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Betweenness centrality is a centrality measure that is widely used, with applications across several disciplines. It is a measure which quantifies the importance of a vertex based on its occurrence in shortest paths between all possible pairs of vertices in a graph. This is a global measure, and in order to find the betweenness centrality of a node, one is(More)
Tumour-repopulating cells (TRCs) are a self-renewing, tumorigenic subpopulation of cancer cells critical in cancer progression. However, the underlying mechanisms of how TRCs maintain their self-renewing capability remain elusive. Here we show that relatively undifferentiated melanoma TRCs exhibit plasticity in Cdc42-mediated mechanical stiffening, histone(More)
Mammalian inner cell mass cells undergo lineage-specific differentiation into germ layers of endoderm, mesoderm and ectoderm during gastrulation. It has been a long-standing challenge in developmental biology to replicate these organized germ layer patterns in culture. Here we present a method of generating organized germ layers from a single mouse(More)
We consider a generalization of the capacitated vehicle routing problem known as the cumulative vehicle routing problem in the literature. Cumulative VRPs are known be a simple model for fuel consumption in VRPs. We examine four variants of the problem, and give constant factor approximation algorithms. Our results are based on a well-known heuristic of(More)
Mechanical forces play critical roles in the function of living cells. However, the underlying mechanisms of how forces influence nuclear events remain elusive. Here, we show that chromatin deformation as well as force-induced transcription of a green fluorescent protein (GFP)-tagged bacterial-chromosome dihydrofolate reductase (DHFR) transgene can be(More)
Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen broad and increasing applications across several disciplines of late. Amongst a plethora of application specific definitions available in the literature to rank the vertices, closeness centrality, betweenness centrality and eigenvector centrality (page-rank) have(More)
—Centrality measures, erstwhile popular amongst the sociologists and psychologists, has seen wide and increasing applications across several disciplines of late. In conjunction with the big data problems there came the need to analyze big networks and in this connection, centrality measures became of great interest to the community of mathematicians,(More)
Cells' ability to sense and interpret mechanical signals from the extracellular milieu modulates the degree of cell spreading. Yet how cells detect such signals and activate downstream signaling at the molecular level remain elusive. Herein, we utilize tension gauge tether (TGT) platform to investigate the underlying molecular mechanism of cell spreading.(More)