Zircon ages in granulite facies rocks: decoupling from geochemistry above 850 °C?

Granulite facies rocks frequently show a large spread in their zircon ages, the interpretation of which raises questions: Has the isotopic system been disturbed? By what process(es) and conditions did the alteration occur? Can the dates be regarded as real ages, reflecting several growth episodes? Furthermore, under some circumstances of (ultra-)high-temperature metamorphism, decoupling of zircon U–Pb dates from their trace element geochemistry has been reported. Understanding these processes is crucial to help interpret such dates in the context of the P–T history. Our study presents evidence for decoupling in zircon from the highest grade metapelites (> 850 °C) taken along a continuous high-temperature metamorphic field gradient in the Ivrea Zone (NW Italy). These rocks represent a well-characterised segment of Permian lower continental crust with a protracted high-temperature history. Cathodoluminescence images reveal that zircons in the mid-amphibolite facies preserve mainly detrital cores with narrow overgrowths. In the upper amphibolite and granulite facies, preserved detrital cores decrease and metamorphic zircon increases in quantity. Across all samples we document a sequence of four rim generations based on textures. U–Pb dates, Th/U ratios and Ti-in-zircon concentrations show an essentially continuous evolution with increasing metamorphic grade, except in the samples from the granulite facies, which display significant scatter in age and chemistry. We associate the observed decoupling of zircon systematics in high-grade non-metamict zircon with disturbance processes related to differences in behaviour of non-formula elements (i.e. Pb, Th, U, Ti) at high-temperature conditions, notably differences in compatibility within the crystal structure

Kinematics and Age of Syn-Intrusive Detachment Faulting in the Southern Alps: Evidence for Early Permian Crustal Extension and Implications for the Pangea A Versus B Controversy

Permian basin formation and magmatism in the Southern Alps of Italy have been interpreted as expressions of a WSW‐ENE‐trending, dextral megashear zone transforming Early Permian Pangea B into Late Permian Pangea A between ~285 and 265 Ma. In an alternative model, basin formation and magmatism resulted from N‐S crustal extension. To characterize Permian tectonics, we studied the Grassi Detachment Fault, a low‐angle extensional fault in the central Southern Alps. The footwall forms a metamorphic core complex affected by upward‐increasing, top‐to‐the‐southeast mylonitization. Two granitoid intrusions occur in the core complex, the synmylonitic Val Biandino Quartz Diorite and the postmylonitic Valle San Biagio Granite. U‐Pb zircon dating yielded crystallization ages of 289.1 ± 4.5 Ma for the former and 286.8 ± 4.9 Ma for the latter. Consequently, detachment‐related mylonitic shearing took place during the Early Permian and ended at ~288 Ma, but kinematically coherent brittle faulting continued. Considering 30° anticlockwise rotation of the Southern Alps since Early Permian, the extension direction of the Grassi Detachment Fault was originally ~N‐S. Even though a dextral continental wrench system has long been regarded as a viable model at regional scale, the local kinematic evidence is inconsistent with this and, rather, supports N‐S extensional tectonics. Based on a compilation of >200 U‐Pb zircon ages, we discuss the evolution and tectonic framework of Late Carboniferous to Permian magmatism in the Alps

Multidimensional signals and analytic flexibility: Estimating degrees of freedom in human speech analyses

Recent empirical studies have highlighted the large degree of analytic flexibility in data analysis which can lead to substantially different conclusions based on the same data set. Thus, researchers have expressed their concerns that these researcher degrees of freedom might facilitate bias and can lead to claims that do not stand the test of time. Even greater flexibility is to be expected in fields in which the primary data lend themselves to a variety of possible operationalizations. The multidimensional, temporally extended nature of speech constitutes an ideal testing ground for assessing the variability in analytic approaches, which derives not only from aspects of statistical modeling, but also from decisions regarding the quantification of the measured behavior. In the present study, we gave the same speech production data set to 46 teams of researchers and asked them to answer the same research question, resulting insubstantial variability in reported effect sizes and their interpretation. Using Bayesian meta-analytic tools, we further find little to no evidence that the observed variability can be explained by analysts’ prior beliefs, expertise or the perceived quality of their analyses. In light of this idiosyncratic variability, we recommend that researchers more transparently share details of their analysis, strengthen the link between theoretical construct and quantitative system and calibrate their (un)certainty in their conclusions

Some remarks to the formal and local theory of the generalized Dhombres functional equation

We are looking for local analytic respectively formal solutions of the generalized Dhombres functional equation $f(zf(z))=\varphi(f(z))$ in the complex domain. First we give two proofs of the existence theorem about solutions $f$ with $f(0) = w_0$ and $w_0 \in \mathbb{C}^\star \setminus \mathbb{E}$ where $\mathbb{E}$ denotes the group of complex roots of $1$. Afterwards we represent solutions $f$ by means of infinite products where we use on the one hand the canonical convergence of complex analysis, on the other hand we show how solutions converge with respect to the weak topology. In this section we also study solutions where the initial value $z_0$ is different from zero