BackgroundVarious aspects of genome organization have been explored based on data from distinct technologies, including histone modification ChIP-Seq, 3C, and its derivatives. Recently developed Hi-C techniques enable the genome wide mapping of DNA interactomes, thereby providing the opportunity to study genome organization in detail, but these methods also pose challenges in methodology development.ResultsWe developed Genome Segmentation from Intra Chromosomal Associations, or GeSICA, to explore genome organization and applied the method to Hi-C data in human GM06990 and K562 cells. GeSICA calculates a simple logged ratio to efficiently segment the human genome into regions with two distinct states that correspond to rich and poor functional element states. Inside the rich regions, Markov Clustering was subsequently applied to segregate the regions into more detailed clusters. The binding sites of the insulator, cohesion, and transcription complexes are enriched in the boundaries between neighboring clusters, indicating that inferred clusters may have fine organizational features.ConclusionsOur study presents a novel analysis method, known as GeSICA, which gives insight into genome organization based on Hi-C data. GeSICA is open source and freely available at: http://web.tongji.edu.cn/~zhanglab/GeSICA/

After randomly reflecting on two hyperplanes, a new iteration method is established by making use of the circumceter of the reflective points from the viewpoint of geometry. The linear combination could be non-convex when the angle between the hyperplances is small. Theoretical analysis show that the proposed method converges and the convergence rate in expectation is also addressed in detail. The relation between our method and block Kaczmarz method is well discussed. Numerical experiments further verify that the new algorithms is efficient, and outperform the existing randomized Kaczmarz methods and randomized reflection methods in terms of the number of iterations and CPU time, especially when the coefficient matrix has highly coherent rows.

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