1,468 research outputs found
Bounds for the Twin-width of Graphs
No full textBonnet, Kim, Thomass\'{e}, and Watrigant (2020) introduced the twin-width of
a graph. We show that the twin-width of an -vertex graph is less than
, and the twin-width of an -edge graph
for a positive is less than . Conference graphs of order (when such graphs
exist) have twin-width at least , and we show that Paley graphs
achieve this lower bound. We also show that the twin-width of the
Erd\H{o}s-R\'{e}nyi random graph with is
larger than
asymptotically almost surely for any positive . Lastly, we
calculate the twin-width of random graphs with for a
constant , determining the thresholds at which the twin-width jumps from
to and from to .Comment: 22 pages, 1 figur
The Relationship between R&D and Market Share: Schumpeterian Hypotheses and Its Implications
No full text
Pyruvate kinase isozyme type M2 (PKM2) interacts and cooperates with Oct-4 in regulating transcription
No full textThe Oct-4 gene encodes a transcription factor that plays an important role in maintaining the pluripotent state of embryonic stem cells and may prevent expression of genes activated during differentiation. Although its role in maintaining embryonic stem cell pluripotency is well established, there is still little known about the binding partners that regulate its function. To identify proteins that control Oct-4 function, we used affinity chromatography on immobilized Oct-4 (POU) together with MALDI-TOF (matrix-assisted laser-desorption ionization-time-of-flight) MS (mass spectrometry) and isolated a novel Oct-4-interacting protein, pyruvate kinase type M2 (PKM2 or M2-PK). PKM2 is an isozyme of pyruvate kinase that is specifically expressed in proliferating cells, such as embryonic stem cells, embryonic carcinoma cells, as well as cancer cells. Oct-4 and PKM2 were co-affinity precipitated from cell extracts, and glutathione S-transferase pull-down assays revealed that the POU DNA binding domain of Oct-4 was required for interaction with PKM2. In addition, the C-terminal domain of PKM2 (amino acids 307-531) was involved in binding to Oct-4. Moreover, ectopic expression of the PKM2 enhanced Oct-4-mediated transcription. These observations indicate that the transactivation potential of the Oct-4 transcription factor is positively modulated by PKM2. (C) 2007 Elsevier Ltd. All rights reserved.This research was supported by a grant (SC2090) from the Stem Cell Research Center of the 21st Century Frontier Research Program funded by the Ministry of Science and Technology, Republic of Korea, by a grant (Code #20070501034009) from BioGreen21 Program, Rural Development Administration, Republic of Korea, and by the Seoul Research and Business Development Program (10816), Republic of Korea. JL was a recipient of Seoul Science Fellowships and of a research fellowship BK21 from the Ministry of Education and Human Resources Development
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