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Abstract The plate tectonic cycle produces chemically distinct mid-ocean ridge basalts and arc volcanics, with the latter enriched in elements such as Ba, Rb, Th, Sr and Pb and depleted in Nb owing to the water-rich flux from the subducted slab. Basalts from back-arc basins, with intermediate compositions, show that such a slab flux can be transported behind the volcanic front of the arc and incorporated into mantle flow. Hence it is puzzling why melts of subduction-modified mantle have rarely been recognized in mid-ocean ridge basalts. Here we report the first mid-ocean ridge basalt samples with distinct arc signatures, akin to back-arc basin basalts, from the Arctic Gakkel Ridge. A new high precision dataset for 576 Gakkel samples suggests a pervasive subduction influence in this region. This influence can also be identified in Atlantic and Indian mid-ocean ridge basalts but is nearly absent in Pacific mid-ocean ridge basalts. Such a hemispheric-scale upper mantle heterogeneity reflects subduction modification of the asthenospheric mantle which is incorporated into mantle flow, and whose geographical distribution is controlled dominantly by a “subduction shield” that has surrounded the Pacific Ocean for 180 Myr. Simple modeling suggests that a slab flux equivalent to ~13% of the output at arcs is incorporated into the convecting upper mantle. 

We study gains from trade in multi-dimensional two-sided markets. Specifically, we focus on a setting with n heterogeneous items, where each item is owned by a different seller i, and there is a constrained-additive buyer with feasibility constraint ℱ. Multi-dimensional settings in one-sided markets, e.g. where a seller owns multiple heterogeneous items but also is the mechanism designer, are well-understood. In addition, single-dimensional settings in two-sided markets, e.g. where a buyer and seller each seek or own a single item, are also well-understood. Multi-dimensional two-sided markets, however, encapsulate the major challenges of both lines of work: optimizing the sale of heterogeneous items, ensuring incentive-compatibility among both sides of the market, and enforcing budget balance. We present, to the best of our knowledge, the first worst-case approximation guarantee for gains from trade in a multi-dimensional two-sided market. Our first result provides an O(log(1/r))-approximation to the first-best gains from trade for a broad class of downward-closed feasibility constraints (such as matroid, matching, knapsack, or the intersection of these). Here r is the minimum probability over all items that a buyer's value for the item exceeds the seller's cost. Our second result removes the dependence on r and provides an unconditional O(log n)-approximation to the second-best gains from trade. We extend both results for a general constrained-additive buyer, losing another O(log n)-factor en-route. The first result is achieved using a fixed posted price mechanism, and the analysis involves a novel application of the prophet inequality or a new concentration inequality. Our second result follows from a stitching lemma that allows us to upper bound the second-best gains from trade by the first-best gains from trade from the “likely to trade” items (items with trade probability at least 1/n) and the optimal profit from selling the “unlikely to trade” items. We can obtain an O(log n)-approximation to the first term by invoking our O(log(1/r))-approximation on the “likely to trade” items. We introduce a generalization of the fixed posted price mechanism—seller adjusted posted price—to obtain an O(log n)-approximation to the optimal profit for the “unlikely to trade” items. Unlike fixed posted price mechanisms, not all seller adjusted posted price mechanisms are incentive compatible and budget balanced. We develop a new argument based on “allocation coupling” to show the seller adjusted posted price mechanism used in our approximation is indeed budget balanced and incentive-compatible. 

ABSTRACT Photometric and spectroscopic data for two Low Luminosity Type IIP Supernovae (LL SNe IIP) 2020cxd and 2021aai are presented. SN 2020cxd was discovered 2 d after explosion at an absolute magnitude of Mr  = −14.02 ± 0.21 mag, subsequently settling on a plateau which lasts for ∼120 d. Through the luminosity of the late light curve tail, we infer a synthesized 56Ni mass of (1.8 ± 0.5) × 10−3 M⊙. During the early evolutionary phases, optical spectra show a blue continuum ($T\, \gt $8000 K) with broad Balmer lines displaying a P Cygni profile, while at later phases, Ca ii, Fe ii, Sc ii, and Ba ii lines dominate the spectra. Hydrodynamical modelling of the observables yields $R\, \simeq$ 575 R⊙ for the progenitor star, with Mej  = 7.5 M⊙ and $E\, \simeq$ 0.097 foe emitted during the explosion. This low-energy event originating from a low-mass progenitor star is compatible with both the explosion of a red supergiant (RSG) star and with an Electron Capture Supernova arising from a super asymptotic giant branch star. SN 2021aai reaches a maximum luminosity of Mr  = −16.57 ± 0.23 mag (correcting for AV = 1.92 mag), at the end of its remarkably long plateau (∼140 d). The estimated 56Ni mass is (1.4 ± 0.5) × 10−2 M⊙. The expansion velocities are compatible with those of other LL SNe IIP (few 103 km s−1). The physical parameters obtained through hydrodynamical modelling are $R\, \simeq$ 575 R⊙, Mej = 15.5 M⊙, and E = 0.4 foe. SN 2021aai is therefore interpreted as the explosion of an RSG, with properties that bridge the class of LL SNe IIP with standard SN IIP events. 

New phases of matter emerge at the edge of magnetic instabilities, which can occur in materials with moments that are localized, itinerant or intermediate between these extremes. In local moment systems, such as heavy fermions, the magnetism can be tuned towards a zero-temperature transition at a quantum critical point (QCP) via pressure, chemical doping, and, rarely, magnetic field. By contrast, in itinerant moment systems, QCPs are more rare, and they are induced by pressure or doping; there are no known examples of field induced transitions. This means that no universal behaviour has been established across the whole itinerant-to-local moment range—a substantial gap in our knowledge of quantum criticality. Here we report an itinerant antiferromagnet, Ti₃Cu₄, that can be tuned to a QCP by a small magnetic field. We see signatures of quantum criticality and the associated non-Fermi liquid behaviour in thermodynamic and transport measurements, while band structure calculations point to an orbital-selective, spin density wave ground state, a consequence of the square net structural motif in Ti₃Cu₄. Ti₃Cu₄thus provides a platform for the comparison and generalisation of quantum critical behaviour across the whole spectrum of magnetism.

 

We present photometric and spectroscopic data on three extragalactic luminous red novae (LRNe): AT 2018bwo , AT 2021afy , and AT 2021blu . AT 2018bwo was discovered in NGC 45 (at about 6.8 Mpc) a few weeks after the outburst onset. During the monitoring period, the transient reached a peak luminosity of 10 40 erg s −1 . AT 2021afy , hosted by UGC 10043 (∼49.2 Mpc), showed a double-peaked light curve, with the two peaks reaching a similar luminosity of 2.1(±0.6)×10 41 erg s −1 . Finally, for AT 2021blu in UGC 5829 (∼8.6 Mpc), the pre-outburst phase was well-monitored by several photometric surveys, and the object showed a slow luminosity rise before the outburst. The light curve of AT 2021blu was sampled with an unprecedented cadence until the object disappeared behind the Sun, and it was then recovered at late phases. The light curve of LRN AT 2021blu shows a double peak, with a prominent early maximum reaching a luminosity of 6.5 × 10 40 erg s −1 , which is half of that of AT 2021afy . The spectra of AT 2021afy and AT 2021blu display the expected evolution for LRNe: a blue continuum dominated by prominent Balmer lines in emission during the first peak, and a redder continuum consistent with that of a K-type star with narrow absorption metal lines during the second, broad maximum. The spectra of AT 2018bwo are markedly different, with a very red continuum dominated by broad molecular features in absorption. As these spectra closely resemble those of LRNe after the second peak, AT 2018bwo was probably discovered at the very late evolutionary stages. This would explain its fast evolution and the spectral properties compatible with that of an M-type star. From the analysis of deep frames of the LRN sites years before the outburst, and considerations of the light curves, the quiescent progenitor systems of the three LRNe were likely massive, with primaries ranging from about 13 M ⊙ for AT 2018bwo , to 14 −1 +4 M ⊙ for AT 2021blu , and over 40 M ⊙ for AT 2021afy .