Harness processes and harmonic crystals

In the Hammersley harness processes the real-valued height at each site i in Z^d is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in Z^d. With this representation we compute covariances and show L^2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L^2 at speed t^{1-d/2} (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process.Comment: 21 pages. Revised version with minor changes. Version almost identical to the one to be published in SP

Initial characterisation of commercially available ELISA tests and the immune response of the clinically correlated SARS-CoV-2 biobank "SERO-BL-COVID-19" collected during the pandemic onset in Switzerland

Background To accurately measure seroprevalance in the population, both the expected immune response as well as the assay performances have to be well characterised. Here, we describe the collection and initial characterisation of a blood and saliva biobank obtained after the initial peak of the SARS-CoV-2 pandemic in Switzerland.Methods Two laboratory ELISAs measuring IgA & IgG (Euroimmun), and IgM & IgG (Epitope Diagnostics) were used to characterise the biobank collected from 349 re- and convalescent patients from the canton of Basel-Landschaft.Findings The antibody response in terms of recognized epitopes is diverse, especially in oligosymptomatic patients, while the average strength of the antibody response of the population does correlate with the severity of the disease at each time point.Interpretation The diverse immune response presents a challenge when conducting epidemiological studies as the used assays only detect ∼90% of the oligosymptomatic cases. This problem cannot be rectified by using more sensitive assay setting as they concomitantly reduce specificity.Funding Funding was obtained from the "Amt für Gesundheit" of the canton Basel-Landschaft, Switzerland.Competing Interest StatementThe authors have declared no competing interest.Funding StatementThis study was sponsored by Jurg Sommer, head of the Amt fur Gesundheit, and the logistics of the sample collection were provided by the crisis staff and the civil protection service of the canton Basel-Landschaft.Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesThe details of the IRB/oversight body that provided approval or exemption for the research described are given below:This study is part of the project COVID-19 in Baselland Investigation and Validation of Serological Diagnostic Assays and Epidemiological Study of Sars-CoV-2 specific Antibody Responses (SERO-BL-COVID-19) approved by the ethics board Ethikkommission Nordwest- und Zentralschweiz (EKNZ), Hebelstrasse 53, 4056 Basel representative of Swissethics under the number (2020-00816).All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesData are available upon reques

Harness processes and harmonic crystals

We consider the long-term behaviour of infinite-volume Hammersley’s harness processes in continuous time. In this process, the height at each site is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We show that the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure. When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process. The construction is used to show almost sure and L² versions of the infinite volume limit of those fields

Harness processes and harmonic crystals

In the Hammersley harness processes the -valued height at each site is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in . With this representation we compute covariances and show L2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L2 at speed t1-d/2 (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process.Harness process Linear Gaussian processes Surface dynamics

The serial harness interacting with a wall

The serial harnesses introduced by Hammersley describe the motion of a hypersurface of dimension d embedded in a space of dimension d+1. The height assigned to each site i of is updated by taking a weighted average of the heights of some of the neighbors of i plus a "noise" (a centered random variable). The surface interacts by exclusion with a "wall" located at level zero: the updated heights are not allowed to go below zero. We show that for any distribution of the noise variables and in all dimensions, the surface delocalizes. This phenomenon is related to the so-called "entropic repulsion". For some classes of noise distributions, characterized by their tail, we give explicit bounds on the speed of the repulsion.Harness Surface dynamics Entropic repulsion

Implementation of a mandatory donor RHD screening in Switzerland

Starting in 2013, blood donors must be tested at least using: (1) one monoclonal anti-D and one anti-CDE (alternatively full RhCcEe phenotyping), and (2) all RhD negative donors must be tested for RHD exons 5 and 10 plus one further exonic, or intronic RHD specificity, according to the guidelines of the Blood Transfusion Service of the Swiss Red Cross (BTS SRC). In 2012 an adequate stock of RHD screened donors was built. Of all 25,370 RhD negative Swiss donors tested in 2012, 20,015 tested at BTS Berne and 5355 at BTS Zürich, showed 120 (0.47%) RHD positivity. Thirty-seven (0.15%) had to be redefined as RhD positive. Routine molecular RHD screening is reliable, rapid and cost-effective and provides safer RBC units in Switzerland