Submegabase-size topologically associating domains (TAD) have been observed in high-throughput chromatin interaction data (Hi-C). However, accurate detection of TADs depends on ultra-deep sequencing and sophisticated normalization procedures. Here we propose a fast and normalization-free method to decode the domains of chromosomes (deDoc) that utilizes structural information theory. By treating Hi-C contact matrix as a representation of a graph, deDoc partitions the graph into segments with minimal structural entropy. We show that structural entropy can also be used to determine the proper bin size of the Hi-C data. By applying deDoc to pooled Hi-C data from 10 single cells, we detect megabase-size TAD-like domains. This result implies that the modular structure of the genome spatial organization may be fundamental to even a small cohort of single cells. Our algorithms may facilitate systematic investigations of chromosomal domains on a larger scale than hitherto have been possible.

In this study, we propose a method for constructing cell sample networks from gene expression profiles, and a structural entropy minimisation principle for detecting natural structure of networks and for identifying cancer cell subtypes. Our method establishes a three-dimensional gene map of cancer cell types and subtypes. The identified subtypes are defined by a unique gene expression pattern, and a three-dimensional gene map is established by defining the unique gene expression pattern for each identified subtype for cancers, including acute leukaemia, lymphoma, multi-tissue, lung cancer and healthy tissue. Our three-dimensional gene map demonstrates that a true tumour type may be divided into subtypes, each defined by a unique gene expression pattern. Clinical data analyses demonstrate that most cell samples of an identified subtype share similar survival times, survival indicators and International Prognostic Index (IPI) scores and indicate that distinct subtypes identified by our algorithms exhibit different overall survival times, survival ratios and IPI scores. Our three-dimensional gene map establishes a high-definition, one-to-one map between the biologically and medically meaningful tumour subtypes and the gene expression patterns, and identifies remarkable cells that form singleton submodules.One of the challenges of cancer treatment is targeting specific therapies to pathogenetically distinct tumour types to maximise treatment efficacy and minimise toxicity. Traditionally, cancer classification has been based on the morphological appearance of the tumour; however, this approach has serious limitations. Tumours with similar histopathological appearances can have different clinical courses and exhibit different responses to therapy. Molecular heterogeneity within individual cancer diagnostic categories is also evident in the variable presence of chromosomal translocations, tumour suppressor genes deletions and numerical chromosomal abnormalities. Cancer classification is difficult because the classification relies on specific biological insights, instead of on systematic, comprehensive, global and unbiased methods for identifying tumour subtypes.Over the past decade, the increased availability of large-scale gene expression profiles have led researchers to propose a number of new approaches for classifying tumour types or subtypes based on gene expression analyses. Golub et al. 1 have proposed a neighbour analysis to distinct known types, and a "class predictor" that assigns a new sample to a known class purely based on the gene expression profiles, and have verified their methods using an acute leukaemia dataset. Alizadeh et al. 2 have proposed a method based on hierarchical clustering, which divides the type of diffuse large B-cell lymphomas into two subtypes. Ramaswamy et al. 3 have proposed a "classifier" based on a support vector machine (SVM) and have analysed the accuracy of true type predictions for both the snap-frozen human tumour and normal tissue specimens. Yeoh et al. 4 have analysed sets ...

It has been a challenge to understand the formation and roles of social groups or natural communities in the evolution of species, societies and real world networks. Here, we propose the hypothesis that homophyly/kinship is the intrinsic mechanism of natural communities, introduce the notion of the affinity exponent and propose the homophyly/kinship model of networks. We demonstrate that the networks of our model satisfy a number of topological, probabilistic and combinatorial properties and, in particular, that the robustness and stability of natural communities increase as the affinity exponent increases and that the reciprocity of the networks in our model decreases as the affinity exponent increases. We show that both homophyly/kinship and reciprocity are essential to the emergence of cooperation in evolutionary games and that the homophyly/kinship and reciprocity determined by the appropriate affinity exponent guarantee the emergence of cooperation in evolutionary games, verifying Darwin’s proposal that kinship and reciprocity are the means of individual fitness. We propose the new principle of structure entropy minimisation for detecting natural communities of networks and verify the functional module property and characteristic properties by a healthy tissue cell network, a citation network, some metabolic networks and a protein interaction network.