Martin Maiwald | Searcharxiv

arXiv2023

Quasi-processes for branching Markov chains

Potential theory is a central tool to understand and analyse Markov processes. In this article, we develop its probabilistic counterpart for branching Markov chains. Specifically, we examine versions of quasi-processes or interlacements that incorporate branching, referred to as branching quasi-processes. These processes are characterized by their occupation measures. If a certain decorability condition is fulfilled, there's an isomorphism between the set of branching quasi-processes and the set of excessive measures, where the excessive measures correspond to the occupation measures of the branching quasi-processes. Utilizing a branching quasi-process as an intensity measure for a Poisson point process leads to the formulation of random interlacements with branching. In cases where individuals reproduce with an average rate of one or less, we detail a construction that draws on classical interlacements. Our approach significantly employs the additive structure of branching Markov chains, with the spinal representation of the branching processes serving as a crucial technical tool.

math.PR↗

arXiv2020

Wide Field Spectral Imaging with Shifted Excitation Raman Difference Spectroscopy Using the Nod and Shuffle Technique

Wide field Raman imaging using the integral field spectroscopy approach was used as a fast, one shot imaging method for the simultaneous collection of all spectra composing a Raman image. For the suppression of autofluorescence and background signals such as room light, shifted excitation Raman difference spectroscopy (SERDS) was applied to remove background artifacts in Raman spectra. To reduce acquisition times in wide field SERDS imaging, we adapted the nod and shuffle technique from astrophysics and implemented it into a wide field SERDS imaging setup. In our adapted version, the nod corresponds to the change in excitation wavelength, whereas the shuffle corresponds to the shifting of charges up and down on a Charge-Coupled Device (CCD) chip synchronous to the change in excitation wavelength. We coupled this improved wide field SERDS imaging setup to diode lasers with 784.4/785.5 and 457.7/458.9 nm excitation and applied it to samples such as paracetamol and aspirin tablets, polystyrene and polymethyl methacrylate beads, as well as pork meat using multiple accumulations with acquisition times in the range of 50 to 200 ms. The results tackle two main challenges of SERDS imaging: gradual photobleaching changes the autofluorescence background, and multiple readouts of CCD detector prolong the acquisition time.

physics.ins-det↗