Toward a radiometric ice clock: uranium ages of the Dome C ice core

Ice sheets and deep ice cores have yielded a wealth of paleoclimate information based on continuous dating methods while independent radiometric ages of ice have remained elusive. Here we demonstrate the application of (234U/238U) measurements to dating the EPICA Dome C ice core based on the accumulation of 234U in the ice matrix from recoil during 238U decay out of dust bound within the ice. Measured (234U/238U) activity ratios within the ice generally increase with depth while the surface areas of the dust grains are relatively constant. Using a newly designed device for measuring surface area for small samples, we were able to estimate reliably the recoil efficiency of nuclides from dust to ice. The resulting calculated radiometric ages range between 80 ka and 870 ka. Measured samples in the upper 3100 m fall on the previously published age-depth profile. Samples in the 3200–3255 m section show a marked change from 723–870 ka to 85 ka indicating homogenization of the deep ice prior to resetting of the (234U/238U) age in the basal layers. The mechanism for homogenization is likely enhanced lateral ice flow due to high basal melting and geothermal heat flux

Unital quantum operators on the Bloch ball and Bloch region

For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that govern when a ``diagonal'' superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.Comment: Revised and corrected, to appear in Physical Review

τ→ρππν\tau\to\rho\pi\pi\nu decays

Effective chiral theory of mesons is applied to study the four decay modes of $\tau\to\rho\pi\pi\nu$. Theoretical values of the branching ratios are in agreement with the data. The theory predicts that the $a_{1}$ resonance plays a dominant role in these decays. There is no new parameter in this study.Comment: 12 pages and one figur

Melting of a Two-component Source beneath Iceland

New trace element and Hf-Nd isotope data on post-glacial basalts from Iceland's main rift zones are used in conjunction with literature data to evaluate the relative importance of source heterogeneity and the melting process for the final melt composition. Correlations between Hf and Nd isotope compositions and trace element ratios indicate that at least two source components are sampled systematically as a function of the degree and pressure of melting beneath Iceland. Strong depletion in Rb, Ba, U and Th and enrichment in Nb and Ta compared with La in the most enriched samples from the Reykjanes Peninsula and Western Rift Zone suggests that the enriched source component is similar to ancient recycled enriched mid-ocean ridge basalt (E-MORB) crust. Highly incompatible trace element ratios such as Nb/La and Nb/U and Pb isotope ratios are variable across Iceland. This observation suggests that either the enriched component is intrinsically heterogeneous, or that there is a larger proportion of the enriched source component beneath the Southwestern Rift Zone compared with the Northern Rift Zone. The relative effect of source heterogeneity and melting on the final melt composition was evaluated with a one-dimensional polybaric melt mixing model in which accumulated melts from a depleted MORB mantle and a recycled E-MORB crust are mixed in different ways. Two styles of melt mixing were simulated: (1) complete mixing of melts with variable proportions of the depleted mantle and recycled E-MORB components; (2) incomplete mixing with a fixed initial proportion of the two source components. Calculated pressure-dependent compositional changes using these simple two-component melting models can explain the observed trends in trace element ratio and isotope ratio diagrams for Icelandic basalts, even in cases where conventional binary mixing models would require more than two source components. The example of Iceland demonstrates that melt mixing during extraction from the mantle is a key process for controlling the trace element and isotope variability observed in basaltic lavas and must be evaluated before inferring the presence of multiple source component

Southern Ocean control of silicon stable isotope distribution in the deep Atlantic Ocean

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Geochemical Cycles 26 (2012): GB2035, doi:10.1029/2011GB004141.The fractionation of silicon (Si) stable isotopes by biological activity in the surface ocean makes the stable isotope composition of silicon (δ30Si) dissolved in seawater a sensitive tracer of the oceanic biogeochemical Si cycle. We present a high-precision dataset that characterizes the δ30Si distribution in the deep Atlantic Ocean from Denmark Strait to Drake Passage, documenting strong meridional and smaller, but resolvable, vertical δ30Si gradients. We show that these gradients are related to the two sources of deep and bottom waters in the Atlantic Ocean: waters of North Atlantic and Nordic origin carry a high δ30Si signature of ≥+1.7‰ into the deep Atlantic, while Antarctic Bottom Water transports Si with a low δ30Si value of around +1.2‰. The deep Atlantic δ30Si distribution is thus governed by the quasi-conservative mixing of Si from these two isotopically distinct sources. This disparity in Si isotope composition between the North Atlantic and Southern Ocean is in marked contrast to the homogeneity of the stable nitrogen isotope composition of deep ocean nitrate (δ15N-NO3). We infer that the meridional δ30Si gradient derives from the transport of the high δ30Si signature of Southern Ocean intermediate/mode waters into the North Atlantic by the upper return path of the meridional overturning circulation (MOC). The basin-scale deep Atlantic δ30Si gradient thus owes its existence to the interaction of the physical circulation with biological nutrient uptake at high southern latitudes, which fractionates Si isotopes between the abyssal and intermediate/mode waters formed in the Southern Ocean.This work was supported by Swiss National Science Foundation grants 200021-116473 and 200020-130361.2012-12-1

Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the Asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.Comment: 17 pages, 8 figures. During preparation of this manuscript the authors became aware of the work of Mileyko at al., concurrently submitted for publicatio

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure

Weighted composition operators on Korenblum type spaces of analytic functions

[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ and $$L^{p-}$$. Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces $$ces(p+), 1\le p\le \infty$$. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces $$ces(p-), 1\le p\le \infty$$. Descriptive topology and functional analysis. II, 43–67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1–32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263–276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70–79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101–118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561–580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41–60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and $$H^\infty$$ spaces. J. Math. Anal. Appl. 445, 1300–1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form $$uC_{\varphi }$$. Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872–884 (2000)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Childhood acute illness and nutrition (CHAIN) network: A protocol for a multi-site prospective cohort study to identify modifiable risk factors for mortality among acutely ill children in Africa and Asia

Introduction: Children admitted to hospitals in resource-poor settings remain at risk of both inpatient and post-discharge mortality. While known risk factors such as young age and nutritional status can identify children at risk, they do not provide clear mechanistic targets for intervention. The Childhood Acute Illness and Nutrition (CHAIN) cohort study aims to characterise the biomedical and social risk factors for mortality in acutely ill children in hospitals and after discharge to identify targeted interventions to reduce mortality.Methods and analysis: The CHAIN network is currently undertaking a multi-site, prospective, observational cohort study, enrolling children aged 1 week to 2 years at admission to hospitals at nine sites located in four African and two South Asian countries. The CHAIN Network supports the sites to provide care according to national and international guidelines. Enrolment is stratified by anthropometric status and children are followed throughout hospitalisation and for 6 months after discharge. Detailed clinical, demographic, anthropometric, laboratory and social exposures are assessed. Scheduled visits are conducted at 45, 90 and 180 days after discharge. Blood, stool and rectal swabs are collected at enrolment, hospital discharge and follow-up. The primary outcome is inpatient or post-discharge death. Secondary outcomes include readmission to hospital and nutritional status after discharge. Cohort analysis will identify modifiable risks, children with distinct phenotypes, relationships between factors and mechanisms underlying poor outcomes that may be targets for intervention. A nested case-control study examining infectious, immunological, metabolic, nutritional and other biological factors will be undertaken.Ethics and dissemination: This study protocol was reviewed and approved primarily by the Oxford Tropical Research Ethics Committee, and the institutional review boards of all partner sites. The study is being externally monitored. Results will be published in open access peer-reviewed scientific journals and presented to academic and policy stakeholders