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

Localizing the Sustainable Development Goals for Marine and Coastal Management in Norway: A Venture Overdue

Meeting global challenges requires regional and local alignment of institutional and business practices. The purpose of our work is to understand, using qualitative systems analysis, how the Sustainable Development Goals can be achieved through local, cross-sectoral solutions. In this chapter, we start by reviewing the status quo of marine and coastal management in Norway and contrast with the United Nations’ expectations for localization of the Sustainable Development Goals. One key finding is that despite vast knowledge on ocean and coastal use and management, Norway has very few examples of actual localization of the Sustainable Development Goals. We present a case study from Andøy Municipality where we use Social-Ecological Systems mapping to spawn awareness and spur local businesses to harness relevant sustainability targets at the local level.publishedVersio

Temperature window for encapsulation of an enzyme into thermally shrunk, CaCO 3 templated polyelectrolyte multilayer capsules

Encapsulation of enzymes allows to preserve their biological activities in various environmental conditions, such as exposure to elevated temperature or to proteases. This is particularly relevant for in vivo applications, where proteases represent a severe obstacle to maintaining the activity of enzymes. Polyelectrolyte multilayer capsules are suitable for enzyme encapsulation, where CaCO3 particles and temperature‐dependent capsule formation are the best templates and the most adequate method, respectively. In this work, these two areas are combined and, ALP (alkaline phosphatase), which is a robust and therapeutically relevant enzyme, is encapsulated into thermally shrunk polyelectrolyte multilayer (PDADMAC/PSS)4 capsules templated on calcium carbonate particles (original average diameter: ≈3.5 µm). The activity of the encapsulated enzyme and the optimal temperature range for encapsulation are investigated. The enzymatic activity is almost four times higher upon encapsulation when the temperature range for encapsulation is situated just above the glass transition temperature (40 °C), while its optimal conditions are dictated, on the one hand, by the enzyme activity (better at lower temperatures) and, on the other hand, by the size and mechanical properties of capsules (better at higher temperatures)

One-sided chronic intervillositis of unknown etiology in dizygotic twins: a description of 3 cases

Chronic intervillositis of unknown etiology (CIUE) is a rare, poorly understood, histopathological diagnosis of the placenta that is frequently accompanied by adverse pregnancy outcomes including miscarriage, fetal growth restriction, and intrauterine fetal death. CIUE is thought to have an immunologically driven pathophysiology and may be related to human leukocyte antigen mismatches between the mother and the fetus. Dizygotic twins with one-sided CIUE provide an interesting context to study the influence of immunogenetic differences in such cases. The main immune-cell subsets were investigated using immunohistochemistry. We identified three dizygotic twin pregnancies in which CIUE was present in only one of the two placentas. Two of the pregnancies ended in term delivery and one ended in preterm delivery. Presence of CIUE was correlated with lower placental weight and lower birthweight. Relative number of CD68, CD56, CD20, and CD3 positive cells were comparable between co-twins. The presence of one-sided CIUE in dizygotic twin pregnancy was associated with selective growth restriction in the affected twin. This suggests a unique fetal immunogenetic contribution to the pathogenesis of CIUE. Further study of dizygotic and monozygotic placentas affected by CIUE could identify new insights into its pathophysiology and into the field of reproductive immunology.Research into fetal development and medicin

A modern pollen-climate calibration set from central-western Mongolia and its application to a late glacial-Holocene record

Aim Fossil pollen spectra from lake sediments in central and western Mongolia have been used to interpret past climatic variations, but hitherto no suitable modern pollen–climate calibration set has been available to infer past climate changes quantitatively. We established such a modern pollen dataset and used it to develop a transfer function model that we applied to a fossil pollen record in order to investigate: (1) whether there was a significant moisture response to the Younger Dryas event in north-western Mongolia; and (2) whether the early Holocene was characterized by dry or wet climatic conditions. Location Central and western Mongolia. Methods We analysed pollen data from surface sediments from 90 lakes. A transfer function for mean annual precipitation (Pann) was developed with weighted averaging partial least squares regression (WA-PLS) and applied to a fossil pollen record from Lake Bayan Nuur (49.98° N, 93.95° E, 932 m a.s.l.). Statistical approaches were used to investigate the modern pollen–climate relationships and assess model performance and reconstruction output. Results Redundancy analysis shows that the modern pollen spectra are characteristic of their respective vegetation types and local climate. Spatial autocorrelation and significance tests of environmental variables show that the WA-PLS model for Pann is the most valid function for our dataset, and possesses the lowest root mean squared error of prediction. Main conclusions Precipitation is the most important predictor of pollen and vegetation distributions in our study area. Our quantitative climate reconstruction indicates a dry Younger Dryas, a relatively dry early Holocene, a wet mid-Holocene and a dry late Holocene