Markus P. Müller,1, 2, ∗ David Gross,3, † and Jens Eisert2, 4, ‡ 1Institute of Mathematics, Technical University of Berlin, 10623 Berlin, Germany 2Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany 3Institute for Theoretical Physics, Leibniz University Hannover, 30167 Hannover, Germany 4Institute for Advanced Study Berlin, 14193 Berlin, Germany (Dated: October 22,...

Mutant prevention concentration (MPC) has been proposed as a new measure of antibiotic potency by which the ability to restrict selection of resistant mutants is evaluated. To determine whether MPC provides potency information unavailable from the more customary measurement of the MIC, 18 fluoroquinolones were examined for their ability to block the growth of Mycobacterium smegmatis and to sele...

During the last two decades, concentration of measure has been a subject of various exciting developments in convex geometry, functional analysis, statistical physics, high-dimensional statistics, probability theory, information theory, communications and coding theory, computer science, and learning theory. One common theme which emerges in these fields is probabilistic stability: complicated,...

where m(f(X)) is a median of f(X) and where Φ is the (one–dimensional) standard normal distribution function. The inequality (1) has seen many extensions and to date, most of the conditions under which these developments hold require the existence of finite exponential moments for the underlying vector X . It is thus natural to explore the robustness of this “concentration phenomenon” and to st...

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value. AMS 2000 Subject Classification: 60E07, 60F10, 15A42, 15A52

In malaria-endemic areas, Plasmodium falciparum parasitemia is common in apparently healthy children and severe malaria is commonly misdiagnosed in patients with incidental parasitemia. We assessed whether the plasma Plasmodium falciparum DNA concentration is a useful datum for distinguishing uncomplicated from severe malaria in African children and Asian adults. P. falciparum DNA concentration...

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

We consider the problem of reasoning about the probability of assertion violations in straight-line, nonlinear computations involving uncertain quantities modeled as random variables. Such computations are quite common in many areas such as cyber-physical systems and numerical computation. Our approach extends probabilistic affine forms, an interval-based calculus for precisely tracking how the...

The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation. This phenomenon is most completely understood when the arguments are mutually independent random variables, and there exist several powerful complementary me...

We have developed a new radioligand binding assay method to measure the concentration of nonradiolabeled drugs in the brain ex vivo. This new method fuses the concepts of standard competition and saturation binding assays and uses a transformed version of the Cheng-Prusoff equation (Biochem Pharmacol 22:3099-3108, 1973) to calculate the drug concentration. After testing the validity of this met...