Egalitarianism under Earmark Constraints

Agents with single-peaked preferences share a resource coming from different suppliers; each agent is connected to only a subset of suppliers. Examples include workload balancing, sharing earmarked funds, and rationing utilities after a storm. Unlike in the one supplier model, in a Pareto optimal allocation agents who get more than their peak from underdemanded suppliers, coexist with agents who get less from overdemanded suppliers. Our Egalitarian solution is the Lorenz dominant Pareto optimal allocation. It treats agents with equal demands as equally as the connectivity constraints allow. Together, Strategyproofness, Pareto Optimality, and Equal Treatment of Equals, characterize our solution.

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

Petrogenesis of rift-related tephrites, phonolites and trachytes (Central European Volcanic Province, Rhon, FRG): Constraints from Sr, Nd, Pb and O isotopes

The volcanic rocks of the Rhön area (Central European Volcanic Province, Germany) belong to a moderately alkali basaltic suite that is associated with minor tephriphonolites, phonotephrites, tephrites, phonolites and trachytes. Based on isotope sytematics (87Sr/86Sr: 0.7033–0.7042; 143Nd/144Nd: 0.51279–0.51287; 206Pb/204Pb: 19.1–19.5), the inferred parental magmas formed by variable degrees of partial melting of a common asthenospheric mantle source (EAR: European Asthenospheric Reservoir of Cebriá and Wilson, 1995). Tephrites, tephriphonolites, phonotephrites, phonolites and trachytes show depletions and enrichments in some trace elements (Sr, Ba, Nb, Zr, Y) indicating that they were generated by broadly similar differentiation processes that were dominated by fractionation of olivine, clinopyroxene, amphibole, apatite and titaniferous magnetite ± plagioclase ± alkalifeldspar. The fractionated samples seem to have evolved by two distinct processes. One is characterized by pure fractional crystallization indicated by increasing Nb (and other incompatible trace element) concentrations at virtually constant 143Nd/144Nd ~ 0.51280 and 87Sr/86Sr ~ 0.7035. The other process involved an assimilation–fractional crystallization (AFC) process where moderate assimilation to crystallization rates produced evolved magmas characterized by higher Nb concentrations at slightly lower 143Nd/144Nd down to 0.51275. Literature data for some of the evolved rocks show more variable 87Sr/86Sr ranging from 0.7037 to 0.7089 at constant 143Nd/144Nd ~ 0.51280. These features may result from assimilation of upper crustal rocks by highly differentiated low-Sr (< 100 ppm Sr) lavas. However, based on the displacement of the differentiated rocks from this study towards lower 143Nd/144Nd ratios and modeled AFC processes in 143Nd/144Nd vs. 87Sr/86Sr and 207Pb/204Pb vs. 143Nd/144Nd space assimilation of lower crustal rocks seems more likely. The view that assimilation of lower crustal rocks played a role is confirmed by high-precision double-spike Pb isotope data that reveal higher 207Pb/204Pb ratios (15.62–15.63) in the differentiated rocks than in the primitive basanites (15.58–15.61). This is compatible with incorporation of radiogenic Pb from lower crustal xenoliths (207Pb/204Pb: 15.63–15.69) into the melt. However, 206Pb/204Pb ratios are similar for the differentiated rocks (19.13–19.35) and the primitive basanites (19.12–19.55) implying that assimilation involved an ancient crustal end member with a higher U/Pb ratio than the mantle source of the basanites. In addition, alteration-corrected δ18O values of the differentiated rocks range from c. 5 to 7‰ which is the same range as observed in the primitive alkaline rocks. This study confirms previous interpretations that highlighted the role of AFC processes in the evolution of alkaline volcanic rocks in the Rhön area of the Central European Volcanic Province.