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1. Transversal Ck -factors in subgraphs of the balanced blow-up of Ck

   https://doi.org/10.1017/S0963548322000086  

   Ergemlidze, Beka ; Molla, Theodore ( November 2022 , Combinatorics, Probability and Computing)

   For a subgraph$G$of the blow-up of a graph$F$, we let$\delta ^*(G)$be the smallest minimum degree over all of the bipartite subgraphs of$G$induced by pairs of parts that correspond to edges of$F$. Johansson proved that if$G$is a spanning subgraph of the blow-up of$C_3$with parts of size$n$and$\delta ^*(G) \ge \frac{2}{3}n + \sqrt{n}$, then$G$contains$n$vertex disjoint triangles, and presented the following conjecture of Häggkvist. If$G$is a spanning subgraph of the blow-up of$C_k$with parts of size$n$and$\delta ^*(G) \ge \left(1 + \frac 1k\right)\frac n2 + 1$, then$G$contains$n$vertex disjoint copies of$C_k$such that each$C_k$intersects each of the$k$parts exactly once. A similar conjecture was also made by Fischer and the case$k=3$was proved for large$n$by Magyar and Martin.

   In this paper, we prove the conjecture of Häggkvist asymptotically. We also pose a conjecture which generalises this result by allowing the minimum degree conditions in each bipartite subgraph induced by pairs of parts of$G$to vary. We support this new conjecture by proving the triangle case. This result generalises Johannson’s result asymptotically.

    

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2. Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up

   https://doi.org/10.1515/crelle-2017-0019  

   Isenberg, James ; Wu, Haotian ( September 2019 , Journal für die reine und angewandte Mathematik (Crelles Journal))

   null (Ed.)

   Abstract We study the phenomenon of Type-II curvature blow-up in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions enveloping formal solutions with prescribed behavior, we show that for each initial hypersurface considered, a mean curvature flow solution exhibits the following behavior near the “vanishing” time T : (1) The highest curvature concentrates at the tip of the hypersurface (an umbilic point), and for each choice of the parameter {\gamma>\frac{1}{2}} , there is a solution with the highest curvature blowing up at the rate {(T-t)^{{-(\gamma+\frac{1}{2})}}} . (2) In a neighborhood of the tip, the solution converges to a translating soliton which is a higher-dimensional analogue of the “Grim Reaper” solution for the curve-shortening flow. (3) Away from the tip, the flow surface approaches a collapsing cylinder at a characteristic rate dependent on the parameter γ. 

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3. On Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome Model

   https://doi.org/10.3390/axioms11030120  

   Takyi, Eric M. ; Beauregard, Matthew A. ; Griffin, Thomas ; Bobo, Landrey ; Parshad, Rana D. ( March 2022 , Axioms)

   The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX–XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive population to skew the sex ratio over time, causing local extinction. We consider the three species TYC reaction diffusion model, and show that introduction of supermales above certain thresholds, and for certain initial data, solutions can blow-up in finite time. Thus, in order to have biologically meaningful solutions, one needs to restrict parameter and initial data regimes, in TYC type models. 

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4. A striking relationship between dust extinction and radio detection in DESI QSOs: evidence for a dusty blow-out phase in red QSOs

   https://doi.org/10.1093/mnras/stad2603  

   Fawcett, V. A. ; Alexander, D. M. ; Brodzeller, A. ; Edge, A. C. ; Rosario, D. J. ; Myers, A. D. ; Aguilar, J. ; Ahlen, S. ; Alfarsy, R. ; Brooks, D. ; et al ( September 2023 , Monthly Notices of the Royal Astronomical Society)

   We present the first eight months of data from our secondary target programme within the ongoing Dark Energy Spectroscopic Instrument (DESI) survey. Our programme uses a mid-infrared and optical colour selection to preferentially target dust-reddened quasi-stellar objects (QSOs) that would have otherwise been missed by the nominal DESI QSO selection. So far, we have obtained optical spectra for 3038 candidates, of which ∼70 per cent of the high-quality objects (those with robust redshifts) are visually confirmed to be Type 1 QSOs, consistent with the expected fraction from the main DESI QSO survey. By fitting a dust-reddened blue QSO composite to the QSO spectra, we find they are well-fitted by a normal QSO with up to AV ∼ 4 mag of line-of-sight dust extinction. Utilizing radio data from the LOFAR Two-metre Sky Survey (LoTSS) DR2, we identify a striking positive relationship between the amount of line-of-sight dust extinction towards a QSO and the radio detection fraction, that is not driven by radio-loud systems, redshift and/or luminosity effects. This demonstrates an intrinsic connection between dust reddening and the production of radio emission in QSOs, whereby the radio emission is most likely due to low-powered jets or winds/outflows causing shocks in a dusty environment. On the basis of this evidence, we suggest that red QSOs may represent a transitional ‘blow-out’ phase in the evolution of QSOs, where winds and outflows evacuate the dust and gas to reveal an unobscured blue QSO.

    

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5. Conditional knockdown of transformer in sheep blow fly suggests a role in repression of dosage compensation and potential for population suppression

   https://doi.org/10.1371/journal.pgen.1009792  

   Williamson, Megan E. ; Yan, Ying ; Scott, Maxwell J. ( October 2021 , PLOS Genetics)

   Palli, Subba Reddy (Ed.)

   The transformer ( tra ) gene is essential for female development in many insect species, including the Australian sheep blow fly, Lucilia cuprina . Sex-specific tra RNA splicing is controlled by Sex lethal ( Sxl ) in Drosophila melanogaster but is auto-regulated in L . cuprina . Sxl also represses X chromosome dosage compensation in female D . melanogaster . We have developed conditional Lctra RNAi knockdown strains using the tet-off system. Four strains did not produce females on diet without tetracycline and could potentially be used for genetic control of L . cuprina . In one strain, which showed both maternal and zygotic tTA expression, most XX transformed males died at the pupal stage. RNAseq and qRT-PCR analyses of mid-stage pupae showed increased expression of X-linked genes in XX individuals. These results suggest that Lctra promotes somatic sexual differentiation and inhibits X chromosome dosage compensation in female L . cuprina . However, XX flies homozygous for a loss-of-function Lctra knockin mutation were fully transformed and showed high pupal eclosion. Two of five X-linked genes examined showed a significant increase in mRNA levels in XX males. The stronger phenotype in the RNAi knockdown strain could indicate that maternal Lctra expression may be essential for initiation of dosage compensation suppression in female embryos. 

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