Various L2-signatures and a topological L2-signature theorem

For a normal covering over a closed oriented topological manifold we give a proof of the L2-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C^*_max-version of the Baum-Connes conjecture imply the L2-signature theorem for a normal covering over a Poincar space, provided that the group of deck transformations is torsion-free. We discuss the various possible definitions of L2-signatures (using the signature operator, using the cap product of differential forms, using a cap product in cellular L2-cohomology,...) in this situation, and prove that they all coincide.Comment: comma in metadata (author field) added

L^2-torsion of hyperbolic manifolds of finite volume

Suppose $\bar{M}$ is a compact connected odd-dimensional manifold with boundary, whose interior $M$ comes with a complete hyperbolic metric of finite volume. We will show that the $L^2$-topological torsion of $\bar{M}$ and the $L^2$-analytic torsion of the Riemannian manifold $M$ are equal. In particular, the $L^2$-topological torsion of $\bar{M}$ is proportional to the hyperbolic volume of $M$, with a constant of proportionality which depends only on the dimension and which is known to be nonzero in dimension 3, 5 and 7. In dimension 3 this proves the conjecture Of Lott and Lueck which gives a complete calculation of the $L^2$-topological torsion of compact $L^2$-acyclic 3-manifolds which admit a geometric torus-decomposition. In an appendix we give a counterexample to an extension of the Cheeger-Mueller theorem to manifolds with boundary: if the metric is not a product near the boundary, in general analytic and topological torsion are not equal, even if the Euler characteristic of the boundary vanishes. Keywords: L^2-torsion, hyperbolic manifolds, 3-manifoldsComment: 42 pages, AMS-Latex2e V2: identical with published version, in particular including an additional appendix with examples for non-trivial anomaly for analytic torsion on manifolds with boundar

Approximating L^2-signatures by their compact analogues

:Let G be a group together with an descending nested sequence of normal subgroups G=G_0, G_1, G_2 G_3, ... of finite index [G:G_k] such the intersection of the G_k-s is the trivial group. Let (X,Y) be a compact 4n-dimensional Poincare' pair and p: (\bar{X},\bar{Y}) \to (X,Y) be a G-covering, i.e. normal covering with G as deck transformation group. We get associated $G/_k$-coverings (X_k,Y_k) \to (X,Y). We prove that sign^{(2)}(\bar{X},\bar{Y}) = lim_{k\to\infty} \frac{sign(X_k,Y_k)}{[G : G_k]}, where sign or sign^{(2)} is the signature or L^2-signature, respectively, and the convergence of the right side for any such sequence (G_k)_k is part of the statement

Novikov-Shubin invariants for arbitrary group actions and their positivity

We extend the notion of Novikov-Shubin invariant for free G-CW-complexes of finite type to spaces with arbitrary G-actions and prove some statements about their positivity. In particular we apply this to classifying spaces of discrete groups.Comment: 18 pages, metadata change

Electronic thermal conductivity of disordered metals

We calculate the thermal conductivity of interacting electrons in disordered metals. In our analysis we point out that the interaction affects thermal transport through two distinct mechanims, associated with quantum interference corrections and energy exchange of the quasi particles with the electromagnetic environment, respectively. The latter is seen to lead to a violation of the Wiedemann-Franz law. Our theory predicts a strong enhancement of the Lorenz ratio $\kappa /\sigma T$ over the value which is predicted by the Wiedemann-Franz law, when the electrons encounter a large environmental impedance.Comment: 4 page

Utilizing Proximity for Increasing Student Knowledge Retention: A Near-Peer Tutoring Program Needs Study

The purpose of this study was to demonstrate the desire and need for peer-to-peer tutoring programs at Division 1 Dell Medical School at the University of Texas. Materials and Methods. Two sets of surveys were created and sent to students at the Dell Medical School, University of Texas, USA. One survey asking about the need or desire to engage with a peer tutor was sent to first-year students, and another one asking about the desire to provide these services to underclassmen as a potential leadership course option was sent to third-year students. Results. For the first-year student survey, 52.9% of respondents disagreed or strongly disagreed of being aware of near-peer tutoring and 70.5% of respondents either agreed or strongly agreed that it would be an option utilized by students. For the third-year student survey, 75% of students either disagreed or felt neutral in being aware of near-peer tutoring as an option to serve underclassmen, whereas 65% of upperclassmen either agreed or strongly agreed that if near-peer tutoring had been offered, they would have chosen this leadership course option in the effort to teach their underclassmen peers. Conclusions. Numerous studies have demonstrated peer-to-peer tutorial options to be of high utility to students in the medical education space. This particular paper obtained results demonstrating students’ desire to engage in peer tutoring voluntarily for their own course success goals and upperclassmen’s desire to participate as near-peer tutors for the benefit of underclassmen

Basiliximab induction therapy in kidney transplantation: Benefits for long term allograft function after 10 years?

The interleukin-2 receptor antagonist basiliximab has proven in large clinical trials to be safe and effective to reduce acute rejections in the first year after renal transplantation. Since acute rejections are a risk factor for chronic graft loss, their effective reduction might have a positive effect on long term allograft survival. So far data is spares to prove this hypothesis and 10-year follow up on basiliximab induction therapy is not available. In our center, 41 patients were enrolled in the multicenter trial CHIB201 in 1995/96 comparing basiliximab vs no induction therapy after renal transplantation. We retrospectively analyzed the outcome of these patients after 10 years. The main reason for patient death with functioning graft were infectious complications (basiliximab: 3/20, placebo 1/19), 21% of all patients developed cancer without an obvious correlation to specific immunosuppression. Death censored 10-year graft survival was equivalent in both groups: 65% in the basiliximab and 68% in the placebo group with a mean s-creatinine-clearance of 60 and 44 ml/min. In this small study patient and graft survival was equivalent 10 years after transplantation comparing basiliximab induction therapy and placebo

Explicit and Implicit Semantic Ranking Framework

The core challenge in numerous real-world applications is to match an inquiry to the best document from a mutable and finite set of candidates. Existing industry solutions, especially latency-constrained services, often rely on similarity algorithms that sacrifice quality for speed. In this paper we introduce a generic semantic learning-to-rank framework, Self-training Semantic Cross-attention Ranking (sRank). This transformer-based framework uses linear pairwise loss with mutable training batch sizes and achieves quality gains and high efficiency, and has been applied effectively to show gains on two industry tasks at Microsoft over real-world large-scale data sets: Smart Reply (SR) and Ambient Clinical Intelligence (ACI). In Smart Reply, $sRank$ assists live customers with technical support by selecting the best reply from predefined solutions based on consumer and support agent messages. It achieves 11.7% gain in offline top-one accuracy on the SR task over the previous system, and has enabled 38.7% time reduction in composing messages in telemetry recorded since its general release in January 2021. In the ACI task, sRank selects relevant historical physician templates that serve as guidance for a text summarization model to generate higher quality medical notes. It achieves 35.5% top-one accuracy gain, along with 46% relative ROUGE-L gain in generated medical notes