Reverse mathematics, well-quasi-orders, and Noetherian spaces

A quasi-order Q induces two natural quasi-orders on P(Q) P(Q) , but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on P(Q) P(Q) preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on P(Q) P(Q) are Noetherian, which means that they contain no infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) P(Q) P(Q) is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA0 over RCA0. To state these theorems in RCA0 we introduce a new framework for dealing with second-countable topological spaces

Well-partial-orderings and the big Veblen number

In this article we characterize a countable ordinal known as the big Veblen number in terms of natural well-partially ordered tree-like structures. To this end, we consider generalized trees where the immediate subtrees are grouped in pairs with address-like objects. Motivated by natural ordering properties, extracted from the standard notations for the big Veblen number, we investigate different choices for embeddability relations on the generalized trees. We observe that for addresses using one finite sequence only, the embeddability coincides with the classical tree-embeddability, but in this article we are interested in more general situations (transfinite addresses and well-partially ordered addresses). We prove that the maximal order type of some of these new embeddability relations hit precisely the big Veblen ordinal ϑΩΩ . Somewhat surprisingly, changing a little bit the well-partially ordered addresses (going from multisets to finite sequences), the maximal order type hits an ordinal which exceeds the big Veblen number by far, namely ϑΩΩΩ . Our results contribute to the research program (originally initiated by Diana Schmidt) on classifying properties of natural well-orderings in terms of order-theoretic properties of the functions generating the orderings

Scintillation and irregularities from the nightside part of a Sun-aligned polar cap arc

In this paper we study the presence of irregularities and scintillation in relation to the nightside part of a long-lived, Sun-aligned transpolar arc on 15 January 2015. The arc was observed in DMSP UV and particle data and lasted at least 3 h between 1700 and 2000 UT. The arc was more intense than the main oval during this time. From all-sky imagers on Svalbard we were able to study the evolution of the arc, which drifted slowly westward toward the dusk cell. The intensity of the arc as observed from ground was 10-17 kR in 557.7 nm and 2-3.5 kR in 630.0 nm, i.e., significant emissions in both green and red emission lines. We have used high-resolution raw data from global navigation satellite systems (GNSS) receivers and backscatter from Super Dual Auroral Radar Network (SuperDARN) radars to study irregularities and scintillation in relation to the polar cap arc. Even though the literature has suggested that polar cap arcs are potential sources for irregularities, our results indicate only very weak irregularities. This may be due to the background density in the northward IMF polar cap being too low for significant irregularities to be created

An order-theoretic characterization of the Howard-Bachmann-hierarchy

In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face Π₁¹-comprehension

Combined loss of HLA I and HLA II expression is more common in the non-GCB type of diffuse large B cell lymphoma

As an immune escape mechanism tumor cells may downregulate expression of Human Leukocyte Antigens (HLA). Loss of HLA class I and class II has been described in various subtypes of diffuse large B cell lymphoma (DLBCL), including the not otherwise specified (NOS) subgroup. 1,2 We analyzed HLA class I and class II expression in DLBCL not otherwise specified (NOS) to investigate whether there is an association between HLA expression, cell of origin (COO) and the recently reported FOXP1 expression in non-GCB DLBCL. 3 This article is protected by copyright. All rights reserved

Cell-cell interactions during the formation of primordial follicles in humans

Gametogenesis is a complex and sex-specific multistep process during which the gonadal somatic niche plays an essential regulatory role. One of the most crucial steps during human female gametogenesis is the formation of primordial follicles, the functional unit of the ovary that constitutes the pool of follicles available at birth during the entire reproductive life. However, the relation between human fetal germ cells (hFGCs) and gonadal somatic cells during the formation of the primordial follicles remains largely unexplored. We have discovered that hFGCs can form multinucleated syncytia, some connected via interconnecting intercellular bridges, and that not all nuclei in hFGC-syncytia were synchronous regarding meiotic stage. As hFGCs progressed in development, pre-granulosa cells formed protrusions that seemed to progressively constrict individual hFGCs, perhaps contributing to separate them from the multinucleated syncytia. Our findings highlighted the cell-cell interaction and molecular dynamics between hFGCs and (pre)granulosa cells during the formation of primordial follicles in humans. Knowledge on how the pool of primordial follicle is formed is important to understand human infertility.</p

Classification of Atretic Small Antral Follicles in the Human Ovary

The reproductive lifespan in humans is regulated by a delicate cyclical balance between follicular recruitment and atresia in the ovary. The majority of the small antral follicles present in the ovary are progressively lost through atresia without reaching dominance, but this process remains largely underexplored. In our study, we investigated the characteristics of atretic small antral follicles and proposed a classification system based on molecular changes observed in granulosa cells, theca cells, and extracellular matrix deposition. Our findings revealed that atresia spreads in the follicle with wave-like dynamics, initiating away from the cumulus granulosa cells. We also observed an enrichment of CD68+ macrophages in the antrum during the progression of follicular atresia. This work not only provides criteria for classifying three stages of follicular atresia in small antral follicles in the human ovary but also serves as a foundation for understanding follicular degeneration and ultimately preventing or treating premature ovarian failure. Understanding follicular remodeling in the ovary could provide a means to increase the number of usable follicles and delay the depletion of the follicular reserve, increasing the reproductive lifespan.</p