Quantum random walks with history dependence

We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased random walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.Comment: 8 pages, 6 figures, RevTe

Magnetic resonance lung function – a breakthrough for lung imaging and functional assessment? A phantom study and clinical trial

BACKGROUND: Chronic lung diseases are a major issue in public health. A serial pulmonary assessment using imaging techniques free of ionizing radiation and which provides early information on local function impairment would therefore be a considerably important development. Magnetic resonance imaging (MRI) is a powerful tool for the static and dynamic imaging of many organs. Its application in lung imaging however, has been limited due to the low water content of the lung and the artefacts evident at air-tissue interfaces. Many attempts have been made to visualize local ventilation using the inhalation of hyperpolarized gases or gadolinium aerosol responding to MRI. None of these methods are applicable for broad clinical use as they require specific equipment. METHODS: We have shown previously that low-field MRI can be used for static imaging of the lung. Here we show that mathematical processing of data derived from serial MRI scans during the respiratory cycle produces good quality images of local ventilation without any contrast agent. A phantom study and investigations in 85 patients were performed. RESULTS: The phantom study proved our theoretical considerations. In 99 patient investigations good correlation (r = 0.8; p ≤ 0.001) was seen for pulmonary function tests and MR ventilation measurements. Small ventilation defects were visualized. CONCLUSION: With this method, ventilation defects can be diagnosed long before any imaging or pulmonary function test will indicate disease. This surprisingly simple approach could easily be incorporated in clinical routine and may be a breakthrough for lung imaging and functional assessment

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)