We prove that the L 2 -Betti numbers of a unimodular locally compact group G coincide, up to a natural scaling constant, with the L 2 -Betti numbers of the countable equivalence relation induced on a cross section of any essentially free ergodic probability measure preserving action of G. As a consequence, we obtain that the reduced and un-reduced L 2 -Betti numbers of G agree and that the L 2 -Betti numbers of a lattice Γ in G equal those of G up to scaling by the covolume of Γ in G. We also deduce several vanishing results, including the vanishing of the reduced L 2 -cohomology for amenable locally compact groups.
The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute to the general theory of L2‐Betti numbers of totally disconnected groups and provide exact computations of the L2‐Betti numbers of the Neretin group and Chevalley groups over the field of Laurent series over a finite field and their lattices.
We introduce a refined version of group cohomology for locally compact, second countable groups which is naturally related to the space of polynomials on the group in question. In the case of trivial coefficients it is proven that the polynomial cohomology admits a description in terms of ordinary cohomology with polynomial coefficients and that the first polynomial cohomology admits a description given directly in terms polynomials. We furthermore give a complete description of the polynomials on a connected, simply connected nilpotent Lie group identifying these with the classical algebra of regular functions.2010 Mathematics Subject Classification. 57M07, 22E41, 22E25.
Coated activated charcoal haemoperfusion (CAC-HP) is a well-known treatment modality. Case reports have revealed conflicting results about the efficacy of CAC-HP in the treatment of amitriptyline (AT) poisoning, and no randomized clinical trials have been identified in the literature. This study aimed at quantifying the efficacy of modern CAC-HP as an adjunctive treatment of AT intoxication compared with standard care alone. Fourteen female Danish landrace pigs were randomized to either standard care or standard care plus 4 hr of CAC-HP. The pigs were anaesthetized, and vital parameters were continuously recorded. Amitriptyline infusion (7.5 mg/kg) was completed in 20 min. Thirty minutes after AT infusion, activated charcoal was instilled orally in both groups. In the intervention group, CAC-HP was initiated 60 min. after AT infusion. Blood and urine samples were collected as were vital parameters at specific time intervals. The protocol was approved by the Danish Experimental Animal Expectorate and complied with the NIH guide for care and use of laboratory animals. Data were managed according to the ARRIVE guidelines. No statistical significant differences between intervention and control groups were found when analysing for differences in AT levels in plasma at any time-point. Furthermore, significant differences between the control and intervention groups in regard to vital parameters could not be found either. In our animal model, the addition of CAC-HP did not improve the clearance of AT compared with standard treatment alone. We suggest that the effect of modern CAC-HP as a treatment modality in AT-poisoned human patients may be inadequate.
Abstract-For an arbitrary ordered set, we consider the model of all distributions P for which an element which precedes another element is considered the more significant one in the sense that the implication a ≤ b ⇒ P (a) ≥ P (b) holds. It will be shown that if the ordered set is a finite co-tree, then the universal predictor for the indicated model or, equivalently, the corresponding universal code, can be determined exactly via an algorithm of reasonably low complexity.
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