Address clustering tries to construct the one-to-many mapping from entities to addresses in the Bitcoin system. Simple heuristics based on the micro-structure of transactions have proved very effective in practice. In this paper we describe the primary reasons behind this effectiveness: address reuse, avoidable merging, super-clusters with high centrality, and the incremental growth of address clusters. We quantify their impact during Bitcoin's first seven years of existence.

ObjectiveAn inadequate host response to the intestinal microbiota likely contributes to the manifestation and progression of human inflammatory bowel disease (IBD). However, molecular approaches to unravelling the nature of the defective crosstalk and its consequences for intestinal metabolic and immunological networks are lacking. We assessed the mucosal transcript levels, splicing architecture and mucosa-attached microbial communities of patients with IBD to obtain a comprehensive view of the underlying, hitherto poorly characterised interactions, and how these are altered in IBD.DesignMucosal biopsies from Crohn's disease and patients with UC, disease controls and healthy individuals (n=63) were subjected to microbiome, transcriptome and splicing analysis, employing next-generation sequencing. The three data levels were integrated by different bioinformatic approaches, including systems biology-inspired network and pathway analysis.ResultsMicrobiota, host transcript levels and host splicing patterns were influenced most strongly by tissue differences, followed by the effect of inflammation. Both factors point towards a substantial disease-related alteration of metabolic processes. We also observed a strong enrichment of splicing events in inflamed tissues, accompanied by an alteration of the mucosa-attached bacterial taxa. Finally, we noted a striking uncoupling of the three molecular entities when moving from healthy individuals via disease controls to patients with IBD.ConclusionsOur results provide strong evidence that the interplay between microbiome and host transcriptome, which normally characterises a state of intestinal homeostasis, is drastically perturbed in Crohn's disease and UC. Consequently, integrating multiple OMICs levels appears to be a promising approach to further disentangle the complexity of IBD.

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Few-node subgraphs are the smallest collective units in a network that can be investigated. They are beyond the scale of individual nodes but more local than, for example, communities. When statistically over-or under-represented, they are called network motifs. Network motifs have been interpreted as building blocks that shape the dynamic behaviour of networks. It is this promise of potentially explaining emergent properties of complex systems with relatively simple structures that led to an interest in network motifs in an ever-growing number of studies and across disciplines. Here, we discuss artefacts in the analysis of network motifs arising from discrepancies between the network under investigation and the pool of random graphs serving as a null model. Our aim was to provide a clear and accessible catalogue of such incongruities and their effect on the motif signature. As a case study, we explore the metabolic network of Escherichia coli and show that only by excluding ever more artefacts from the motif signature a strong and plausible correlation with the essentiality profile of metabolic reactions emerges.

Information on biological networks can greatly facilitate the function-orientated interpretation of high-throughput molecular data. Genome-wide metabolic network models of human cells, in particular, can be employed to contextualize gene expression profiles of patients with the goal of both, a better understanding of individual etiologies and an educated reclassification of (clinically defined) phenotypes. We analyzed publicly available expression profiles of intestinal tissues from treatment-naive pediatric inflammatory bowel disease (IBD) patients and age-matched control individuals, using a reaction-centric metabolic network derived from the Recon2 model. By way of defining a measure of ‘coherence’, we quantified how well individual patterns of expression changes matched the metabolic network. We observed a bimodal distribution of metabolic network coherence in both patients and controls, albeit at notably different mixture probabilities. Multidimensional scaling analysis revealed a bisectional pattern as well that overlapped widely with the metabolic network-based results. Expression differences driving the observed bimodality were related to cellular transport of thiamine and bile acid metabolism, thereby highlighting the crosstalk between metabolism and other vital pathways. We demonstrated how classical data mining and network analysis can jointly identify biologically meaningful patterns in gene expression data.

We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but non-random networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.

Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.

The pattern of over- and under-representations of three-node subgraphs has become a standard method of characterizing complex networks and evaluating how this intermediate level of organization contributes to network function. Understanding statistical properties of subgraph counts in random graphs, their fluctuations, and their interdependences with other topological attributes is an important prerequisite for such investigations. Here we introduce a formalism for predicting subgraph fluctuations induced by perturbations of unidirectional and bidirectional edge densities. On this basis we predict the over- and under-representation of subgraphs arising from a density mismatch between a network and the corresponding pool of randomized graphs serving as a null model. Such mismatches occur, for example, in modular and hierarchical graphs.