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11:00-12:00 Session 9: Poster III
Simulating the evolution of citation network: A case study in Information Science

ABSTRACT. The citation network, which indicates the citation relationship between the citing paper and the cited one, can be expressed by a directed graph. We proposed a distributed graph model to simulate the evolution of citation network in the field of Information Science, in which the papers are represented by nodes and the citing behaviors by edges linking up to two nodes. The model is motivated by the exponential nature of papers' out-degree distribution and the attraction rule between the citing papers and cited ones in a citation network. We assume that the probability of one published paper attracting the citations from others can be defined by its reputation and the distance, the former expressed by the in-degree while the latter by the age gap and topic relevance between the citing and cited paper. We focus on the papers published in seventeen journals of Information Science obtained from Web of Science Core Collection database. The empirical results show that the model promises effective simulation of the citation network evolution and well performance on the fitting of in-degree and out-degree distributions. There exists a potential for this model extended to explore the pattern of citation behavior in more wider fields, to make the model pragmatic.

Influence of disease and information interactive action on the transmission of respiratory infectious diseases via UAU-SEIR duplex network model

ABSTRACT. In real life, the spreading and prevention of infectious diseases is usually accompanied by the spreading of related disease popularization and prevention and control awareness information. In order to verify the inhibitory effect of effective information dissemination on epidemic spread, this paper constructed online information dissemination network and offline student social contact network, and coupled these two networks to form a typical duplex network model. Based on the typical UAU-SEIR model, a numerical simulation study was carried out on the spreading process of disease prevention and control awareness of individuality on the social network. Relevant results obtained here has some reference and guidance value for the public's COVID-19 vaccination and national awareness of sequential vaccination in the context of the continuous spread of the global epidemic. In the simulation parts, this paper also uses the method of microscale Markov chain to describe the states’ change of individual diseases and information at different times. At the same time, the spreading range of the disease and the time to reach the maximum number of infections were analyzed by statistics methods. In order to verify the inhibition effect of the public's awareness of epidemic prevention and control on the spread of diseases in the interpersonal network, the comparison of the final number of infections produced by the disease and information coupling network and the single-layer network under the same experimental conditions was also studied, and some valuable reference conclusions were obtained.

Analysis on the diffusion characteristics of disease prevention and control consciousness on multilayer social networks

ABSTRACT. In daily life, the diffusion of information is divided into various channels, such as mass media, social software (mobile apps), and face-to-face communication. This paper divides primary school students' access to information on epidemic prevention and control into three channels: online friend WeChat communication, online work-class group communication, and offline face-to-face communication, creating a typical three-layer coupling network to describe the real interpersonal communication network. Based on this social network topology, the classic SIR information spreading model is used to analyze the spreading dynamics of epidemic prevention and control awareness on this multiplex network. We simulated the specific process of epidemic prevention and control awareness spreading. Particularly, we used regeneration matrix method to give a precise theoretical analysis of the basic regeneration number generated in the epidemic propagation process. At the same time, by setting different communication times and initial infection node proportions in different network layers, the coverage level and scope of prevention and control awareness in the three-layer network are investigated on details.

Image2network: A new geometric algorithm framework for image data analysis based on complex network theory

ABSTRACT. In recent years, network science has been developed into an important research tool for describing the relationship between structure and function of typical complex systems. It has been successfully applied in modelling and analysis of complex systems. From the perspective of mutual representation of image and complex network, this paper carried out the investigation of the construction of associated complex network of image data, new algorithm for feature extraction of associated complex network graph, and optimization of the image classification operation process based on graph feature extraction. The application of industrial practice will also be reported, too. Focus of this paper includes two main parts: 1 Geometric representation of texture and contour image data and its applications; 2. Construction of a generalized image visibility graph scheme (GIVGS) and its performance comparison. 3. Construction of a unified image2network scheme for future research on geometric analysis of image data. Different pooling strategies are also used here to deal with high resolution images.

China's Textile Enterprises' Overseas Investment Path Network and Investment Position Analysis of Countries Along One Belt and One Road

ABSTRACT. By using 43,115 record data from the Ministry of Commerce's "Outbound Investment Enterprise (Institution) Recording Results Public Directory", We extracts 460 textile companies from 46 countries (regions) (including 19 “Belt and Road” countries) from 308 records to further study. Based on the historical investment records, we have built a network of overseas investment paths for Chinese textile companies. A preliminary analysis was made on the structure of the overseas investment path network and the economic status of the countries along the "Belt and Road" in the investment network via network analysis method. Results shows that the path for Chinese textile companies to invest globally around the whole world is not random, but rather a preference for popular countries or regions. In the overseas investment path network of Chinese textile enterprises, the largest connected branch contains 334 nodes, which account for 66.01% of all network nodes, and 342 investment contacts account for 69.8% of all investment contacts. It represents that the most popular countries for investing in and the most important individual textile enterprises (institutions) of the Chinese textile enterprises. These enterprises (institutions) play a pivotal role in the "going out" strategy of Chinese textile enterprises. In the largest connected component, the investment environment of the countries (regions) involved in the investment path is generally similar. Through the analysis of the centrality of the investment path network node (via the analysis of the PR value), community structure detection, and the network phantom distribution analysis, our article reveals that: the Chinese textile companies (institutions) have obvious preference for investment countries (regions). In addition, our study found that the most popular areas for Chinese textile companies to invest in countries along the “Belt and Road” are Vietnam, Cambodia, Myanmar, Bangladesh, Indonesia, Turkey and other countries, but textile companies conduct overseas investment meetings in these popular countries with mature investment environments and they will face stronger competition. In those countries with only one or two Chinese textile companies among along the “Belt and Road” who have implemented overseas investment, the investment environment and system may not be perfect. If under the conditions of correct market assessment, new companies that carry out targeted overseas investment may face relatively less intense business competition, and they might have more investment prospects.

Network Modeling and Resilience Analysis of Combat Systems-of-systems Based on Kill Web

ABSTRACT. Resilience is a comprehensive index to measure the stability of the network structure, whether it can complete tasks under attack, and the ability of self-organization and self-adaptation [1]. A reasonable assessment of combat systems-of-systems (CSoS) resilience is of great value to the improvement and optimization of the CSoS structure, to improve weapon construction efficiency, and building a weapon systems-of-systems (WSoS) that adapts to intelligent warfare requirements and fulfills missions [2]. From the SoS point of view, this paper proposes a CSoS modeling and resilience analysis based on the kill web based on supernetwork theory. First, the interaction relationship between CSoS is analyzed. Based on supernetwork theory, a three-layer supernetwork model is constructed from three aspects: the logical interaction relationship of weapon nodes, the influence relationship of weapon indicators, and the physical relationship of weapon operations. This is the basis for a network resilience assessment. Second, the scope of resilience assessment is divided according to performance changes. The combat effectiveness, which considers the number of combat loops, combat capabilities, and time efficiency, is used as an index to measure performance changes. According to the changes in combat effectiveness, a multi-stage resilience assessment method is constructed that considers performance degradation and performance recovery. The performance degradation stage corresponds to the anti-jamming capability, and the performance recovery node corresponds to the recovery capability. Finally, a military example is used to calculate the resilience index to verify the feasibility and effectiveness of the proposed method. Strike strategies considering the priority of attacking high node degree and high-capacity weapon, and a recovery strategy considering the constraints of weapon node degree and weapon interface distance are constructed in this example. Compare the anti-jamming, recovery, and resilience values of CSoS under different strike strategies. The results show that functional redundancy is important for improving resilience; compared with highly integrated weapons, decentralization is more conducive to maintaining SoS stability.

Collective firing patterns of neuronal networks with short-term synaptic plasticity

ABSTRACT. We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition (see Fig.1). The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Modeling the impact of floods on multi-level road network systems in the context of climate change

ABSTRACT. The negative impact of climate change continues to escalate flood risk. Floods directly and indirectly damage road systems and disturb the socioeconomic order. In this study, we propose three different approaches to quantitatively assess how floods impact a road system from the national structure, function and city level. Firstly, we develop a failure model to study the effect of floods on road networks in China and the United States. Secondly, we propose an integrated approach to quantitatively assess how floods impact the functioning of a highway system in China. Finally, an integrated resilience assessment model of urban transportation network: a case study of 40 cities in China is studied. These results have critical implications for transport sector policies and can be used to guide road design and infrastructure protection. The approach can be extended to analyze other networks with spatial vulnerability, and it is an effective quantitative tool for reducing systemic disaster risk.

Symmetric synergy in the threshold model on social networks

ABSTRACT. The threshold model has been widely adopted as a prototype for studying peer influence in social networks. Existing studies, however, focused mainly on the linear response function. This paper generalized the linear threshold model to the nonlinear case by considering the model on social networks with symmetric synergistic effects. A heterogeneous mean-field approach has been developed to calculate the final prevalence which determines whether a global cascade occurs or not. Compared to the situation without synergy, it is found that the constructive synergy enhances the contagion prevalence and thus weakens the systematic robustness. The interfering synergy, however, plays an opposite role. In ompetition with heterogeneity, it turns out that the constructive synergy shows a larger effect on cascade propagation than the degree heterogeneity, while the effect of the interfering synergy is smaller than that of the threshold heterogeneity. Simulations on synthetic and empirical networks verify analytical predictions.

Application of Network theory In Bioelectrical Signal Analysis

ABSTRACT. Preterm birth is the leading cause of neonatal morbidity and mortality. Early identification of high-risk patients followed by medical interventions is essential to the prevention of preterm birth. Based on the relationship between uterine contraction and the fundamental electrical activities of muscles, we extracted effective features from EHG signals recorded from pregnant women, and use them to train classifiers with the purpose of providing high precision in classifying term and preterm pregnancies. Methods: To characterize changes from irregularity tocoherence of the uterine activity during the whole pregnancy, network representations of the original electrohysterogram (EHG) signals are established by applying the Horizontal Visibility Graph (HVG ) algorithm, from which we extract network degree density and distribution, clustering coefficient and assortativity coefficient. Concerns on the interferences of different noise sources embedded in the EHG signal, we apply Short-Time Fourier Transform (STFT) to expand the original signal in the time-frequency domain. This allows a network representation and the extraction of related features on each frequency component. Feature selection algorithms are then used to filter out unrelated frequency components. We further apply the proposed feature extraction method to EHG signals available in the Term-Preterm EHG database (TPEHG), and use them to train classifiers. We adopt the Partition-Synthesis scheme which splits the original imbalanced dataset into two sets and synthesizes artificial samples separately within each subset to solve the problem of dataset imbalance. Results: The optimally selected network-based features, not only contribute to the identification of the essential frequency components of uterine activities related to preterm birth, but also to improved performance in classifying term/preterm pregnancies, i.e., the SVM (Support Vector Machine) classifier trained with the available samples in the TPEHG gives sensitivity, specificity, overall accuracy, and auc values as high as 0.89, 0.93, 0.91, and 0.97, respectively.

TEGDetector: A Phishing Detector that Knows Evolving Transaction Behaviors

ABSTRACT. Recently, phishing scams have posed a significant threat to blockchains. Phishing detectors direct their efforts in hunting phishing addresses. Most of the detectors extract target addresses’ transaction behavior features by random walking or constructing static subgraphs. The random walking methods, unfortunately, usually miss structural information due to limited sampling sequence length, while the static subgraph methods tend to ignore temporal features lying in the evolving transaction behaviors. More importantly, their performance undergoes severe degradation when the malicious users intentionally hide phishing behaviors. To address these challenges, we propose TEGDetector, a dynamic graph classifier that learns the evolving behavior features from transaction evolution graphs(TEGs). First, we cast the transaction series into multiple time slices, capturing the target address’s transaction behaviors in different periods. Then, we provide a fast non-parametric phishing detector to narrow down the search space of suspicious addresses. Finally, TEGDetector considers both the spatial and temporal evolutions towards a complete characterization of the evolving transaction behaviors. Moreover, TEGDetector utilizes adaptively learnt time coefficient to pay distinct attention to different periods, which provides several novel insights. Extensive experiments on the large-scale Ethereum transaction dataset demonstrate that the proposed method achieves state-of-the-art detection performance.

The dynamics of SEIR model on time-varying higher-order networks

ABSTRACT. Static higher-order networks have become an important framework for understanding the dynamics of epidemic spreading at present. Some non-trivial phenomena have been discovered, such as explosive transitions and bistable state, which are difficult to occur on the network with pairwise interactions. However, the temporal evolution, which is less taken into account for higher-order networks, is the more general pattern and deeply influences the spreading dynamics in the real world. For example, changes in contact networks caused by human activities may affect the spread of diseases within a population. To further investigate the role of temporal evolution of topology on higher-order networks, we extend the epidemic spreading model to time-varying higher-order networks. In addition, considering diseases with the latent characteristics, the susceptible-exposed-infectious-recovered (SEIR) model is adopted as the baseline model. Taking use of the microscopic Markov chain approach, we obtain the evolutionary equations and outbreak threshold of the proposed model. Through large quantities of theoretical analyses and numerical simulations, we discuss the effects of time evolution and exposed (E) states on the phase transition and stable state on higher-order networks and the interplay between them. Furthermore, we verified the consistency of the theoretical approach and numerical simulation. Finally, we further simulate the results in a time-varying higher-order network constructed based on real wireless network data, which can be used to describe the long-term population activities. Taking together, our work will help to better understand the disease spreading behavior within the real-world population.

Network-based methods to quantify COVID-19 importation risk: A rapid review

ABSTRACT. The ongoing global pandemic of COVID-19 (SARS-CoV-2) has caused incredible global disruption and challenges, in addition to its substantial health impact. The importation risk of COVID-19 from epicenters to the global destinations is a major concern during the early pandemic. For regions facing high importation risk, quantifying the real-time importation risk and applying stringent measures based on that is urgent and imperative to trigger public health responses. We aim to conduct a rapid review to identify the main existing network-based methods of quantifying importation risk to provide the estimation and prevention of COVID-19 importation risk.

A novel switching event-triggered control for secure consensus of linear multi-agent systems subject to cyber-physical attacks

ABSTRACT. This paper studies the secure consensus problem of the linear multi-agent systems subject to a series of arranged cyber-physical attacks. It is firstly worthy noting that a novel switching controller is designed under the event-triggered scheme and it is fully distributed which only uses the local neighbours' information. Then, an algorithm is constructed to design the control gain matrix of the controller and the event-triggered condition which gives the asynchronous event-triggered time of different nodes. The secure consensus could be achieved although the networks may not contain a directed spanning tree because of the cyber attacks and the Zeno behavior is excluded. In addition, the upper bounds of the attack frequencies and the swelling time of the attacks are obtained and it is deeply investigated the effect of the attack on the secure consensus. Finally, the effectiveness of the theoretical results could be verified by numerical simulations.

Containment Control of Heterogeneous Liner Singular Multi-Agent Systems by Distributed Event/Self-Triggered Control

ABSTRACT. This paper investigates the containment control of singular heterogeneous multi-agent systems by distributed event/self-triggered control strategy. Firstly, an adaptive observers and a state-feedback controller are proposed to obtain the leader-following consensus of heterogeneous liner singular MASs. Then, to avoid continuous monitoring, a novel distributed event/self-triggered control strategy is designed without considering the global topology information and the event/self-triggered control could solve the containment control problem of the heterogeneous liner singular MASs. Furthermore, it is proved that the inter-event times are lower bounded by a positive constant and then the Zeno behavior is excluded. Finally, an example is given to verify the effectiveness of the control strategy.

Evolution of cooperation in prisoner’s dilemma game under the coupling of aspiration and imitation rules

ABSTRACT. Considering the important roles played by aspiration and imitation rules, we explore how cooperation evolves in the spatial prisoner’s dilemma game. In detail, the strategy updating rule couples the inner aspiration payoff and the external neighbors payoff through the parameter α. Intriguingly, we find that there exists an optimal value of α leading to the highest density of cooperators for a given aspiration level. By analyzing the dynamical strategy changes of system, we find that an optimal α helps individuals form cooperator clusters and curbs the further spread of high-payoff defectors, and thus improves the density of cooperators. Moreover, when when the aspiration level A ≤ 0.5, the optimal value of α which leads to the highest density of cooperators, decreases with A, the optimal range of α gradually expands and the highest cooperation level is on the rise.

Structure of cross-correlation between stock and oil markets

ABSTRACT. We displayed in this paper the structure of cross-correlation between the S\&P 500 stock market and the Brent Oil market and its evolutionary behavior. Technically, the ensemble empirical mode decomposition is adopted to separate the two series into components. Let a window slide along the multi-variate series of the components, generating a series of segments. For each segment, one calculates the mutual entropies between the components to describe the coupling strengths, resulting into a network between/within the two markets. The networks corresponding to the successive segments form a temporal network. It is found that the characteristic period of intrinsic mode for each series grows exponentially from several days to more than ten years. The couplings between long-term components (with periods larger than one year) form the stable backbone of the network. The shocks of short-term events on the long-term components determine mainly the evolutionary behavior, especially the changes of the coupling structure. This method can be extended straightly to display the cross-correlation structures and their evolutions for complex systems composing of multi-subsystems.

Exploring Community Structure of Sample-based Music through Bipartite Network Analysis

ABSTRACT. Musical sampling is a composition technique of popular music that borrows from existing recordings to produce new songs. All components of a song such melody lines, drum parts, and vocals a cappella can be sampled. Thus the sampled song is deeply related to the identity of the newly created music. For example, G-Funk, the dominant subgenre of American West Coast hip-hop in the '90s, featured its own groove borne out of sampling of George Clinton and many other funk musicians. We can therefore surmise that the sampling practice of an artist reflects the characteristics of the subgenre or music community to which the artist belongs, so that analyzing the sampling relationships can help us understand the origin and evolution of different styles of sample-based music. In this study, we present a network analysis of the communities of artists based on sampling relationships. We establish an artist-song bipartite network of artists who perform the sampling and songs that are subject of sampling, and detect communities. The communities comprise artists and the songs they sampled. We show that sample-based music has a clear community structure where each community features artists (nodes) with high centrality that allows us to identify the musical styles of the community. We also define and visualize the similarities between communities of distinct generations to observe how sample-based musical styles have evolved or “handed off” to later time periods. This study not only enhances our understanding of sampling-based music, but also presents a novel application of network community structures to creative enterprises.

Network Analysis of Science Fiction Subjects

ABSTRACT. How can we explore the relationship between literary works? With recent advances in Natural Language Processing (NLP), it is becoming increasingly feasible to identify connections between written works based on content itself. This `machine reading' enables us to characterize the structure of the network in literature in large scale. In this study we analyze the topical subjects in SF (science fiction) appearing the classical pulp magazine Amazing Stories. To this end we employ `topic modeling' to identify the underlying topics of the SF novels, then form the network of SF stories based on their topical similarity. An analysis of the network reveals the type of topics in SF and how they are used in conjunction. We also define measures of an author's distinctiveness and diversity of topic usage, which allow us to understand the writer's literary characteristics. Based on this work we anticipate a more robust quantitative framework for the evolution of ideas and the transmission of messages in stories that can further illuminate many network aspects of literary works.

Exploring The Network Origin of Creativity In Music

ABSTRACT. Creativity is the foundation of all artistic and intellectual innovations, but it is not yet well characterized. As creativity is increasingly believed to be the ability to make novel connections between concepts in many enterprises, exploring the actual patterns of connections in creative artifacts is gaining attention. While some works exist on semantic memory networks and linguistic creativity, there have been fewer works on the network patterns of musical and artistic creativity, a topic of intrigue especially in the current era of computer-generated music and art driven by advances in AI and deep learning. Here we present the patterns of melodic creativity in the classical piano works composed between the Baroque and the modern periods. After computing the network-based creativity scores of the works reflecting novelty and influence~[1], we measure various topological properties of the network of compositional elements and study how they correlate to one another. We find that clustered melodic transitions implies high creativity, whereas longer distances and higher modularity--the existence of distinct groups connected preferentially internally--imply low creativity, showing that creativity is manifest in the ready ability to scale the whole space of compositional elements and establish new connections, supporting the Flatter Association Hierarchies of Mednick' hypothesis~[2] and paralleling previous comparative studies on linguistic creativity~[3,4,5]. Our paper demonstrates the possibility of an intriguing and novel understanding of artistic creativity from the perspective of network science.

12:00-13:30 Session 10A: Biological Networks II
Feature-rich multiplex lexical networks unveil cognitive strategies of early language learning

ABSTRACT. Knowledge in the human mind exhibits a dualistic vector/network nature. Modelling words as vectors is key to natural language processing, whereas networks of word associations can map the nature of semantic memory. We reconcile these paradigms - fragmented across linguistics, psychology and computer science - by introducing FEature-Rich MUltiplex LEXical (FERMULEX) networks. This novel framework merges structural similarities in networks and vector features of words, which can be combined or explored independently. Similarities model heterogenous word associations across semantic/syntactic/phonological aspects of knowledge. Words are enriched with multi-dimensional feature embeddings including frequency, age of acquisition, length and polysemy. These aspects enable unprecedented explorations of cognitive knowledge. Through CHILDES data, we use FERMULEX networks to model normative language acquisition by 1000 toddlers between 18 and 30 months. Similarities and embeddings capture word homophily via conformity, which measures assortative mixing via distance and features. Conformity unearths a language kernel of frequent/polysemous/short nouns and verbs key for basic sentence production, supporting recent evidence of children's syntactic constructs emerging at 30 months. This kernel is invisible to network core-detection and feature-only clustering: It emerges from the dual vector/network nature of words. Our quantitative analysis reveals two key strategies in early word learning. Modelling word acquisition as random walks on FERMULEX topology, we highlight non-uniform filling of communicative developmental inventories (CDIs). Conformity-based walkers lead to accurate (75\%), precise (55\%) and partially well-recalled (34\%) predictions of early word learning in CDIs, providing quantitative support to previous empirical findings and developmental theories.

Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes

ABSTRACT. Cascading phenomena over spatially embedded networks, such as social contagions, neuronal activations and infrastructure failures etc., exhibit two competing spreading mechanisms, local wavefront propagation (WFP) and nonlocal appearance of new clusters (ANC), which occur due to the presence of both short- and long-range edges. We are extending this field to understand the effects of higher-order interactions on such cascades. We introduce a simplicial threshold model (STM) for analyzing such systems with dyadic, triadic and higher-order dependencies. We utilize topological building blocks, k-simplex, to encode the interactions of dimension k and simulate cascades in which vertex v(i) gets activated if the surrounding activity of k-simplices exceeds a certain threshold, T. We show that higher-order interactions and thresholding cooperatively guide cascades along multidimensional geometrical channels. We study WTM cascades on a C. Elegans neuronal complex, which we construct using an empirical synapse network, showing that higher-order interactions enhance the memory capacity and efficiency of STM cascades. We support our findings with bifurcation theory to predict wavefront speeds and cluster appearance rates. Our framework and findings show that dynamical/structural interplay of higher-order nonlinearity and the multidimensional geometry of simplicial complexes to be a fruitful direction for uncovering the multiscale mechanisms that orchestrate higher-order processing within complex systems.

Reorganization of Negative “Anti-Rich Clubs” in Autism Brain Networks

ABSTRACT. Autism Spectrum Disorder (ASD) is a developmental disability that causes serious social and communication difficulties and impacts an estimated 1 in 44 youth in the USA. The nascent field of network neuroscience allows us to frame various brain disorders and diseases as dysconnectivity problems. ASD is associated with differences in the organization of whole brain networks, most notably a reduction in connection density and changes in hub connectivity. Yet, we still lack reliable network-level biomarkers of ASD. In this study, we develop a rich club based analysis to characterize connectivity changes in ASD. We obtained resting state functional magnetic resonance imaging (rs-fMRI) data from the Autism Brain Imaging Data Exchange (ABIDE) study. We derived functional connectomes for 66 children under 10 diagnosed with ASD and 71 typically developing controls (TD), and separated positive and negative edges to form two networks for each child. Studies in structural networks have demonstrated the existence of a densely connected rich club of hub regions in the brain that plays a key role in the integration and segregation of the information processing. In our functional networks, the rich club appears very different. The positive hubs forming the rich club are densely connected and have high efficiency, but are largely constrained to individual modules and exhibit low participation coefficients (they are provincial hubs). This is consistent with the literature. Interestingly, considering the negative networks revealed a secondary component to the club. The negative hubs preferentially attach to low degree nodes outside of their own modules and have low efficiency, high betweenness, and high participation coefficients (they are connector hubs). Furthermore, these hubs avoid sharing connections with each other – creating an “anti-rich club” of negatively weighted edges. We found that the negative anti-rich clubs are more pronounced in ASD, while the positive rich clubs are not discernible from the TD group. We measured prominence of the negative anti-rich club by calculating the minimum value of the rich club coefficient, Φ(k)norm. We found that a lower min(Φ(k)norm) was associated with higher social, communication, and total ADOS (Autism Diagnostic Observation Schedule) scores. That is, the more pronounced the negative anti-rich cub, the greater the symptom burden. Our results provide a new understanding of the rich club of hub nodes in the brain. We find that the club of functional hubs of the human brain can be split into two components according to positive and negative edges – i.e., excitatory and inhibitory connections. We show that an atypical negative anti-rich club is associated with social and communication difficulties in ASD, highlighting the role of excess inhibitory connections in ASD and paving the way for quantitative diagnosis and novel therapeutics.

Entropic Feature Representation for Brain Connectivity Networks in Alzheimeter's Disease

ABSTRACT. The complex network provides us with powerful tools to study the advanced functions of the human brain. It can get deep insight into brain disease pathogenesis, such as using brain networks to diagnose mild cognitive impairment of Alzheimer's disease. However, there is a tough and fundamental issue for network-based analysis about how to simply and effectively characterize brain networks. In this paper, we apply fMRI to construct brain networks and propose entropy as a feature representation for brain connectivity networks. Specifically, we compute the global entropy of the networks from a statistical point of view and then decompose it into edges. Extensive experiments on Alzheimer’s Disease Neuroimaging Initiative(ADNI) datasets demonstrate the potential of our proposed methods. Moreover, our proposed framework achieves superior classification accuracy compared to several state-of-art methods. To the best of our knowledge, we use a robust preprocessing pipeline for fMRI data with a large number of subjects. we also apply the concept of thermodynamics to characterize the brain networks of patients with Alzheimer's disease.

Using Differential Network Analysis and the GRAND Database for Drug Repurposing in Colon Cancer

ABSTRACT. Biological states, or phenotypes, and the transition between them, are decontrolled through complex networks of interacting elements within the cell. Gene regulatory networks (GRNs) consist of regulatory proteins (transcription factors; TFs) and their target genes and shape cellular processes in many contexts, including disease and response to drug exposure. Using computational tools form the Network Zoo (netZoo;, we built more than 20,000 GRN models across human conditions that include cancer, healthy tissues, and cell lines, as well as in exposure to more than 20,000 small molecules, and collected the Gene Regulatory Network Database (GRAND; We used this unparalleled collection of regulatory network models to develop a drug repurposing approach called CLUEreg (Figure 1) based on comparing regulatory network features between healthy and disease states and accounting for regulatory changes to drug treatment. As a demonstration of the value of such a resource, we considered regulatory response to drug treatment with the goal of identifying compounds in other indications that could be useful in treating colon cancer. We compared normal colon and colon cancer networks to find altered regulatory processes, compared those to drug response networks to identify disease-associated regulatory processes that are reversed by drug treatment, and ranked compounds based on their reversal scores. We identified the Aurora-A kinase inhibitor MK-5108, a compound that has shown efficacy in clinical trials in lung cancer, as a potential drug candidate for treatment of colon cancer; this drug was not identified using other techniques, such as exploring changes in gene expression. Tools to conduct this analysis have been incorporated in GRAND, allowing others to use networks search for candidates for drug repurposing in other diseases.

Hypergraphs Demonstrate Anastomoses During Divergent Integration

ABSTRACT. During the development of an embryo, cells divide and differentiate, eventually forming tissues and physiological systems. This process has typically been characterized using tree-like structures, the most famous example being the lineage tree. The cells of an embryo can also be characterized as a complex network [1] and is useful in understanding phenomena such as intercellular signaling and geometric/spatial constraints. Furthermore, these embryo networks tend to diverge as cells differentiate, migrate, and form structures such as tissues and organs. The resulting functional and structural divergence is called divergent integration [2]. During divergent integration, components of the network diverge in both function and connectivity but retain a small number of connections while remaining part of the same system. But how do we characterize this process across time and, more importantly, across cell births, deaths, and respecification of cell fate? A hypergraph structure will be used to graphically represent these processes and provides a means to quantify these dynamics. To demonstrate hypergraphs in a developmental context, we will present a hypothetical embryogenetic hypergraph with the simplicity of C. elegans embryo but with the regulative potential of vertebrate embryos. Embryogenetic hypergraphs also represent the process of anastomosis. Anastomoses are cross-connections between subgraphs representing the differentiated subgraphs of an embryo network. These connections reveal exchanges of cells between subgraphs as they change identity from one functional cell category to another. This model of hypergraph exchange and subgraph partitioning can be further understood with the density-bifurcation model, which proposes a developmentally specific model of node attachment. This work is particularly relevant to building spatiotemporal representations of embryo dynamics.

References [1] Alicea, B. and Gordon R. (2018). Cell Differentiation Processes as Spatial Networks: identifying four-dimensional structure in embryogenesis. BioSystems, 173, 235-246.

[2] Alicea, B. and Cialfi, D. Embryo Networks as Generative Divergent Integration. NetSci 2021.

12:00-13:30 Session 10B: Dynamics I
Analysis and Visualization of High-Dimensional Dynamical Systems’ Phase Space Using a Network-Based Approach

ABSTRACT. The concept of attractors is considered critical in the study of dynamical systems as they represent the set of states that a system gravitates toward. However, it is generally difficult to analyze attractors in complex systems due to multiple reasons including chaos, high-dimensionality and stochasticity. This paper explores a novel approach to analyzing attractors in complex systems by utilizing networks to represent phase spaces. We accomplish this by discretizing phase space and defining node associations with attractors by finding sink-strongly connected components (SSCCs) within these networks. Moreover, the network representation of phase space facilitates the use of well-established techniques of network analysis to study the phase space of a complex system. We show the latter by introducing a new node-based metric called attractivity which can be used in conjunction with the SSCC as they are highly correlated. We demonstrate the proposed method by applying it to several chaotic dynamical systems and a large-scale agent-based social simulation model.

Edge-snapping in presence of limited resources

ABSTRACT. See attached file

Dynamic stability of complex networks

ABSTRACT. Will a large complex system be stable? This question, first posed by May in 1972, captures a long-standing challenge, fueled by a seeming contradiction between theory and practice. While empirical reality answers with an astounding yes, the mathematical analysis, based on linear stability theory, seems to suggest the contrary - that a sufficiently large complex system, will inevitably become unstable - hence, the diversity-stability paradox. What, then, are the naturally emerging organizing principles, or in May’s original wording - what are nature’s devious strategies, to achieve dynamic stability in complex systems?

Initial clues began to unveil with the mapping of empirical networks, which uncovered universally recurring topological characteristics that can potentially impact the system’s dynamics. For example, degree heterogeneity, community structure and topological symmetries - all naturally emerging features of real-world networks - indeed, impact the system’s dynamics. However, on their own, these topological features are insufficient to ensure stability, leaving May’s mathematical challenge unresolved.

In this talk we present a solution to this dichotomy, by considering the interplay between the network topology Aij and system’s intrinsic nonlinear dynamics. We show that this interplay leads to the emergence of non-random patterns in the system's stability matrix Jij (the Jacobian). Specifically, we show that the diagonal and off-diagonal terms of the Jacobian scale as Jii∼-k_i^μ, Jij∼k_i^ν k_j^ρ, where k_i,k_j are the weighted degrees of i and j, and the exponents μ,ν,ρ are rooted in the specific form of the system’s dynamics, e.g., social, biological or technological. Hence, for example, when μ=1 or 2, the diagonal terms associated with hub nodes are large, while, under the same network, if μ=-1, these terms asymptotically vanish. This represents a previously unmapped link between Aij and Jij. Such patterns stands in sharp contrast with the prevailing random matrix-based paradigm, thus offering a new matrix ensemble, by which to capture the dynamic stability of real-world systems.

This ensemble helps us analytically identify the (few) relevant control parameters that predict a system's stability, exposing three broad dynamic classes: In the asymptotically unstable class, diversity, indeed, leads to instability a là May's paradox. However, we also expose an asymptotically stable class, the class in which most real systems reside, where diversity not only does not prohibit, but, in fact, enhances dynamic stability. Together, our theory uncovers the naturally emerging rules of complex system stability, helping us reconcile the paradox that has eluded us for decades.

Exploring the impact of positive and negative information on green behavior diffusion based on two-layered networks

ABSTRACT. The increasing global warming effect has aroused widespread concern about climate issues. In addition to reducing carbon emissions in industrial production, some individual green behaviors (e.g., green travel and garbage sorting) can also play a non-negligible role in reducing greenhouse gas emissions. The dynamical properties of positive and negative information and individual green behavior are investigated on the basis of two-layer networks, where one layer is used to represent the two kinds of information and the other layer is explored to describe the individual green behavior diffusion. The positive information can motivate individuals to adopt green behaviors, while the negative information can hinder individuals from practicing green behaviors. The dissemination of positive and negative information related to green behavior is characterized by means of the epidemic model. Considering that individuals may be affected by the benefits when practicing green behaviors, a public goods game model is introduced to describe the diffusion of individual green behavior. Moreover, the impact of green credit on the diffusion of individual green behavior is also considered in the model. The individual green behavior diffusion is quantitatively analyzed by using a large number of simulation experiments. The results show that promoting the spread of positive information and inhibiting the spread of negative information can play a very beneficial role in enhancing the spread of individual green behavior. Selecting nodes with high degree centrality as the initial dissemination nodes of positive information is also an effective means to promote the diffusion of individual green behavior. Furthermore, reducing the individual sensitivity to the income difference and increasing the individual's emphasis on green credit can also increase the willingness of individual to adopt individual green behavior. The current work could help to a deeper understanding of the dynamics of the coupled diffusion of multiple information and individual green behavior.

Opinion dynamics can be unknowingly distorted in complex networks

ABSTRACT. see the attached PDF file.

A Multi-Type Branching Process Method for Modelling Complex Contagion on Clustered Networks

ABSTRACT. Online social networks such as Twitter, Facebook, Instagram and TikTok serve as media for the spread of information between their users. We are interested in developing models for this information diffusion to gain a greater understanding of its drivers. Some models for the spread of online behaviour and information assume that the information behaves similarly to a virus, where infection is equally likely after each exposure, these dynamics are known as a simple contagion. In a simple contagion, the exposures are independent of each other. However, online adoption of some behaviour and content has been empirically observed to be more likely after multiple exposures from their network neighbours [1-2], the exposures are not independent of each other, we refer to this as a complex contagion. Analytically tractable descriptions of complex contagions have been developed for continuous-time dynamics. These extend mean-field and pair approximation methods to account for clustering in the network topologies [3]; however, no such analogous treatments for discrete-time cascade processes exist using branching processes. We describe a novel definition of complex contagion adoption dynamics and show how to construct multi-type branching processes which account for clustering on networks [4]. We achieve this by tracking the evolution of a cascade via different classes of clique motifs which contain different numbers of active, inactive and removed nodes. This description allows for accurate analytical calculation of cascade sizes, determination of critical behaviour and we also describe how the branching process description allows us, using probability generating functions, to derive full distributions of cascade sizes and other quantities of interest from the model.

[1] D. Centola, The spread of behavior in an online social network experiment, Science 329, 1194 (2010). [2] D. M. Romero, B. Meeder, and J. Kleinberg, Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter, in Proceedings of the 20th international conference on World wide web (2011) pp. 695–704. [3] D. J. P. O’Sullivan, G. J. O’Keeffe, P. G. Fennell, and J. P. Gleeson, Mathematical modeling of complex contagion on clustered networks, Frontiers in Physics 3,10.3389/fphy.2015.00071 (2015). [4] Keating, L.A., Gleeson, J.P. and O'Sullivan, D. J.P. A multi-type branching process method for modelling complex contagion on clustered networks. arXiv preprint arXiv:2107.10134 (2021).

12:00-13:30 Session 10C: Emerging Networks I
Thermodynamic efficiency of autocatalytic networks

ABSTRACT. An autocatalytic network is a reaction network modelling a set of chem- ical species that mutually catalyse each other’s production through chem- ical reactions, starting from a finite set of species assumed to be available from the environment. Autocatalytic networks are capable of spon- taneous emergence and self-reproduction, and are supposed to be chemical networks at the basis of life. In this work, I investigate the thermodynamic features of autocatalytic networks. In particular, I use recent results on nonequilibrium thermody- namics of Chemical Reaction Networks in order to study the con- nection between the topological constrains a network must satisfy to be autocatalytic, and its ability to store the chemical work performed by the surrounding environment, i.e., its thermodynamic efficiency:

eta = 1−EP/Wc.

Here EP is the entropy production and Wc is the chemical work performed by the environment on the chemical network. By studying the evolution of simple autocatalytic networks, I observe that the topology of an autocatalytic network does not strongly constrain the thermodynamic properties of the system, allowing different networks to exhibit various thermodynamic behaviours. Furthermore, the obtained results suggest that the effects of catalyses on thermodynamic flows may result in an advantage for autocatalytic networks over other systems in storing energy.

Helios-Web: An interactive framework to explore large complex networks on the web

ABSTRACT. Network science emerged as a proper framework to represent, analyze and model a diverse range of complex systems. Still, investigating such structures can become considerably challenging when they encompass many nodes and edges. Moreover, it is typical these elements to be associated with metadata and other features, further increasing the complexity and dimensionality of the problem. In this context, interactive visualization can streamline the data exploration process by facilitating the discovery of hidden patterns and providing intuitive interpretations of the system under analysis. However, most of the existing tools can not handle large networks comprising more than 10,000 nodes in real-time, which is a reflection of their lack of both rendering capabilities and continuous layout algorithms. Here, we developed a new network visualization and exploration tool, Helios-web ( ) that incorporates GPU-based rendering and continuous force-directed layouts that can visualize networks of millions of nodes. This is attained by using a variety of rendering techniques, such as billboards, signed distance fields, and GPU-based picking. The tool also includes an API and interactivity features to search, filter and highlight nodes or edges according to their associated attributes. Helios-web is being developed for a web environment and can be integrated into portals and websites. We illustrate the usefulness of the tool through an exploration of scholarly networks obtained from the APS, Microsoft Academic Graph, and OpenAlex datasets.

Phishing Detection on Ethereum via Attributed Ego-graph Embedding

ABSTRACT. In recent years, the losses caused by phishing scams on Ethereum have reached a level that cannot be ignored. In such a phishing detection scenario, network embedding is seen as an effective solution. In this paper, we propose an attributed ego-graph embedding framework to distinguish phishing accounts. We first obtain the account labels from an authority site and the transaction records from Ethereum on-chain blocks. Then we extract ego-graphs for each labeled account to represent it. To learn representations for ego-graphs, we utilize non-linear substructures sampled from ego-graphs and use a skip-gram model. Finally, a classifier is applied to graph embeddings to predict phishing accounts. To overcome the limit that transaction attributes are not encoded into ego-graph embeddings, we give nodes and subgraphs with richer attribute-based semantics. Specifically, we propose a novel node relabeling strategy based on Ethereum transaction attributes including transaction amount, number, and direction, and differentiating nodes and subgraphs by new labels. Through this, structural and attributed features of the Ethereum transaction networks can be learned at the same time. Experimental results show that our framework achieves effective performance on class imbalanced phishing detection on Ethereum.

A multiplex analysis of phonological and orthographic networks

ABSTRACT. The study of natural language using a network approach has made it possible to characterize novel properties ranging from the level of individual words to phrases or sentences. A natural way to quantitatively evaluate similarities and differences between spoken and written language is by means of a multiplex network defined in terms of a similarity distance between words. Here, we use a multiplex representation of words based on orthographic or phonological similarity to evaluate their structure.

As a continuation of our work [Lara-Martínez, P., Obregón-Quintana, B., Reyes-Manzano, C. F., López-Rodríguez, I., & Guzmán-Vargas, L. (2021). Comparing phonological and orthographic networks: A multiplex analysis. Plos one, 16(2), e0245263.], we adjust the way of assigning links so that these links show the morphological similarity in a better way.

We find that from the analysis of topological properties of networks, there are different levels of local and global similarity when comparing written vs. spoken structure across 12 natural languages from 4 language families (Romance, Germanic, Slavic and Uralic), by analyzing 50000 different words of each language. In particular, it is found that differences between the phonetic and written layers is markedly higher for French and English, while for the other languages analyzed, this separation is relatively smaller.

Specifying some results, we find the following: (i) a Weibull behavior in the degree distribution, (ii) clustering by degree distribution retrieves the language family, (iii) the behavior of each language in finding communities that maximize modularity is similar in each language family separately, and (iv) differences between linguistic families in robustness (for example a marked difference in the Germanic language between layers).

We conclude that the multiplex approach allows us to explore additional properties of the interaction between spoken and written language.

Peer learner networks impact study-abroad second language acquisition: Insights from mixed-methods SNA

ABSTRACT. Social networks play a vital role in SLA. Combining computational and anthropological Social Network Analysis (SNA), we investigate the influence of peer interaction dynamics and social graph topology on measurable outcomes in two intensive language courses: a 5-week course of German for Erasmus+ exchange students in Baden-Württemberg (n=40), and two editions of a 4-week summer course of the Polish language and culture in Warsaw (n=332). Unlike previous Study Abroad social network research concentrating on i) the micro-level of individual learners’ egocentric networks, presenting an emic view only, and ii) primarily TL native-speaker contacts, we demonstrate how and why peer learner networks can be examined in their entirety, complementing an etic perspective. In particular, we focus on the moderating role of the social network (mesoscopic explanatory variable)—in turn influenced by engagement with the TL-speaking culture (macroscopic explanatory variable)—on L2 progress (microscopic response variable). The study addresses the following overarching questions: RQ1: Is the learners’ L2 progress influenced by their position in the peer interaction network (center vs. periphery) and community membership? RQ2: Which types of interaction revealed in the social graph structure are the most important predictors of L2 progress: - unidirectional or reciprocal? - overall (irrespective of the language(s) used) or in the TL? - incoming or outgoing? RQ3: With respect to TL use, is a more important factor the absolute numbers of immersion hours in the language, or the proportion of L2 use to total communication? RQ4: Is there a relationship between participants’ language progress and the intensity of their contacts with same-L1 users (investigation of homophily effects; cf. Lazarsfeld & Merton, 1954; McPherson et al., 2001)? RQ5: Do the students prefer to socialize with peers demonstrating a similar or different level of L2 proficiency? RQ6: Is TL progress conditioned by network-external factors such as motivation or competence in other (background) languages? The quantitative component of the project showed among others i) that outgoing interactions in the TL are a stronger predictor of progress than incoming interactions, ii) a clear detrimental effect of interactions with same-L1 speakers (routgoing=−.31[-0.63, 0.00],p=.048), iii) the strongest influence of the network in the domains of pronunciation and lexis, where degree centrality in the TL positively correlates with progress (routdegree=.258,p=.001 for pronunciation; routdegree=.304,p=.0002 and rindegree=.263,p=.001 for vocabulary), while betweenness in total communication is significantly anticorrelated (r=−.242,p=.003 and r=−.204,p=.01, respectively). iv) This mirrors the impact of closeness centrality (ease of access to other students). v) Combined with the deleterious influence on SLA of a high in-degree, this underscores the importance of the network’s structural properties. In turn, structured interviews carried out with course participants and their instructors yielded valuable information on the formation and types of the networks the learners engaged in and the purposes these networks served. The presentation will thus illustrate the benefits of combining computational (quantitative) and anthropological (qualitative) social network analysis. Lastly, we shall also compare two face-to-face iterations of one of the courses with its online edition during the COVID-19 pandemic.

Variable selection aided by correlation networks: Revealing behavioral immunity landscapes

ABSTRACT. Mapping in vivo the different states of immune cells is an important open problem in biology. In this work, using data from movement and shape of over 100\,000 cells, we found that supervised selection of morpho-kinetic variables guided by a combination of wrapper and filter methods captured the behavioral landscapes of active inflammation [1]. Our mathematical modeling, based on logistic and decision tree models, as well as correlation networks, provided distributions on graphs which allowed us to identify the most important variables for immune cell prediction. The Euclidean projection was made using multidimensional scaling, employing Pearson’s distances as entries of the dissimilarity matrix.

12:00-13:30 Session 10D: Higher-Order Interactions
The impact of directed higher order interactions on synchronization

ABSTRACT. The study of higher-order structures has seen a growing interest in the complex systems and network science communities, due to the vast number of dynamical phenomena encoded by the many-body interactions, which escaped the classical pairwise description. These systems have been used to investigate various dynamical processes, such as random walks, synchronization and consensus, to name a few. However, the above framework is not general enough to describe systems where the group interactions are intrinsically asymmetric. For instance, group pressure or bullying in social systems, (bio)chemical reactions or microbial communities all show an asymmetric nature, due to the fact that group interactions are addressed towards one or more individuals but not necessarily reciprocated. Here, we introduce the concept of M-directed hypergraphs, a general class of directed higher-order structures, which allow to investigate dynamical systems coupled through directed group interactions. As an application we study the synchronization of Rössler oscillators on 1-directed hypergraphs. A 1-directed d-hyperedge, where the source nodes j_1, j_2, ..., j_d point toward node i, can be represented by an adjacency tensor A^(d) with the following property

A_{ij_1\dots j_d}^{(d)}=1 \Rightarrow A_{i\pi(j_1\dots j_d)}^{(d)}=1

where \pi(j_1,...,j_d) is any permutation of the indices j_1,..., j_d.

With the above formalism, we generalize the Master Stability Function approach, proving that the stability of the synchronous state depends on the spectrum of a generalized Laplacian matrix. We find that directed higher-order interactions can prevent synchronization, in a scenario where the synchronized state would be stable with undirected ones.

Existence of higher-order components in hypergraphs

ABSTRACT. We investigate the higher-order components that ubiquitously exist in the real-world hypergraphs but have not received much attention, and we propose a solvable random hypergraph model having the higher-order components. We introduce m-th-order connectivity in hypergraphs as the connectivity between two hyperedges sharing m common nodes and m-th-order component as the connected component only through m-th- or higher-order connectivities. We examined seventeen real-world hypergraphs from various fields and confirmed that the higher-order largest component exists ubiquitously. Moreover, we also examined the randomized real-world hypergraphs, which preserves the hyperdegee distribution and size distribution like the configuration model. As a result, it was confirmed that the m-th-order largest component of the real-world hypergraphs was larger at relatively higher m, the m-th-order largest component of the randomized counterparts was larger at relatively lower m. In other words, the higher-order largest components in the real-world hypergraphs could not be explained simply by their hyperdegree distribution and size distribution. To this end, we propose a novel random hypergraph model in which higher-order components substantially exist. The concept of the subgroup consisting of randomly preassigned nodes is introduced in the model. First, prepare N nodes, H hyperedges, and G subgroups. Then, our hypergraph model evolves by recruiting either a random node (with probability 1-p) or a random group (with probability p) to a random hyperedge until the desired mean degree is reached. We analytically calculate the properties of the model hypergraphs, such as the m-th-order giant component size, supported by numerical simulations. We applied an SIS-based simple higher-order contagion model to our hypergraph model to understand the effect of the higher-order connectivity on dynamics. In this model, the rate beta_n at which all nodes in a hyperedge will be infected is determined according to the number of infected nodes n in the hyperedge, and the infected nodes become susceptible at the rate mu. We confirmed that the extensive presence of the higher-order connectivities decreases of the phase transition point in an SIS-based simple higher-order contagion model. We anticipate that this model could provide a framework for exploring the higher-order architectures in hypergraphs.

Connecting Hodge and Sakaguchi-Kuramoto : a mathematical framework for coupled oscillators on simplicial complexes

ABSTRACT. The Kuramoto model is a popular dynamical system, capable of reproducing a wide range of observed synchronisation behaviours. Here, we formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order $k$. Crucially, we introduce linear and non-linear frustration terms that are independent of the orientation of the $k+1$ simplices, providing a natural generalization of the Sakaguchi-Kuramoto model. While the formulation of the model is general, we focus our interest on the edge simplicial frustrated Kuramoto model: \begin{align} \dot \theta^{(1)} = -\alpha_1 - N_0\mathrm{sin}\left ( N_0^* \theta^{(1)}\right) \nonumber- (N_1^*V_2)^- \mathrm{sin}\left (V_2 N_1 \theta^{(1)} + \alpha_2\right). \label{eq:edge_frustrated_kuramoto} \end{align} The coboundary operator $N_k$ and its dual $N_k^*$ on a simplicial complex are defined using the generalized incidence matrices $B_k^T\in M^{n_{k}\times n_{k+1}}$ which encode the topology of a simplicial complex, and the weight matrices $W_k$, which are diagonal matrices of the $k$-simplices weights: $N_k = B_k\, ,\ N_k^* = W_{k} B_k^T W^{-1}_{k+1}$. The lift matrices $V_k = \begin{pmatrix} I_{n_k}\\ -I_{n_k} \end{pmatrix}\,$ create duplicates of simplices of order $k$ with an orientation opposite to the original one, the sign projection operator $X_{ij}^\pm = \frac12 \big(X_{ij} \pm \left |X_{ij}\right |\big )\,\ \forall ij$ ensures the sign of the orientation relative to the frustration is consistent so that the model is independent of the orientation of the faces and is consistent with the node Sakaguchi-Kuramoto model. We choose the negative projection so that close to synchronisation, we follow consensus dynamics.

\indent We further propose a generalized formulation of the Kuramoto higher-order parameter as a potential function to write the dynamics as a gradient flow. The generalised order parameter measures synchronisation with respect to the distance to the kernel of the Laplacian that drives the dynamics close to synchronisation. In the node Kuramoto case, the kernel is the constant eigenvector, corresponding to full synchronisation. In higher-order models, equal phase synchronisation will in general not be in the kernel of the Laplacian and full synchronisation will be akin to phase-locking.

\indent We study the properties of the dynamics of the edge simplicial Sakaguchi-Kuramoto model using a selection of simplicial complexes of increasingly complex structure, to highlight the complexity of dynamical behaviors emerging from even simple simplicial complexes. In particular, using the Hodge decomposition of the solution, we highlight how the nonlinear frustration couples the dynamics in orthogonal subspaces. We discover various dynamical phenomena related to the simplicial complex topological properties, such as the partial loss of synchronization in subspaces aligned with the Hodge subspaces and the emergence of simplicial phase re-locking in regimes of high frustration (see Figure \ref{fig}).

Identifying vital nodes through random walks on higher-order networks

ABSTRACT. Empirical complex networks possess considerable heterogeneity of nodes connections, resulting in that a small portion of nodes playing far crucial rules in network structure and function. How to characterize nodes’ influence and identify vital nodes is by far still unclear in the study of networks with higher-order interactions. In this paper, we represented higher-order interacting networks with a variant of bipartite graph and proposed a two-sided random walk-based approach to identify vital nodes. The bipartite graph comprised of two distinct node sets (U, W) and an edge set E containing edges between U and W, where U is the set of the original nodes and W is the set of interactions. Different from usual bipartite representations of higher-order networks, we also enable the interactions between the nodes in U by adding edges among the nodes in U (Fig. 1 (a-b)). This novel representation can preserve as much information of the higher-interacting network as possible. Then random walk process was applied to this bipartite representation to identify vital nodes. A tunning parameter was introduced to coordinate the probability of walks going along pairwise or higher-order interactions. Results showed that the proposed method helps solve the localization problem of centrality measures, e.g., Eigenvector centrality, in networks (Fig. 1 (c)). In addition, results suggested that more random walks along pairwise interactions would help find vital nodes that accelerate spreading in networks. In contrast, more walks along higher-order interactions would help find vital nodes that expand the spreading scope (Fig. 1(d)). The proposed bipartite representation of the higher-order interacting network and the random walk model give us a better understanding of the influence of higher-order interactions on network functionality and shed light on the design of more robust networked systems.

Higher-order motif analysis in hypergraphs

ABSTRACT. A deluge of new data on real-world networks suggests that interactions among system units are not limited to pairs, but often involve a higher number of nodes. To properly encode higher-order interactions, richer mathematical frameworks such as hypergraphs are needed, where hyperedges describe interactions among an arbitrary number of nodes. Here we systematically investigate higher-order motifs, defined as small connected subgraphs in which vertices may be linked by interactions of any order, and propose an efficient algorithm to extract complete higher-order motif profiles from empirical data. We identify different families of hypergraphs, characterized by distinct higher-order connectivity patterns at the local scale. We also propose a set of measures to study the nested structure of hyperedges and provide evidences of structural reinforcement, a mechanism that associates higher strengths of higher-order interactions for the nodes that interact more at the pairwise level. Our work highlights the informative power of higher-order motifs, providing a principled way to extract higher-order fingerprints in hypergraphs at the network microscale.

Optimizing higher-order network topology for synchronization of coupled phase oscillators

ABSTRACT. Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned to optimize synchronization. Previous studies showed that the optimized conventional network with pairwise interactions favors a homogeneous degree distribution of nodes when the interaction is undirected, and is always structurally asymmetric when the interaction is directed. However, the optimal control on synchronization for networks with prevailing higher-order interactions is less explored. Here, by considering the higher-order interactions in a hypergraph and the Kuramoto model with 2-hyperlink interactions, we find that the network topology with optimized synchronizability may have distinct properties. For the undirected interaction, optimized networks with 2-hyperlink interactions by simulated annealing tend to become homogeneous in the nodes' generalized degree, consistent with 1-hyperlink (pairwise) interactions. We further define the directed hyperlink, and rigorously demonstrate that for the directed interaction, the structural symmetry can be preserved in the optimally synchronizable network with 2-hyperlink interactions, in contrast to the conclusion for 1-hyperlink interactions. The results suggest that controlling the network topology of higher-order interactions leads to synchronization phenomena beyond pairwise interactions.

12:00-13:30 Session 10E: Geometric
Switchover phenomenon induced by epidemic seeding on geometric networks

ABSTRACT. It is a fundamental question in disease modeling how the initial seeding of an epidemic, spreading over a network, determines its final outcome. One important goal has been to find the seed configuration, which infects the most individuals. Although the identified optimal configurations give insight into how the initial state affects the outcome of an epidemic, they are unlikely to occur in real life.

In this talk, we identify two important seeding scenarios, both motivated by historical data, that reveal a complex phenomenon [1]. In one scenario, the seeds are concentrated on the central nodes of a network, while in the second one, they are spread uniformly in the population. We challenge the intuition that an epidemic from the most tightly connected, central nodes of a network always leads to a larger epidemic in the long run, in terms of the number of final infected people. Through data-driven and synthetic simulations on real and modelled geometric metapopulation networks, we find that when the basic reproduction number R0 is close to 1, more individuals become infected in the central seeding scenario, but for larger values of R0, the uniform seeding scenario is more dangerous (see the figure). We find that this switchover phenomenon is amplified by the geometric nature of the underlying network by simulations on a variant of the Hyperbolic Random Graph model [2], which features both spacial properties and a scale-free degree distribution, similarly to real metapopulation networks. Based on an equivalence between metapopulation models and bond percolation established by [3], we also provide mathematically rigorous proofs of the switchover phenomenon in analytically tractable network models such as the Configuration Model and the Stochastic Block Model.

Our results expand on the previous finding that in case of a single seed, the central scenario is always more dangerous, and further our understanding why the sizes of consecutive waves of a pandemic can differ even if their epidemic characters are similar. We highlight the importance to follow not only the rate but also the spatial distribution of new infection cases during an ongoing pandemic.

References [1] G.Ódor, D.Czifra, J.Komjáthy, L.Lovász, and M.Karsai,“Switchover phenomenon induced by epidemic seeding on geometric networks,” Proceedings of the National Academy of Sciences, vol. 118, no. 41, 2021. [2] D. Krioukov, F. Papadopoulos, M. Kitsak, A. Vahdat, and M. Boguná, “Hyperbolic geometry of complex networks,” Physical Review E, vol. 82, no. 3, p. 036106, 2010. [3] M. Barthélemy, C. Godreche, and J.-M. Luck, “Fluctuation effects in metapopulation models: percolation and pandemic threshold,” Journal of theoretical biology, vol. 267, no. 4, pp. 554–564, 2010.

Modeling human proximity networks with random hyperbolic graphs

ABSTRACT. Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Understanding their properties is critical because they affect the behavior of disease and information spreading, as well as the formation and evolution of communities. Interestingly, a simple model of mobile agents, which assumes the agents perform random walks, reproduces a wide variety of these properties. However, until recently the mechanisms responsible for more complex social behavior remained elusive. Specifically, random walks cannot reproduce the recurrent formation of groups of the same people, which originate from human motion patterns that are far from random. We show that many of the properties of proximity networks, including the formation of recurrent groups (components), emerge naturally and simultaneously in a simple latent space model, called dynamic-S1. The dynamic-S1 does not model agent mobility, but captures their connectivity in each snapshot--each snapshot in the model is a realization of the S1 model of traditional complex networks, which is isomorphic to random hyperbolic graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, inter-contact and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Furthermore, the behavior of compartmental epidemic spreading processes, such as SIS and SEIR, is remarkably similar in real and modeled networks. We have also shown that the time-aggregated representation of real human proximity networks can be meaningfully embedded into hyperbolic space, using methods developed for the S1 model. Using the resulting embeddings one can identify communities, facilitate greedy routing on the temporal network, and predict future links. Taken altogether, our results indicate that dynamic random hyperbolic graphs are adequate null models of human proximity networks.

Dimension matters when modelling network communities in hyperbolic spaces

ABSTRACT. See attached PDF file.

Nearest-neighbour network in hyperbolic space: a simple model of a directed network with asymmetric degree distribution

ABSTRACT. Reference and recommendation networks are ubiquitous: encyclopedia articles and scientific papers refer to each other, people recommend each other books, films and music, online shops are full of “people who like this also like that” recommendations. Such networks are substantially asymmetric: the rules according to which a node becomes a source are different from those according to which it becomes a target. Often, the number of recommendations given is effectively bounded, while the number of times a node is recommended (in-degree) is unlimited and has a wide distribution.

Here we suggest a relatively simple model of a directed network with asymmetric degree distribution: narrow distribution of out degree and (generally speaking) wide distribution of the in degree, and study its structural properties. Our model belong to the hyperbolic class [1,2] and is a direct generalization of nearest-neighbor models studied extensively for the case of Euclidean metric spaces.

Consider a disk on a hyperbolic space, put a large number of points onto the disk uniformly at random, and then connect each point by directed links to a fixed number $m$ of its nearest neighbors. We study the properties of resulting networks in the limit when the area of the disk diverges while the dimensionless density of the points (measured in the space curvature units) remains constant. We show that the resulting networks consist of two distinct parts (see figure), a central core where the in-degree has an approximately Poissonian distribution with average $m$, and peripheral part, where the average in-degree is position-dependent and increases exponentially with increasing distance from the periphery of the disk. The distribution of nodes between core and periphery is controlled by the dimensionless density of the nodes: in high-density networks the core dominates, while the low-density are dominated by the periphery.

The resulting overall in-degree distribution is a truncated power law with exponent -3, the width of the power-law region depends on the density, in the limit of low density the distribution becomes a true power law. Notably, in contrast with the model presented in [1] average in-degree of the network remain finite and equal to $m$ in the thermodynamic limit. Similarly to [1] the exponent of the in-degree distribution can be regulated by switching to a quasi-uniform distribution of nodes.

We calculate additional structural properties of the network, such as the fraction of bidirectional links, and show how it can be regulated by introducing an additional temperature-like parameter governing the probability of link formation.

1. Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., Boguñá, M., Hyperbolic geometry of complex networks, Phys. Rev. E 82, 036106 (2010) .

2. Papadopoulos, F., Kitsak, M., Serrano, M.Á., Boguná, M., Krioukov, M. Popularity versus similarity in growing networks, Nature 489, 537 (2012).

Model-independent embedding of directed networks into geometric spaces
PRESENTER: Bianka Kovács

ABSTRACT. Hyperbolic network models are known to be able of generating networks that are scale-free, highly clustered, and small-world, and can even have a pronounced community structure as well. The success of the hyperbolic network models provides a strong motivation for the development of hyperbolic embedding algorithms that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network topology. However, the previous hyperbolic embedding methods were developed for undirected graphs and can not grasp the asymmetry of the connections occurring in directed networks. Here, we propose a general framework for embedding directed networks into both Euclidean and hyperbolic spaces, where two positions are assigned for each node in the system: one representing its behaviour as a source and one that characterises it as a target of links. Contrary to previous methods, our newly introduced Euclidean-hyperbolic conversion transforms Euclidean embeddings into hyperbolic ones without assuming any specific hyperbolic model as the generator of the network to be embedded.

Scaling up real networks by geometric branching growth

ABSTRACT. Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or species. Here, we provide empirical evidence for self-similar growth of network structure in the evolution of real systems---the journal citation network and the world trade web---and present the Geometric Branching Growth model, which predicts this evolution and explains the symmetries observed. The model produces multiscale unfolding of a network in a sequence of scaled-up replicas preserving network features, including clustering and community structure, at all scales. Practical applications in real instances include the tuning of network size for best response to external influence and finite-size scaling to assess critical behavior under random link failures.

12:00-13:30 Session 10F: Theory II
When and how can models of collective social phenomena benefit from data-driven individual-level models?

ABSTRACT. Complexity science has explained the emergence of diverse collective social phenomena by identifying individual-level mechanisms that reproduce the large-scale behaviors of interest. On the other hand, fields such as social psychology, behavioral economics, and consumer behavior are traditionally concerned with detailed modeling of how individuals make choices, often via utility-based models of individual choices. Bridging the two modeling philosophies remains elusive. Because of this, it remains unclear when and how individual-level models may benefit predictions of collective social phenomena, and inform successful interventions to steer the collective dynamics toward desired states.

Here, we show that popular collective adoption theories (preferential attachment models, threshold models of social diffusion, and epidemic spreading models) can be derived from individual-level choice models traditionally used in microeconomics and consumer behavior. This theoretical result enables the calibration of collective adoption models with individual-level discrete-choice experiments. To this end, based on the widely-studied threshold model of diffusion, we find analytically a simple formula that links individuals' threshold to the utility function's coefficients. We collect individual-level data from two discrete-choice experiments on information spreading and new product adoption, respectively, and use the derived formula to infer individual-level thresholds. Analysis of simulated choice data show that our threshold estimation procedure is accurate and reasonably robust with respect to noise.

We demonstrate the implications of these results for success predictions and seeding policies to maximize the reach of social diffusion. Specifically, by calibrating agent-based simulations with the individual-level experimental results, we determine under which conditions individual-level detailed modeling improves predictions and seeding policies compared to network structural properties and traditional agent-based models. When comparing different products across different networks, we find that individual-level detailed information improves success predictions as long as behavioral noise stay sufficiently low. At the same time, when considering the spreading of a single product on a given network, seeding policies only benefit from individual-level data for high-threshold alternatives that face high levels of social resistance (see Fig. 1 in the enclosed pdf). We illustrate the implications of this result for preventing the spreading of false information and promoting sustainable consumption. For example, although sustainable products face higher levels of social resistance, they might spread wider than non-sustainable alternatives if their diffusion starts in the centers of clusters of highly-susceptible potential adopters.

Ensemble nonequivalence and Bose-Einstein condensation in weighted networks

ABSTRACT. The asymptotic (non)equivalence of canonical and microcanonical ensembles, describing systems with soft and hard constraints respectively, is a central concept in statistical physics. Traditionally, the breakdown of ensemble equivalence (EE) has been associated with nonvanishing relative canonical fluctuations of the constraints in the thermodynamic limit. Recently, it has been reformulated in terms of a nonvanishing relative entropy density between microcanonical and canonical probabilities. The earliest observations of EE violation required phase transitions or long-range interactions. More recent research on binary networks found that an extensive number of local constraints can also break EE, even in absence of phase transitions. Here we study for the first time ensemble nonequivalence in weighted networks with local constraints. Unlike their binary counterparts, these networks can undergo a form of Bose-Einstein condensation (BEC) producing a core-periphery structure where a finite fraction of the link weights concentrates in the core. This phenomenon creates a unique setting where local constraints coexist with a phase transition. We find surviving relative fluctuations only in the condensed phase, as in more traditional BEC settings. However, we also find a non-vanishing relative entropy density for all temperatures, signalling a breakdown of EE due to the presence of an extensive number of constraints, irrespective of BEC. Therefore, in presence of extensively many local constraints, vanishing relative fluctuations no longer guarantee EE.

Random graph models with fixed centrality patterns and degree sequence

ABSTRACT. The Onion Decomposition (OD) offers a reliable and rapid way to obtain information about the micro-, meso- and macroscopic organization of a network. Following its introduction a few years ago, it has been successfully used in various contexts, such as network reconstruction, network embedding, as a tool to quantify spreading processes and as a tool to accurately predict bond percolation thresholds. While it is often used to obtain insights on a graph at a macroscopic level, OD also contains rich information at the scale of individual nodes; a simple set of rules on the immediate neighbors of a node can be used to entirely describe its position in the OD. Using these rules brings about an easy-to-implement mechanism by which we can explore ensembles of graphs that are constrained to a specific centrality structure.

We develop a new set of such ensembles, starting with the Layered Configuration Model (LCM). We define the LCM to be the ensemble containing all graphs with both a fixed degree sequence and a fixed OD sequence. Following from the LCM, we then define ensembles with node type correlations that we call the Layered and Correlated Configuration Models (LCCMs). In these ensembles we conserve either the degree to degree correlations, the layer to layer correlations or the layer-degree to layer-degree correlations. We also diversify the different LCCMs by imposing either hard constraints on the correlations, where we preserve exactly the correlations at every swap, or by imposing soft constraints, where we preserve the correlations on average only.

We propose a set of Markov Chain Monte Carlo algorithms based on edge swapping to generate samples from this collection of graph ensembles. We discuss how to uniformly sample the ensembles with hard constraints, and non-uniformly sample the ensembles to respect the soft constraints. To encourage the use of these null models, we present a complete C++ and Python library that samples graphs from our ensembles. Finally, we compare the different ensembles with already existing ones, underlining the foundational role of centrality in the overall organization of real networks.

Random Matrix Analysis of Multiplex Networks

ABSTRACT. We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the combined multiplex network exhibit superposition of two Gaussian orthogonal ensemble (GOE)s for very small multiplexing strength followed by a smooth transition to the GOE statistics with an increase in the multiplexing strength. Interestingly, randomness in the connection architecture, introduced by random rewiring to 1D lattice, of at least one layer may govern nearest neighbor spacing distribution (NNSD) of the entire multiplex network, and in fact, can drive to a transition from the Poisson to the GOE statistics or vice versa. Notably, this transition transpires for a very small number of the random rewiring corresponding to the small-world transition. Ergo, only one layer being represented by the small-world network is enough to yield GOE statistics for the entire multiplex network. Spectra of adjacency matrices of underlying interaction networks have been contemplated to be related with dynamical behavior of the corresponding complex systems, the investigations presented here have implications in achieving better structural and dynamical control to the systems represented by multiplex networks against structural perturbation in only one of the layers.

Weighted Belief Networks Unify Simple and Complex Contagion

ABSTRACT. From the spreading of infectious diseases to the diffusion of ideas, innovations, beliefs, and behaviors, contagion is one of the most fundamental dynamical processes in social systems. The dynamics of social contagion broadly fall into two classes—simple and complex contagion. Most social contagion models make an apriori assumption about the contagion dynamics being 'simple' or 'complex'. This is particularly troubling given that a single social system can exhibit a spectrum of contagion dynamics—from simple to complex—simultaneously.

In this work, we demonstrate that both behaviors of social contagion, simple and complex, can emerge from a single model of weighted belief network that is rooted in a fundamental cognitive desire to achieve internal coherence. This finding is reinforced by the observation of optimal modularity, a counter-intuitive phenomenon that can only occur with complex contagion.

Simple and complex contagion can be differentiated by the spreading sequence, but not by the spreading dynamics

ABSTRACT. The terms simple contagion and complex contagion usually refer to two categories of spreading mechanisms, where the latter involves social reinforcement while the former does not. Despite their clear difference at the microscopic level, it is unclear to what extent the observed macroscopic patterns are different and consequently distinguishable. Estimating the spreading mechanism is of significant importance, as it guilds us on how to interpret the empirical data, model the future spreading, control the rumor, and promote beneficial innovations. Here we focus on susceptible–infected (SI) model and linear threshold (LT) model, which are respectively the typical example of simple and complex contagion. We first analyze the evolution of the portion of the infected population $I(t)$ at time $t$, capturing the spreading dynamics at the macroscopic level. We find that $I(t)$ from simple and complex contagion can overlap when the parameters are properly chosen. Hence, one can not distinguish the two spreading mechanisms from $I(t)$, as it can be well fitted by both the mechanisms. We then analyze the spreading dynamics at the microscopic level, characterized by the percentage of infected neighbors $\phi$ when a node becomes infected. As complex contagion requires more than one active neighbor to trigger the adoption, it is intuitively expected that $\phi$ would be higher in LT model than that in SI model. However, this hypothesis is not supported by the simulation. When the property of the network changes, $\phi$ generated by the LT model can be higher or lower than that generated by the SI model. Hence, different from our intuitions, we find that the two distinct models can not be differentiated by the spreading dynamics with confounding factors such as different initiator size, time evolution, and network topology. Instead, we propose that the temporal order in the spreading sequence can differentiate the two models, following the argument that complex contagion is apt to influence the local community whereas simple contagion can spread further and form a long spreading path. Using a simple machine learning tool, we confirm that the two spreading models can be accurately and robustly classified with different confounding factors whereas the baseline methods relying on the macroscopic and microscopic dynamics in general fail to accomplish the classification. We also demonstrate how the method can be applied to real data to identify the underlying spreading mechanism. Taken together, we bring evidence that our common approaches to identify simple and complex contagion are inherently incapable. By utilizing the temporal order in the spreading sequence, however, we can accurately and efficiently distinguish the two spreading mechanisms.

13:45-14:55 Session 11: Invited Talks (A. Motter & F. Valdovinos)
Complex Contagion: Unfolding and Control
How do ecological networks respond to global change?
16:25-17:25 Session 12: Poster IV
The network signature of constellation line figures

ABSTRACT. In current and historical astronomies across the world, groups of stars in the night sky were linked into constellations represented as line figures: spatial networks on the fixed background of stars. We analyse 1591 line figures from 50 cultures spanning all continents. We define and measure their visual signature: a set of network, spatial, and brightness features. We cluster the constellations by signature, and assess whether the shapes are unique to a culture (are abstract chain-like structures typical only to the medieval Chinese?), or to a phylogeny (for example, Mesopotamian). A signature may also simply be universal in some parts of the sky, so driven by the pattern of stars. We investigate these possibilities across the cultures.

Perturbation-based graph theory to the rescue of weighted networks

ABSTRACT. Built on the shoulders of graph theory the field of complex networks has become a central tool for understanding complex systems. Represented as a graph, empirical systems across domains can thus be studied using the same concepts and the same metrics. However, this simplicity is also a major limitation since graph theory is defined for a binary and symmetric description where the only relevant information is whether a link exists or not between two vertices. Adaptation to directed links was successful but the application to weighted networks has been rather clumsy. It is common practice to threshold empirical networks in order to obtain the binary representation needed for classical graph analysis. Many weighted versions of graph metrics have been developed replacing the binary entries in the equations of a metric by real valued entries. Such ad-hoc approaches fundamentally ignore the fact that link weights are not only numerical values but physical or statistical quantities.

Here, we propose a dynamical reformulation of graph theory that can help aleviate these limitations, valid at least for the class of networks that accept propagation. First, we show that classical graph metrics are derived from a simple but common generative dynamical model (a discrete cascade) governing how perturbations propagate along the network. From this perspective graph metrics are no longer regarded as combinatorial attributes of a graph, but they correspond to spatio-temporal properties of the network's response to external perturbations. We learn that the difficulties of graph theory to deal with weighted networks are more a consequence of the constrains of its underlying dynamical model than a limitation of the binary representation. Therefore, these limitation can be leveraged by replacing the underlying discrete cascade by other generative dynamical models which, for example, allow for the propagation of continuous variables, in continuous time.

Given an adjacency matrix A, it is well-known that the powers A^d encode the number of walks, of length d, that traverse between two nodes. From the dynamical perspective proposed here, the set of power matrices C(t) = {A^1, A^2, A^3, … , A^t} represent the network response to unit external perturbations – the Green's function – at consecutive discrete times t. Also, all the relevant information needed to describe the network, and to define graph metrics, is unfolded via the generative dynamics from the adjaceny matrix onto the set of power matrices C(t). Replacing the discrete cascade by other generative models (either discrete or continuous, conservative or non-conservative) and one can redefine the graph metrics from the cor-responding Green's function C(t).

In summary, we propose a dynamical generalization of graph theory in which the underlying generative model is explicit and tunable. This allows to define metrics in which both directionality and link weights are natural, built-in aspects of the metrics. It also provides the oportunity to calibrate network analyses by choosing generative models that are better suited for the particular system under study; thus balancing between simplicity and interpretability of results. Many past efforts have employed a variety of dynamics to study complex networks by navigating on them, e.g., random walkers or routing. We envision that the perturbative formulation here proposed serves to enclose all those efforts under a common umbrella.

Cascades of delays and diffusion algorithms on the railway network

ABSTRACT. As population grows, create and project better infrastructures has become a global priority. Mobility is recognized as a key area of policy intervention. How can quantitative studies improve well-being in socioeconomic environments? I try to assess this problem. The techniques are taken from Network Science and Agent-Based Modelling. In particular, how can delay cascades be analyzed and modeled? The study focuses onto applying diffusion and epidemic spreading models to railway mobility.

Propagation of disruptions in supply networks of essential goods: A population-centered perspective of systemic risk

ABSTRACT. The Covid-19 pandemic drastically emphasized the fragility of national and international supply networks (SNs), leading to significant supply shortages of essential goods for people, such as food and medical equipment. Severe disruptions that propagate along complex SNs can expose the population of entire regions or even countries to these risks. A lack of both, data and quantitative methodology, has hitherto hindered us to empirically quantify the vulnerability of the population to disruptions. Here we develop a data-driven simulation methodology to locally quantify actual supply losses for the population that result from the cascading of supply disruptions. We demonstrate the method on a large food SN of a European country including 22,938 business premises, 44,355 supply links and 116 local administrative districts. We rank the business premises with respect to their criticality for the districts’ population with the proposed systemic risk index, SRIcrit, to identify around 30 premises that—in case of their failure—are expected to cause critical supply shortages in sizable fractions of the population. The new methodology is immediately policy relevant as a fact-driven and generalizable crisis management tool. This work represents a starting point for quantitatively studying SN disruptions focused on the well-being of the population.

A Potential Mechanism for Low Tolerance Feedback Loops in Social Media Flagging Systems

ABSTRACT. Many people use social media as a primary information source, but their questionable reliability has pushed platforms to contain misinformation via crowdsourced flagging systems. Such systems, however, assume that users are impartial arbiters of truth. This assumption might be unwarranted, as users might be influenced by their own political biases and tolerance for opposing points of view, besides considering the truth value of a news item. In this paper we simulate a scenario in which users on one side of the polarity spectrum have different tolerance levels for the opinions of the other side. We create a model based on some assumptions about online news consumption, including echo chambers, selective exposure, and confirmation bias. A consequence of such a model is that news sources on the opposite side of the intolerant users attract more flags. We extend the base model in two ways: (i) by allowing news sources to find the path of least resistance that leads to a minimization of backlash, and (ii) by allowing users to change their tolerance level in response to a perceived lower tolerance from users on the other side of the spectrum. With these extensions, in the model we see that intolerance is attractive: news sources are nudged to move their polarity to the side of the intolerant users. Such a model does not support high-tolerance regimes: these regimes are out of equilibrium and will converge towards empirically-supported low-tolerance states under the assumption of partisan but rational users.

In Figure 1, phi_r is a parameter regulating the tolerance of the right side of the spectrum (positive opinion value), while phi_l is the tolerance of the left side of the spectrum (negative opinion value).

The Weighted Bitcoin Lightning Network

ABSTRACT. The Bitcoin Lightning Network (BLN) was launched in 2018 to scale up the number of transactions between Bitcoin owners. Although several contributions concerning the analysis of the BLN binary structure have recently appeared in the literature, the properties of its weighted counterpart are still largely unknown. The present contribution aims at filling this gap, by considering the Bitcoin Lightning Network over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, and focusing on its weighted, undirected, daily snapshot representation. As the study of the BLN weighted structural properties reveals, it is becoming increasingly ‘centralised’ at different levels, just as its binary counterpart: 1) the Nakamoto coefficient shows that the percentage of nodes whose degrees/strengths ‘enclose’ the 51% of the total number of links/total weight is rapidly decreasing; 2) the Gini coefficient confirms that several weighted centrality measures are becoming increasingly unevenly distributed; 3) the weighted BLN topology is becoming increasingly compatible with a core-periphery structure, with the largest nodes ‘by strength’ constituting the core of such a network, whose size keeps shrinking as the BLN evolves. Further inspection of the resilience of the weighted BLN shows that removing such hubs leads to the network fragmentation into many components, an evidence indicating potential security threats - as the ones represented by the so called ‘split attacks’.

Network medicine and its promises for complex human diseases

ABSTRACT. Biomedical researches at the era of precision medicine are improved by Network medicine. This new field research combines principles and approaches of systems biology in trying to understand the basis of human diseases, to set up new biomarkers and to develop new therapeutics. Using the tools of network science and focusing on the molecular biology and omics data at the cellular level, Network medicine is now ble to reveal the complex liaisons and interactions between human patho-phenotypes molecular mediators to determine human diseases. Network medicine is a “holistic approach trying to look at the whole system at once rather than trying to find a single magic treatment bullet, which is the principle behind so many reductionist approaches to disease”. Diseases are considered arising because of the perturbation of one or many disease-perturbed biological networks through genetic and/or environmental changes. Many different networks underling human diseases can be studied such as networks of protein-protein interactions, or networks of expressed genes following changes in expression of messenger RNA. Biological variants among molecular mediators of the molecular biological networks can be interpreted in several ways. Here, we will discuss through literature review network-based signatures in neuro-endocrine cancers that put a person at risk for such complex diseases.

Network-based cancer precision medicine : A new emerging paradigm

ABSTRACT. The complex interactions in biological systems have been shown to affect the response to single-targeted therapies which were initially developed under the "reductionist paradigm “of cancer precision medicine, the "reductionist paradigm “as a scientific approach consists of splitting reality into separate entities and studying their functioning. To deal with the fundamental problems, great efforts have been dedicated from a network perspective to explore the tumorigenesis, its mechanisms and progression. As a complex disease, the understanding of cancer has to be extended by exploiting new advances in cancer diagnosis, prevention and treatment. Many factors, such as availability of targeted drugs, advances in laboratory science, and improved information systems, converged to make precision medicine research possible on a large scale at the National Cancer Institute. This study abridges the novelty of network applications in cancer precision medicine research, including biomarker identification, cancer patient stratification and network target recognition, highlights network-based systematic integrations across macro and micro networks, and discusses the tremendous potential of this new emerging network-based "systems paradigm" for precision medicine, which would ultimately make substantial progress for fighting cancer. But until then, all clinicians are challenged to make sense of an overabundance of information when managing individual patients.

Cancer and epigenetic

ABSTRACT. Cancer is a serious pathology whose detection at an early stage and its avoidance are the major objectives of modern medicine in the field of oncology. Thus, to understand the development of cancer, researchers have long focused on gene mutations, by sequencing as many cancer cells as possible.

A new player is now identified: epigenetic modifications, which govern the way genetic information is read and used by the cell. This aspect of research is improving, while the means for “reading” the variations of the epigenome are multiplying.

These modifications, which do not change the DNA itself, act as a chef, express or use the dosage of certain "ingredients" in the cell. Epigenetic marks include proteins, histones, kinds of coils around DNA wraps. By arranging themselves in a more or less condensed way, histones change the accessibility and therefore the readability of genes. Various chemical marks regulate the degree of condensation of "chromatin", the complex formed by DNA and histones. These marks can also be molecules (methyl groups), which are grafted onto certain places in the genome and block the expression of a given gene.

The idea then is to identify the epigenetic actor responsible for the cancer in question and to react in order to prevent it occurrence.

Epigenetic, Slowing Biological Aging

ABSTRACT. Aging is the biggest risk factor for many chronic diseases, including cardiovascular disease, cancer, neurodegeneration, and diabetes type2. BUT, If these people eat an abundance of vegetables, do not smoke, maintain a healthy lifestyle, a normal weight, are physically active,increase eating too much meat or processed foods, and moderate alcohol consumption, this life expectancy will definitely getting improved.

What is the implication of epigenetics in this improvement? .

As we grow older, several changes are made in our genetic material and alter the expression of certain genes. These modifications, which are called "epigenetic", often consume the form of methyl groups (CH3) which are added to a base of DNA (cytosine) to either prevent or increase the expression of a gene. It has been found that the degree of methylation of certain regions of DNA is strongly correlated with aging and analytical techniques (DNAmAge) have been developed to estimate the biological age of a person by specified methylation levels of these regions. **The secret of people who live long and healthy lives is therefore not a question of genetics, but rather of epigenetics, that is to say the set of factors associated with lifestyle which, collectively, modulates the expression of our genes. This is encouraged, because it means that our destiny is generally not fixed at birth and that we can really take control of our health by modifying our lifestyle.

Graph similarity learning for change-point detection in dynamic networks

ABSTRACT. Dynamic networks are ubiquitous objects that model sequential graph-structured data, e.g., brain connectome, population flows between geographical areas and online messages in social networks. In this work, we consider dynamic networks that are temporal sequences of graph snapshots, and aim at detecting abrupt changes in their structure. This task is often denoted network change-point detection (NCPD) and has numerous applications, such as fraud detection or physical motion monitoring. In an online setting, change-points are detected while the graph snapshots are collected, and one usually aims at doing so with minimal detection delay. Leveraging a graph neural network model, we design a method to perform online NCPD that can adapt to the specific network domain and localise changes with no delay. More precisely, we train a Siamese graph neural network architecture to learn an adequate graph similarity function, and then compute an average similarity score via a sliding window. This method allows for the detection of significant changes between the current graph and its recent history, without prior knowledge on the network distribution and types of change-points; moreover, our method can be applied to a large variety of networks, that include for instance edge weights and node attributes. We demonstrate the effectiveness of our method on synthetic data generated from a dynamic stochastic block model with different change-point settings, and on two real data sets, namely stock returns in the S&P 500 index and sensor data from a physical activity experiment. We show that our method enjoys a number of benefits: it is able to learn an adequate similarity measure for NCPD, requires a shorter data history to detect changes, and leads to smaller detection delays than most existing state-of-the-art baselines.

Trophic Analysis On Production Network: Applying The Idea Of Food Chains To Economic data

ABSTRACT. This study aims to understand the position of economic sectors and regional supplier-buyer relationships between countries by studying the flow of goods within the production network built from the World Input-Output Table. We use the newly improved version of trophic levels and related concept trophic incoherence to investigate the flow structure of the production network. Unlike works using centrality measures to identify key economic sectors, this work relies purely on the flow of goods and focuses on the ranking of sectors and countries. We present the trophic structures of different scales and their time evolution. In addition, understanding the cycles structure within the network helps the study of economic growth and shock propagation. Further using the trophic levels, we decompose the original network into the circular flow and potential flow. The Circular flow extracts the cycle structure from the original network. With the circular part, we find important economic clusters using flow-based community detection techniques. We also propose a circular flow-based edge importance measure to find important transactions within the network. This work brings the idea of trophic analysis to economic networks and contributes to the empirical study of the global production networks.

Opinion Diversity and Cooperation in Dynamical Networks

ABSTRACT. In various aspects of life on earth, cooperation can be observed in action. This can range from man-made concepts such as the economy and politics to aspects of the natural world, including animal social groups and cellular mechanics. In the field of game theory, the act of cooperation is considered as the act of an individual producing some form of benefit/commodity that can be utilised by others they are associated with, which comes at some personal cost.

Ideally, all individuals within such a scenario will engage in cooperation to look out for each other and collectively take advantage of the benefits produced, outweighing the downsides of the incurred costs. However, as historical events, such as the tragedy of commons, and certain games illustrate, this altruistic behaviour can be taken advantage of by opportunistic cheaters. In game theory, a cheater is considered as an individual not does not produce any benefits for others and not incurring any costs. A cheater will still take advantage of the benefits produced by others whilst giving nothing in return.

In [1], we explore how the implementation of simulated diversity of opinion can potentially contribute to the structure and mechanics of a dynamical network model and to the resilience of cooperation, where individuals joining the network are able to make use of private and publicly available information when deciding which individual, they should associate themselves with before engaging in a game of the Prisoner’s Dilemma. Our results [1] show that increasing this diversity of opinion, in general, leads to more stable but less interconnected and prosperous networks and leads to the emergence of more frequent, but shallower, information cascades.

References: [1] - Miles AL, Cavaliere M. Opinion Diversity and the Resilience of Cooperation in Dynamical Networks. Mathematics;9(15):1801

Changes in Mobility Network Structure Drove Experienced Segregation During the Pandemic

ABSTRACT. Using origin-destination flows for each month of 2020 and 2021, I construct spatial interaction networks for the 100 largest metropolitan areas in the United States. Building on Athey et al. (2021) and Moro et al. (2021), I document changes in “experienced” segregation—the degree to which individuals of one group will interact with individuals of another during daily life—through the pandemic. I begin by showing that assortativity by income and race, measured at the level of the Census block group, peaked in April of 2020 when orders to remain at home were most stringent, at that assortativity by race is higher than assortativity by income. This holds for both 1st- and 2nd-order assortativity (Zhou et al. 2008): people visit neighborhoods similar to their own neighborhood, and people visit neighborhoods where other people from neighborhoods similar to theirs visit. Next, we partition the network in each month using both random walks and modularity for comparison, tracking changes to communities across months using a technique employed by Gao et al. (2018), which identifies central nodes and feeds labels forward in time based on these shared central nodes, as well as partition quality across time following Straulino et al. (2021). Community size decreased as concentration by race and income increased. While assortativity measures have still not returned to their prepandemic conditions, community structure is noisier. In addition to describing differences in experienced segregation across the country and across time, I explore several possible explanations, finding marked spatial patterns. Building a multiplex network with each layer corresponding to a type of visit—restaurants, shops, offices—I show that restaurants play an important role in mixing and the loss of dining during the pandemic contributed to changes in urban integration; the life or death of downtown may be an important determinant of experienced segregation moving forward, and one for urban policy to consider.

Network Analysis of Population Flows and Socioeconomic Homophily in Neighbourhood Shootings Dynamics

ABSTRACT. Gun violence related theories posit stability and concentration of gun violence and predict contagious diffusion into surrounding areas. Recent empirical studies have produced mounting evidence of spatiotemporal diffusion of gun violence. However, previous research has mainly focused on the gun violence spatiotemporal diffusion from a spatial perspective and overlooked the underlying mechanisms that foster shootings co-movement. Also, empirical investigations into the underlying factors driving shooting trajectories in similar but non-contiguous neighbourhoods are scarce and rely on inappropriate methods. Using network analysis, this research explores the potential drivers of shooting incident dynamics by investigating the role of people movement, spatial proximity, and social distance between neighbourhoods. Using shooting incidents data from Chicago, IL, USA, a Mobile Phone Origin Destination (MPOD) dataset, and US census data, we estimate a set of Exponential Random Graph Models to investigate the attributes of neighbourhoods that foster shooting incidents co-movement. The analyses show that higher movement flows between neighbourhoods and socio-economic similarity of neighbourhoods increase the likelihood of shootings co-movement ties irrespective of spatial proximity between neighbourhoods. Identifying the potential drivers of shootings co-movement between neighbourhoods is important because it will help to deepen our understanding of why neighbourhood shooting rates move together.