hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

A Global Trend towards Democratic Convergence? A Lijphartian Analysis of Advanced Democracies.

The article offers a systematic analysis of the comparative trajectory of international democratic change. In particular, it focuses on the resulting convergence or divergence of political systems, borrowing from the literatures on institutional change and policy convergence. To this end, political-institutional data in line with Arend Lijphart’s (1999, 2012) empirical theory of democracy for 24 developed democracies between 1945 and 2010 are analyzed. Heteroscedastic multilevel models allow for directly modeling the development of the variance of types of democracy over time, revealing information about convergence, and adding substantial explanations. The findings indicate that there has been a trend away from extreme types of democracy in single cases, but no unconditional trend of convergence can be observed. However, there are conditional processes of convergence. In particular, economic globalization and the domestic veto structure interactively influence democratic convergence.

Remarks on the convergence of pseudospectra

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant resolvent norm on an open set. We extend the class of operators for which it is known that the latter cannot happen by showing that if the resolvent norm is constant on an open set, then this constant is the global minimum. We present a number of examples exhibiting various resolvent norm behaviours and illustrating the applicability of this characterisation compared to known results.

Quick divergence but slow convergence during ecotype formation in lake and stream stickleback pairs of variable age

When genetic constraints restrict phenotypic evolution, diversification can be predicted to evolve along so-called lines of least resistance. To address the importance of such constraints and their resolution, studies of parallel phenotypic divergence that differ in their age are valuable. Here, we investigate the parapatric evolution of six lake and stream threespine stickleback systems from Iceland and Switzerland, ranging in age from a few decades to several millennia. Using phenotypic data, we test for parallelism in ecotypic divergence between parapatric lake and stream populations and compare the observed patterns to an ancestral-like marine population. We find strong and consistent phenotypic divergence, both among lake and stream populations and between our freshwater populations and the marine population. Interestingly, ecotypic divergence in low-dimensional phenotype space (i.e. single traits) is rapid and seems to be often completed within 100 years. Yet, the dimensionality of ecotypic divergence was highest in our oldest systems and only there parallel evolution of unrelated ecotypes was strong enough to overwrite phylogenetic contingency. Moreover, the dimensionality of divergence in different systems varies between trait complexes, suggesting different constraints and evolutionary pathways to their resolution among freshwater systems.

Topology of the ambient boundary and the convergence of causal curves

We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric topology but with the Zeeman fine topology. This then places severe constraints to the convergence of a sequence of causal curves and the extraction of a limit curve, and also to our ability to formulate conditions for singularity formation.

The Almost Person: Myth, Narrative and The Doctor

Paul Ricœur describes selfhood as the product of a communal narrative. Communal narratives structured as symbolic myths provide a narrative identity and an ethic of selfhood. The psychologist Jerome Bruner, for instance, places the source of such a narrative identity in the family, where ‘canonical stories’ are formed. ‘Home’ becomes a mode of discourse, a way of recognizing ourselves in the narratives given to us by others. This paper will draw on these concepts of narrative identity in order to investigate the problems to selfhood which face the character of The Doctor in the BBC series Doctor Who. I will identify The Doctor as a character who acts within a self-constructed narrative vacuum, reading the character by contrasting two types of personal myth-making, one ‘real’, as in a lived narrative, and one ‘counterfeit’; a conjured myth to replace and obscure the lived self. The paper will pay particular attention to the twenty-first century reincarnations of Doctor Who. I will argue that the writing of Russell T. Davis and later Steven Moffat in particular directly address this tension of myth and selfhood, as The Doctor struggles between his self-imposed role as a modern Prometheus and the insistent haunting and return of his own story. In these incarnations, his companions become mirrors to The Doctor, bringing with them their own narrative and ethical identities. In turn, it is through his companions that The Doctor is able to build his own lived narrative of sorts, which challenges his self-created ‘mythology’. In contrast to the weeping angels, whose horrific agency manifests only when not apprehended, the Doctor’s story continues to become more real the more he is ‘perceived’, both by the human race and by the viewer.

Estimating whole-lake fish catch per unit effort

The European standard for gillnetsampling to characterize lake fish communities stratifies sampling effort (i.e., number of nets) within depth strata. Nets to sample benthic habitats are randomly distributed throughout the lake within each depth strata. Pelagic nets are also stratified by depth, but are set only at the deepest point of the lake. Multiple authors have suggested that this design under-represents pelagic habitats, resulting in estimates of whole-lake CPUE and community composition which are disproportionately influenced by ecological conditions of littoral and benthic habitats. To address this issue, researchers have proposed estimating whole-lake CPUE by weighting the catch rate in each depth-compartment by the proportion of the volume of the lake contributed by the compartment. Our study aimed to assess the effectiveness of volume-weighting by applying it to fish communities sampled according to the European standard (CEN), and by a second whole-lake gillnetting protocol (VERT), which prescribes additional fishing effort in pelagic habitats. We assume that convergence between the protocols indicates that volume-weighting provides a more accurate estimate of whole-lake catch rate and community composition. Our results indicate that volume-weighting improves agreement between the protocols for whole-lake total CPUE, estimated proportion of perch and roach and the overall fish community composition. Discrepancies between the protocols remaining after volume-weighting maybe because sampling under the CEN protocol overlooks horizontal variation in pelagic fish communities. Analyses based on multiple pelagic-set VERT nets identified gradients in the density and biomass of pelagic fish communities in almost half the lakes that corresponded with the depth of water at net-setting location and distance along the length of a lake. Additional CEN pelagic sampling effort allocated across water depths and distributed throughout the lake would therefore help to reconcile differences between the sampling protocols and, in combination with volume-weighting, converge on a more accurate estimate of whole-lake fish communities.

The DESCARTES-Nantes survey of kidney transplant recipients displaying clinical operational tolerance identifies 35 new tolerant patients and 34 almost tolerant patients.

BACKGROUND Kidney recipients maintaining a prolonged allograft survival in the absence of immunosuppressive drugs and without evidence of rejection are supposed to be exceptional. The ERA-EDTA-DESCARTES working group together with Nantes University launched a European-wide survey to identify new patients, describe them and estimate their frequency for the first time. METHODS Seventeen coordinators distributed a questionnaire in 256 transplant centres and 28 countries in order to report as many 'operationally tolerant' patients (TOL; defined as having a serum creatinine <1.7 mg/dL and proteinuria <1 g/day or g/g creatinine despite at least 1 year without any immunosuppressive drug) and 'almost tolerant' patients (minimally immunosuppressed patients (MIS) receiving low-dose steroids) as possible. We reported their number and the total number of kidney transplants performed at each centre to calculate their frequency. RESULTS One hundred and forty-seven questionnaires were returned and we identified 66 TOL (61 with complete data) and 34 MIS patients. Of the 61 TOL patients, 26 were previously described by the Nantes group and 35 new patients are presented here. Most of them were noncompliant patients. At data collection, 31/35 patients were alive and 22/31 still TOL. For the remaining 9/31, 2 were restarted on immunosuppressive drugs and 7 had rising creatinine of whom 3 resumed dialysis. Considering all patients, 10-year death-censored graft survival post-immunosuppression weaning reached 85% in TOL patients and 100% in MIS patients. With 218 913 kidney recipients surveyed, cumulative incidences of operational tolerance and almost tolerance were estimated at 3 and 1.5 per 10 000 kidney recipients, respectively. CONCLUSIONS In kidney transplantation, operational tolerance and almost tolerance are infrequent findings associated with excellent long-term death-censored graft survival.