Linnik's problems and maximal entropy methods

We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas and follow techniques presented by Einsiedler, Lindenstrauss, Michel and Venkatesh in 2011

Simultaneous supersingular reductions of CM elliptic curves

We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show -- under additional congruence assumptions on the CM order -- that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order becomes large. This variant of the equidistribution theorems of Duke and Cornut-Vatsal is an(other) application of the recent work of Einsiedler and Lindenstrauss on the classification of joinings of higher-rank diagonalizable actions.Comment: 46 pages. Revised according to the referee's comment

Einsatz der Matrix-Assisted Laser Desorption/ionisation-Time of Flight Massenspektrometrie (MALDI-TOF MS) in der mikrobiologischen Routinediagnostik

Very recently a novel method for differentiation of bacteria and fungi has been developed, that is, identification by means of matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOF MS). This differentiation relies on the exact measurement of species-specific protein spectra of ribosomal proteins. It is at least as accurate as conventional biochemical differentiation methods, but provides results within minutes. In addition to differentiation of bacteria and yeasts grown on agar plates, direct identification is feasible from positive blood cultures as well as from urine samples of patients suffering from urinary tract infections. Future developments of MALDI-TOF MS for clinical microbiological purposes include the detection of beta-lactamase and carbapenemase activity as well as genotyping of bacteria below the species level

Attentional threat biases and their role in anxiety: A neurophysiological perspective

One of the most important function of selective attention is the efficient and accurate detection and identification of cues associated with threat. However, in pathological anxiety, this attentional mechanism seems to be dysfunctional, which leads to an exaggeration of threat processing and significant functional impairment. This attentional threat bias (ATB) has been proposed as a key mechanism in the etiology and maintenance of anxiety disorders. Recently, evidence has accumulated that the behavioral assessment of ATB by means of reaction times is compromised by conceptual and methodological problems. In this review paper we argue that a brain-based assessment of ATB, which includes different mechanistic aspects of biased attention, may provide neuromechanistic knowledge regarding the etiology and maintenance of anxiety, and potentially start identifying different targets for effective treatment. We summarize examples for such an approach, highlighting the strengths of electrophysiological measurements, which include the sensitivity to time dynamics, specificity to specific neurocomputational mechanisms, and the continuous/dimensional nature of the resulting variables. These desirable properties are a prerequisite for developing trans-diagnostic biomarkers of attentional bias, and hence may inform individually tailored treatment approaches

Clinical and laboratory considerations: determining an antibody-based composite correlate of risk for reinfection with SARS-CoV-2 or severe COVID-19

Much of the global population now has some level of adaptive immunity to SARS-CoV-2 induced by exposure to the virus (natural infection), vaccination, or a combination of both (hybrid immunity). Key questions that subsequently arise relate to the duration and the level of protection an individual might expect based on their infection and vaccination history. A multi-component composite correlate of risk (CoR) could inform individuals and stakeholders about protection and aid decision making. This perspective evaluates the various elements that need to be accommodated in the development of an antibody-based composite CoR for reinfection with SARS-CoV-2 or development of severe COVID-19, including variation in exposure dose, transmission route, viral genetic variation, patient factors, and vaccination status. We provide an overview of antibody dynamics to aid exploration of the specifics of SARS-CoV-2 antibody testing. We further discuss anti-SARS-CoV-2 immunoassays, sample matrices, testing formats, frequency of sampling and the optimal time point for such sampling. While the development of a composite CoR is challenging, we provide our recommendations for each of these key areas and highlight areas that require further work to be undertaken

Planes in four space and four associated CM points

To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement and the second two essentially arise from the accidental local isomorphism between SO(4) and SO(3)xSO(3). As an application of a recent result of Einsiedler and Lindenstrauss on algebraicity of joinings we prove simultaneous equidistribution of all of these objects under two splitting conditions