://dx.doi.org/10.3390/e22040425.
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Identifying communities in dynamic networks is essential for exploring the latent network structures, understanding network functions, predicting network evolution, and discovering abnormal network events. Many dynamic community detection methods have been proposed from different viewpoints. However, identifying the community structure in dynamic networks is very challenging due to the difficulty of parameter tuning, high time complexity and detection accuracy decreasing as time slices increase. In this paper, we present a dynamic community detection framework based on information dynamics and develop a dynamic community detection algorithm called DCDID (dynamic community detection based on information dynamics), which uses a batch processing technique to incrementally uncover communities in dynamic networks. DCDID employs the information dynamics model to simulate the exchange of information among nodes and aims to improve the efficiency of community detection by filtering out the unchanged subgraph. To illustrate the effectiveness of DCDID, we extensively test it on synthetic and real-world dynamic networks, and the results demonstrate that the DCDID algorithm is superior to the representative methods in relation to the quality of dynamic community detection.
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Levin, Ilya, Mark Korenblit, and Vadim Talis. "STUDY OF SOCIAL NETWORKS’ DYNAMICS BY SIMULATION WITHIN THE NODEXL-EXCEL ENVIRONMENT." Problems of Education in the 21st Century 54, no. 1 (June 20, 2013): 125–37. http://dx.doi.org/10.33225/pec/13.54.125.
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The present study is an analysis of the learning activity, which constitutes simulation of networks and studying their functioning and dynamics. The study is based on using network-like learning environments. Such environments allow building computer models of the network graphs. According to the suggested approach, the students construct dynamic computer models of the networks' graphs, thus implementing various algorithms of such networks’ dynamics. The suggested tool for building the models is the software environment comprising network analysis software NodeXL and a standard spreadsheet Excel. The proposed approach enables the students to visualize the network's dynamics. The paper presents specific examples of network models and various algorithms of the network's dynamics, which were developed based on the proposed approach. Key words: learning environments, modelling, social networks.
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Melamed, David, Ashley Harrell, and Brent Simpson. "Cooperation, clustering, and assortative mixing in dynamic networks." Proceedings of the National Academy of Sciences 115, no. 5 (January 16, 2018): 951–56. http://dx.doi.org/10.1073/pnas.1715357115.
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Humans’ propensity to cooperate is driven by our embeddedness in social networks. A key mechanism through which networks promote cooperation is clustering. Within clusters, conditional cooperators are insulated from exploitation by noncooperators, allowing them to reap the benefits of cooperation. Dynamic networks, where ties can be shed and new ties formed, allow for the endogenous emergence of clusters of cooperators. Although past work suggests that either reputation processes or network dynamics can increase clustering and cooperation, existing work on network dynamics conflates reputations and dynamics. Here we report results from a large-scale experiment (total n = 2,675) that embedded participants in clustered or random networks that were static or dynamic, with varying levels of reputational information. Results show that initial network clustering predicts cooperation in static networks, but not in dynamic ones. Further, our experiment shows that while reputations are important for partner choice, cooperation levels are driven purely by dynamics. Supplemental conditions confirmed this lack of a reputation effect. Importantly, we find that when participants make individual choices to cooperate or defect with each partner, as opposed to a single decision that applies to all partners (as is standard in the literature on cooperation in networks), cooperation rates in static networks are as high as cooperation rates in dynamic networks. This finding highlights the importance of structured relations for sustained cooperation, and shows how giving experimental participants more realistic choices has important consequences for whether dynamic networks promote higher levels of cooperation than static networks.
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Nie, Chun-Xiao. "Hurst analysis of dynamic networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 2 (February 2022): 023130. http://dx.doi.org/10.1063/5.0070170.
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The sequence of network snapshots with time stamps is an effective tool for describing system dynamics. First, this article constructs a multifractal analysis of a snapshot network, in which the Hurst integral is used to describe the fractal structure hidden in structural dynamics. Second, we adjusted the network model and conducted comparative analysis to clarify the meaning of the Hurst exponent and found that the snapshot network usually includes multiple fractal structures, such as local and global fractal structures. Finally, we discussed the fractal structure of two real network datasets. We found that the real snapshot network also includes rich dynamics, which can be distinguished by the Hurst exponent. In particular, the dynamics of financial networks includes multifractal structures. This article provides a perspective to study the dynamic networks, thereby indirectly describing the fractal characteristics of complex system dynamics.
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Iedema, Rick, Raj Verma, Sonia Wutzke, Nigel Lyons, and Brian McCaughan. "A network of networks." Journal of Health Organization and Management 31, no. 2 (April 10, 2017): 223–36. http://dx.doi.org/10.1108/jhom-07-2016-0146.
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Purpose To further our insight into the role of networks in health system reform, the purpose of this paper is to investigate how one agency, the NSW Agency for Clinical Innovation (ACI), and the multiple networks and enabling resources that it encompasses, govern, manage and extend the potential of networks for healthcare practice improvement. Design/methodology/approach This is a case study investigation which took place over ten months through the first author’s participation in network activities and discussions with the agency’s staff about their main objectives, challenges and achievements, and with selected services around the state of New South Wales to understand the agency’s implementation and large system transformation activities. Findings The paper demonstrates that ACI accommodates multiple networks whose oversight structures, self-organisation and systems change approaches combined in dynamic ways, effectively yield a diversity of network governances. Further, ACI bears out a paradox of “centralised decentralisation”, co-locating agents of innovation with networks of implementation and evaluation expertise. This arrangement strengthens and legitimates the role of the strategic hybrid – the healthcare professional in pursuit of change and improvement, and enhances their influence and impact on the wider system. Research limitations/implications While focussing the case study on one agency only, this study is unique as it highlights inter-network connections. Contributing to the literature on network governance, this paper identifies ACI as a “network of networks” through which resources, expectations and stakeholder dynamics are dynamically and flexibly mediated and enhanced. Practical implications The co-location of and dynamic interaction among clinical networks may create synergies among networks, nurture “strategic hybrids”, and enhance the impact of network activities on health system reform. Social implications Network governance requires more from network members than participation in a single network, as it involves health service professionals and consumers in a multi-network dynamic. This dynamic requires deliberations and collaborations to be flexible, and it increasingly positions members as “strategic hybrids” – people who have moved on from singular taken-as-given stances and identities, towards hybrid positionings and flexible perspectives. Originality/value This paper is novel in that it identifies a critical feature of health service reform and large system transformation: network governance is empowered through the dynamic co-location of and collaboration among healthcare networks, particularly when complemented with “enabler” teams of people specialising in programme implementation and evaluation.
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Galizia, Roberto, and Petri T. Piiroinen. "Regions of Reduced Dynamics in Dynamic Networks." International Journal of Bifurcation and Chaos 31, no. 06 (May 2021): 2150080. http://dx.doi.org/10.1142/s0218127421500802.
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We consider complex networks where the dynamics of each interacting agent is given by a nonlinear vector field and the connections between the agents are defined according to the topology of undirected simple graphs. The aim of the work is to explore whether the asymptotic dynamic behavior of the entire network can be fully determined from the knowledge of the dynamic properties of the underlying constituent agents. While the complexity that arises by connecting many nonlinear systems hinders us to analytically determine general solutions, we show that there are conditions under which the dynamical properties of the constituent agents are equivalent to the dynamical properties of the entire network. This feature, which depends on the nature and structure of both the agents and connections, leads us to define the concept of regions of reduced dynamics, which are subsets of the parameter space where the asymptotic solutions of a network behave equivalently to the limit sets of the constituent agents. On one hand, we discuss the existence of regions of reduced dynamics, which can be proven in the case of diffusive networks of identical agents with all-to-all topologies and conjectured for other topologies. On the other hand, using three examples, we show how to locate regions of reduced dynamics in parameter space. In simple cases, this can be done analytically through bifurcation analysis and in other cases we exploit numerical continuation methods.
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Wu, Wei, and Xuemeng Zhai. "DyLFG: A Dynamic Network Learning Framework Based on Geometry." Entropy 25, no. 12 (November 30, 2023): 1611. http://dx.doi.org/10.3390/e25121611.
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Dynamic network representation learning has recently attracted increasing attention because real-world networks evolve over time, that is nodes and edges join or leave the networks over time. Different from static networks, the representation learning of dynamic networks should not only consider how to capture the structural information of network snapshots, but also consider how to capture the temporal dynamic information of network structure evolution from the network snapshot sequence. From the existing work on dynamic network representation, there are two main problems: (1) A significant number of methods target dynamic networks, which only allow nodes to increase over time, not decrease, which reduces the applicability of such methods to real-world networks. (2) At present, most network-embedding methods, especially dynamic network representation learning approaches, use Euclidean embedding space. However, the network itself is geometrically non-Euclidean, which leads to geometric inconsistencies between the embedded space and the underlying space of the network, which can affect the performance of the model. In order to solve the above two problems, we propose a geometry-based dynamic network learning framework, namely DyLFG. Our proposed framework targets dynamic networks, which allow nodes and edges to join or exit the network over time. In order to extract the structural information of network snapshots, we designed a new hyperbolic geometry processing layer, which is different from the previous literature. In order to deal with the temporal dynamics of the network snapshot sequence, we propose a gated recurrent unit (GRU) module based on Ricci curvature, that is the RGRU. In the proposed framework, we used a temporal attention layer and the RGRU to evolve the neural network weight matrix to capture temporal dynamics in the network snapshot sequence. The experimental results showed that our model outperformed the baseline approaches on the baseline datasets.
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Chen, Kevin S. "Optimal Population Coding for Dynamic Input by Nonequilibrium Networks." Entropy 24, no. 5 (April 25, 2022): 598. http://dx.doi.org/10.3390/e24050598.
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The efficient coding hypothesis states that neural response should maximize its information about the external input. Theoretical studies focus on optimal response in single neuron and population code in networks with weak pairwise interactions. However, more biological settings with asymmetric connectivity and the encoding for dynamical stimuli have not been well-characterized. Here, we study the collective response in a kinetic Ising model that encodes the dynamic input. We apply gradient-based method and mean-field approximation to reconstruct networks given the neural code that encodes dynamic input patterns. We measure network asymmetry, decoding performance, and entropy production from networks that generate optimal population code. We analyze how stimulus correlation, time scale, and reliability of the network affect optimal encoding networks. Specifically, we find network dynamics altered by statistics of the dynamic input, identify stimulus encoding strategies, and show optimal effective temperature in the asymmetric networks. We further discuss how this approach connects to the Bayesian framework and continuous recurrent neural networks. Together, these results bridge concepts of nonequilibrium physics with the analyses of dynamics and coding in networks.
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Chen, Kevin S. "Optimal Population Coding for Dynamic Input by Nonequilibrium Networks." Entropy 24, no. 5 (April 25, 2022): 598. http://dx.doi.org/10.3390/e24050598.
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The efficient coding hypothesis states that neural response should maximize its information about the external input. Theoretical studies focus on optimal response in single neuron and population code in networks with weak pairwise interactions. However, more biological settings with asymmetric connectivity and the encoding for dynamical stimuli have not been well-characterized. Here, we study the collective response in a kinetic Ising model that encodes the dynamic input. We apply gradient-based method and mean-field approximation to reconstruct networks given the neural code that encodes dynamic input patterns. We measure network asymmetry, decoding performance, and entropy production from networks that generate optimal population code. We analyze how stimulus correlation, time scale, and reliability of the network affect optimal encoding networks. Specifically, we find network dynamics altered by statistics of the dynamic input, identify stimulus encoding strategies, and show optimal effective temperature in the asymmetric networks. We further discuss how this approach connects to the Bayesian framework and continuous recurrent neural networks. Together, these results bridge concepts of nonequilibrium physics with the analyses of dynamics and coding in networks.
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Chen, Kevin S. "Optimal Population Coding for Dynamic Input by Nonequilibrium Networks." Entropy 24, no. 5 (April 25, 2022): 598. http://dx.doi.org/10.3390/e24050598.
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The efficient coding hypothesis states that neural response should maximize its information about the external input. Theoretical studies focus on optimal response in single neuron and population code in networks with weak pairwise interactions. However, more biological settings with asymmetric connectivity and the encoding for dynamical stimuli have not been well-characterized. Here, we study the collective response in a kinetic Ising model that encodes the dynamic input. We apply gradient-based method and mean-field approximation to reconstruct networks given the neural code that encodes dynamic input patterns. We measure network asymmetry, decoding performance, and entropy production from networks that generate optimal population code. We analyze how stimulus correlation, time scale, and reliability of the network affect optimal encoding networks. Specifically, we find network dynamics altered by statistics of the dynamic input, identify stimulus encoding strategies, and show optimal effective temperature in the asymmetric networks. We further discuss how this approach connects to the Bayesian framework and continuous recurrent neural networks. Together, these results bridge concepts of nonequilibrium physics with the analyses of dynamics and coding in networks.
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Foley, Michael, Patrick Forber, Rory Smead, and Christoph Riedl. "Conflict and convention in dynamic networks." Journal of The Royal Society Interface 15, no. 140 (March 2018): 20170835. http://dx.doi.org/10.1098/rsif.2017.0835.
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An important way to resolve games of conflict (snowdrift, hawk–dove, chicken) involves adopting a convention: a correlated equilibrium that avoids any conflict between aggressive strategies. Dynamic networks allow individuals to resolve conflict via their network connections rather than changing their strategy. Exploring how behavioural strategies coevolve with social networks reveals new dynamics that can help explain the origins and robustness of conventions. Here, we model the emergence of conventions as correlated equilibria in dynamic networks. Our results show that networks have the tendency to break the symmetry between the two conventional solutions in a strongly biased way. Rather than the correlated equilibrium associated with ownership norms (play aggressive at home, not away), we usually see the opposite host–guest norm (play aggressive away, not at home) evolve on dynamic networks, a phenomenon common to human interaction. We also show that learning to avoid conflict can produce realistic network structures in a way different than preferential attachment models.
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Kuhn, Fabian, and Rotem Oshman. "Dynamic networks." ACM SIGACT News 42, no. 1 (March 21, 2011): 82–96. http://dx.doi.org/10.1145/1959045.1959064.
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Yan, Xian. "Key Factors Influencing Network Resilience in Dynamical Networks." Frontiers in Computing and Intelligent Systems 3, no. 3 (May 17, 2023): 99–101. http://dx.doi.org/10.54097/fcis.v3i3.8577.
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There has been much recent research focusing on the resilience of networks, providing theoretical insights into the effective response of real-world systems systems to disasters. However, few studies have analyzed the factors that affect the resilience of networks. And the network operation process varies greatly so that the dynamic behavior of the network is a factor that has to be considered. To bridge these gaps, we analyze the factors affecting dynamic network resilience in terms of network dynamics. There are two main influencing factors: differentiation of failure probability, differentiation of impact. We build a generic resilience model for the network and validate these influencing factors by simulating them in different networks. By summarizing these factors, we point out constructive strategies. These strategies can help dynamic networks enhance network resilience, which is an important criterion for reducing network failures in real-world systems.
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Harrell, Ashley, David Melamed, and Brent Simpson. "The strength of dynamic ties: The ability to alter some ties promotes cooperation in those that cannot be altered." Science Advances 4, no. 12 (December 2018): eaau9109. http://dx.doi.org/10.1126/sciadv.aau9109.
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Dynamic networks, where ties can be shed and new ties can be formed, promote the evolution of cooperation. Yet, past research has only compared networks where all ties can be severed to those where none can, confounding the benefits of fully dynamic networks with the presence of some dynamic ties within the network. Further, humans do not live in fully dynamic networks. Instead, in real-world networks, some ties are subject to change, while others are difficult to sever. Here, we consider whether and how cooperation evolves in networks containing both static and dynamic ties. We argue and find that the presence of dynamic ties in networks promotes cooperation even in static ties. Consistent with previous work demonstrating that cooperation cascades in networks, our results show that cooperation is enhanced in networks with both tie types because the higher rate of cooperation that occurs following the dynamics process “spills over” to those relations that are more difficult to alter. Thus, our findings demonstrate the critical role that dynamic ties play in promoting cooperation by altering behavioral outcomes even in non-dynamic relations.
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Wadhwa, Pooja, and M. P. S. Bhatia. "Community Detection Approaches in Real World Networks." International Journal of Virtual Communities and Social Networking 6, no. 1 (January 2014): 35–51. http://dx.doi.org/10.4018/ijvcsn.2014010103.
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Online social networks have been continuously evolving and one of their prominent features is the evolution of communities which can be characterized as a group of people who share a common relationship among themselves. Earlier studies on social network analysis focused on static network structures rather than dynamic processes, however, with the passage of time, the networks have also evolved and the researchers have started to focus on the aspect of studying dynamic behavior of networks. This paper aims to present an overview of community detection approaches graduating from static community detection methods towards the methods to identify dynamic communities in networks. The authors also present a classification of the existing dynamic community detection algorithms along the dimension of studying the evolution as either a two-step approach comprising of community detection via static methods and then applying temporal dynamics or a unified approach which comprises of dynamic detection of communities along with their evolutionary characteristics.
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Goyal, Ravi, and Victor De Gruttola. "Dynamic network prediction." Network Science 8, no. 4 (July 9, 2020): 574–95. http://dx.doi.org/10.1017/nws.2020.24.
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AbstractWe present a statistical framework for generating predicted dynamic networks based on the observed evolution of social relationships in a population. The framework includes a novel and flexible procedure to sample dynamic networks given a probability distribution on evolving network properties; it permits the use of a broad class of approaches to model trends, seasonal variability, uncertainty, and changes in population composition. Current methods do not account for the variability in the observed historical networks when predicting the network structure; the proposed method provides a principled approach to incorporate uncertainty in prediction. This advance aids in the designing of network-based interventions, as development of such interventions often requires prediction of the network structure in the presence and absence of the intervention. Two simulation studies are conducted to demonstrate the usefulness of generating predicted networks when designing network-based interventions. The framework is also illustrated by investigating results of potential interventions on bill passage rates using a dynamic network that represents the sponsor/co-sponsor relationships among senators derived from bills introduced in the U.S. Senate from 2003 to 2016.
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Muneepeerakul, Rachata, Jeffrey C. Johnson, Michael J. Puma, and Michael A. Zurek-Ost. "Triadic signatures of global human mobility networks." PLOS ONE 19, no. 2 (February 23, 2024): e0298876. http://dx.doi.org/10.1371/journal.pone.0298876.
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Global refugee and migrant flows form complex networks with serious consequences for both sending and receiving countries as well as those in between. While several basic network properties of these networks have been documented, their finer structural character remains under-studied. One such structure is the triad significance profile (TSP). In this study, the TSPs of global refugee and migrant flow networks are assessed. Results indicate that the migrant flow network’s size and TSP remain stable over the years; its TSP shares patterns with social networks such as trade networks. In contrast, the refugee network has been more dynamic and structurally unstable; its TSP shares patterns with networks in the information-processing superfamily, which includes many biological networks. Our findings demonstrate commonality between migrant and social networks as well as between refugee and biological networks, pointing to possible interdisciplinary collaboration—e.g., application of biological network theories to refugee network dynamics—, potentially furthering theoretical development with respect to both network theory and theories on human mobility.
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Ponraj, Ranjana, and George Amalanathan. "Dynamic Capacity Routing in Networks with MTSP." International Journal of Computer and Communication Engineering 5, no. 6 (2016): 465–72. http://dx.doi.org/10.17706/ijcce.2016.5.6.465-472.
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Elamurugu, V., and D. J. Evanjaline. "DynAuthRoute: Dynamic Security for Wireless Sensor Networks." Indian Journal Of Science And Technology 17, no. 13 (March 25, 2024): 1323–30. http://dx.doi.org/10.17485/ijst/v17i13.49.
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Objectives: The research aims to design an architecture for secure transmission of data in wireless sensor networks. Methods: The method involves three main pillars: authentication, data encryption, and dynamic routing. Extensive simulations have been conducted to evaluate the suggested method in terms of energy consumption, memory footprint, packet delivery ratio, end-to-end latency, execution time, encryption time, and decryption time. Findings: For authentication, a dynamic key is used to power an improved salt password hashing method. Data encryption is performed using format-preserving encryption (FPE) with the appended salt key. Dynamic routing is implemented using a cluster-based routing technique to enhance network efficiency in terms of power consumption and security. The execution time for MD5 ranges from 15 to 22 milliseconds, while for SHA-1 it ranges from 16 to 23 milliseconds and for the proposed salt key generation it is 1 to 5 milliseconds. Similarly, in terms of energy consumption, memory footprint, packet delivery ratio, end-to-end latency, execution time, encryption time, and decryption time the proposed method shows promising results in ensuring the integrity and security of transmitted encrypted data. Novelty: The presents a novel architecture with enhanced cluster head-based selection algorithm that combines dynamic key-based authentication and secure data routing to establish a safe environment for data transmission in wireless sensor networks. This research works offers a method for encrypting text with a dynamic salt key that is safe, energy-efficient, and lightweight. Keywords: Wireless Sensor Network, Dynamic Key, Authentication, Hash function, Salt algorithm, Dynamic routing, Node clustering, Format-preserving encryption
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Bryden, John, Sebastian Funk, Nicholas Geard, Seth Bullock, and Vincent A. A. Jansen. "Stability in flux: community structure in dynamic networks." Journal of The Royal Society Interface 8, no. 60 (December 2010): 1031–40. http://dx.doi.org/10.1098/rsif.2010.0524.
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The structure of many biological, social and technological systems can usefully be described in terms of complex networks. Although often portrayed as fixed in time, such networks are inherently dynamic, as the edges that join nodes are cut and rewired, and nodes themselves update their states. Understanding the structure of these networks requires us to understand the dynamic processes that create, maintain and modify them. Here, we build upon existing models of coevolving networks to characterize how dynamic behaviour at the level of individual nodes generates stable aggregate behaviours. We focus particularly on the dynamics of groups of nodes formed endogenously by nodes that share similar properties (represented as node state) and demonstrate that, under certain conditions, network modularity based on state compares well with network modularity based on topology. We show that if nodes rewire their edges based on fixed node states, the network modularity reaches a stable equilibrium which we quantify analytically. Furthermore, if node state is not fixed, but can be adopted from neighbouring nodes, the distribution of group sizes reaches a dynamic equilibrium, which remains stable even as the composition and identity of the groups change. These results show that dynamic networks can maintain the stable community structure that has been observed in many social and biological systems.
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Mundher, Zaid. "A Method for Investigating Coverage Area Issue in Dynamic Networks." Technium: Romanian Journal of Applied Sciences and Technology 4, no. 3 (April 16, 2022): 19–27. http://dx.doi.org/10.47577/technium.v4i3.6342.
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Coverage area in dynamic networks is considered an important issue that affects their general performance. It also affects the delay time when exchanging data and the consumption of resources in the network. Moreover, the coverage area issue in dynamic networks is directly affected by the distributions of nodes within the environment. Movement patterns may also affect the performance when it comes to coverage area. Therefore, this work develops a method that simulates different scenarios. These scenarios include a variety of settings and parameters that are believed to affect the coverage area issue of dynamic networks. These experiments enable network developers to be aware of the optimal conditions that maximize the coverage area of dynamic network nodes and eventually improve the overall performance of the network. Three distributions are used in the experiments namely, Cauchy distribution, Power-Law distribution, and Normal distribution. Also, the simulations incorporate the correlation mobility model for nodes dynamics. The findings show that Cauchy distribution is not appropriate for simulating dynamic networks due to the large uncovered areas by nodes communications. Also, the stability of an approach is considered an important factor when measuring the performance of a dynamic network. The results of this research are important to avoid wasting network resources.
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West, Bruce J., Paolo Grigolini, Scott E. Kerick, Piotr J. Franaszczuk, and Korosh Mahmoodi. "Complexity Synchronization of Organ Networks." Entropy 25, no. 10 (September 28, 2023): 1393. http://dx.doi.org/10.3390/e25101393.
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The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks. Information flows from dynamic networks at a higher level of complexity to those at lower levels of complexity, as summarized in the `complexity matching effect’, and the flow is maximally efficient when the complexities are equal. Herein, we use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks’ multifractal dimensions.
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Jardón-Kojakhmetov, Hildeberto, and Christian Kuehn. "On Fast–Slow Consensus Networks with a Dynamic Weight." Journal of Nonlinear Science 30, no. 6 (June 5, 2020): 2737–86. http://dx.doi.org/10.1007/s00332-020-09634-9.
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Abstract We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take values over the whole real numbers, and that its behaviour depends on the nodes it connects and on an extrinsic slow variable. We show that, under mild conditions on the weight, there exists a reduction such that the dynamics of the network are organized by a transcritical singularity. As such, we detail a slow passage through a transcritical singularity for a simple network, and we observe that an exchange between consensus and clustering of the nodes is possible. In contrast to the classical planar fast–slow transcritical singularity, the network structure of the system under consideration induces the presence of a maximal canard. Our main tool of analysis is the blow-up method. Thus, we also focus on tracking the effects of the blow-up transformation on the network’s structure. We show that on each blow-up chart one recovers a particular dynamic network related to the original one. We further indicate a numerical issue produced by the slow passage through the transcritical singularity.
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Gao, Hongwei, Han Qiao, Artem Sedakov, and Lei Wang. "A Dynamic Formation Procedure of Information Flow Networks." Journal of Systems Science and Information 3, no. 2 (April 25, 2015): 97–110. http://dx.doi.org/10.1515/jssi-2015-0097.
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AbstractA characterization of the equilibrium of information flow networks and the dynamics of network formation are studied under the premise of local information flow. The main result of this paper is that it gives the dynamic formation procedure in the local information flow network. The research shows that core-periphery structure is the most representative equilibrium network in the case of the local information flow without information decay whatever the cost of information is homogeneous or heterogeneous. If the profits and link costs of local information flow networks with information decay are homogeneous empty network and complete network are typical equilibrium networks, which are related to the costs of linking.
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Thamizhmaran, K. "Efficient Dynamic Acknowledgement Scheme for Manet." Journal of Advanced Research in Embedded System 07, no. 3&4 (July 3, 2021): 1–6. http://dx.doi.org/10.24321/2395.3802.202005.
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Mobile Adhoc Networks (MANET) is the decentralized type of network and it does not rely on pre-existing infrastructure. All nodes work as routers and take path in discovery and maintenance of routes to other nodes in the network. The Energy Efficiency continues to be a key factor in limitingthe deploy ability of ad-hoc networks. Deployingan energy efficient system exploiting themaximum life time of the network has remained agreat challenge since years. The major concern inWireless network in recent days is Energy Consumption. There are numerous algorithms proposed to overcome this issue. In this paper proposed a new intrusion detection system is Enhanced Adaptive 3 Acknowledgement (EA3ACK) using Energy Efficiency Dynamic State (EEDS) algorithm. This algorithmis designed to increase the network lifetime and remaining energy bycontinuously monitoring the individual nodes inthe network, thereby it increases the quality ofservice of the network. Network Simulator (NS2) is used to implement & test our proposed system. The proposed EEDS- EA3ACK algorithm provides secure transmission & further it improves network performance.
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Bunimovich, Leonid, D. J. Passey, Dallas Smith, and Benjamin Webb. "Spectral and Dynamic Consequences of Network Specialization." International Journal of Bifurcation and Chaos 30, no. 06 (May 2020): 2050091. http://dx.doi.org/10.1142/s0218127420500911.
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One of the hallmarks of real networks is the ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the function(s) they perform. A recent model of network growth based on this notion of specialization has been able to reproduce some of the most well-known topological features found in real-world networks including right-skewed degree distributions, the small world property, modular as well as hierarchical topology, etc. Here we describe how specialization under this model also effects the spectral properties of a network. This allows us to give the conditions under which a network is able to maintain its dynamics as its topology evolves. Specifically, we show that if a network is intrinsically stable, which is a stronger version of the standard notion of global stability, then the network maintains this type of dynamics as the network evolves. This is one of the first steps toward unifying the rigorous study of the two types of dynamics exhibited by networks. These are the dynamics of a network, which is the topological evolution of the network’s structure, modeled here by the process of network specialization, and the dynamics on a network, which is the changing state of the network elements, where the type of dynamics we consider is global stability. The main examples we apply our results to are recurrent neural networks, which are the basis of certain types of machine learning algorithms.
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Zhang, Guoyin, Xu Fan, and Yanxia Wu. "Minimal Increase Network Coding for Dynamic Networks." PLOS ONE 11, no. 2 (February 11, 2016): e0148725. http://dx.doi.org/10.1371/journal.pone.0148725.
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Dawaliby, Samir, Abbas Bradai, and Yannis Pousset. "Adaptive dynamic network slicing in LoRa networks." Future Generation Computer Systems 98 (September 2019): 697–707. http://dx.doi.org/10.1016/j.future.2019.01.042.
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Gupta, Pramod, and Naresh K. Sinha. "Modeling Robot Dynamics Using Dynamic Neural Networks." IFAC Proceedings Volumes 30, no. 11 (July 1997): 755–59. http://dx.doi.org/10.1016/s1474-6670(17)42936-3.
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Dumpis, Martynas. "ARTIFICIAL NEURAL NETWORKS WITH DYNAMIC SYNAPSES: A REVIEW." Mokslas - Lietuvos ateitis 15 (November 8, 2023): 1–8. http://dx.doi.org/10.3846/mla.2023.20144.
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Artificial neural networks (ANNs) are widely applied to solve real-world problems. Most of the actions we take and the processes around us are time-varying. ANNs with dynamic properties allow processing time-dependent data and solving tasks such as speech and text processing, prediction models, face and emotion recognition, game strategy development. Dynamics in neural networks can appear in the input data, the architecture of the neural network, and the individual elements of the neural network – synapses and neurons. Unlike static synapses, dynamic synapses can change their connection strength based on incoming information. This is a fundamental principle allows neural networks to perform complex tasks like word processing or face recognition more efficiently. Dynamic synapses play a key role in the ability of artificial neural networks to learn from experience and change over time, which is one of the key aspects of artificial intelligence. The scientific works examined in this article show that there are no literature sources that review and compare dynamic DNTs according to their synapses. To fill this gap, the article reviews and groups DNTs with dynamic synapses. Dynamic neural networks are defined by providing a general mathematical expression. A dynamic synapse is described by specifying its main properties and presenting a general mathematical expression. Also an explanation, how these synapses can be modelled and integrated into 11 different dynamic ANNs is shown. Moreover, structures of dynamic ANNs are compared according to the properties of dynamic synapses.
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Lordan, Oriol, and Jose M. Sallan. "Dynamic measures for transportation networks." PLOS ONE 15, no. 12 (December 3, 2020): e0242875. http://dx.doi.org/10.1371/journal.pone.0242875.
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Most complex network analyses of transportation systems use simplified static representations obtained from existing connections in a time horizon. In static representations, travel times, waiting times and compatibility of schedules are neglected, thus losing relevant information. To obtain a more accurate description of transportation networks, we use a dynamic representation that considers synced paths and that includes waiting times to compute shortest paths. We use the shortest paths to define dynamic network, node and edge measures to analyse the topology of transportation networks, comparable with measures obtained from static representations. We illustrate the application of these measures with a toy model and a real transportation network built from schedules of a low-cost carrier. Results show remarkable differences between measures of static and dynamic representations, demonstrating the limitations of the static representation to obtain accurate information of transportation networks.
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Cheng, Hui. "Dynamic Genetic Algorithms with Hyper-Mutation Schemes for Dynamic Shortest Path Routing Problem in Mobile Ad Hoc Networks." International Journal of Adaptive, Resilient and Autonomic Systems 3, no. 1 (January 2012): 87–98. http://dx.doi.org/10.4018/jaras.2012010105.
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In recent years, the static shortest path (SP) routing problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks (ANNs), genetic algorithms (GAs), particle swarm optimization (PSO), etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile ad hoc network (MANET), wireless mesh network (WMN), etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time due to energy conservation or node mobility. Therefore, the SP routing problem in MANETs turns out to be a dynamic optimization problem. This paper proposes to use two types of hyper-mutation GAs to solve the dynamic SP routing problem in MANETs. The authors consider MANETs as target systems because they represent new generation wireless networks. The experimental results show that the two hyper-mutation GAs can quickly adapt to the environmental changes (i.e., the network topology change) and produce good solutions after each change.
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Sekara, Vedran, Arkadiusz Stopczynski, and Sune Lehmann. "Fundamental structures of dynamic social networks." Proceedings of the National Academy of Sciences 113, no. 36 (August 23, 2016): 9977–82. http://dx.doi.org/10.1073/pnas.1602803113.
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Social systems are in a constant state of flux, with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding the spreading of influence or diseases, formation of friendships, and the productivity of teams. Although there has been much progress on understanding complex networks over the past decade, little is known about the regularities governing the microdynamics of social networks. Here, we explore the dynamic social network of a densely-connected population of ∼1,000 individuals and their interactions in the network of real-world person-to-person proximity measured via Bluetooth, as well as their telecommunication networks, online social media contacts, geolocation, and demographic data. These high-resolution data allow us to observe social groups directly, rendering community detection unnecessary. Starting from 5-min time slices, we uncover dynamic social structures expressed on multiple timescales. On the hourly timescale, we find that gatherings are fluid, with members coming and going, but organized via a stable core of individuals. Each core represents a social context. Cores exhibit a pattern of recurring meetings across weeks and months, each with varying degrees of regularity. Taken together, these findings provide a powerful simplification of the social network, where cores represent fundamental structures expressed with strong temporal and spatial regularity. Using this framework, we explore the complex interplay between social and geospatial behavior, documenting how the formation of cores is preceded by coordination behavior in the communication networks and demonstrating that social behavior can be predicted with high precision.
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Lyons, Rowanne, Larissa Hammer, Alexis André, Charles-André Fustin, Renaud Nicolaÿ, and Evelyne van Ruymbeke. "Equilibration dynamics of a dynamic covalent network diluted in a metallosupramolecular polymer matrix." Journal of Rheology 66, no. 6 (November 1, 2022): 1349–64. http://dx.doi.org/10.1122/8.0000473.
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We investigate the viscoelastic properties of double dynamic networks (DDNs) based on side-functionalized P nBA chains. One of these networks is highly crosslinked by metal-ligand junctions characterized by a fast association/dissociation dynamics, while the other network is sparsely crosslinked with slow dynamic covalent networks (DCNs). We first show that modulating the dynamics of the metallosupramolecular networks, by playing with the temperature, the density of reversible junctions, or the stress applied, has direct consequences on the local equilibration of the DCN. The latter takes place by a constraint release Rouse process at the rhythm of the association/dissociation of the metal-ligand junctions. Then, based on creep-recovery experiments, we investigate the ability of the DDNs to recover their initial shape after a creep test and show again the important role played by the metallosupramolecular network. In particular, the sample recovery strongly depends on the network connectivity, which is enhanced if a denser metallosupramolecular network is used as it reduces the possible creep of the double dynamic network and increases its elastic memory. The sample recovery also depends on the association-dissociation dynamics of the metallosupramolecular bonds as it fixes how fast the stretched DCN can come back to its equilibrium conformation and can recover its initial shape after a large deformation has been applied. Adjusting the dynamics of the weak network is thus a key process to govern the viscoelastic response of the slow network.
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Yu, Haichao, Haoxiang Li, Gang Hua, Gao Huang, and Humphrey Shi. "Boosted Dynamic Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (June 26, 2023): 10989–97. http://dx.doi.org/10.1609/aaai.v37i9.26302.
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Early-exiting dynamic neural networks (EDNN), as one type of dynamic neural networks, has been widely studied recently. A typical EDNN has multiple prediction heads at different layers of the network backbone. During inference, the model will exit at either the last prediction head or an intermediate prediction head where the prediction confidence is higher than a predefined threshold. To optimize the model, these prediction heads together with the network backbone are trained on every batch of training data. This brings a train-test mismatch problem that all the prediction heads are optimized on all types of data in training phase while the deeper heads will only see difficult inputs in testing phase. Treating training and testing inputs differently at the two phases will cause the mismatch between training and testing data distributions. To mitigate this problem, we formulate an EDNN as an additive model inspired by gradient boosting, and propose multiple training techniques to optimize the model effectively. We name our method BoostNet. Our experiments show it achieves the state-of-the-art performance on CIFAR100 and ImageNet datasets in both anytime and budgeted-batch prediction modes. Our code is released at https://github.com/SHI-Labs/Boosted-Dynamic-Networks.
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Liao, Wei, Yun-Shuang Fan, Siqi Yang, Jiao Li, Xujun Duan, Qian Cui, and Huafu Chen. "Preservation Effect: Cigarette Smoking Acts on the Dynamic of Influences Among Unifying Neuropsychiatric Triple Networks in Schizophrenia." Schizophrenia Bulletin 45, no. 6 (December 17, 2018): 1242–50. http://dx.doi.org/10.1093/schbul/sby184.
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Abstract Objective The high prevalence of cigarette smoking in schizophrenia (SZ) is generally explained by the self-medication theory. However, its neurobiological mechanism remains unclear. The impaired dynamic of influences among unifying neuropsychiatric triple networks in SZ, including the central executive network (CEN), the default mode network (DMN), and the salience network (SN), might explain the nature of their syndromes, whereas smoking could regulate the dynamics within networks. Therefore, this study examined whether cigarette smoking could elicit a distinct improvement in the dynamics of triple networks in SZ and associated with the alleviation of symptoms. Methods Four groups were recruited, namely, SZ smoking (n = 22)/nonsmoking (n = 25), and healthy controls smoking (n = 22)/nonsmoking (n = 21). All participants underwent a resting-state functional magnetic resonance imaging (fMRI). The dynamics among unifying neuropsychiatric triple networks were measured using Granger causality analysis on the resting-sate fMRI signal. Interaction effects between SZ and smoking on dynamics were detected using 2-way analysis of covariance, correcting for sex, age, and education level. Results Whereas smoking reduced SN→DMN dynamic in healthy controls, it preserved the dynamic in SZ, thus suggesting a preservation effect. Moreover, smoking additionally increased DMN→CEN dynamic in SZ. Conclusions This finding from neural pathways shed new insights into the prevailing self-medication hypothesis in SZ. More broadly, this study elaborates on the neurobiological dynamics that may assist in the treatment of the symptomatology of SZ.
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Torgashev, Valery Antony. "Dynamic Automata Networks." SPIIRAS Proceedings 4, no. 27 (March 17, 2014): 23. http://dx.doi.org/10.15622/sp.27.2.
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Donner, Amy. "GRBing dynamic networks." Nature Chemical Biology 7, no. 9 (August 17, 2011): 576. http://dx.doi.org/10.1038/nchembio.650.
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Kuperman, M. N., M. Ballard, and F. Laguna. "Dynamic domain networks." European Physical Journal B 50, no. 3 (April 2006): 513–20. http://dx.doi.org/10.1140/epjb/e2006-00148-3.
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van Assen, M. A. L. M., and Arnout van de Rijt. "Dynamic exchange networks." Social Networks 29, no. 2 (May 2007): 266–78. http://dx.doi.org/10.1016/j.socnet.2006.12.003.
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Khalili, A. M. "Dynamic Switching Networks." Complex Systems 28, no. 1 (March 15, 2019): 77–96. http://dx.doi.org/10.25088/complexsystems.28.1.77.
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Yue, Liang, Shan Wang, Verena Wulf, Sivan Lilienthal, Françoise Remacle, R. D. Levine, and Itamar Willner. "Consecutive feedback-driven constitutional dynamic networks." Proceedings of the National Academy of Sciences 116, no. 8 (February 6, 2019): 2843–48. http://dx.doi.org/10.1073/pnas.1816670116.
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Cellular transformations are driven by environmentally triggered complex dynamic networks, which include signal-triggered feedback processes, cascaded reactions, and switchable transformations. We apply the structural and functional information encoded in the sequences of nucleic acids to construct signal-triggered constitutional dynamic networks (CDNs) that mimic the functions of natural networks. Using predesigned hairpin structures as triggers, the network generates functional strands, which stabilize one or the other of the constituents of the network, leading to feedback-driven reconfiguration and time-dependent equilibration of the networks. Using structurally designed hairpins, positive-feedback or negative-feedback mechanisms operated by the CDNs are demonstrated. With two predesigned hairpins, the coupled consecutive operations of negative/positive- or positive/positive- feedback cascades are accomplished. The time-dependent composition changes of the networks are well reproduced by chemical kinetics simulations that provide predictive behaviors of the network, under variable auxiliary conditions. Beyond mimicking natural network properties and functions by means of the synthetic nucleic-acid–based CDNs, the systems introduce versatile perspectives for the design of amplified sensors (sensing of miRNA-376a) and the development of logic gate circuits.
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WIT, ERNST, and ANTONINO ABBRUZZO. "Factorial graphical models for dynamic networks." Network Science 3, no. 1 (February 12, 2015): 37–57. http://dx.doi.org/10.1017/nws.2015.2.
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AbstractDynamic network models describe many important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Until now, the literature has focused on static networks, which lack specific temporal interpretations.We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links, and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We illustrate the flexibility of the method on both synthetic and real data.
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Yan, Yu-Wei, Yuan Jiang, Song-Qing Yang, Rong-Bin Yu, and Cheng Hong. "Network failure model based on time series." Acta Physica Sinica 71, no. 8 (2022): 088901. http://dx.doi.org/10.7498/aps.71.20212106.
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With the development of network science, the static network has been unable to clearly characterize the dynamic process of the network. In real networks, the interaction between individuals evolves rapidly over time. This network model closely links time to interaction process. Compared with static networks, dynamic networks can clearly describe the interaction time of nodes, which has more practical significance. Therefore, how to better describe the behavior changes of networks after being attacked based on time series is an important problem in the existing cascade failure research. In order to better answer this question, a failure model based on time series is proposed in this paper. The model is constructed according to time, activation ratio, number of edges and connection probability. By randomly attacking nodes at a certain time, the effects of four parameters on sequential networks are analyzed. In order to validate the validity and scientificity of this failure model, we use small social networks in the United States. The experimental results show that the model is feasible. The model takes into account the time as well as the spreading dynamics and provides a reference for explaining the dynamic networks in reality.
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Britton, Tom, and Mathias Lindholm. "Dynamic Random Networks in Dynamic Populations." Journal of Statistical Physics 139, no. 3 (March 24, 2010): 518–35. http://dx.doi.org/10.1007/s10955-010-9952-5.
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Parmelee, Caitlyn, Samantha Moore, Katherine Morrison, and Carina Curto. "Core motifs predict dynamic attractors in combinatorial threshold-linear networks." PLOS ONE 17, no. 3 (March 4, 2022): e0264456. http://dx.doi.org/10.1371/journal.pone.0264456.
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Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. In prior work, we have developed a detailed mathematical theory relating stable and unstable fixed points of CTLNs to graph-theoretic properties of the underlying network. Here we find that a special type of fixed points, corresponding to core motifs, are predictive of both static and dynamic attractors. Moreover, the attractors can be found by choosing initial conditions that are small perturbations of these fixed points. This motivates us to hypothesize that dynamic attractors of a network correspond to unstable fixed points supported on core motifs. We tested this hypothesis on a large family of directed graphs of size n = 5, and found remarkable agreement. Furthermore, we discovered that core motifs with similar embeddings give rise to nearly identical attractors. This allowed us to classify attractors based on structurally-defined graph families. Our results suggest that graphical properties of the connectivity can be used to predict a network’s complex repertoire of nonlinear dynamics.
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Braun, Urs, Axel Schäfer, Henrik Walter, Susanne Erk, Nina Romanczuk-Seiferth, Leila Haddad, Janina I. Schweiger, et al. "Dynamic reconfiguration of frontal brain networks during executive cognition in humans." Proceedings of the National Academy of Sciences 112, no. 37 (August 31, 2015): 11678–83. http://dx.doi.org/10.1073/pnas.1422487112.
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The brain is an inherently dynamic system, and executive cognition requires dynamically reconfiguring, highly evolving networks of brain regions that interact in complex and transient communication patterns. However, a precise characterization of these reconfiguration processes during cognitive function in humans remains elusive. Here, we use a series of techniques developed in the field of “dynamic network neuroscience” to investigate the dynamics of functional brain networks in 344 healthy subjects during a working-memory challenge (the “n-back” task). In contrast to a control condition, in which dynamic changes in cortical networks were spread evenly across systems, the effortful working-memory condition was characterized by a reconfiguration of frontoparietal and frontotemporal networks. This reconfiguration, which characterizes “network flexibility,” employs transient and heterogeneous connectivity between frontal systems, which we refer to as “integration.” Frontal integration predicted neuropsychological measures requiring working memory and executive cognition, suggesting that dynamic network reconfiguration between frontal systems supports those functions. Our results characterize dynamic reconfiguration of large-scale distributed neural circuits during executive cognition in humans and have implications for understanding impaired cognitive function in disorders affecting connectivity, such as schizophrenia or dementia.
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Shepherd, Patrick, and Judy Goldsmith. "A Reinforcement Learning Approach to Strategic Belief Revelation with Social Influence." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (April 3, 2020): 13734–35. http://dx.doi.org/10.1609/aaai.v34i10.7139.
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The study of social networks has increased rapidly in the past few decades. Of recent interest are the dynamics of changing opinions over a network. Some research has investigated how interpersonal influence can affect opinion change, how to maximize/minimize the spread of opinion change over a network, and recently, if/how agents can act strategically to effect some outcome in the network's opinion distribution. This latter problem can be modeled and addressed as a reinforcement learning problem; we introduce an approach to help network agents find strategies that outperform hand-crafted policies. Our preliminary results show that our approach is promising in networks with dynamic topologies.
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Vernon, Matthew C., and Matt J. Keeling. "Representing the UK's cattle herd as static and dynamic networks." Proceedings of the Royal Society B: Biological Sciences 276, no. 1656 (October 14, 2008): 469–76. http://dx.doi.org/10.1098/rspb.2008.1009.
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Network models are increasingly being used to understand the spread of diseases through sparsely connected populations, with particular interest in the impact of animal movements upon the dynamics of infectious diseases. Detailed data collected by the UK government on the movement of cattle may be represented as a network, where animal holdings are nodes, and an edge is drawn between nodes where a movement of animals has occurred. These network representations may vary from a simple static representation, to a more complex, fully dynamic one where daily movements are explicitly captured. Using stochastic disease simulations, a wide range of network representations of the UK cattle herd are compared. We find that the simpler static network representations are often deficient when compared with a fully dynamic representation, and should therefore be used only with caution in epidemiological modelling. In particular, due to temporal structures within the dynamic network, static networks consistently fail to capture the predicted epidemic behaviour associated with dynamic networks even when parameterized to match early growth rates.