Forming Probably Stable Communities with Limited Interactions

A community needs to be partitioned into disjoint groups; each community member has an underlying preference over the groups that they would want to be a member of. We are interested in finding a stable community structure: one where no subset of members $S$ wants to deviate from the current structure. We model this setting as a hedonic game, where players are connected by an underlying interaction network, and can only consider joining groups that are connected subgraphs of the underlying graph. We analyze the relation between network structure, and one's capability to infer statistically stable (also known as PAC stable) player partitions from data. We show that when the interaction network is a forest, one can efficiently infer PAC stable coalition structures. Furthermore, when the underlying interaction graph is not a forest, efficient PAC stabilizability is no longer achievable. Thus, our results completely characterize when one can leverage the underlying graph structure in order to compute PAC stable outcomes for hedonic games. Finally, given an unknown underlying interaction network, we show that it is NP-hard to decide whether there exists a forest consistent with data samples from the network.Comment: 11 pages, full version of accepted AAAI-19 pape

Axiomatic Characterization of Data-Driven Influence Measures for Classification

We study the following problem: given a labeled dataset and a specific datapoint x, how did the i-th feature influence the classification for x? We identify a family of numerical influence measures - functions that, given a datapoint x, assign a numeric value phi_i(x) to every feature i, corresponding to how altering i's value would influence the outcome for x. This family, which we term monotone influence measures (MIM), is uniquely derived from a set of desirable properties, or axioms. The MIM family constitutes a provably sound methodology for measuring feature influence in classification domains; the values generated by MIM are based on the dataset alone, and do not make any queries to the classifier. While this requirement naturally limits the scope of our framework, we demonstrate its effectiveness on data

Continental Magmatism and Uplift as the Primary Driver for First-Order Oceanic 87Sr/86Sr Variability with Implications for Global Climate and Atmospheric Oxygenation

Oceans cover 70% of Earth\u27s surface, setting it apart from the other terrestrial planets in the solar system, but the mechanisms driving oceanic chemical evolution through time remain an important unresolved problem. Imbalance in the strontium cycle, introduced, for example, by increases in continental weathering associated with mountain building, has been inferred from shifts in marine carbonate 87Sr/86Sr ratios. There are, however, uncertainties about the spatial and temporal patterns of crustal evolution in Earth\u27s past, particularly for the period leading up to the Cambrian explosion of life. Here we show that U-Pb age and trace element data from a global compilation of detrital zircons are consistent with marine carbonate 87Sr/86Sr ratios, suggesting changes in radiogenic continental input into Earth\u27s oceans over time. Increases in riverine Sr input were related to the break-up and dispersal of continents, with increased weathering and erosion of a higher proportion of radiogenic rocks and high-elevation continental crust. Tectonic processes exert a strong influence on the chemical evolution of the planet\u27s oceans over geologic time scales and may have been a key driver for concomitant increases in atmosphere-ocean oxygenation and global climate cooling

Rapid magma generation or shared magmatic reservoir? Petrology and geochronology of the Rat Creek and Nelson Mountain Tuffs, CO, USA

This study was supported by the ETH Research Grant ETH-34 15-2 (JS).Large-volume silicic volcanism poses global hazards in the form of proximal pyroclastic density currents, distal ash fall and short-term climate perturbations, which altogether warrant the study of how silicic magma bodies evolve and assemble. The southern rocky mountain volcanic field (SRMVF) is home to some of the largest super-eruptions in the geological record, and has been studied to help address the debate over how quickly eruptible magma batches can be assembled–whether in decades to centuries, or more slowly over 100’s of kyr. The present study focuses on the San Luis caldera complex within the SRMVF, and discusses the paradigms of rapid magma generation vs. rapid magma assembly. The caldera complex consists of three overlapping calderas that overlie the sources of three large-volume mid-Cenozoic ignimbrites: first, the Rat Creek Tuff (RCT; zoned dacite-rhyolite, 150 km3), followed by the Cebolla Creek Tuff (mafic dacite, 250 km3) and finally, the Nelson Mountain Tuff (NMT; zoned dacite-rhyolite, 500 km3), which are all indistinguishable in age by 40Ar/39Ar dating. We argue for a shared magmatic history for the three units on the basis of (1) similar mineral trace element compositions in the first and last eruptions (plagioclase, sanidine, biotite, pyroxene, amphibole, titanite, and zircon), (2) overlapping zircon U-Pb ages in all three units, and (3) similar thermal rejuvenation signatures visible in biotite (low-Mn, high-Ba) and zircon (low-Hf, low-U) geochemistry within the RCT and NMT. It is postulated that the NMT was sourced from a pre-existing magma reservoir to the northeast, which is corroborated by the formation of the nearby Cochetopa Caldera during the eruption of the NMT. The inferred lateral magma transport has two important implications: (1) it demonstrates long-distance transport of highly viscosity magmas at volumes (100’s of km3) not previously recorded, and (2) the sourcing of magma from a nearby pre-existing magma reservoir greatly reduces the rate of magma generation necessary to explain the close coincidence of three overlapping, large-volume magma systems. Additionally, the concept of magmatic “flux” (km3 kyr−1) is discussed in this context, and it is argued that an area-normalized flux (km3 kyr–1 km−2) provides a more useful number for measuring magma production rates: it is expected that magmatic volumes will scale with footprint of the thermal anomaly, and not taking this into account may lead to errant volumetric flux (km3 kyr−1) estimates. Meanwhile, area-normalized flux estimates in a given area are similar between units, consistent with evolution in a relatively constant thermal regime. Such estimates also demonstrate similar fluxes for ∼cogenetic volcanic and plutonic units.Publisher PDFPeer reviewe

Outboard Onset of Ross Orogen Magmatism and Subsequent Igneous and Metamorphic Cooling Linked to Slab Rollback during Late-Stage Gondwana Assembly

Changes in magmatism and sedimentation along the late Neoproterozoic-early Paleozoic Ross orogenic belt in Antarctica have been linked to the cessation of convergence along the Mozambique belt during the assembly of East-West Gondwana. However, these interpretations are non-unique and are based, in part, on limited thermochronological data sets spread out along large sectors of the East Antarctic margin. We report new 40Ar/39Ar hornblende, muscovite, and biotite age data for plutonic (n = 13) and metasedimentary (n = 3) samples from the Shackleton–Liv Glacier sector of the Queen Maud Mountains in Antarctica. Cumulative 40Ar/39Ar age data show polymodal age peaks (510 Ma, 491 Ma, 475 Ma) that lag peaks in U-Pb igneous crystallization ages, suggesting igneous and metamorphic cooling following magmatism within the region. The 40Ar/39Ar ages are similar to ages in other sectors of the Ross orogen, but younger than detrital mineral 40Ar/39Ar cooling ages indicative of older magmatism and cooling of unexposed inboard areas along the margin. Detrital zircon trace element abundances suggest that the widespread onset of magmatism in outboard localities of the orogen correlates with a ~560–530 Ma decrease in crustal thickness. The timing of crustal thinning recorded by zircon in magmas overlaps with other evidence for the timing of crustal extension, suggesting that the regional onset of magmatism with subsequent igneous and metamorphic cooling probably reflects slab rollback that coincided with possible global plate motion changes induced during the final assembly of Gondwana

Distinguishing the vegetation and soil component of δ13C variation in speleothem records from degassing and prior calcite precipitation effects

The carbon isotopic signature inherited from soil/epikarst processes may be modified by degassing and prior calcite precipitation (PCP) before its imprint on speleothem calcite. Despite laboratory demonstration of PCP effects on carbon isotopes and increasingly sophisticated models of the governing processes, to date, there has been limited effort to deconvolve the dual PCP and soil/epikarst components in measured speleothem isotopic time series. In this contribution, we explore the feasibility, advantages, and disadvantages of using trace element ratios and &delta;44Ca to remove the overprinting effect of PCP on measured &delta;13C to infer the temporal variations in the initial &delta;13C of dripwater. In 8 examined stalagmites, the most widely utilized PCP indicators Mg/Ca and &delta;44Ca covary as expected. However, Sr/Ca does not show consistent relationships with &delta;44Ca so PCP is not universally the dominant control on Sr/Ca. From &delta;44Ca and Mg/Ca, our calculation of PCP as fCa, fraction of initial Ca remaining at the deposition of the stalagmite layer, yields multiple viable solutions depending on the assumed &delta;44Ca fractionation factor and inferred variation in DMg. Uncertainty in the effective fractionation of &delta;13C during degassing and precipitation contributes to uncertainty in the absolute value of estimated initial &delta;13C. Nonetheless, the trends in initial &delta;13C are less sensitive to these uncertainties. In coeval stalagmites from the same cave spanning 94 to 82 ka interval, trends in calculated initial &delta;13C are more similar than those in measured &delta;13C, and reveal a common positive anomaly initial &delta;13C during a stadial cooling event. During deglaciations, the trend of greater respiration rates and higher soil CO2 is captured in the calculated initial &delta;13C, despite the tendency of higher interglacial dripwater situation to favor more extensive PCP.</p

Refining LA-ICP-MS Data Acquisition and Interpretation Methods for the Zircon Geochronometer in Tertiary Magmatic Systems

Understanding the mechanisms that govern the evolution of magmatic systems necessitates a firm grasp on their respective timescales. To this end, a variety of mineral chronometers is employed, most notably the U-Pb system in zircon. While high-resolution methods such as isotope dilution thermal ionization mass spectrometry (ID-TIMS) provide unparalleled insight into the temporal evolution of silicic magmatic systems, the time-intensive and specialized nature of these techniques often hinders their utility. Laser ablation inductively-coupled-plasma mass spectrometry (LA-ICP-MS) is a widely-available technique that combines high throughput with an ever-increasing degree of precision, but suffers some inherent technical and methodological drawbacks. The resolution of these issues and the expansion of LA-ICP-MS as a trusted source of geochronological data in magmatic petrology is considered here. First, the application of LA-ICP-MS to U-Th zircon dating of young (< 350 ka) zircons has been historically limited due to the difficulty of detecting the low-abundance 230Th isotope (particularly on the backdrop of the much more abundant 232Th), and distinguishing it from isobaric Zr2O3 interferences on mass 230. A novel analytical routine and data reduction scheme are developed, wherein a series of corrections are applied to arrive at an accurate (230Th/238U). These combined methods are applied to a variety of reference materials at secular equilibrium and a series of young zircons, reproducing (230Th/238U) values at secular equilibrium in the former case, and the SIMS-derived ages in the latter. Next, the application of LA-ICP-MS to U-Pb is considered for relatively young zircons ( 350 ka), where age determination is hindered by strong differences in crystal lattice properties relative to older and more radiation-damaged zircon reference materials. A relationship between the α particle radiation dosage and the apparent age offset is systematically characterized on a number of reference materials, and a novel multi-reference material-based data reduction software (Dose_Corrector.ipf) is developed for the commonly-used IgorPro platform. A detailed discussion of excess variance in LA-ICP-MS U-Pb dating follows, focusing on identifying the sources of excess uncertainty and analytical bias that ultimately limit the inter-session and inter-laboratory reproducibility of the method to ~2% (relative), despite individual analyses having uncertainties as good as 0.5%. A series of guidelines are proposed that are meant to limit the degree of excess uncertainty caused by analytical parameters, and a series of recommendations are made that take a conservative approach to propagating uncertainties in order to increase the reliability of LA-ICP-MS data interpretations. Lastly, a systematic study of trace elements in thermally annealed and unannealed zircons is carried out by LA-ICP-MS, demonstrating the dependence of Li concentration on thermal perturbation and calling into question the validity of applying Li-in-zircon as a geospeedometer. In particular, it is suggested that the incorporation of Li in zircon is directly linked to H in the crystal lattice, which together work to charge balance trivalent rare earth elements. Both Li and H, present in high concentrations within melt inclusions, are mobilized during thermal events and diffuse through the crystal lattice at rates much faster than previously determined