Apoptosis in mouse fetal and neonatal oocytes during meiotic prophase one

Background The vast majority of oocytes formed in the fetal ovary do not survive beyond birth. Possible reasons for their loss include the elimination of non-viable genetic constitutions arising through meiosis, however, the precise relationship between meiotic stages and prenatal apoptosis of oocytes remains elusive. We studied oocytes in mouse fetal and neonatal ovaries, 14.5–21 days post coitum, to examine the relationship between oocyte development and programmed cell death during meiotic prophase I. Results Microspreads of fetal and neonatal ovarian cells underwent immunocytochemistry for meiosis- and apoptosis-related markers. COR-1 (meiosis-specific) highlighted axial elements of the synaptonemal complex and allowed definitive identification of the stages of meiotic prophase I. Labelling for cleaved poly-(ADP-ribose) polymerase (PARP-1), an inactivated DNA repair protein, indicated apoptosis. The same oocytes were then labelled for DNA double strand breaks (DSBs) using TUNEL. 1960 oocytes produced analysable results. . Oocytes at all stages of meiotic prophase I stained for cleaved PARP-1 and/or TUNEL, or neither. Oocytes with fragmented (19.8%) or compressed (21.2%) axial elements showed slight but significant differences in staining for cleaved PARP-1 and TUNEL to those with intact elements. However, fragmentation of axial elements alone was not a good indicator of cell demise. Cleaved PARP-1 and TUNEL staining were not necessarily coincident, showing that TUNEL is not a reliable marker of apoptosis in oocytes. Conclusions Our data indicate that apoptosis can occur throughout meiotic prophase I in mouse fetal and early postnatal oocytes, with greatest incidence at the diplotene stage. Careful selection of appropriate markers for oocyte apoptosis is essential

A homological interpretation of the transverse quiver Grassmannians

In recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second-named author to introduce a variety called transverse quiver Grassmannian and the first-named and third-named authors to consider the smooth loci of quiver Grassmannians. In this paper, we prove that, for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable representation M is the set of points N in the quiver Grassmannian of M such that Ext^1(N,M/N)=0. As a corollary we prove that the transverse quiver Grassmannian coincides with the smooth locus of the irreducible components of minimal dimension in the quiver Grassmannian.Comment: final version, 7 pages, corollary 1.2 has been modifie

Chronicles of Oklahoma

Article describes life in territorial Skullyville, Oklahoma, a town that was the original location of the first agency for the Choctaws in Indian Territory. G. E. Hartshorne, M.D. uses personal recollections of the town to describe its layout and people

Log canonical thresholds of Del Pezzo Surfaces in characteristic p

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic $0$. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than $4$ are K-semistable.Comment: 21 pages. Thorough rewrite following referee's suggestions. To be published in Manuscripta Mathematic

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.Comment: 8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc

The hidden costs of dietary restriction: Implications for its evolutionary and mechanistic origins

Dietary restriction (DR) extends life span across taxa. Despite considerable research, universal mechanisms of DR have not been identified, limiting its translational potential. Guided by the conviction that DR evolved as an adaptive, pro-longevity physiological response to food scarcity, biomedical science has interpreted DR as an activator of pro-longevity molecular pathways. Current evolutionary theory predicts that organisms invest in their soma during DR, and thus when resource availability improves, should outcompete rich-fed controls in survival and/or reproduction. Testing this prediction in Drosophila melanogaster (N > 66,000 across 11 genotypes), our experiments revealed substantial, unexpected mortality costs when flies returned to a rich diet following DR. The physiological effects of DR should therefore not be interpreted as intrinsically pro-longevity, acting via somatic maintenance. We suggest DR could alternatively be considered an escape from costs incurred under nutrient-rich conditions, in addition to costs associated with DR

On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor correction

A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes

The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In particular, we show that the normalized volume of the free sum of full dimensional polytopes is precisely the product of the normalized volumes of the summands.Comment: Published in the proceedings of 2017 Southern Regional Algebra Conferenc

Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata)

We give an effective upper bound of |Bir(X)| for the birational automorphism group of an irregular n-fold (with n = 3) of general type in terms of the volume V = V(X) under an ''albanese smoothness and simplicity'' condition. To be precise, |Bir(X)| < d_3 V^{10}. An optimum linear bound |Bir(X)|-1 < (1/3)(42)^3 V is obtained for those 3-folds with non-maximal albanese dimension. For all n > 2, a bound |Bir(X)| < d_n V^{10} is obtained when alb_X is generically finite, alb(X) is smooth and Alb(X) is simple.Comment: Mathematische Annalen, to appea