Unveiling Explosive Vulnerability of Networks through Edge Collective Behavior

Edges, binding together nodes within networks, have the potential to induce dramatic transitions when specific collective failure behaviors emerge. These changes, initially unfolding covertly and then erupting abruptly, pose substantial, unforeseeable threats to networked systems, and are termed explosive vulnerability. Thus, identifying influential edges capable of triggering such drastic transitions, while minimizing cost, is of utmost significance. Here, we address this challenge by introducing edge collective influence (ECI), which builds upon the optimal percolation theory applied to line graphs. ECI embodies features of both optimal and explosive percolation, involving minimized removal costs and explosive dismantling tactic. Furthermore, we introduce two improved versions of ECI, namely IECI and IECIR, tailored for objectives of hidden and fast dismantling, respectively, with their superior performance validated in both synthetic and empirical networks. Finally, we present a dual competitive percolation (DCP) model, whose reverse process replicates the explosive dismantling process and the trajectory of the cost function of ECI, elucidating the microscopic mechanisms enabling ECI's optimization. ECI and the DCP model demonstrate the profound connection between optimal and explosive percolation. This work significantly deepens our comprehension of percolation and provides valuable insights into the explosive vulnerabilities arising from edge collective behaviors.Comment: 19 pages, 11 figures, 2 table

Duplication Models for Biological Networks

Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks), and is fundamentally different from the mechanisms thought to dominate the growth of most non-biological networks (such as the internet [1-4]). The preferential choice models non-biological networks like web graphs can only produce power-law graphs with exponents greater than 2 [1-4,8]. We use combinatorial probabilistic methods to examine the evolution of graphs by duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph

The Giant component in a Random Subgraph of a Given Graph

Abstract We consider a random subgraph G p of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function of G) for which a giant component emerges. Suppose G satisfies some (mild) conditions depending on its spectral gap and higher moments of its degree sequence. We define the second order average degreed to bed = v

The Giant component in a Random Subgraph of a Given Graph

Abstract. We consider a random subgraph Gp of a host graph G formed by retaining each edge of G with probability p. We address the question of determining the critical value p (as a function of G) for which a giant component emerges. Suppose G satisfies some (mild) conditions depending on its spectral gap and higher moments of its degree sequence. We define the second order average degreed to bed where dv denotes the degree of v. We prove that for any > 0, if p > (1 + )/d then asymptotically almost surely the percolated subgraph Gp has a giant component. In the other direction, if p < (1 − )/d then almost surely the percolated subgraph Gp contains no giant component

Mitochondrial Genome of an 8,400-Year-Old Individual from Northern China Reveals a Novel Sub-Clade under C5d

Ancient DNA studies have always refreshed our understanding of the human past that can’t be tracked by modern DNA alone. Until recently, ancient mitochondrial genomic studies in East Asia are still very limited. Here, we retrieved the whole mitochondrial genome of an 8,400-year- old individual from Inner Mongolia, China. Phylogenetic analyses show that the individual belongs to a previously undescribed clade under haplogroup C5d that was most probably originated in northern Asia and may have a very low frequency in extant populations that is not yet sampled. We further characterized the demographic history of mitochondrial haplogroups C5 and C5d, and found that C5 experienced a sharp increase in population size starting from around 4,000 years before present (BP). The time when intensive millet farming was built by populations who are associated with the lower Xiajiadian culture and was widely adopted in northern China. We caution that people related to haplogroup C5 may added this farming technology to their original way of life and that the various subsistence may provide abundant food sources and may further contribute to the increase of the population size

Local dominance unveils clusters in networks

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data

Eye movement characteristics in a mental rotation task presented in virtual reality

IntroductionEye-tracking technology provides a reliable and cost-effective approach to characterize mental representation according to specific patterns. Mental rotation tasks, referring to the mental representation and transformation of visual information, have been widely used to examine visuospatial ability. In these tasks, participants visually perceive three-dimensional (3D) objects and mentally rotate them until they identify whether the paired objects are identical or mirrored. In most studies, 3D objects are presented using two-dimensional (2D) images on a computer screen. Currently, visual neuroscience tends to investigate visual behavior responding to naturalistic stimuli rather than image stimuli. Virtual reality (VR) is an emerging technology used to provide naturalistic stimuli, allowing the investigation of behavioral features in an immersive environment similar to the real world. However, mental rotation tasks using 3D objects in immersive VR have been rarely reported.MethodsHere, we designed a VR mental rotation task using 3D stimuli presented in a head-mounted display (HMD). An eye tracker incorporated into the HMD was used to examine eye movement characteristics during the task synchronically. The stimuli were virtual paired objects oriented at specific angular disparities (0, 60, 120, and 180°). We recruited thirty-three participants who were required to determine whether the paired 3D objects were identical or mirrored.ResultsBehavioral results demonstrated that the response times when comparing mirrored objects were longer than identical objects. Eye-movement results showed that the percent fixation time, the number of within-object fixations, and the number of saccades for the mirrored objects were significantly lower than that for the identical objects, providing further explanations for the behavioral results.DiscussionIn the present work, we examined behavioral and eye movement characteristics during a VR mental rotation task using 3D stimuli. Significant differences were observed in response times and eye movement metrics between identical and mirrored objects. The eye movement data provided further explanation for the behavioral results in the VR mental rotation task