Topological graph clustering with thin position

Johnson, Jesse

doi:10.1007/s10711-013-9848-z

Cited by 8 publications

(29 citation statements)

References 11 publications

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Section: Introductionmentioning

confidence: 99%

“…In [14] another topological approach to graph clustering was suggested, based on the idea of thin position for knots and 3-manifolds [9,20]. In the context of 3-manifolds, thin position determines minimal genus Heegaard splittings, which are related to minimal surfaces [19] and the Cheeger constant [15].…”

Section: Introductionmentioning

confidence: 99%

“…In the context of 3-manifolds, thin position determines minimal genus Heegaard splittings, which are related to minimal surfaces [19] and the Cheeger constant [15]. In [14] thin position was translated into the framework of graph partitioning/clustering. The present paper describes and studies the resulting algorithm that we will call TILO (for Topologically Intrinsic Lexicographic Ordering).…”

Section: Introductionmentioning

confidence: 99%

“…In section 2, the mathematical foundation from [14] is summarized and the TILO algorithm is presented. In section 3, we propose a new measure called pinch ratio which is based on concept of a topological thin position and thick width.…”

Section: Introductionmentioning

confidence: 99%

“…The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise.The TILO portion of the algorithm progressively improves a linear ordering of the points in a data set until the ordering satisfies a topological condition called strongly irreducible. The PRC algorithm then divides the data set based on this ordering and a heuristic metric called the pinch ratio.…”

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confidence: 99%

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Pinch Ratio Clustering from a Topologically Intrinsic Lexicographic Ordering

Heisterkamp¹,

Johnson²

2013

Proceedings of the 2013 SIAM International Conference on Data Mining

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This paper introduces an algorithm for determining data clusters called TILO/PRC (Topologically Intrinsic Lexicographic Ordering/Pinch Ratio Clustering). The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise.The TILO portion of the algorithm progressively improves a linear ordering of the points in a data set until the ordering satisfies a topological condition called strongly irreducible. The PRC algorithm then divides the data set based on this ordering and a heuristic metric called the pinch ratio.We demonstrate the effectiveness of TILO/PRC for finding clusters in a wide variety of real and synthetic data sets and compare the results to existing clustering methods. Moreover, because the output of TILO depends on the initial ordering, we consider the effects of different random orderings on the final clusters defined by PRC, and show that choosing an initial ordering based on a different clustering algorithm can improve the final clusters. These results verify that both the theoretical foundations of TILO and the heuristic notion of pinch ratio are reasonable.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Pinch Ratio Clustering from a Topologically Intrinsic Lexicographic Ordering

Heisterkamp¹,

Johnson²

2013

Proceedings of the 2013 SIAM International Conference on Data Mining

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HMGB1 coordinates SASP-related chromatin folding and RNA homeostasis on the path to senescence

Sofiadis

Nikolić

Zirkel

et al. 2019

Preprint

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Spatial organization and gene expression of mammalian chromosomes are maintained and regulated in conjunction with cell cycle progression. This link is perturbed once cells enter senescence. The highly abundant HMGB1 protein, known to associate with bent and looped DNA, is actively depleted from senescent cell nuclei to act as an extracellular proinflammatory stimulus. Despite its physiological importance, we still lack understanding of the positioning and functional roles of HMGB1 on chromatin in vivo. To address this, we mapped HMGB1 binding genome-wide in different primary cells using a tailored protocol. We then integrated ChIP-seq and Hi-C data with a knot theory approach to uncover HMGB1 demarcation at the boundaries of particular topologically-associating domains (TADs). These TADs harbor genes involved in the key proinflammatory leg of the senescent transcriptional program. Moreover, we used sCLIP and siRNA-mediated knockdown to show that HMGB1 is a bona fide RNAbinding protein also affecting splicing choices. Together, our findings highlight a broader than hitherto assumed role for HMGB1 in chromatin homeostasis connected to cell cycle potency, and allow us to postulate a "rheostat" model for HMGB function with implications in cancer biology.

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HMGB1 coordinates SASP‐related chromatin folding and RNA homeostasis on the path to senescence

Sofiadis

Josipović

Nikolić

et al. 2021

Molecular Systems Biology

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Spatial organization and gene expression of mammalian chromosomes are maintained and regulated in conjunction with cell cycle progression. This is perturbed once cells enter senescence and the highly abundant HMGB1 protein is depleted from nuclei to act as an extracellular proinflammatory stimulus. Despite its physiological importance, we know little about the positioning of HMGB1 on chromatin and its nuclear roles. To address this, we mapped HMGB1 binding genome-wide in two primary cell lines. We integrated ChIP-seq and Hi-C with graph theory to uncover clustering of HMGB1-marked topological domains that harbor genes involved in paracrine senescence. Using simplified Cross-Linking and Immuno-Precipitation and functional tests, we show that HMGB1 is also a bona fide RNA-binding protein (RBP) binding hundreds of mRNAs. It presents an interactome rich in RBPs implicated in senescence regulation. The mRNAs of many of these RBPs are directly bound by HMGB1 and regulate availability of SASPrelevant transcripts. Our findings reveal a broader than hitherto assumed role for HMGB1 in coordinating chromatin folding and RNA homeostasis as part of a regulatory loop controlling cellautonomous and paracrine senescence.

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Topological graph clustering with thin position

Cited by 8 publications

References 11 publications

Pinch Ratio Clustering from a Topologically Intrinsic Lexicographic Ordering

Pinch Ratio Clustering from a Topologically Intrinsic Lexicographic Ordering

HMGB1 coordinates SASP-related chromatin folding and RNA homeostasis on the path to senescence

HMGB1 coordinates SASP‐related chromatin folding and RNA homeostasis on the path to senescence

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