Search

Nowadays, morphology and molecular analyses at the single-cell level have a fundamental role in understanding biology better. These methods are utilized for cell phenotyping and in-depth studies of cellular processes, such as mitosis. Fluorescence microscopy and optical spectroscopy techniques, including Raman micro-spectroscopy, allow researchers to examine biological samples at the single-cell level in a non-destructive manner. Fluorescence microscopy can give detailed morphological information about the localization of stained molecules, while Raman microscopy can produce label-free images at the subcellular level; thus, it can reveal the spatial distribution of molecular fingerprints, even in live samples. Accordingly, the combination of correlative fluorescence and Raman microscopy (CFRM) offers a unique approach for studying cellular stages at the single-cell level. However, subcellular spectral maps are complex and challenging to interpret. Artificial intelligence (AI) may serve as a valuable solution to characterize the molecular backgrounds of phenotypes and biological processes by finding the characteristic patterns in spectral maps. The major contributions of the manuscript are: (I) it gives a comprehensive review of the literature focusing on AI techniques in Raman-based cellular phenotyping; (II) via the presentation of a case study, a new neural network-based approach is described, and the opportunities and limitations of AI, specifically deep learning, are discussed regarding the analysis of Raman spectroscopy data to classify mitotic cellular stages based on their spectral maps. [ABSTRACT FROM AUTHOR]

Precise asymptotics for Christoffel functions are established for power type weights on unions of Jordan curves and arcs. The asymptotics involve the equilibrium measure of the support of the measure. The result at the endpoints of arc components is obtained from the corresponding asymptotics for internal points with respect to a different power weight. On curve components the asymptotic formula is proved via a sharp form of Hilbert's lemniscate theorem while taking polynomial inverse images. The situation is completely different on arc components, where the local asymptotics is obtained via a discretization of the equilibrium measure with respect to the zeros of an associated Bessel function. The proofs are potential-theoretical, and fast decreasing polynomials play an essential role in them. [ABSTRACT FROM AUTHOR]

In this paper the asymptotic behavior of a critical multi-type branching process with immigration is described when the offspring mean matrix is irreducible, in other words, when the process is indecomposable. It is proved that sequences of appropriately scaled random step functions formed from periodic subsequences of a critical indecomposable multi-type branching process with immigration converge weakly towards a process supported by a ray determined by the Perron vector of the offspring mean matrix. The types can be partitioned into nonempty mutually disjoint subsets (according to communication of types) such that the coordinate processes belonging to the same subset are multiples of the same squared Bessel process, and the coordinate processes belonging to different subsets are independent. [ABSTRACT FROM AUTHOR]