Network higher-order structure dismantling

Diverse higher-order structures, foundational for supporting a network's "meta-functions", play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been consistently overlooked. In this paper, we introduce the concept of dismantling higher-order structures, with the objective of disrupting not only network connectivity but also eradicating all higher-order structures in each branch, thereby ensuring thorough functional paralysis. Given the diversity and unknown specifics of higher-order structures, identifying and targeting them individually is not practical or even feasible. Fortunately, their close association with k-cores arises from their internal high connectivity. Thus, we transform higher-order structure measurement into measurements on k-cores with corresponding orders. Furthermore, we propose the Belief Propagation-guided High-order Dismantling (BPDH) algorithm, minimizing dismantling costs while achieving maximal disruption to connectivity and higher-order structures, ultimately converting the network into a forest. BPDH exhibits the explosive vulnerability of network higher-order structures, counterintuitively showcasing decreasing dismantling costs with increasing structural complexity. Our findings offer a novel approach for dismantling malignant networks, emphasizing the substantial challenges inherent in safeguarding against such malicious attacks.Comment: 14 pages, 5 figures, 2 table

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

In vitro biofilm formation of Gardnerella vaginalis and Escherichia coli associated with bacterial vaginosis and aerobic vaginitis

ObjectiveTo determine the optimum biofilm formation ratio of Gardnerella vaginalis (G. vaginalis) in a mixed culture with Escherichia coli (E. coli).MethodsG. vaginalis ATCC14018, E. coli ATCC25922, as well as five strains of G. vaginalis were selected from the vaginal sources of patients whose biofilm forming capacity was determined by the Crystal Violet method. The biofilm forming capacity of E. coli in anaerobic and non-anaerobic environments were compared using the identical assay. The Crystal Violet method was also used to determine the biofilm forming capacity of a co-culture of G. vaginalis and E. coli in different ratios. After Live/Dead staining, biofilm thickness was measured using confocal laser scanning microscopy, and biofilm morphology was observed by scanning electron microscopy.ResultsThe biofilm forming capacity of E. coli under anaerobic environment was similar to that in a 5% CO2 environment. The biofilm forming capacity of G. vaginalis and E. coli was stronger at 106:105 CFU/mL than at other ratios (P<0.05). Their thicknesses were greater at 106:105 CFU/mL than at the other ratios, with the exception of 106:102 CFU/mL (P<0.05), under laser scanning microscopy. Scanning electron microscopy revealed increased biofilm formation at 106:105 CFU/mL and 106:102 CFU/mL, but no discernible E. coli was observed at 106:102 CFU/mL.ConclusionG. vaginalis and E. coli showed the greatest biofilm forming capacity at a concentration of 106:105 CFU/mL at 48 hours and could be used to simulate a mixed infection of bacterial vaginosis and aerobic vaginitis in vitro

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