ALBERT

Description: The paper is devoted to the optimal state filtering of the finite-state Markov jump processes, given indirect continuous-time observations corrupted by Wiener noise. The crucial feature is that the observation noise intensity is a function of the estimated state, which breaks forthright filtering approaches based on the passage to the innovation process and Girsanov’s measure change. We propose an equivalent observation transform, which allows usage of the classical nonlinear filtering framework. We obtain the optimal estimate as a solution to the discrete–continuous stochastic differential system with both continuous and counting processes on the right-hand side. For effective computer realization, we present a new class of numerical algorithms based on the exact solution to the optimal filtering given the time-discretized observation. The proposed estimate approximations are stable, i.e., have non-negative components and satisfy the normalization condition. We prove the assertions characterizing the approximation accuracy depending on the observation system parameters, time discretization step, the maximal number of allowed state transitions, and the applied scheme of numerical integration.

Description: Fluorescent tagging is a popular method in biomedical research. Using multiple taggants of different but resolvable fluorescent spectra simultaneously (multiplexing), it is possible to obtain more comprehensive and faster information about various biochemical reactions and diseases, for example, in the method of flow cytometry. Here we report on a first demonstration of the synthesis of ultrabright fluorescent silica nanoporous nanoparticles (Star-dots), which have a large number of complex fluorescence spectra suitable for multiplexed applications. The spectra are obtained via simple physical mixing of different commercially available fluorescent dyes in a synthesizing bath. The resulting particles contain dye molecules encapsulated inside of cylindrical nanochannels of the silica matrix. The distance between the dye molecules is sufficiently small to attain Forster resonance energy transfer (FRET) coupling within a portion of the encapsulated dye molecules. As a result, one can have particles of multiple spectra that can be excited with just one wavelength. We show this for the mixing of five, three, and two dyes. Furthermore, the dyes can be mixed inside of particles in different proportions. This brings another dimension in the complexity of the obtained spectra and makes the number of different resolvable spectra practically unlimited. We demonstrate that the spectra obtained by different mixing of just two dyes inside of each particle can be easily distinguished by using a linear decomposition method. As a practical example, the errors of demultiplexing are measured when sets of a hundred particles are used for tagging.