Edge Dynamics Research Articles

Evolutionary dynamics under interactive diversity

As evidenced by many cases in human societies, individuals often make different behavior decisions in different interactions, and adaptively adjust their behavior in changeable interactive scenarios. However, up to now, how such diverse interactive behavior affects cooperation dynamics has still remained unknown. Here we develop a general framework of interactive diversity, which models individuals’ separated behavior against distinct opponents and their adaptive adjustment in response to opponents’ strategies, to explore the evolution of cooperation. We find that interactive diversity enables individuals to reciprocate every single opponent, and thus sustains large-scale reciprocal interactions. Our work witnesses an impressive boost of cooperation for a notably extensive range of parameters and for all pairwise games. These results are robust against well-mixed and various networked populations, and against degree-normalized and cumulative payoff patterns. From the perspective of network dynamics, distinguished from individuals competing for nodes in most previous work, in this paper, the system evolves in the form of behavior disseminating along edges. We propose a theoretical method based on evolution of edges, which predicts well both the frequency of cooperation and the compact cooperation clusters. Our thorough investigation clarifies the positive role of interactive diversity in resolving social dilemmas and highlights the significance of understanding evolutionary dynamics from the viewpoint of edge dynamics.

Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics

This paper studies the robust proportional-integral-derivative (PID) consensus control for a class of linear multi-agent systems (MASs) with external disturbances. Different from the existing results, both the consensus analysis and the transient performance characteristics for high-order linear MASs are considered. Based on a factorization of Laplacian matrix, the initial MAS is firstly transformed into the so-called weighted edge dynamics, and then a design equivalence between the proposed PID consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results. Furthermore, by combining Lyapunov theory and Barbalat’s Lemma, it is proved that both the stabilization of weighted edge dynamics and the consensus of MAS can be guaranteed even in the presence of external disturbances. In particular, some relationships between the transient time performance of weighted edge dynamics and the PID design parameters are given. Finally, some numerical examples on LC oscillator network are provided to illustrate the validity of theoretical results.

Forward reachable sets: Analytically derived properties of connected components for dynamic networks.

Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration. FRS are defined as the set of nodes that can be reached from an initial seed via a path of temporally ordered edges; a natural extension of connected component measures to dynamic networks. Working in a stochastic framework, we derive closed-form expressions for the mean and variance of the exponential growth rate of the FRS for temporal networks with both edge and node dynamics. For networks with node dynamics, we calculate thresholds for the growth of the FRS. The effects of finite population size are explored via simulation and approximation. We examine how these properties vary by edge duration and different cross-sectional degree distributions that characterize a range of scientifically interesting normative outcomes (Poisson and Bernoulli). The size of the forward reachable set gives an upper bound for the epidemic size in disease transmission network models, relating this work to epidemic modeling (Ferguson, 2000; Eames, 2004).

Universal framework for edge controllability of complex networks

Dynamical processes occurring on the edges in complex networks are relevant to a variety of real-world situations. Despite recent advances, a framework for edge controllability is still required for complex networks of arbitrary structure and interaction strength. Generalizing a previously introduced class of processes for edge dynamics, the switchboard dynamics, and exploit- ing the exact controllability theory, we develop a universal framework in which the controllability of any node is exclusively determined by its local weighted structure. This framework enables us to identify a unique set of critical nodes for control, to derive analytic formulas and articulate efficient algorithms to determine the exact upper and lower controllability bounds, and to evaluate strongly structural controllability of any given network. Applying our framework to a large number of model and real-world networks, we find that the interaction strength plays a more significant role in edge controllability than the network structure does, due to a vast range between the bounds determined mainly by the interaction strength. Moreover, transcriptional regulatory networks and electronic circuits are much more strongly structurally controllable (SSC) than other types of real-world networks, directed networks are more SSC than undirected networks, and sparse networks are typically more SSC than dense networks.

Controllable subspace of edge dynamics in complex networks

For the edge dynamics in some real networks, it may be neither feasible nor necessary to be fully controlled. An accompanying issue is that, when the external signal is applied to a few nodes or even a single node, how many edges can be controlled? In this paper, for the edge dynamics system, we propose a theoretical framework to determine the controllable subspace and calculate its generic dimension based on the integer linear programming. This framework allows us not only to analyze the control centrality, i.e., the ability of a node to control, but also to uncover the controllable centrality, i.e., the propensity of an edge to be controllable. The simulation results and analytic calculation show that dense and homogeneous networks tend to have larger control centrality of nodes and controllable centrality of edges, but the negatively correlated in- and out-degrees of nodes or edges can reduce the two centrality. The positive correlation between the control centrality of node and its out-degree leads to that the distribution of control centrality, instead of that of controllable centrality, is encoded by the out-degree distribution of networks. Meanwhile, the positive correlation indicates that the nodes with high out-degree tend to play more important roles in control.

Improving the interpretability of climate landscape metrics: An ecological risk analysis of Japan's Marine Protected Areas.

Conservation efforts strive to protect significant swaths of terrestrial, freshwater and marine ecosystems from a range of threats. As climate change becomes an increasing concern, these efforts must take into account how resilient-protected spaces will be in the face of future drivers of change such as warming temperatures. Climate landscape metrics, which signal the spatial magnitude and direction of climate change, support a convenient initial assessment of potential threats to and opportunities within ecosystems to inform conservation and policy efforts where biological data are not available. However, inference of risk from purely physical climatic changes is difficult unless set in a meaningful ecological context. Here, we aim to establish this context using historical climatic variability, as a proxy for local adaptation by resident biota, to identify areas where current local climate conditions will remain extant and future regional climate analogues will emerge. This information is then related to the processes governing species' climate-driven range edge dynamics, differentiating changes in local climate conditions as promoters of species range contractions from those in neighbouring locations facilitating range expansions. We applied this approach to assess the future climatic stability and connectivity of Japanese waters and its network of marine protected areas (MPAs). We find 88% of Japanese waters transitioning to climates outside their historical variability bounds by 2035, resulting in large reductions in the amount of available climatic space potentially promoting widespread range contractions and expansions. Areas of high connectivity, where shifting climates converge, are present along sections of the coast facilitated by the strong latitudinal gradient of the Japanese archipelago and its ocean current system. While these areas overlap significantly with areas currently under significant anthropogenic pressures, they also include much of the MPA network that may provide stepping-stone protection for species that must shift their distribution because of climate change.

K-shell photoabsorption edge of strongly coupled aluminum driven by laser-converted radiation

The first observation of the K-shell photoabsorption edge of strongly coupled aluminum generated by intense x-ray radiation-driven shocks is reported. By using a “dog bone” gold hohlraum as an x-ray converter, colliding shocks compression and preheating shielding are achieved to generate an unexplored state with a density of 5.5 g/cm3 and temperature of 0.43 eV (the ion-ion coupling parameter is around 240). The time-resolved K-shell photoabsorption edges are measured with a crystal spectrometer using a short x-ray backlighter. The broadenings and redshifts of the edges are studied by using the slope fitting of the edge and quantum molecular dynamics calculations. This work shows that the K-edge of aluminum driven by laser-converted radiation provides a novel capability to probe WDM at extended conditions.

Fat2 and Lar Define a Basally Localized Planar Signaling System Controlling Collective Cell Migration

Collective migration of epithelial cells underlies diverse tissue-remodeling events, but the mechanisms that coordinate individual cell migratory behaviors for collective movement are largely unknown. Studying the Drosophila follicular epithelium, we show that the cadherin Fat2 and the receptor tyrosine phosphatase Lar function in a planar signaling system that coordinates leading and trailing edge dynamics between neighboring cells. Fat2 signals from each cell's trailing edge to induce leading edge protrusions in the cell behind, in part by stabilizing Lar's localization in these cells. Conversely, Lar signals from each cell's leading edge to stimulate trailing edge retraction in the cell ahead. Fat2/Lar signaling is similar to planar cell polarity signaling in terms of sub-cellular protein localization; however, Fat2/Lar signaling mediates short-range communication between neighboring cells instead of transmitting long-range information across a tissue. This work defines a key mechanism promoting epithelial migration and establishes a different paradigm for planar cell-cell signaling.

Unraveling the martian water cycle with high-resolution global climate simulations

Global climate modeling of the Mars water cycle is usually performed at relatively coarse resolution (200−300km), which may not be sufficient to properly represent the impact of waves, fronts, topography effects on the detailed structure of clouds and surface ice deposits. Here, we present new numerical simulations of the annual water cycle performed at a resolution of 1° × 1° (∼ 60 km in latitude). The model includes the radiative effects of clouds, whose influence on the thermal structure and atmospheric dynamics is significant, thus we also examine simulations with inactive clouds to distinguish the direct impact of resolution on circulation and winds from the indirect impact of resolution via water ice clouds. To first order, we find that the high resolution does not dramatically change the behavior of the system, and that simulations performed at ∼ 200 km resolution capture well the behavior of the simulated water cycle and Mars climate. Nevertheless, a detailed comparison between high and low resolution simulations, with reference to observations, reveal several significant changes that impact our understanding of the water cycle active today on Mars. The key northern cap edge dynamics are affected by an increase in baroclinic wave strength, with a complication of northern summer dynamics. South polar frost deposition is modified, with a westward longitudinal shift, since southern dynamics are also influenced. Baroclinic wave mode transitions are observed. New transient phenomena appear, like spiral and streak clouds, already documented in the observations. Atmospheric circulation cells in the polar region exhibit a large variability and are fine structured, with slope winds. Most modeled phenomena affected by high resolution give a picture of a more turbulent planet, inducing further variability. This is challenging for long-period climate studies.

Sparse identification of a predator-prey system from simulation data of a convection model

The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a reduced model from simulation data of a convection problem. A convection model with a pressure source centered at the inner boundary models the edge dynamics of a magnetically confined plasma. The convection problem undergoes a sequence of bifurcations as the strength of the pressure source increases. The time evolution of the energies of the pressure profile, the turbulent flow, and the zonal flow capture the fundamental dynamic behavior of the full system. By applying the sparse identification of nonlinear dynamics (SINDy) method, we identify a predator-prey type dynamical system that approximates the underlying dynamics of the three energy state variables. A bifurcation analysis of the system reveals consistency between the bifurcation structures, observed for the simulation data, and the identified underlying system.

Reduced-Order Distributed Consensus Controller Design via Edge Dynamics

This paper proposes a novel approach to design reduced-order distributed consensus controllers for multi-agent systems (MASs) with identical linear dynamics of agents. A new model namely edge dynamics representing the differences on agents' states is first presented. Then the distributed consensus controller design is shown to be equivalent to the synthesis of a distributed stabilizing controller for this edge dynamics. Consequently, based on LQR approach, the globally optimal and locally optimal distributed stabilizing controller designs are proposed, of which the locally distributed stabilizing controller for the edge dynamics results in a distributed consensus controller for the MAS with no conservative bound on the coupling strength. This approach is next further developed to obtain reduced-order distributed consensus controllers for linear MASs. Several numerical examples are introduced to illustrate the theoretical results.

Evidence for Global Edge–Core Interplay in Fusion Plasmas

Large-scale reactor-relevant fusion plasmas are likely to operate near marginal stability. In this regime, we show clear evidence of interplay between core and edge regions of the plasma. This result illustrates aspects of the controversial 'shortfall problem' in the far-core, near-edge so-called 'No Man's Land' region and a possible route to resolve this issue. More generally, it emphasises global-scale organisation of turbulence and relevance of edge dynamics to core confinement.

Optimizing controllability of edge dynamics in complex networks by perturbing network structure

Using the minimum input signals to drive the dynamics in complex networks toward some desired state is a fundamental issue in the field of network controllability. For a complex network with the dynamical process defined on its edges, the controllability of this network is optimal if it can be fully controlled by applying one input signal to an arbitrary non-isolated vertex of it. In this paper, the adding-edge strategy and turning-edge strategy are proposed to optimize the controllability by minimum structural perturbations. Simulations and analyses indicate that the minimum number of adding-edges required for the optimal controllability is equal to the minimum number of turning-edges, and networks with positively correlated in- and out-degrees are easier to achieve optimal controllability. Furthermore, both the strategies have the capacity to reveal the relationship between certain structural properties of a complex network and its controllability of edge dynamics.

Network Unfolding Map by Vertex-Edge Dynamics Modeling.

The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network, which are called particles, to solve semisupervised learning problems. Three actions govern the particles' dynamics: generation, walking, and absorption. Labeled vertices generate new particles that compete against rival particles for edge domination. Active particles randomly walk in the network until they are absorbed by either a rival vertex or an edge currently dominated by rival particles. The result from the model evolution consists of sets of edges arranged by the label dominance. Each set tends to form a connected subnetwork to represent a data class. Although the intrinsic dynamics of the model is a stochastic one, we prove that there exists a deterministic version with largely reduced computational complexity; specifically, with linear growth. Furthermore, the edge domination process corresponds to an unfolding map in such way that edges "stretch" and "shrink" according to the vertex-edge dynamics. Consequently, the unfolding effect summarizes the relevant relationships between vertices and the uncovered data classes. The proposed model captures important details of connectivity patterns over the vertex-edge dynamics evolution, in contrast to the previous approaches, which focused on only vertex or only edge dynamics. Computer simulations reveal that the new model can identify nonlinear features in both real and artificial data, including boundaries between distinct classes and overlapping structures of data.

Robustness of controlling edge dynamics in complex networks against node failure.

The robustness of controlling complex networks is significant in network science. In this paper, we focus on evaluating and analyzing the robustness of controlling edge dynamics in complex networks against node failure. Using three categories of all nodes to quantify the robustness, we find that the percentages of the three types of nodes are mainly related to the degree distribution of networks. The simulation results of model networks and analytic calculations show that the sparse inhomogeneous networks, which emerge in many real complex networks, have strong control robustness from the point of the number of ordinary nodes, but the strong positive correlation between in and out degrees reduces the control robustness. Evaluation of real-world networks indicates that most of them have few or no critical nodes, that is, they do not need to increase driver nodes to maintain control for most of node failures. Then an adding circuit-link strategy is proposed to optimize the robustness of edge controllability.

Interactive diversity promotes the evolution of cooperation in structured populations

Evolutionary games on networks traditionally assume that each individual adopts an identical strategy to interact with all its neighbors in each generation. Considering the prevalent diversity of individual interactions in the real society, here we propose the concept of interactive diversity, which allows individuals to adopt different strategies against different neighbors in each generation. We investigate the evolution of cooperation based on the edge dynamics rather than the traditional nodal dynamics in networked systems. The results show that, without invoking any other mechanisms, interactive diversity drives the frequency of cooperation to a high level for a wide range of parameters in both well-mixed and structured populations. Even in highly connected populations, cooperation still thrives. When interactive diversity and large topological heterogeneity are combined together, however, in the relaxed social dilemma, cooperation level is lower than that with just one of them, implying that the combination of many promotive factors may make a worse outcome. By an analytical approximation, we get the condition under which interactive diversity provides more advantages for cooperation than traditional evolutionary dynamics does. Numerical simulations validating the approximation are also presented. Our work provides a new line to explore the latent relation between the ubiquitous cooperation and individuals’ distinct responses in different interactions. The presented results suggest that interactive diversity should receive more attention in pursuing mechanisms fostering cooperation.

Liprin-α1 and ERC1 control cell edge dynamics by promoting focal adhesion turnover.

Liprin-α1 and ERC1 are interacting scaffold proteins regulating the motility of normal and tumor cells. They act as part of plasma membrane-associated platforms at the edge of motile cells to promote protrusion by largely unknown mechanisms. Here we identify an amino-terminal region of the liprin-α1 protein (liprin-N) that is sufficient and necessary for the interaction with other liprin-α1 molecules. Similar to liprin-α1 or ERC1 silencing, expression of the liprin-N negatively affects tumor cell motility and extracellular matrix invasion, acting as a dominant negative by interacting with endogenous liprin-α1 and causing the displacement of the endogenous ERC1 protein from the cell edge. Interfering with the localization of ERC1 at the cell edge inhibits the disassembly of focal adhesions, impairing protrusion. Liprin-α1 and ERC1 proteins colocalize with active integrin β1 clusters distinct from those colocalizing with cytoplasmic focal adhesion proteins, and influence the localization of peripheral Rab7-positive endosomes. We propose that liprin-α1 and ERC1 promote protrusion by displacing cytoplasmic adhesion components to favour active integrin internalization into Rab7-positive endosomes.

Epidemic processes over adaptive state-dependent networks.

In this paper we study the dynamics of epidemic processes taking place in adaptive networks of arbitrary topology. We focus our study on the adaptive susceptible-infected-susceptible (ASIS) model, where healthy individuals are allowed to temporarily cut edges connecting them to infected nodes in order to prevent the spread of the infection. In this paper we derive a closed-form expression for a lower bound on the epidemic threshold of the ASIS model in arbitrary networks with heterogeneous node and edge dynamics. For networks with homogeneous node and edge dynamics, we show that the resulting lower bound is proportional to the epidemic threshold of the standard SIS model over static networks, with a proportionality constant that depends on the adaptation rates. Furthermore, based on our results, we propose an efficient algorithm to optimally tune the adaptation rates in order to eradicate epidemic outbreaks in arbitrary networks. We confirm the tightness of the proposed lower bounds with several numerical simulations and compare our optimal adaptation rates with popular centrality measures.

Social contact processes and the partner model

We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determines the set of contacts at each moment in time. We identify a basic reproduction number $R_0$ with the property that if $R_0<1$ the infection dies out by time $O(\log N)$, while if $R_0>1$ the infection survives for an amount of time $e^{\gamma N}$ for some $\gamma>0$ and hovers around a uniquely determined metastable proportion of infectious individuals. The proof in both cases relies on comparison to a set of mean-field equations when the infection is widespread, and to a branching process when the infection is sparse.

Ratiometric Imaging Using a Single Dye Enables Simultaneous Visualization of Rac1 and Cdc42 Activation.

Biosensors that report endogenous protein activity in vivo can be based on environment-sensing fluorescent dyes. The dyes can be attached to reagents that bind selectively to a specific conformation of the targeted protein, such that binding leads to a fluorescence change. Dyes that are sufficiently bright for use at low, nonperturbing intracellular concentrations typically undergo changes in intensity rather than the shifts in excitation or emission maxima that would enable precise quantitation through ratiometric imaging. We report here mero199, an environment-sensing dye that undergoes a 33 nm solvent-dependent shift in excitation. The dye was used to generate a ratiometric biosensor of Cdc42 (CRIB199) without the need for additional fluorophores. CRIB199 was used in the same cell with a FRET sensor of Rac1 activation to simultaneously observe Cdc42 and Rac1 activity in cellular protrusions, indicating that Rac1 but not Cdc42 activity was reduced during tail retraction, and specific protrusions had reduced Cdc42 activity. A novel program (EdgeProps) used to correlate localized activation with cell edge dynamics indicated that Rac1 was specifically reduced during retraction.