The fundamental advantages of temporal networks

Compressing the Chronology of a Temporal Network with Graph Commutators

Studies of dynamics on temporal networks often represent the network as a series of "snapshots," static networks active for short durations of time. We argue that successive snapshots can be aggregated if doing so has little effect on the overlying dynamics. We propose a method to compress network chronologies by progressively combining pairs of snapshots whose matrix commutators have the smallest dynamical effect. We apply this method to epidemic modeling on real contact tracing data and find that it allows for significant compression while remaining faithful to the epidemic dynamics.

Sequential stacking link prediction algorithms for temporal networks

Link prediction algorithms are indispensable tools in many scientific applications by speeding up network data collection and imputing missing connections. However, in many systems, links change over time and it remains unclear how to optimally exploit such temporal information for link predictions in such networks. Here, we show that many temporal topological features, in addition to having high computational cost, are less accurate in temporal link prediction than sequentially stacked static network features. This sequential stacking link prediction method uses 41 static network features that avoid detailed feature engineering choices and is capable of learning a highly accurate predictive distribution of future connections from historical data. We demonstrate that this algorithm works well for both partially observed and completely unobserved target layers, and on two temporal stochastic block models achieves near-oracle-level performance when combined with other single predictor methods as an ensemble learning method. Finally, we empirically illustrate that stacking multiple predictive methods together further improves performance on 19 real-world temporal networks from different domains.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Temporal rich club phenomenon and its formation mechanisms

The temporal rich club (TRC) phenomenon is widespread in real systems, forming a tight and continuous collection of the prominent nodes that control the system. However, there is still a lack of sufficient understanding of the mechanisms of TRC formation. Here we use the international N-nutrient trade network as an example of an in-depth identification, analysis, and modeling of its TRC phenomenon. The system exhibits a statistically significant TRC phenomenon, with eight economies forming the cornerstone club. Our analysis reveals that node degree is the most influential factor in TRC formation compared to other variables. The mathematical evolution models we constructed propose that the TRC in the N-nutrient trade network arises from the coexistence of degree-homophily and path-dependence mechanisms. By comprehending these mechanisms, we introduce a different perspective on TRC formation. Although our analysis is limited to the international trade system, the methodology can be extended to analyze the mechanisms underlying TRC emergence in other systems.

Systematic loss in biotic heterogeneity but not biodiversity across multiple trophic levels in Erhai lake, China

Anthropogenic disturbances and climate change have significantly altered the biotic composition across many ecosystems, leading to changes in biodiversity and even ecological collapse. An ecosystem comprises multiple trophic levels, and the issue how these disturbances affect their assembly processes remains unclear. Ecological stability of assemblages was maintained by their structure, and thus, revealing structure changes across trophic levels could improve our understanding of how ecosystems response to disturbances as a whole. In this study, we combined methods from palaeolimnology, ecology and network analysis, and observed the changes of biodiversity and network structure of two trophic levels (algae - diatoms and zoobenthos - chironomids) in Erhai lake, Southwest China over the last century. Results showed nutrient enrichment induced shifts in diatom and chironomid assemblages at ∼2001 CE, suggesting that the shift in Erhai lake may have occurred at multiple trophic levels. We found biodiversity exhibit different trends across trophic levels as it decreased in diatoms but increased in chironomids. However, network skewness declined in both trophic levels, indicating the common loss of biotic heterogeneity. The consistent decline of skewness among trophic levels long before the compositional shift is a potential parameter to warn of the shifts in lake ecosystems.

Constructing temporal networks with bursty activity patterns

Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One of the key statistics to summarize temporal patterns is the inter-event time, namely the duration between successive pairwise interactions. Empirical studies have found inter-event time distributions that are heavy-tailed, for both physical and digital interactions. But it is difficult to construct theoretical models of time-varying activity on a network that reproduce the burstiness seen in empirical data. Here we develop a spanning-tree method to construct temporal networks and activity patterns with bursty behavior. Our method ensures any desired target inter-event time distributions for individual nodes and links, provided the distributions fulfill a consistency condition, regardless of whether the underlying topology is static or time-varying. We show that this model can reproduce burstiness found in empirical datasets, and so it may serve as a basis for studying dynamic processes in real-world bursty interactions.

Fixation probability in evolutionary dynamics on switching temporal networks

Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks.

Target control of complex networks: How to save control energy

Controlling complex networks has received much attention in the past two decades. In order to control complex networks in practice, recent progress is mainly focused on the control energy required to drive the associated system from an initial state to any final state within finite time. However, one of the major challenges when controlling complex networks is that the amount of control energy is usually prohibitively expensive. Previous explorations on reducing the control energy often rely on adding more driver nodes to be controlled directly by external control inputs, or reducing the number of target nodes required to be controlled. Here we show that the required control energy can be reduced exponentially by appropriately setting the initial states of uncontrollable nodes for achieving the target control of complex networks. We further present the energy-optimal initial states and theoretically prove their existence for any structure of network. Moreover, we demonstrate that the control energy could be saved by reducing the distance between the energy-optimal states set and the initial states of uncontrollable nodes. Finally, we propose a strategy to determine the optimal time to inject the control inputs, which may reduce the control energy exponentially. Our conclusions are all verified numerically, and shed light on saving control energy in practical control.

Burstiness and information spreading in active particle systems

We construct a temporal network using the two-dimensional Vicsek model. The bursts of the interevent times for a specific pair of particles are investigated numerically. We found that, for different noise strengths, the distribution of the interevent times of a target edge follows a heavy tail, revealing the burstiness of the signals. To further characterize the nature of the burstiness, we calculate the burstiness parameters and the memory coefficients. The results show that, near the phase transition points of the Vicsek model, the burstiness parameters reach the minimum values for each density, indicating a relationship between the phase transition of the Vicsek model and the bursty nature of the signals. Furthermore, we investigate the spreading dynamics on our temporal network using a susceptible-infected model and observe a positive correlation between them.

Analysing dynamic work systems using DynEAST: a demonstration of concept

The capability of current Ergonomics methods to capture dynamism is limited, stifling our understanding of work-as-done, distributed situational awareness and organisational drift. This paper provides a demonstration of concept of DynEAST; an extension of the EAST framework underpinned by principles from Dynamic Network Analysis, to capture elements of dynamism within work systems. The DynEAST concept is applied to a railway maintenance case study. Case study findings demonstrate how DynEAST outputs can be used to advance our understanding of the aforementioned phenomena and better equip practitioners for current and future Ergonomics challenges.Practitioner summary: This paper introduces the DynEAST method. DynEAST enables HF/E practitioners to model and analyse dynamic features of complex work systems. The development of DynEAST is timely due to the concurrent proliferation of increasingly complex sociotechnical systems and stagnation of HF/E methods development; particularly those able to model systemic dynamism. Abbreviations: DynEAST: dynamic event analysis of systemic teamwork; EAST: dynamic event analysis of systemic teamwork; HF/E: human factors and ergonomics; HF: human factors; DNA: dynamic network analysis; HTA: hierarchal task analysis; CWA: cognitive work analysis; CAST: causal analysis based on system theory; STAMP: system theoretic accident model and processes; FRAM: functional resonance analysis method; SNA: social network analysis; DSA: distributed situational awareness; PPO: possession protection officer; PO: protection officer; RTS: railway track signals; LPA: local possession authority; SMEs: subject matter experts.

Stability of multi-layer ecosystems

Community structure is reported to play a critical role in ecosystem stability, which indicates the ability of a system to return to equilibrium after perturbations. However, current studies rely on the assumption that the community consists of only a single-layer structure. In practice, multi-layer structures are common in ecosystems, e.g. the distributions of both microorganisms in strata and fish in the ocean usually stratify into multi-layer structures. Here we use multi-layer networks to model species interactions within each layer and between different layers, and study the stability of multi-layer ecosystems under different interaction types. We show that competitive interactions within each layer have a more substantial stabilizing effect in multi-layer ecosystems relative to their impact in single-layer ecosystems. Surprisingly, between different layers, we find that competition between species destabilizes the ecosystem. We further provide a theoretical analysis of the stability of multi-layer ecosystems and confirm the robustness of our findings for different connectances between layers, numbers of species in each layer, and numbers of layers. Our work provides a general framework for investigating the stability of multi-layer ecosystems and uncovers the double-sided role of competitive interactions in the stability of multi-layer ecosystems.

Covariation of brain and skull shapes as a model to understand the role of crosstalk in development and evolution

Covariation among discrete phenotypes can arise due to selection for shared functions, and/or shared genetic and developmental underpinnings. The consequences of such phenotypic integration are far-reaching and can act to either facilitate or limit morphological variation. The vertebrate brain is known to act as an "organizer" of craniofacial development, secreting morphogens that can affect the shape of the growing neurocranium, consistent with roles for pleiotropy in brain-neurocranium covariation. Here, we test this hypothesis in cichlid fishes by first examining the degree of shape integration between the brain and the neurocranium using three-dimensional geometric morphometrics in an F₅ hybrid population, and then genetically mapping trait covariation using quantitative trait loci (QTL) analysis. We observe shape associations between the brain and the neurocranium, a pattern that holds even when we assess associations between the brain and constituent parts of the neurocranium: the rostrum and braincase. We also recover robust genetic signals for both hard- and soft-tissue traits and identify a genomic region where QTL for the brain and braincase overlap, implicating a role for pleiotropy in patterning trait covariation. Fine mapping of the overlapping genomic region identifies a candidate gene, notch1a, which is known to be involved in patterning skeletal and neural tissues during development. Taken together, these data offer a genetic hypothesis for brain-neurocranium covariation, as well as a potential mechanism by which behavioral shifts may simultaneously drive rapid change in neuroanatomy and craniofacial morphology.

Temporal networks in biology and medicine: a survey on models, algorithms, and tools

The use of static graphs for modelling and analysis of biological and biomedical data plays a key role in biomedical research. However, many real-world scenarios present dynamic behaviours resulting in both node and edges modification as well as feature evolution. Consequently, ad-hoc models for capturing these evolutions along the time have been introduced, also referred to as dynamic, temporal, time-varying graphs. Here, we focus on temporal graphs, i.e., graphs whose evolution is represented by a sequence of time-ordered snapshots. Each snapshot represents a graph active in a particular timestamp. We survey temporal graph models and related algorithms, presenting fundamentals aspects and the recent advances. We formally define temporal graphs, focusing on the problem setting and we present their main applications in biology and medicine. We also present temporal graph embedding and the application to recent problems such as epidemic modelling. Finally, we further state some promising research directions in the area. Main results of this study include a systematic review of fundamental temporal network problems and their algorithmic solutions considered in the literature, in particular those having application in computational biology and medicine. We also include the main software developed in this context.

Analysis of cattle movement networks in Paraguay: Implications for the spread and control of infectious diseases

Beef exports represent a substantial part of Paraguay's agricultural sector. Cattle movements involve a high risk due to the possible spread of bovine diseases that can have a significant impact on the country's economy. We analyzed cattle movements from 2014 to 2018 using the networks analysis methodology at the holding and district levels at different temporal scales. We built two types of networks to identify network characteristics that may contribute to the spread of two diseases with different epidemiological characteristics: i) a network including all cattle movements to consider the transmission of a disease of rapid spread like foot and mouth disease, and ii) a network including only cow movements to account for bovine brucellosis, a disease of slow spread that occurs mainly in adult females. Network indicators did not vary substantially among the cattle and cow only networks. The holdings/districts included in the largest strongly connected components were distributed throughout the country. Percolation analysis performed at the holding level showed that a large number of holdings should be removed to make the largest strongly connected component disappear. Higher values of the centrality indicators were found for markets than for farms, indicating that they may play an important role in the spread of an infectious disease. At the holding level (but not at the district level), the networks exhibited characteristics of small-world networks. This property may facilitate the spread of foot and mouth disease in case of re-emergence, or of bovine brucellosis in the country through cattle movements. They should be taken into account when implementing surveillance or control measures for these diseases.

Modeling Real-Life Urban Sensor Networks Based on Open Data

Epidemics and pandemics dramatically affect mobility trends around the world, which we have witnessed recently and expect more of in the future. A global energy crisis is looming ahead on the horizon and will redefine the transportation and energy usage patterns, in particular in large cities and metropolitan areas. As the trend continues to expand, the need to efficiently monitor and manage smart city infrastructure, public transportation, service vehicles, and commercial fleets has become of higher importance. This, in turn, requires new methods for dissemination, collection, and processing of data from massive number of already deployed sensing devices. In order to transmit these data efficiently, it is necessary to optimize the connection structure in wireless networks. Emerging open access to real data from different types of networked and sensing devices should be leveraged. It enables construction of models based on frequently updated real data rather than synthetic models or test environments. Hence, the main objective of this article is to introduce the concept of network modeling based on publicly available geographic location data of heterogeneous nodes and to promote the use of real-life diverse open data sources as the basis of novel research related to urban sensor networks. The feasibility of designed modeling architecture is discussed and proved with numerous examples of modeled spatial and spatiotemporal graphs, which are essential in opportunistic routing-related studies using the methods which rely on graph theory. This approach has not been considered before in similar studies and in the literature.

Uncovering the biological basis of control energy: Structural and metabolic correlates of energy inefficiency in temporal lobe epilepsy

Network control theory is increasingly used to profile the brain's energy landscape via simulations of neural dynamics. This approach estimates the control energy required to simulate the activation of brain circuits based on structural connectome measured using diffusion magnetic resonance imaging, thereby quantifying those circuits' energetic efficiency. The biological basis of control energy, however, remains unknown, hampering its further application. To fill this gap, investigating temporal lobe epilepsy as a lesion model, we show that patients require higher control energy to activate the limbic network than healthy volunteers, especially ipsilateral to the seizure focus. The energetic imbalance between ipsilateral and contralateral temporolimbic regions is tracked by asymmetric patterns of glucose metabolism measured using positron emission tomography, which, in turn, may be selectively explained by asymmetric gray matter loss as evidenced in the hippocampus. Our investigation provides the first theoretical framework unifying gray matter integrity, metabolism, and energetic generation of neural dynamics.

Spatial evolution of cooperation with variable payoffs

In the evolution of cooperation, the individuals' payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual's payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner's dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals' normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals' exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.

Effects of time-varying habitat connectivity on metacommunity persistence

Network structure or connectivity patterns are critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure, though most real network structures change in time, forming time-varying networks. This raises the question, in metacommunities, how does the pattern of synchrony vary with temporal evolution in the network structure. The synchronous dynamics among species are known to reduce metacommunity persistence. Here we consider a time-varying metacommunity small-world network consisting of a chaotic three-species food chain oscillator in each patch or node. The rate of change in the network connectivity is determined by the natural frequency or its subharmonics of the constituent oscillator to allow sufficient time for the evolution of species in between successive rewirings. We find that over a range of coupling strengths and rewiring periods, even higher rewiring probabilities drive a network from asynchrony towards synchrony. Moreover, in networks with a small rewiring period, an increase in average degree (more connected networks) pushes the asynchronous dynamics to synchrony. On the other hand, in networks with a low average degree, a higher rewiring period drives the synchronous dynamics to asynchrony resulting in increased species persistence. Our results also follow the calculation of synchronization time and are robust across other ecosystem models. Overall, our study opens the possibility of developing temporal connectivity strategies to increase species persistence in ecological networks.

How zealots affect the energy cost for controlling complex social networks

The controllability of complex networks may be applicable for understanding how to control a complex social network, where members share their opinions and influence one another. Previous works in this area have focused on controllability, energy cost, or optimization under the assumption that all nodes are compliant, passing on information neutrally without any preferences. However, the assumption on nodal neutrality should be reassessed, given that in networked social systems, some people may hold fast to their personal beliefs. By introducing some stubborn agents, or zealots, who hold steadfast to their beliefs and seek to influence others, the control energy is computed and compared against those without zealots. It was found that the presence of zealots alters the energy cost at a quadratic rate with respect to their own fixed beliefs. However, whether or not the zealots' presence increases or decreases the energy cost is affected by the interplay between different parameters such as the zealots' beliefs, number of drivers, final control time regimes, network effects, network dynamics, and number and configurations of neutral nodes influenced by the zealots. For example, when a network dynamics is linear but does not have conformity behavior, it could be possible for a contrarian zealot to assist in reducing control energy. With conformity behavior, a contrarian zealot always negatively affects network control by increasing energy cost. The results of this paper suggest caution when modeling real networked social systems with the controllability of networked linear dynamics since the system dynamical behavior is sensitive to parameter change.

Hidden dependence of spreading vulnerability on topological complexity

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time-commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its "spreading vulnerability," is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the "entropy of temporal entanglement" as a quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological, and engineered systems.

Control theory illustrates the energy efficiency in the dynamic reconfiguration of functional connectivity

The brain’s functional connectivity fluctuates over time instead of remaining steady in a stationary mode even during the resting state. This fluctuation establishes the dynamical functional connectivity that transitions in a non-random order between multiple modes. Yet it remains unexplored how the transition facilitates the entire brain network as a dynamical system and what utility this mechanism for dynamic reconfiguration can bring over the widely used graph theoretical measurements. To address these questions, we propose to conduct an energetic analysis of functional brain networks using resting-state fMRI and behavioral measurements from the Human Connectome Project. Through comparing the state transition energy under distinct adjacent matrices, we justify that dynamic functional connectivity leads to 60% less energy cost to support the resting state dynamics than static connectivity when driving the transition through default mode network. Moreover, we demonstrate that combining graph theoretical measurements and our energy-based control measurements as the feature vector can provide complementary prediction power for the behavioral scores (Combination vs. Control: t = 9.41, p = 1.64e−13; Combination vs. Graph: t = 4.92, p = 3.81e−6). Our approach integrates statistical inference and dynamical system inspection towards understanding brain networks.

A framework that allows for the statistical investigation of the dynamic aspect of functional connectivity derived from resting-state fMRI is developed that is shown to complementarily predict individual differences in behavioral measurements compared to existing approaches.

Quantifying agent impacts on contact sequences in social interactions

Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of interactions—since the topology of the network, containing who is in contact with whom, when, for how long, and in which precise sequence, varies (rapidly) in time—analyzing them requires developing network methods and metrics that respect temporal variability, in contrast to those developed for static (i.e., time-invariant) networks. Here, by means of event mapping, we propose a method to quantify how quickly agents mingle by transforming temporal network data of agent contacts. We define a novel measure called contact sequence centrality, which quantifies the impact of an individual on the contact sequences, reflecting the individual’s behavioral potential for spreading. Comparing contact sequence centrality across agents allows for ranking the impact of agents and identifying potential ‘behavioral super-spreaders’. The method is applied to social interaction data collected at an art fair in Amsterdam. We relate the measure to the existing network metrics, both temporal and static, and find that (mostly at longer time scales) traditional metrics lose their resemblance to contact sequence centrality. Our work highlights the importance of accounting for the sequential nature of contacts when analyzing social interactions.

Temporal exponential random graph models of longitudinal brain networks after stroke

Plasticity after stroke is a complex phenomenon. Functional reorganization occurs not only in the perilesional tissue but throughout the brain. However, the local connection mechanisms generating such global network changes remain largely unknown. To address this question, time must be considered as a formal variable of the problem rather than a simple repeated observation. Here, we hypothesized that the presence of temporal connection motifs, such as the formation of temporal triangles (T) and edges (E) over time, would explain large-scale brain reorganization after stroke. To test our hypothesis, we adopted a statistical framework based on temporal exponential random graph models (tERGMs), where the aforementioned temporal motifs were implemented as parameters and adapted to capture global network changes after stroke. We first validated the performance on synthetic time-varying networks as compared to standard static approaches. Then, using real functional brain networks, we showed that estimates of tERGM parameters were sufficient to reproduce brain network changes from 2 weeks to 1 year after stroke. These temporal connection signatures, reflecting within-hemisphere segregation (T) and between hemisphere integration (E), were associated with patients' future behaviour. In particular, interhemispheric temporal edges significantly correlated with the chronic language and visual outcome in subcortical and cortical stroke, respectively. Our results indicate the importance of time-varying connection properties when modelling dynamic complex systems and provide fresh insights into modelling of brain network mechanisms after stroke.

Coordination and equilibrium selection in games: the role of local effects

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in two-player coordination games. We investigate three update rules - the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). For the pure coordination game with two equivalent strategies we find a transition from a disordered state to coordination for a critical value of connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU it is system-size-dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

Network rewiring and plasticity promotes synchronization of suprachiasmatic nucleus neurons

In mammals, circadian rhythms throughout the body are orchestrated by the master clock in the hypothalamic suprachiasmatic nucleus (SCN), where SCN neurons are coupled with neurotransmitters to generate a uniform circadian rhythm. How the SCN circadian rhythm is so robust and flexible is, however, unclear. In this paper, we propose a temporal SCN network model and investigate the effects of dynamical rewiring and flexible coupling due to synaptic plasticity on the synchronization of the neural network in SCN. In networks consisting of simple Poincaré oscillators and complex circadian clocks, we found that dynamical rewiring and coupling plasticity enhance the synchronization in inhomogeneous networks. We verified the effect of enhanced synchronization in different architectures of random, scale-free, and small-world networks. A simple mean-field analysis for synchronization in plastic networks is proposed. Intuitively, the synchronization is greatly enhanced because both the random rewiring and coupling plasticity in the heterogeneous network have effectively increased the coupling strength in the whole network. Our results suggest that a proper network model for the master SCN circadian rhythm needs to take into account the effects of dynamical changes in topology and plasticity in neuron interactions that could help the brain to generate a robust circadian rhythm for the whole body.

Temporal Graphs and Temporal Network Characteristics for Bio-Inspired Networks during Optimization

Temporal network analysis and time evolution of network characteristics are powerful tools in describing the changing topology of dynamic networks. This paper uses such approaches to better visualize and provide analytical measures for the changes in performance that we observed in Voronoi-type spatial coverage, particularly for the example of time-evolving networks with a changing number of wireless sensors being deployed. Specifically, our analysis focuses on the role different combinations of impenetrable obstacles and environmental noise play in connectivity and overall network structure. It is shown how the use of (i) temporal network graphs, and (ii) network centrality and regularity measures illustrate the differences between various options developed for the balancing act of energy and time efficiency in network coverage. Last, we compare the outcome of these measures with the less abstract classification variables, such as percent area covered and cumulative distance traveled.

Altered temporal reachability highlights the role of sensory perception systems in major depressive disorder

BACKGROUND

The latest studies have considered the time-dependent structures in dynamic brain networks. However, the effect of periphery structures on the temporal flow of information remains unexplored in patients with major depressive disorder (MDD). In this work, we aimed to explore the pattern of interactions between brain regions in MDD across space and time.

METHODS

We concentrated on the temporal reachability of nodes in temporal brain networks derived from the resting-state functional magnetic resonance imaging (rs-fMRI) of 55 MDD patients and 62 sex-, age-matched healthy controls. Specifically, temporal connectedness and temporal efficiency (TEF) were estimated based on the length of temporal paths between node pairs. Subsequently, the temporal clustering coefficient (TCC) and temporal distance were jointly employed to explore the patterns in which a node's periphery structure affects its reachability.

RESULTS

Significantly higher TEF and lower TCC were found in temporal brain networks in MDD. Besides, significant between-group differences of nodal TCC were detected in regions of sensory perception systems. Considering the temporal paths that begin or end at these regions, MDD patients showed several altered temporal distances.

CONCLUSION

Our results showed that the temporal reachability of specific brain regions in MDD could be affected as their periphery structures evolve, which may explain the dysfunction of sensory perception systems in the spatiotemporal domain.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Pathologically reduced neural flexibility recovers during psychotherapy of OCD patients

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Psychiatric impairment is associated with decreased neural flexibility.

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Psychotherapy was able to increase the neural flexibility of the patients.

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Psychotherapy should increase adaptivity of cognitive-emotional-behavioral patterns.

Flexibility is a key feature of psychological health, allowing the individual to dynamically adapt to changing environmental demands, which is impaired in many psychiatric disorders like obsessive–compulsive disorder (OCD). Adequately responding to varying demands requires the brain to switch between different patterns of neural activity, which are represented by different brain network configurations (functional connectivity patterns). Here, we operationalize neural flexibility as the dissimilarity between consecutive connectivity matrices of brain regions (jump length). In total, 132 fMRI scans were obtained from 17 patients that were scanned four to five times during inpatient psychotherapy, and from 17 controls that were scanned at comparable time intervals. Significant negative correlations were found between the jump lengths and the symptom severity scores of OCD, depression, anxiety, and stress, suggesting that high symptom severity corresponds to inflexible brain functioning. Further analyses revealed that impaired reconfiguration (pattern stability) of the brain seems to be more related to general psychiatric impairment rather than to specific symptoms, e.g., of OCD or depression. Importantly, the group × time interaction of a repeated measures ANOVA was significant, as well as the post-hoc paired t-tests of the patients (first vs. last scan). The results suggest that psychotherapy is able to significantly increase the neural flexibility of patients. We conclude that psychiatric symptoms like anxiety, stress, depression, and OCD are associated with an impaired adaptivity of the brain. In general, our results add to the growing evidence that dynamic functional connectivity captures meaningful properties of brain functioning.

Network control principles for identifying personalized driver genes in cancer

To understand tumor heterogeneity in cancer, personalized driver genes (PDGs) need to be identified for unraveling the genotype-phenotype associations corresponding to particular patients. However, most of the existing driver-focus methods mainly pay attention on the cohort information rather than on individual information. Recent developing computational approaches based on network control principles are opening a new way to discover driver genes in cancer, particularly at an individual level. To provide comprehensive perspectives of network control methods on this timely topic, we first considered the cancer progression as a network control problem, in which the expected PDGs are altered genes by oncogene activation signals that can change the individual molecular network from one health state to the other disease state. Then, we reviewed the network reconstruction methods on single samples and introduced novel network control methods on single-sample networks to identify PDGs in cancer. Particularly, we gave a performance assessment of the network structure control-based PDGs identification methods on multiple cancer datasets from TCGA, for which the data and evaluation package also are publicly available. Finally, we discussed future directions for the application of network control methods to identify PDGs in cancer and diverse biological processes.

Energy cost study for controlling complex social networks with conformity behavior

To understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time linear dynamics. However, continuous-time linear dynamics is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modeling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, the energy costs needed for controlling systems with and without conformity are compared, and it was found that controlling networked systems with conformity features always requires less control energy. Finally, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since the conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward toward developing realistic control of complex social systems.

Fuzzy protein theory for disordered proteins

Why proteins are fuzzy? Constant adaptation to the cellular environment requires a wide range of changes in protein structure and interactions. Conformational ensembles of disordered proteins in particular exhibit large shifts to activate or inhibit alternative pathways. Fuzziness is critical for liquid–liquid phase separation and conversion of biomolecular condensates into fibrils. Interpretation of these phenomena presents a challenge for the classical structure-function paradigm. Here I discuss a multi-valued formalism, based on fuzzy logic, which can be applied to describe complex cellular behavior of proteins.

Designing temporal networks that synchronize under resource constraints

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget available in a network to facilitate interaction and communication. Here, we show that introducing temporal variation in the network structure can lead to efficient synchronization even when stable synchrony is impossible in any static network under the given budget, thereby demonstrating a fundamental advantage of temporal networks. The temporal networks generated by our open-loop design are versatile in the sense of promoting synchronization for systems with vastly different dynamics, including periodic and chaotic dynamics in both discrete-time and continuous-time models. Furthermore, we link the dynamic stabilization effect of the changing topology to the curvature of the master stability function, which provides analytical insights into synchronization on temporal networks in general. In particular, our results shed light on the effect of network switching rate and explain why certain temporal networks synchronize only for intermediate switching rate.

The ability of complex networks to synchronize themselves is limited by available coupling resources. Zhang and Strogatz show that allowing temporal variation in the network structure can lead to synchronization even when stable synchrony is impossible in any static network under the fixed budget.

Dynamic hidden-variable network models

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The dynamics is controlled by two parameters: one that tunes the rate of change of hidden variables and another that tunes the rate at which node pairs reevaluate their connections given the current values of hidden variables. Snapshots of networks in the dynamic models are equivalent to networks generated by the static models only if the link reevaluation rate is sufficiently larger than the rate of hidden-variable dynamics or if an additional mechanism is added whereby links actively respond to changes in hidden variables. Otherwise, links are out of equilibrium with respect to hidden variables and network snapshots exhibit structural deviations from the static models. We examine the level of structural persistence in the considered models and quantify deviations from staticlike behavior. We explore temporal versions of popular static models with community structure, latent geometry, and degree heterogeneity. While we do not attempt to directly model real networks, we comment on interesting qualitative resemblances to real systems. In particular, we speculate that links in some real networks are out of equilibrium with respect to hidden variables, partially explaining the presence of long-ranged links in geometrically embedded systems and intergroup connectivity in modular systems. We also discuss possible extensions, generalizations, and applications of the introduced class of dynamic network models.

Heuristic assessment of choices for risk network control

Data-driven risk networks describe many complex system dynamics arising in fields such as epidemiology and ecology. They lack explicit dynamics and have multiple sources of cost, both of which are beyond the current scope of traditional control theory. We construct the global economy risk network by combining the consensus of experts from the World Economic Forum with risk activation data to define its topology and interactions. Many of these risks, including extreme weather and drastic inflation, pose significant economic costs when active. We introduce a method for converting network interaction data into continuous dynamics to which we apply optimal control. We contribute the first method for constructing and controlling risk network dynamics based on empirically collected data. We simulate applying this method to control the spread of COVID-19 and show that the choice of risks through which the network is controlled has significant influence on both the cost of control and the total cost of keeping network stable. We additionally describe a heuristic for choosing the risks trough which the network is controlled, given a general risk network.

Temporal network embedding using graph attention network

Graph convolutional network (GCN) has made remarkable progress in learning good representations from graph-structured data. The layer-wise propagation rule of conventional GCN is designed in such a way that the feature aggregation at each node depends on the features of the one-hop neighbouring nodes. Adding an attention layer over the GCN can allow the network to provide different importance within various one-hop neighbours. These methods can capture the properties of static network, but is not well suited to capture the temporal patterns in time-varying networks. In this work, we propose a temporal graph attention network (TempGAN), where the aim is to learn representations from continuous-time temporal network by preserving the temporal proximity between nodes of the network. First, we perform a temporal walk over the network to generate a positive pointwise mutual information matrix (PPMI) which denote the temporal correlation between the nodes. Furthermore, we design a TempGAN architecture which uses both adjacency and PPMI information to generate node embeddings from temporal network. Finally, we conduct link prediction experiments by designing a TempGAN autoencoder to evaluate the quality of the embedding generated, and the results are compared with other state-of-the-art methods.

The inherent uncertainty of temporal networks is a true challenge for control

Recently, it has been suggested that network temporality can be exploited to substantially reduce the energy required to control complex networks. This somewhat counterintuitive finding was explained through an evocative example of the advantage of temporal networks: when navigating a sailboat, we raise the sails when the wind helps us while lowering them when it works against us. Unfortunately, controlling complex networks inherits a further analogy with navigating a sailboat: having to face the inherent uncertainty of future winds. We rarely, if ever, have deterministic knowledge of the evolution of the network we want to control. Here, our challenge is to exploit the potential advantages of temporality when only a probabilistic description of the future is available. We prove that, in this more realistic setting, exploiting temporality is no more a panacea for network control, but rather an asset of a wider toolbox made available by the scientific community. One that can indeed turn out useful, provided that the temporality of the network structure matches the intrinsic time scales of the nodes we want to control.

A theory of pattern formation for reaction–diffusion systems on temporal networks

Networks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over time. One area of active interest is pattern formation from reaction–diffusion systems, which themselves evolve over temporal networks. We derive analytical conditions for the onset of diffusive spatial and spatio-temporal pattern formation on undirected temporal networks through the Turing and Benjamin–Feir mechanisms, with the resulting pattern selection process depending strongly on the evolution of both global diffusion rates and the local structure of the underlying network. Both instability criteria are then extended to the case where the reaction–diffusion system is non-autonomous, which allows us to study pattern formation from time-varying base states. The theory we present is illustrated through a variety of numerical simulations which highlight the role of the time evolution of network topology, diffusion mechanisms and non-autonomous reaction kinetics on pattern formation or suppression. A fundamental finding is that Turing and Benjamin–Feir instabilities are generically transient rather than eternal, with dynamics on temporal networks able to transition between distinct patterns or spatio-temporal states. One may exploit this feature to generate new patterns, or even suppress undesirable patterns, over a given time interval.

Spreader events and the limitations of projected networks for capturing dynamics on multipartite networks

Many systems of scientific interest can be conceptualized as multipartite networks. Examples include the spread of sexually transmitted infections, scientific collaborations, human friendships, product recommendation systems, and metabolic networks. In practice, these systems are often studied after projection onto a single class of nodes, losing crucial information. Here, we address a significant knowledge gap by comparing transmission dynamics on temporal multipartite networks and on their time-aggregated unipartite projections to determine the impact of the lost information on our ability to predict the systems' dynamics. We show that the dynamics of transmission models can be dramatically dissimilar on multipartite networks and on their projections at three levels: final outcome, the magnitude of the variability from realization to realization, and overall shape of the temporal trajectory. We find that the ratio of the number of nodes to the number of active edges over the time-aggregation scale determines the ability of projected networks to capture the dynamics on the multipartite network. Finally, we explore which properties of a multipartite network are crucial in generating synthetic networks that better reproduce the dynamical behavior observed in real multipartite networks.

Dynamic spatio-temporal patterns of metapopulation occupancy in patchy habitats

Spatio-temporal dynamics in habitat suitability and connectivity among mosaics of heterogeneous wetlands are critical for biological diversity and species persistence in aquatic patchy landscapes. Despite the recognized importance of stochastic hydroclimatic forcing in driving wetlandscape hydrological dynamics, linking such effects to emergent dynamics of metapopulation poses significant challenges. To fill this gap, we propose here a dynamic stochastic patch occupancy model (SPOM), which links parsimonious hydrological and ecological models to simulate spatio-temporal patterns in species occupancy in wetlandscapes. Our work aims to place ecological studies of patchy habitats into a proper hydrologic and climatic framework to improve the knowledge about metapopulation shifts in response to climate-driven changes in wetlandscapes. We applied the dynamic version of the SPOM (D-SPOM) framework in two wetlandscapes in the US with contrasting landscape and climate properties. Our results illustrate that explicit consideration of the temporal dimension proposed in the D-SPOM is important to interpret local- and landscape-scale patterns of habitat suitability and metapopulation occupancy. Our analyses show that spatio-temporal dynamics of patch suitability and accessibility, driven by the stochasticity in hydroclimatic forcing, influence metapopulation occupancy and the topological metrics of the emergent wetlandscape dispersal network. D-SPOM simulations also reveal that the extinction risk in dynamic wetlandscapes is exacerbated by extended dry periods when suitable habitat decreases, hence limiting successful patch colonization and exacerbating metapopulation extinction risks. The proposed framework is not restricted only to wetland studies but could also be applied to examine metapopulation dynamics in other types of patchy habitats subjected to stochastic external disturbances.

Modeling epidemic spreading through public transit using time-varying encounter network

Passenger contact in public transit (PT) networks can be a key mediate in the spreading of infectious diseases. This paper proposes a time-varying weighted PT encounter network to model the spreading of infectious diseases through the PT systems. Social activity contacts at both local and global levels are also considered. We select the epidemiological characteristics of coronavirus disease 2019 (COVID-19) as a case study along with smart card data from Singapore to illustrate the model at the metropolitan level. A scalable and lightweight theoretical framework is derived to capture the time-varying and heterogeneous network structures, which enables to solve the problem at the whole population level with low computational costs. Different control policies from both the public health side and the transportation side are evaluated. We find that people's preventative behavior is one of the most effective measures to control the spreading of epidemics. From the transportation side, partial closure of bus routes helps to slow down but cannot fully contain the spreading of epidemics. Identifying "influential passengers" using the smart card data and isolating them at an early stage can also effectively reduce the epidemic spreading.

Dynamic Functional Connectivity as a complex random walk: Definitions and the dFCwalk toolbox

•We have developed a framework to describe the dynamics of Functional Connectivity (dFC) estimated from brain activity time-series as a complex random walk in the space of possible functional networks. This conceptual and methodological framework considers dFC as a smooth reconfiguration process, combining "liquid" and "coordinated" aspects. Unlike other previous approaches, our method does not require the explicit extraction of discrete connectivity states.•In our previous work, we introduced several metrics for the quantitative characterization of the dFC random walk. First, dFC speed analyses extract the distribution of the time-resolved rate of reconfiguration of FC along time. These distributions have a clear peak (typical dFC speed, that can already serve as a biomarker) and fat tails (denoting deviations from Gaussianity that can be detected by suitable scaling analyses of FC network streams). Second, meta-connectivity (MC) analyses identify groups of functional links whose fluctuations co-vary in time and that define veritable dFC modules organized along specific dFC meta-hub controllers (differing from conventional FC modules and hubs). The decomposition of whole-brain dFC by MC allows performing dFC speed analyses separately for each of the detected dFC modules.•We present here blocks and pipelines for dFC random walk analyses that are made easily available through a dedicated MATLABⓇ toolbox (dFCwalk), openly downloadable. Although we applied such analyses mostly to fMRI resting state data, in principle our methods can be extended to any type of neural activity (from Local Field Potentials to EEG, MEG, fNIRS, etc.) or even non-neural time-series.

An Advanced Deep Generative Framework for Temporal Link Prediction in Dynamic Networks

Temporal link prediction in dynamic networks has attracted increasing attention recently due to its valuable real-world applications. The primary challenge of temporal link prediction is to capture the spatial-temporal patterns and high nonlinearity of dynamic networks. Inspired by the success of image generation, we convert the dynamic network into a sequence of static images and formulate the temporal link prediction as a conditional image generation problem. We propose a novel deep generative framework, called NetworkGAN, to tackle the challenging temporal link prediction task efficiently, which simultaneously models the spatial and temporal features in the dynamic networks via deep learning techniques. The proposed NetworkGAN inherits the advantages of the graph convolutional network (GCN), the temporal matrix factorization (TMF), the long short-term memory network (LSTM), and the generative adversarial network (GAN). Specifically, an attentive GCN is first designed to automatically learn the spatial features of dynamic networks. Second, we propose a TMF enhanced attentive LSTM (TMF-LSTM) to capture the temporal dependencies and evolutionary patterns of dynamic networks, which predicts the network snapshot at next timestamp based on the network snapshots observed at previous timestamps. Furthermore, we employ a GAN framework to further refine the performance of temporal link prediction by using a discriminative model to guide the training of the deep generative model (i.e., TMF-LSTM) in an adversarial process. To verify the effectiveness of the proposed model, we conduct extensive experiments on five real-world datasets. Experimental results demonstrate the significant advantages of NetworkGAN compared to other strong competitors.