Nucleation phenomena and extreme vulnerability of spatial k-core systems.

K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially embedded. Here, we study k-core percolation on two-dimensional spatially embedded networks and show that, in contrast to regular percolation, the length of connections can control the transition type, leading to four different types of phase transitions associated with interesting phenomena and a rich phase diagram. A key finding is the existence of a metastable phase where microscopic localized damage, independent of system size, can cause a macroscopic phase transition, a result which cannot be achieved in traditional percolation. In this case, local failures spontaneously propagate the damage radially until the system collapses, a phenomenon analogous to the nucleation process.

Motif-based community detection in heterogeneous multilayer networks.

Multilayer networks composed of intralayer edges and interlayer edges are an important type of complex networks. Considering the heterogeneity of nodes and edges, it is necessary to design more reasonable and diverse community detection methods for multilayer networks. Existing research on community detection in multilayer networks mainly focuses on multiplexing networks (where the nodes are homogeneous and the edges are heterogeneous), but few studies have focused on heterogeneous multilayer networks where both nodes and edges represent different semantics. In this paper, we studied community detection on heterogeneous multilayer networks and proposed a motif-based detection algorithm. First, the communities and motifs of multilayer networks are defined, especially the interlayer motifs. Then, the modularity of multilayer networks based on these motifs is designed, and the community structure of the multilayer network is detected by maximizing the modularity of multilayer networks. Finally, we verify the effectiveness of the detection algorithm on synthetic networks. In the experiments on synthetic networks, comparing with the classical community detection algorithms (without considering interlayer heterogeneity), the motif-based modularity community detection algorithm can obtain better results under different evaluation indexes, and we found that there exists a certain relationship between motifs and communities. In addition, the proposed algorithm is applied in the empirical network, which shows its practicability in the real world. This study provides a solution for the investigation of heterogeneous information in multilayer networks.

Temporal segmentation of EEG based on functional connectivity network structure.

In the study of brain functional connectivity networks, it is assumed that a network is built from a data window in which activity is stationary. However, brain activity is non-stationary over sufficiently large time periods. Addressing the analysis electroencephalograph (EEG) data, we propose a data segmentation method based on functional connectivity network structure. The goal of segmentation is to ensure that within a window of analysis, there is similar network structure. We designed an intuitive and flexible graph distance measure to quantify the difference in network structure between two analysis windows. This measure is modular: a variety of node importance indices can be plugged into it. We use a reference window versus sliding window comparison approach to detect changes, as indicated by outliers in the distribution of graph distance values. Performance of our segmentation method was tested in simulated EEG data and real EEG data from a drone piloting experiment (using correlation or phase-locking value as the functional connectivity strength metric). We compared our method under various node importance measures and against matrix-based dissimilarity metrics that use singular value decomposition on the connectivity matrix. The results show the graph distance approach worked better than matrix-based approaches; graph distance based on partial node centrality was most sensitive to network structural changes, especially when connectivity matrix values change little. The proposed method provides EEG data segmentation tailored for detecting changes in terms of functional connectivity networks. Our study provides a new perspective on EEG segmentation, one that is based on functional connectivity network structure differences.

Rigorous Criteria for the Collapse of Nonlinear Cooperative Networks.

Many real-world complex systems, when hitting a tipping point, undergo irreversible sudden shifts that can eventually take a great toll on humanity and the natural world, such as ecosystem collapses, disease outbreaks, etc. Previous work has adopted approximations to predict the tipping points, but due to the nature of nonlinearity, this may lead to unexpected errors in predicting real-world systems. Here we obtain the rigorous bounds of the tipping points for general nonlinear cooperative networks. Our results offer two rigorous criteria that determine the collapse and survival of such a system. These two criteria are decided by the combined effect of dynamical parameters and interaction topology.

Long-range connections are crucial for synchronization transition in a computational model of Drosophila brain dynamics.

The synchronization transition type has been the focus of attention in recent years because it is associated with many functional characteristics of the brain. In this paper, the synchronization transition in neural networks with sleep-related biological drives in Drosophila is investigated. An electrical synaptic neural network is established to research the difference between the synchronization transition of the network during sleep and wake, in which neurons regularly spike during sleep and chaotically spike during wake. The synchronization transition curves are calculated mainly using the global instantaneous order parameters S. The underlying mechanisms and types of synchronization transition during sleep are different from those during wake. During sleep, regardless of the network structure, a frustrated (discontinuous) transition can be observed. Moreover, the phenomenon of quasi periodic partial synchronization is observed in ring-shaped regular network with and without random long-range connections. As the network becomes dense, the synchronization of the network only needs to slightly increase the coupling strength g. While during wake, the synchronization transition of the neural network is very dependent on the network structure, and three mechanisms of synchronization transition have emerged: discontinuous synchronization (explosive synchronization and frustrated synchronization), and continuous synchronization. The random long-range connections is the main topological factor that plays an important role in the resulting synchronization transition. Furthermore, similarities and differences are found by comparing synchronization transition research for the Hodgkin-Huxley neural network in the beta-band and gammma-band, which can further improve the synchronization phase transition research of biologically motivated neural networks. A complete research framework can also be used to study coupled nervous systems, which can be extended to general coupled dynamic systems.

Target recovery of the economic system based on the target reinforcement path method.

An effective and stable operation of an economic system leads to a prosperous society and sustainable world development. Unfortunately, the system faces inevitable perturbations of extreme events and is frequently damaged. To maintain the system's stability, recovering its damaged functionality is essential and is complementary to strengthening its resilience and forecasting extreme events. This paper proposes a target recovery method based on network and economic equilibrium theories to defend the economic system against perturbations characterized as localized attacks. This novel method stimulates a set of economic sectors that mutually reinforce damaged economic sectors and is intuitively named the target reinforcement path (TRP) method. Developing a nonlinear dynamic model that simulates the economic system's operation after being perturbed by a localized attack and recovering based on a target recovery method, we compute the relaxation time for this process to quantify the method's efficiency. Furthermore, we adopt a rank aggregation method to comprehensively measure the method's efficiency by studying the target recovery of three country-level economic systems (China, India, and Japan) for 73 different regional attack scenarios. Through a comparative analysis of the TRP method and three other classic methods, the TRP method is shown to be more effective and less costly. Applicatively, the proposed method exhibits the potential to recover other vital complex systems with spontaneous recovery ability, such as immune, neurological, and ecological systems.

Modeling multi-opinion propagation in complex systems with heterogeneous relationships via Potts model on signed networks.

This paper investigates how the heterogenous relationships around us affect the spread of diverse opinions in the population. We apply the Potts model, derived from condensed matter physics on signed networks, to multi-opinion propagation in complex systems with logically contradictory interactions. Signed networks have received increasing attention due to their ability to portray both positive and negative associations simultaneously, while the Potts model depicts the coevolution of multiple states affected by interactions. Analyses and experiments on both synthetic and real signed networks reveal the impact of the topology structure on the emergence of consensus and the evolution of balance in a system. We find that, regardless of the initial opinion distribution, the proportion and location of negative edges in the signed network determine whether a consensus can be formed. The effect of topology on the critical ratio of negative edges reflects two distinct phenomena: consensus and the multiparty situation. Surprisingly, adding a small number of negative edges leads to a sharp breakdown in consensus under certain circumstances. The community structure contributes to the common view within camps and the confrontation (or alliance) between camps. The importance of inter- or intra-community negative relationships varies depending on the diversity of opinions. The results also show that the dynamic process causes an increase in network structural balance and the emergence of dominant high-order structures. Our findings demonstrate the strong effects of logically contradictory interactions on collective behaviors, and could help control multi-opinion propagation and enhance the system balance.

Impactful scientists have higher tendency to involve collaborators in new topics.

In scientific research, collaboration is one of the most effective ways to take advantage of new ideas, skills, and resources and for performing interdisciplinary research. Although collaboration networks have been intensively studied, the question of how individual scientists choose collaborators to study a new research topic remains almost unexplored. Here, we investigate the statistics and mechanisms of collaborations of individual scientists along their careers, revealing that, in general, collaborators are involved in significantly fewer topics than expected from a controlled surrogate. In particular, we find that highly productive scientists tend to have a higher fraction of single-topic collaborators, while highly cited-i.e., impactful-scientists have a higher fraction of multitopic collaborators. We also suggest a plausible mechanism for this distinction. Moreover, we investigate the cases where scientists involve existing collaborators in a new topic. We find that, compared to productive scientists, impactful scientists show strong preference of collaboration with high-impact scientists on a new topic. Finally, we validate our findings by investigating active scientists in different years and across different disciplines.

Ladderpath Approach: How Tinkering and Reuse Increase Complexity and Information.

The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory and exobiology. Many measures of these quantities are either difficult to compute, rely on the statistical notion of information, or can only be applied to strings. Based on assembly theory, we propose the notion of a ladderpath, which describes how an object can be decomposed into hierarchical structures using repetitive elements. From the ladderpath, two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origin of life. The ladderpath approach provides an alternative characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

Classifying Drosophila olfactory projection neuron boutons by quantitative analysis of electron microscopic reconstruction.

In Drosophila melanogaster, olfactory projection neurons (PNs) convey odor information from the antenna lobe to higher brain regions. Recent transcriptomic studies reveal a large diversity of transcription factors, cell-surface molecules, neurotransmitter-coding, and neuropeptide-coding genes in PNs; however, their structural diversity remains unknown. Herein, we achieved a volumetric reconstruction of 89 PN boutons under Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) and quantitatively analyzed the internal presynaptic active zones (PAZs) and dense-core vesicles (DCVs). The ultrastructure-based cluster analysis reveals three morphological distinct bouton subtypes: complex boutons, unilobed boutons, and simple boutons. The complex boutons contain the most PAZs and DCVs, which suggests that they are of the highest capability of releasing neurotransmitters and neuromodulators. By labeling a subset of boutons under FIB-SEM, we found that DCVs are preferentially distributed in certain GH146-positive subtypes. Our study demonstrates that PN boutons display distinct morphology, which may determine their capacity of releasing neurotransmitters and neuromodulators.

Dynamical analysis of evolutionary public goods game on signed networks.

In evolutionary dynamics, the population structure and multiplayer interactions significantly impact the evolution of cooperation levels. Previous works mainly focus on the theoretical analysis of multiplayer games on regular networks or pairwise games on complex networks. Combining these two factors, complex networks and multiplayer games, we obtain the fixation probability and fixation time of the evolutionary public goods game in a structured population represented by a signed network. We devise a stochastic framework for estimating fixation probability with weak mistrust or strong mistrust mechanisms and develop a deterministic replicator equation to predict the expected density of cooperators when the system evolves to the equilibrium on a signed network. Specifically, the most interesting result is that negative edges diversify the cooperation steady state, evolving in three different patterns of fixed probability in Erdös-Rényi signed and Watts-Strogatz signed networks with the new "strong mistrust" mechanism.

Epidemic spreading with migration in networked metapopulation.

Migration plays a crucial role in epidemic spreading, and its dynamic can be studied by metapopulation model. Instead of the uniform mixing hypothesis, we adopt networked metapopulation to build the model of the epidemic spreading and the individuals' migration. In these populations, individuals are connected by contact network and populations are coupled by individuals migration. With the network mean-field and the gravity law of migration, we establish the N-seat intertwined SIR model and obtain its basic reproduction number ℛ 0 . Meanwhile, we devise a non-markov Node-Search algorithm for model statistical simulations. Through the static network migration ansatz and ℛ 0 formula, we discover that migration will not directly increase the epidemic replication capacity. But when ℛ 0 > 1 , the migration will make the susceptive population evolve from metastable state (disease-free equilibrium) to stable state (endemic equilibrium), and then increase the influence area of epidemic. Re-evoluting the epidemic outbreak in Wuhan, top 94 cities empirical data validate the above mechanism. In addition, we estimate that the positive anti-epidemic measures taken by the Chinese government may have reduced 4 million cases at least during the first wave of COVID-19, which means those measures, such as the epidemiological investigation, nucleic acid detection in medium-high risk areas and isolation of confirmed cases, also play a significant role in preventing epidemic spreading after travel restriction between cities.

Guiding propagation to localized target nodes in complex networks.

Spreading is an important type of dynamics in complex networks that can be used to model numerous real processes such as epidemic contagion and information propagation. In the literature, there are many methods in vital node identification and node immunization proposed for controlling the spreading processes. As a novel research problem, target spreading aims to minimize or maximize propagation toward a group of target nodes. In this paper, we consider a situation where the initial spreader emerges randomly in the network and one has to guide the propagation toward localized targets in the network. To this end, we propose a guided propagation and a reversed guided propagation model, which adaptively guides the spreading process by allocating the limited number of recovery nodes in each spreading step. We study in detail the impact of infection rate and recovery rate on the model. Simulation results show the validity of our models in most cases. Finally, we find that this adaptive target spreading can be achieved under situations with multiple groups of target nodes.

Collective Dynamics of Neural Networks With Sleep-Related Biological Drives in Drosophila.

The collective electrophysiological dynamics of the brain as a result of sleep-related biological drives in Drosophila are investigated in this paper. Based on the Huber-Braun thermoreceptor model, the conductance-based neurons model is extended to a coupled neural network to analyze the local field potential (LFP). The LFP is calculated by using two different metrics: the mean value and the distance-dependent LFP. The distribution of neurons around the electrodes is assumed to have a circular or grid distribution on a two-dimensional plane. Regardless of which method is used, qualitatively similar results are obtained that are roughly consistent with the experimental data. During wake, the LFP has an irregular or a regular spike. However, the LFP becomes regular bursting during sleep. To further analyze the results, wavelet analysis and raster plots are used to examine how the LFP frequencies changed. The synchronization of neurons under different network structures is also studied. The results demonstrate that there are obvious oscillations at approximately 8 Hz during sleep that are absent during wake. Different time series of the LFP can be obtained under different network structures and the density of the network will also affect the magnitude of the potential. As the number of coupled neurons increases, the neural network becomes easier to synchronize, but the sleep and wake time described by the LFP spectrogram do not change. Moreover, the parameters that affect the durations of sleep and wake are analyzed.

Fresh teams are associated with original and multidisciplinary research.

Teamwork is one of the most prominent features in modern science. It is now well understood that team size is an important factor that affects the creativity of the team. However, the crucial question of how the character of research studies is related to the freshness of a team remains unclear. Here, we quantify the team freshness according to the absence of prior collaboration among team members. Our results suggest that papers produced by fresher teams are associated with greater originality and a greater multidisciplinary impact. These effects are even stronger in larger teams. Furthermore, we find that freshness defined by new team members in a paper is a more effective indicator of research originality and multidisciplinarity compared with freshness defined by new collaboration relationships among team members. Finally, we show that the career freshness of team members is also positively correlated with the originality and multidisciplinarity of produced papers.

Characterizing dissimilarity of weighted networks.

Measuring the dissimilarities between networks is a basic problem and wildly used in many fields. Based on method of the D-measure which is suggested for unweighted networks, we propose a quantitative dissimilarity metric of weighted network (WD-metric). Crucially, we construct a distance probability matrix of weighted network, which can capture the comprehensive information of weighted network. Moreover, we define the complementary graph and alpha centrality of weighted network. Correspondingly, several synthetic and real-world networks are used to verify the effectiveness of the WD-metric. Experimental results show that WD-metric can effectively capture the influence of weight on the network structure and quantitatively measure the dissimilarity of weighted networks. It can also be used as a criterion for backbone extraction algorithms of complex network.

Interhemispheric Relationship of Genetic Influence on Human Brain Connectivity.

To understand the origins of interhemispheric differences and commonalities/coupling in human brain wiring, it is crucial to determine how homologous interregional connectivities of the left and right hemispheres are genetically determined and related. To address this, in the present study, we analyzed human twin and pedigree samples with high-quality diffusion magnetic resonance imaging tractography and estimated the heritability and genetic correlation of homologous left and right white matter (WM) connections. The results showed that the heritability of WM connectivity was similar and coupled between the 2 hemispheres and that the degree of overlap in genetic factors underlying homologous WM connectivity (i.e., interhemispheric genetic correlation) varied substantially across the human brain: from complete overlap to complete nonoverlap. Particularly, the heritability was significantly stronger and the chance of interhemispheric complete overlap in genetic factors was higher in subcortical WM connections than in cortical WM connections. In addition, the heritability and interhemispheric genetic correlations were stronger for long-range connections than for short-range connections. These findings highlight the determinants of the genetics underlying WM connectivity and its interhemispheric relationships, and provide insight into genetic basis of WM connectivity asymmetries in both healthy and disease states.

Stability of spatially discordant repolarization alternans in cardiac tissue.

Cardiac alternans, a period-2 behavior of excitation and contraction of the heart, is a precursor of ventricular arrhythmias and sudden cardiac death. One form of alternans is repolarization or action potential duration alternans. In cardiac tissue, repolarization alternans can be spatially in-phase, called spatially concordant alternans, or spatially out-of-phase, called spatially discordant alternans (SDA). In SDA, the border between two out-of-phase regions is called a node in a one-dimensional cable or a nodal line in a two-dimensional tissue. In this study, we investigate the stability and dynamics of the nodes and nodal lines of repolarization alternans driven by voltage instabilities. We use amplitude equation and coupled map lattice models to derive theoretical results, which are compared with simulation results from the ionic model. Both conduction velocity restitution induced SDA and non-conduction velocity restitution induced SDA are investigated. We show that the stability and dynamics of the SDA nodes or nodal lines are determined by the balance of the tensions generated by conduction velocity restitution, convection due to action potential propagation, curvature of the nodal lines, and repolarization and coupling heterogeneities. Our study provides mechanistic insights into the different SDA behaviors observed in experiments.

Magnitude and significance of the peak of early embryonic mortality.

Embryonic development is of great importance because it determines congenital anomalies and influences their severity. However, little is known about the actual probabilities of success or failure and about the nature of early embryonic defects. Here, we propose that the analysis of embryonic mortality as a function of post-fertilization time provides a simple way to identify major defects. By reviewing the literature, we show that even small initial defects, e.g., spatial cellular asymmetries or irregularities in the timing of development, carry with them lethal effects in subsequent stages of embryogenesis. Although initially motivated by human study, in this contribution, we review the few embryonic mortality data available for farm animals and highlight zebrafish as a particularly suited organism for such a kind of study because embryogenesis can be followed from its very beginning and observed easily thanks to eggshell transparency. In line with the few other farm animals for which data are available, we provide empirical evidence that embryonic mortality in zebrafish has a prominent peak shortly after fertilization. Indeed, we show how subsequent mortality rates decay according to a power law, supporting the role of the early embryonic mortality peak as a screening process rapidly removing defective embryos.

Increasing trend of scientists to switch between topics.

Despite persistent efforts in understanding the creativity of scientists over different career stages, little is known about the underlying dynamics of research topic switching that drives innovation. Here, we analyze the publication records of individual scientists, aiming to quantify their topic switching dynamics and its influence. We find that the co-citing network of papers of a scientist exhibits a clear community structure where each major community represents a research topic. Our analysis suggests that scientists have a narrow distribution of number of topics. However, researchers nowadays switch more frequently between topics than those in the early days. We also find that high switching probability in early career is associated with low overall productivity, yet with high overall productivity in latter career. Interestingly, the average citation per paper, however, is in all career stages negatively correlated with the switching probability. We propose a model that can explain the main observed features.