A proteinuria cut-off level of 0.7 g /day after 12 months of treatment best predicts long-term renal outcome in lupus nephritis: Data from the MAINTAIN Nephritis Trial

Background: Although an early decrease in proteinuria has been correlated with good long-term renal outcome in lupus nephritis (LN), studies aimed at defining a cut-off proteinuria value are missing, except a recent analysis performed on patients randomised in the Euro-Lupus Nephritis Trial, demonstrating that a target value of 0.8 g/day at month 12 optimised sensitivity and specificity for the prediction of good renal outcome. The objective of the current work is to validate this target in another LN study, namely the MAINTAIN Nephritis Trial (MNT). Methods: Long-term (at least 7 years) renal function data were available for 90 patients randomised in the MNT. Receiver operating characteristic curves were built to test the performance of proteinuria measured within the 1st year as short-term predictor of long-term renal outcome. We calculated the positive and negative predictive values (PPV, NPV). Results: After 12 months of treatment, achievement of a proteinuria <0.7 g/day best predicted good renal outcome, with a sensitivity and a specificity of 71% and 75%, respectively. The PPV was high (94%) but the NPV low (29%). Addition of the requirement of urine red blood cells 645/hpf as response criteria at month 12 reduced sensitivity from 71% to 41%. Conclusions: In this cohort of mainly Caucasian patients suffering from a first episode of LN in most cases, achievement of a proteinuria <0.7 g/day at month 12 best predicts good outcome at 7 years and inclusion of haematuria in the set of criteria at month 12 undermines the sensitivity of early proteinuria decrease for the prediction of good outcome. The robustness of these conclusions stems from the very similar results obtained in two distinct LN cohorts

Asymptotic correlations in gapped and critical topological phases of 1D quantum systems

Topological phases protected by symmetry can occur in gapped and—surprisingly—in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by a topological invariant and a central charge c. We investigate the correlations of string operators, giving insight into the interplay between topology and criticality. In the gapped phases, these non-local string order parameters allow us to extract . Remarkably, ratios of correlation lengths are universal. In the critical phases, the scaling dimensions of these operators serve as an order parameter, encoding and c. We derive exact asymptotics of these correlation functions using Toeplitz determinant theory. We include physical discussion, e.g., relating lattice operators to the conformal field theory. Moreover, we discuss the dual spin chains. Using the aforementioned universality, the topological invariant of the spin chain can be obtained from correlations of local observables

Gapless topological phases and symmetry-enriched quantum criticality

We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants establishing the notion of symmetry-enriched quantum criticality. The charges of nonlocal scaling operators, or more generally, of symmetry defects, are topological and imply the presence of localized edge modes. We primarily focus on the 1+1d case where the edge has a topological degeneracy, whose finite-size splitting can be exponential or algebraic in system size depending on the involvement of additional gapped sectors. An example of the exponential case is given by tuning the spin-1 Heisenberg chain to a symmetry-breaking Ising phase. An example of the algebraic case arises between the gapped Ising and cluster phases: This symmetry-enriched Ising CFT has an edge mode with finite-size splitting scaling as 1/L14. In addition to such new cases, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer—including a complete characterization of symmetry-enriched 1+1d Ising CFTs. Nontrivial topological invariants can also be constructed in higher dimensions, which we illustrate for a symmetry-enriched 2+1d CFT without gapped sectors

Topology and edge modes in quantum critical chains

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk—in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c∈12N, and the topological invariant, ω∈Z. Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder

Statistical localization: From strong fragmentation to strong edge modes

Certain disorder-free Hamiltonians can be nonergodic due to a strong fragmentation of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of "statistically localized integrals of motion" (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to subextensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system while keeping them on the boundary. This results in statistically localized strong zero modes, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a nonintegrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators

An Experimental Approach to the Joint Effects of Relations with Partner, Friends and Parents on Happiness

Personal relations constitute an important life domain and satisfaction therein affects happiness in people. In an experimental approach with a 3×3×3 vignettes study in which 103 first year psychology students participated, the contribution of the quality of relationships with parents, friends, and a partner are studied. It is found that the studied relationships contribute to imagined happiness according to an averaging model with equal weights, whereby relationship with a partner is weighted the most important, followed by the relationship, with friends and parents respectively. The averaging model implies that the impact of the quality of the one kind of relationship can be compensated for by the effect from another kind of relationship. The equal weighting implies that the impact of each kind of relationships (parents, friends, and a partner), within the relationships domain, is constant and so does not depend on its quality. Moreover, it seems that at some high level of satisfaction the positive effect of a very good relationship with a partner cannot further be increased by better relationship with friends. Further research with participants from different age groups is needed to further understand the impact of relations with parents, friends, and a partner on happiness