Results 101 to 110 of about 543,681 (314)
A determinant formula for the Jones polynomial of pretzel knots
, 2012 This paper presents an algorithm to construct a weighted adjacency matrix of a plane bipartite graph obtained from a pretzel knot diagram. The determinant of this matrix after evaluation is shown to be the Jones polynomial of the pretzel knot by way of ...
Burde G., Kauffman L. H., MOSHE COHEN
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On Transforming a Spatial Graph into a Plane Graph [PDF]
Progress of Theoretical Physics Supplement, 2011 This talk is an improved revision of the talk (see [1]) given at the workskp Knots and soft-matter physics, Kyoto, August, 2008 on a complexity of a spatial graph with an emphasis on a transformation of spatial graph into a plane graph. In a research of proteins, molecules, or polymers, it is important to understand geometrically and topologically ...
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Molecular Oncology, EarlyView.Chronic TGF‐β exposure drives epithelial HCC cells from a senescent state to a TGF‐β resistant mesenchymal phenotype. This transition is characterized by the loss of Smad3‐mediated signaling, escape from senescence, enhanced invasiveness and metastatic potential, and upregulation of key resistance modulators such as MARK1 and GRM8, ultimately promoting
Minenur Kalyoncu +11 more
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Every Graph Is an Integral Distance Graph in the Plane
Journal of Combinatorial Theory, Series A, 1997 AbstractWe prove that every finite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.
Norihide Tokushige +2 more
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Molecular Oncology, EarlyView.Dual targeting of AKT and mTOR using MK2206 and RAD001 reduces tumor burden in an intracardiac colon cancer circulating tumor cell xenotransplantation model. Analysis of AKT isoform‐specific knockdowns in CTC‐MCC‐41 reveals differentially regulated proteins and phospho‐proteins by liquid chromatography coupled mass spectrometry. Circulating tumor cells
Daniel J. Smit +19 more
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Facial [r,s,t]-Colorings of Plane Graphs
Discussiones Mathematicae Graph Theory, 2019 Let G be a plane graph. Two edges are facially adjacent in G if they are consecutive edges on the boundary walk of a face of G. Given nonnegative integers r, s, and t, a facial [r, s, t]-coloring of a plane graph G = (V,E) is a mapping f : V ∪ E → {1, . .
Czap Július +3 more
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Electronic Notes in Discrete Mathematics, 2007 Abstract The rainbowness, rb ( G ) , of a connected plane graph G is the minimum number k such that any colouring of vertices of the graph G using at least k colours involves a face all vertices of which receive distinct colours. We give a survey on recent results concerning ranbowness of plane graphs.
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Molecular Oncology, EarlyView.This article advocates integrating temporal dynamics into cancer research. Rather than relying on static snapshots, researchers should increasingly consider adopting dynamic methods—such as live imaging, temporal omics, and liquid biopsies—to track how tumors evolve over time.
Gautier Follain +3 more
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Inhibitor of DNA binding‐1 is a key regulator of cancer cell vasculogenic mimicry
Molecular Oncology, EarlyView.Elevated expression of transcriptional regulator inhibitor of DNA binding 1 (ID1) promoted cancer cell‐mediated vasculogenic mimicry (VM) through regulation of pro‐angiogenic and pro‐cancerous genes (e.g. VE‐cadherin (CDH5), TIE2, MMP9, DKK1). Higher ID1 expression also increased metastases to the lung and the liver.
Emma J. Thompson +11 more
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A note on face coloring entire weightings of plane graphs
Discussiones Mathematicae Graph Theory, 2014 Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _.
Jendrol Stanislav, Šugerek Peter
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