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modAL is a modular active learning framework for Python, aimed to make active learning research and practice simpler. Its distinguishing features are (i) clear and modular object oriented design (ii) full compatibility with scikit-learn models and workflows. These features make fast prototyping and easy extensibility possible, aiding the development of real-life active learning pipelines and novel algorithms as well. modAL is fully open source, hosted on GitHub at https://github.com/cosmic-cortex/modAL. To assure code quality, extensive unit tests are provided and continuous integration is applied. In addition, a detailed documentation with several tutorials are also available for ease of use. The framework is available in PyPI and distributed under the MIT license., 5 pages

In this paper we study the local zero behavior of orthogonal polynomials around an algebraic singularity, that is, when the measure of orthogonality is supported on $ [-1,1] $ and behaves like $ h(x)|x - x_0|^\lambda dx $ for some $ x_0 \in (-1,1) $, where $ h(x) $ is strictly positive and analytic. We shall sharpen the theorem of Yoram Last and Barry Simon and show that the so-called fine zero spacing (which is known for $ \lambda = 0$) unravels in the general case, and the asymptotic behavior of neighbouring zeros around the singularity can be described with the zeros of the function $ c J_{\frac{\lambda - 1}{2}}(x) + d J_{\frac{\lambda + 1}{2}}(x) $, where $ J_a(x) $ denotes the Bessel function of the first kind and order $ a $. Moreover, using Sturm-Liouville theory, we study the behavior of this linear combination of Bessel functions, thus providing estimates for the zeros in question., Comment: 25 pages

In this paper we study the local zero behavior of orthogonal polynomials around an algebraic singularity, that is, when the measure of orthogonality is supported on $ [-1,1] $ and behaves like $ h(x)|x - x_0|^��dx $ for some $ x_0 \in (-1,1) $, where $ h(x) $ is strictly positive and analytic. We shall sharpen the theorem of Yoram Last and Barry Simon and show that the so-called fine zero spacing (which is known for $ ��= 0$) unravels in the general case, and the asymptotic behavior of neighbouring zeros around the singularity can be described with the zeros of the function $ c J_{\frac{��- 1}{2}}(x) + d J_{\frac{��+ 1}{2}}(x) $, where $ J_a(x) $ denotes the Bessel function of the first kind and order $ a $. Moreover, using Sturm-Liouville theory, we study the behavior of this linear combination of Bessel functions, thus providing estimates for the zeros in question., 25 pages

In this paper we establish asymptotic results for Christoffel functions with respect to measures supported on Jordan curves having a Radon-Nikodym derivative with a jump singularity. We extend the results known for measures supported in the interval $ [-1,1] $ to more general sets, for example a system of Jordan curves, using polynomial inverse images. It is shown that the asymptotic limit can be written in terms of the equilibrium measure or Green's function., Comment: 20 pages

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.

Phenotypic image analysis is the task of recognizing variations in cell properties using microscopic image data. These variations, produced through a complex web of interactions between genes and the environment, may hold the key to uncover important biological phenomena or to understand the response to a drug candidate. Today, phenotypic analysis is rarely performed completely by hand. The abundance of high-dimensional image data produced by modern high-throughput microscopes necessitates computational solutions. Over the past decade, a number of software tools have been developed to address this need. They use statistical learning methods to infer relationships between a cell's phenotype and data from the image. In this review, we examine the strengths and weaknesses of non-commercial phenotypic image analysis software, cover recent developments in the field, identify challenges, and give a perspective on future possibilities. The goal of phenotypic image analysis is to recognize variations in cellular properties using image data—either measurements extracted by image analysis software or directly from the raw pixel values. In this review, we describe free and open-source software tools that are currently available for exploring and quantifying phenotypes in image-based cellular assays. We discuss some of the main challenges, current trends, and future research directions in phenotypic image analysis.