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In this paper we show how simple text-driven variations of given statements in mathematics can lead to interesting new problems and push forward a whole theory around simple initial questions. We exemplify this in two cases. Case 1 deals with problem-posing activities suitable for pupils and case 2 is a rational reconstruction of the organisation of mathematical knowledge within problems of graph colorings. Mathematicians learn to systematically look for subsequent problems around a given problem. We argue that this toy-model captures a nontrivial part of professional mathematical research within the pure fields and conjecture that it even grasps high level developments in mathematics. By doing this, we implicitly encourage a very simplistic view on criteria, so to speak a “cowpath” approach to progress in mathematics. The term “cowpath” is borrowed from architecture and software design, where it is commonly used. While we can contemplate which pathways are ideal, we may also just plant grass and see where people choose to walk. Those pathways are also self-enforcing, since we are less hesitant to walk on those rather than criss-cross the landscape.

Repeated carbon isotope excursions and widespread organic-rich shale deposition mark the Middle and Upper Devonian series. Various explanations such as extensive volcanism and land plant evolution have been given for these perturbations and the general sensitivity of the Devonian oceans to the development of anoxia, but their repeated nature suggests that astronomical forcing may have controlled their timing. Here, a cyclostratigraphic study of the Kellwasser Crisis at the Frasnian–Famennian stage boundary (ca. 372 Ma) is carried out. The Kellwasser Crisis was one of the most ecologically impactful of the Devonian perturbations and is ranked among the “Big Five” Phanerozoic mass extinctions. The studied site is the Winsenberg roadcut section in the Rhenish Massif, Germany, which represents a quiet tropical shelf basin setting. Centimetre-scale elemental records, generated by portable X-ray scanning, allow for testing of the hypothesis that a 2.4 Myr eccentricity node preceded the Upper Kellwasser event. The study's results are supportive of this hypothesis. We find enhanced chemical weathering (K2O / Al2O3) during the period leading up to the Upper Kellwasser and a peak in distal detrital input (SiO2 / CaO) and riverine runoff (TiO2 / Al2O3) just prior to the start of the Upper Kellwasser event. We interpret this pattern as the long-term eccentricity minimum facilitating excessive regolith build-up in the absence of strong seasonal contrasts. The Earth's system coming out of this node would have rapidly intensified the hydrological cycle, causing these nutrient-rich regoliths to be eroded and washed away to the oceans, where they resulted in eutrophication and anoxia. An astronomical control on regional climate is observed beyond this single crisis. Wet–dry cycles were paced by 405 kyr eccentricity, with both the Lower and Upper Kellwasser events taking place during comparatively drier times. A precession-sensitive monsoonal climate system prevailed on shorter timescales. Intensification of this monsoonal system following the node may have caused the widespread regolith erosion. We estimate the total duration of the Kellwasser Crisis at ca. 900 kyr, with the individual events lasting for ca. 250 and 100 kyr, respectively. If astronomical control indeed operated via regolith development in monsoonal climates, then land plants may have played an important role. This would not have been through evolutionary steps directly triggering Kellwasser perturbations but by gradually strengthening the climatic response to orbital forcing via soil development – creating soils thick enough to meaningfully respond to orbital forcing – and intensifying the hydrological cycle.

Abstract Online debates and debate spheres challenge our assumptions about democracy, politics, journalism, trust, and truth in ways that make them a necessary object of study. In the present article, we argue that the study of online arguments can benefit from an interdisciplinary approach that combines computational methods for text analysis with conceptual models of opinion dynamics. The article thereby seeks to make a conceptual and methodological contribution to the field by highlighting the role of domain-crossing causal statements in debates of societal interest, and by providing a method for automatically mining such statements from textual corpora on the web. The article illustrates the relevance of this approach for the study of online debates by means of a case study in which we analyse cross-cutting statements on climate change and energy technologies from the comment section of the online newspaper The Guardian. In support of this case study, we use data and methods that are made openly available through the Penelope ecosystem of tools and techniques for computational social science.

Patagonia is ideally situated to reconstruct past migrations of the southern westerly winds (SWWs) due to its southerly maritime location. The SWWs are an important driver of Southern Ocean upwelling and their strength and latitudinal position changed during the Holocene, leading thus to different responses of the vegetation to past climate changes along the Chilean continental margin. A new speleothem record from Cueva Chica (51°S) is investigated to reconstruct past climatic changes throughout the Holocene in conjunction with other marine and paleoenvironmental records of the region and better constrain the regional paleoclimatic evolutions of SWWs. Samples comprising both a flowstone core and a stalagmite were radiometrically dated (Usingle bondTh & 14C) to construct age-depth models for the highly-resolved proxy profiles (δ13C, δ18O, chemical composition). The Cueva Chica record provides a highly-resolved isotopic and elemental curves for the last 12 ka, albeit with a hiatus from 5.8 to 4 ka BP. The multi-proxy analysis suggests three climatic regimes throughout the Holocene in Southern Patagonia: i) an early Holocene wet period (with the exception of two dry excursions at 10.5 ka and 8.5 ka BP), ii) a mid-Holocene dry period and iii), a return to generally wet conditions over the late Holocene. The global drivers for these tri-phased climatic regimes are likely related to oceanic and South polar feedbacks. The early Holocene was the warmest period and might be attributable to changes in global ocean circulation which involved a rise in air T° and a strength in SWW from 50°S, and therefore higher precipitations over landmass. After 9 ka BP, an intensified deglaciation dynamic along the Antarctic Peninsula is concordant with increasing summer insolation in the Southern hemisphere, leading to a poleward shift of the SWWs in response to global warming and thus to a reduction in moisture supply from the Pacific onto the Patagonian shore. After 5 ka BP, a gradual SST decline is consistent with an equatorward shift of the SWWs in response to a cooling Southern hemisphere. The SWW storm tracks extended to lower latitudes, inducing a return to wetter conditions with highly variable moisture patterns along the Patagonian landmass. Clumped isotope (Δ 47) analyses at lower resolution reflect the degree of kinetic isotope fractionation at the time of carbonate deposition, especially during the dry interval around 8.5–5.5 ka BP. Reduced kinetic isotope fractionation is observed since at least 2.6 ka BP, a period marked by (slightly) wetter conditions.

Ultraluminous infrared galaxies (ULIRGs) have infrared luminosities L $_{IR}$ ��� 10$^{12}$ L $_{���}$, making them the most luminous objects in the infrared sky. These dusty objects are generally powered by starbursts with star formation rates that exceed 100 M $_{���}$ yr$^{���1}$, possibly combined with a contribution from an active galactic nucleus. Such environments make ULIRGs plausible sources of astrophysical high-energy neutrinos, which can be observed by the IceCube Neutrino Observatory at the South Pole. We present a stacking search for high-energy neutrinos from a representative sample of 75 ULIRGs with redshift z ��� 0.13 using 7.5 yr of IceCube data. The results are consistent with a background-only observation, yielding upper limits on the neutrino flux from these 75 ULIRGs. For an unbroken E $^{���2.5}$ power-law spectrum, we report an upper limit on the stacked flux at 90% confidence level. In addition, we constrain the contribution of the ULIRG source population to the observed diffuse astrophysical neutrino flux as well as model predictions. The astrophysical journal 926(1), 59 (2022). doi:10.3847/1538-4357/ac3cb6 Published by Univ., Chicago, Ill. [u.a.]

<p>The Pliocene sedimentary record provides a window into Earth’s climate dynamics under warmer-than-present boundary conditions. However, the Pliocene cannot be considered a stable warm climate that constitutes a solid baseline for middle-road future climate projections. Indeed, the increasing availability of time-continuous sedimentary archives (e.g., marine sediment cores) reveals complex temporal and spatial patterns of Pliocene ocean and climate variability on astronomical timescales. The Perth Basin is particularly interesting in that respect because it remains unclear if and how the Leeuwin Current sustained the comparably wet Pliocene climate in West-Australia, as well as how it influenced Southern Hemisphere paleoclimate variability. To constrain Leeuwin Current dynamics in time and space, this project constructed a new orbitally-resolved planktonic foraminifera (<em>Trilobatus sacculifer</em>) stable isotope record (δ<sup>18</sup>O and clumped isotopes Δ<sub>47</sub>) for the Plio-Pleistocene (4–2 Ma) interval of International Ocean Discovery Program (IODP) Site U1459. It complements an existing TEX<sub>86</sub> record from the same site and similar planktonic isotope records from the Northern Carnarvon Basin (ODP Site 763 and IODP Site U1463). The comparison of TEX<sub>86</sub> and Δ<sub>47</sub> paleothermometers reveals that TEX<sub>86</sub> likely reflects sea surface temperatures (SST, 23.8–28.9 °C), whereas <em>T. sacculifer</em> Δ<sub>47</sub> calcification temperatures probably echo the state of the lower mixed layer and upper thermocline at the studied Site U1459 (18.2–20.8 °C). The isotopic δ<sup>18</sup>O gradient along a 19° S–29° S latitudinal transect, between 3.9–2.2 Ma, displays large variability, ranging between 0.5 and 2.0 ‰, whereby a low latitudinal gradient is indicative of a strong Leeuwin Current and vice versa. These results challenge the interpretation that suggested a tectonic event in the Indonesian Throughflow as the cause for the rapid steepening of the isotopic gradient (0.9 to 1.5 ‰) around 3.7 Ma. The tectonic interpretation appears obsolete as it is now clear that the 3.7 Ma steepening of the isotopic gradient is intermittent, with flat latitudinal gradients (~0.5 ‰) restored in the latest Pliocene (2.9–2.6 Ma). Still, the new analysis affirms that a combination of astronomical forcing of wind patterns and eustatic sea level controlled Leeuwin Current intensity. A period of relatively weak Leeuwin Current between 3.7 and 3.1 Ma is advocated; a time interval also marked by cooler conditions throughout the Southern Hemisphere. In conclusion, the intensity of the Leeuwin Current and the latitudinal position of the subtropical front are rooted in the same forcing: Heat transport through the Indonesian Throughflow (ITF) valve propagated to the temperate zone through Indian Ocean poleward heat transport. The common ITF forcing explains the observed coherence of Southern Hemisphere ocean and climate records.</p>