Compact projective planes with homogeneous ovals

Löwen, Rainer

doi:10.1007/bf01380891

Cited by 11 publications

(7 citation statements)

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“…At E7.5, we identified four phosphosites on placental TFs: Ets2 S300, Nfat5 S229, Satb2 S13, and Snai1 S92 (Figure 4b). Snai1 and Nfat5 are implicated in PE 130,131 , while Ets2 and Satb2 are important for trophoblast stem cell renewal 132,133 . The sites on Nfat5, Satb2, and Snai1 were previously found to be phosphorylated in human on NFAT5 S229, SATB2 S13, SNAI1 S92, but had no prior evidence of phosphorylation in mouse (Figure 4b).…”

Section: Discovery Of Novel Phosphositesmentioning

confidence: 99%

Comparative Analysis of the Transcriptome and Proteome during Mouse Placental Development

et al. 2019

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The condition of the placenta is a determinant of the short-and long-term health of the mother and the fetus. However, critical processes occurring in early placental development, such as trophoblast invasion and establishment of placental metabolism, remain poorly understood. To gain a better understanding of the genes involved in regulating these processes, we utilized a multi-omics approach, incorporating transcriptome, proteome, and phosphoproteome data generated from mouse placental tissue collected at two critical developmental timepoints. We found that incorporating information from both the transcriptome and proteome identifies genes associated with timepoint-specific biological processes, unlike using the proteome alone. We further inferred genes upregulated based on the proteome data but not the transcriptome data at each timepoint, leading us to identify 27 genes that we predict to have a role in trophoblast migration or placental metabolism. Finally, using the phosphoproteome dataset, we discovered novel phosphosites that may play crucial roles in the regulation of placental transcription factors. By generating the largest proteome and phosphoproteome datasets in the developing placenta, and integrating transcriptome analysis, we uncovered novel aspects of placental gene regulation.

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Section: Discovery Of Novel Phosphositesmentioning

confidence: 99%

Comparative Analysis of the Transcriptome and Proteome during Mouse Placental Development

et al. 2019

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“…These cases have been treated in [11], [12], with the result that then dim Aut ~ < 5, contrary to our assumption. If • is not locally isomorphic to SL2E, then • ~ SO3 or • ~ Spin3 or dim~ > 6.…”

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confidence: 66%

Four-dimensional compact projective planes with a nonsolvable automorphism group

Löwen

1990

Geom Dedicata

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“…For (I) ~ SO3, we have a complete result from [1][2][3][4][5][6][7][8][9][10][11][12][13]. My next aim was to determine the possibilities for g in this situation, assuming that dim A > 3.…”

Section: Resultsmentioning

confidence: 99%

Actions of spin3 on 4-dimensional stable planes

L�wen

1986

Geom Dedicata

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PLANESWe conclude a series of papers on 4-dimensional stable planes admitting a non-solvable Lie group A of automorphisms. Here we consider the case where A contains a subgroup qb ~ Spin 3. For dim A >~ 6, the possible planes are completely determined (Theorem 5). Apart from classical examples, we get a single new plane, which is analogous to a 2-dimensional plane constructed by Strambach [21]. For dim A = 5, we can determine the action of the group and roughly describe the possible planes. However, there remains a seemingly difficult problem of deciding which planes of this possibly very large class actually exist, or at least to give some examples.Stable planes are a generalization of topological projective planes designed to include geometries similar to hyperbolic planes. There are also examples which are not obtained as subplanes of projective planes, such as Strambach's plane mentioned above and its 4-dimensional analogue; cf. also [5, § 5]. A stable plane ~ = (M,50) consists of two things. One, a point space M, throughout assumed to be locally compact and Hausdorff and of finite covering dimension d > 0. Two, a system 50 of subsets of M, called lines. Different points x,y~M are joined (belong to) a unique line L = x v y. The operation v and its dual/x (intersection of different lines) are continuous with respect to a suitable topology on 5 °, and the domain of definition of ^ is open (stability of intersection). If ^ exists everywhere, then we get a topological projective plane. The following facts can be found in [3]: The smallest possible values old are 2 and 4 (cf. also [10]), and then the pencil 50x of all lines through x~M is homeomorphic to a sphere of dimension d/2. Each line is closed in M and homeomorphic to an open subset of 50~. The automorphism group F of g is a locally compact topological transformation group of M and of 50. It is a Lie group if d = 2 or if d = 4 and dim F ~> 5[4].This group is the main tool for the investigation of planes; in particular, it serves to single out classes of planes which can be completely understood. In most cases, one starts from a condition of the kind 'dim F >~f' and hopes for a complete classification if f is somewhere in the vicinity of 2d, which is about half the maximal value for projective planes. For stable planes with lines homeomorphic to ~2 this works with f= 10 [3], and in fact, f=9 (unpublished).The present paper concludes a series whose results corflbine to show that Geometriae Dedicata 21 (1986), 1-12.

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Compact projective planes with homogeneous ovals

Cited by 11 publications

References 11 publications

Comparative Analysis of the Transcriptome and Proteome during Mouse Placental Development

Comparative Analysis of the Transcriptome and Proteome during Mouse Placental Development

Four-dimensional compact projective planes with a nonsolvable automorphism group

Actions of spin3 on 4-dimensional stable planes

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