We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the scaled critical number of examples below which learning of the direction is impossible. The asymptotic tightness of the bounds suggests an asymptotically optimal ...

Immune monitoring of functional responses is a fundamental parameter to establish correlates of protection in clinical trials evaluating vaccines and therapies to boost antigen-specific responses. The IFNg ELISPOT assay is a well-standardized and validated method for the determination of functional IFNg-producing T-cells in peripheral blood mononuclear cells (PBMC); however, its performance gre...

Diffraction gratings are often used in optical metrology. When an electromagnetic wave is incident on a grating, the periodicity of the grating causes a multiplicity of diffraction orders. In many metrology applications one needs to know the diffraction efficiency of these orders. Since the period of a grating is often of the same order of magnitude as the wavelength, it is needed to solve Maxw...

We introduce KiNetX, a fully automated meta-algorithm for the kinetic simulation and analysis of general (complex and noisy) chemical reaction networks with rigorous uncertainty control. It is designed to cope with method inherent errors in quantum chemical calculations on elementary reaction steps. We developed and implemented KiNetX to possess three features. First, KiNetX identifies and elim...

Enclosure methods are a class of computer-aided proofs used in analysis. They are used increasingly to solve open problems in mathematics. The proposed project will use enclosure methods to address two open statistical decision problems: 1. rigorous parameter estimation in a chaotic statistical experiment, and 2. rigorous point estimation and exact posterior sampling in phylogenetics. To addres...