Upper bounds for number of removed edges in the Erased Configuration Model

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected to half-edges of other nodes at random, and then self-loops are removed and multiple edges are concatenated to make the graph simple. Although asymptotic results for many properties of this model, such as the limiting degree distribution, are known, the exact speed of convergence in terms of the graph sizes remains an open question. We provide a first answer by analyzing the size dependence of the average number of removed edges in the erased configuration model. By combining known upper bounds with a Tauberian Theorem we obtain upper bounds for the number of removed edges, in terms of the size of the graph. Remarkably, when the degree distribution follows a power-law, we observe three scaling regimes, depending on the power law exponent. Our results provide a strong theoretical basis for evaluating finite-size effects in networks

The interplay of microscopic and mesoscopic structure in complex networks

Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models

Evolving Clustered Random Networks

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as generic models for studying the impacts of degree distributions and clustering on dynamical processes as well as null models for detecting other structural properties in empirical networks

Polynomials over quaternions and coquaternions: a unified approach

This paper aims to present, in a unified manner, results which are valid on both the algebras of quaternions and coquaternions and, simultaneously, call the attention to the main differences between these two algebras. The rings of one-sided polynomials over each of these algebras are studied and some important differences in what concerns the structure of the set of their zeros are remarked. Examples illustrating this different behavior of the zero-sets of quaternionic and coquaternionic polynomials are also presented.(undefined)info:eu-repo/semantics/publishedVersio

Neighbor Overlap Is Enriched in the Yeast Interaction Network: Analysis and Implications

The yeast protein-protein interaction network has been shown to have distinct topological features such as a scale free degree distribution and a high level of clustering. Here we analyze an additional feature which is called Neighbor Overlap. This feature reflects the number of shared neighbors between a pair of proteins. We show that Neighbor Overlap is enriched in the yeast protein-protein interaction network compared with control networks carefully designed to match the characteristics of the yeast network in terms of degree distribution and clustering coefficient. Our analysis also reveals that pairs of proteins with high Neighbor Overlap have higher sequence similarity, more similar GO annotations and stronger genetic interactions than pairs with low ones. Finally, we demonstrate that pairs of proteins with redundant functions tend to have high Neighbor Overlap. We suggest that a combination of three mechanisms is the basis for this feature: The abundance of protein complexes, selection for backup of function, and the need to allow functional variation

Identification and Classification of Hubs in Brain Networks

Brain regions in the mammalian cerebral cortex are linked by a complex network of fiber bundles. These inter-regional networks have previously been analyzed in terms of their node degree, structural motif, path length and clustering coefficient distributions. In this paper we focus on the identification and classification of hub regions, which are thought to play pivotal roles in the coordination of information flow. We identify hubs and characterize their network contributions by examining motif fingerprints and centrality indices for all regions within the cerebral cortices of both the cat and the macaque. Motif fingerprints capture the statistics of local connection patterns, while measures of centrality identify regions that lie on many of the shortest paths between parts of the network. Within both cat and macaque networks, we find that a combination of degree, motif participation, betweenness centrality and closeness centrality allows for reliable identification of hub regions, many of which have previously been functionally classified as polysensory or multimodal. We then classify hubs as either provincial (intra-cluster) hubs or connector (inter-cluster) hubs, and proceed to show that lesioning hubs of each type from the network produces opposite effects on the small-world index. Our study presents an approach to the identification and classification of putative hub regions in brain networks on the basis of multiple network attributes and charts potential links between the structural embedding of such regions and their functional roles

Spatio-Temporal Transmission Patterns of Black-Band Disease in a Coral Community

Transmission mechanisms of black-band disease (BBD) in coral reefs are poorly understood, although this disease is considered to be one of the most widespread and destructive coral infectious diseases. The major objective of this study was to assess transmission mechanisms of BBD in the field based on the spatio-temporal patterns of the disease

Simultaneous Genome-Wide Inference of Physical, Genetic, Regulatory, and Functional Pathway Components

Biomolecular pathways are built from diverse types of pairwise interactions, ranging from physical protein-protein interactions and modifications to indirect regulatory relationships. One goal of systems biology is to bridge three aspects of this complexity: the growing body of high-throughput data assaying these interactions; the specific interactions in which individual genes participate; and the genome-wide patterns of interactions in a system of interest. Here, we describe methodology for simultaneously predicting specific types of biomolecular interactions using high-throughput genomic data. This results in a comprehensive compendium of whole-genome networks for yeast, derived from ∼3,500 experimental conditions and describing 30 interaction types, which range from general (e.g. physical or regulatory) to specific (e.g. phosphorylation or transcriptional regulation). We used these networks to investigate molecular pathways in carbon metabolism and cellular transport, proposing a novel connection between glycogen breakdown and glucose utilization supported by recent publications. Additionally, 14 specific predicted interactions in DNA topological change and protein biosynthesis were experimentally validated. We analyzed the systems-level network features within all interactomes, verifying the presence of small-world properties and enrichment for recurring network motifs. This compendium of physical, synthetic, regulatory, and functional interaction networks has been made publicly available through an interactive web interface for investigators to utilize in future research at http://function.princeton.edu/bioweaver/

Plasmodium falciparum: Differential Selection of Drug Resistance Alleles in Contiguous Urban and Peri-Urban Areas of Brazzaville, Republic of Congo

The African continent is currently experiencing rapid population growth, with rising urbanization increasing the percentage of the population living in large towns and cities. We studied the impact of the degree of urbanization on the population genetics of Plasmodium falciparum in urban and peri-urban areas in and around the city of Brazzaville, Republic of Congo. This field setting, which incorporates local health centers situated in areas of varying urbanization, is of interest as it allows the characterization of malaria parasites from areas where the human, parasite, and mosquito populations are shared, but where differences in the degree of urbanization (leading to dramatic differences in transmission intensity) cause the pattern of malaria transmission to differ greatly. We have investigated how these differences in transmission intensity affect parasite genetic diversity, including the amount of genetic polymorphism in each area, the degree of linkage disequilibrium within the populations, and the prevalence and frequency of drug resistance markers. To determine parasite population structure, heterozygosity and linkage disequilibrium, we typed eight microsatellite markers and performed haplotype analysis of the msp1 gene by PCR. Mutations known to be associated with resistance to the antimalarial drugs chloroquine and pyrimethamine were determined by sequencing the relevant portions of the crt and dhfr genes, respectively. We found that parasite genetic diversity was comparable between the two sites, with high levels of polymorphism being maintained in both areas despite dramatic differences in transmission intensity. Crucially, we found that the frequencies of genetic markers of drug resistance against pyrimethamine and chloroquine differed significantly between the sites, indicative of differing selection pressures in the two areas