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Open science is receiving widespread attention globally, and preprinting offers an important way to implement open science practices in scholarly publishing. To develop a systematic understanding of researchers' adoption of and attitudes toward preprinting, we conducted a survey of authors of research papers published in 2021 and early 2022. Our survey results show that the United States and Europe led the way in the adoption of preprinting. The United States and European respondents reported a higher familiarity with and a stronger commitment to preprinting than their colleagues elsewhere in the world. The adoption of preprinting is much stronger in physics and astronomy as well as mathematics and computer science than in other research areas. Respondents identified free accessibility of preprints and acceleration of research communication as the most important benefits of preprinting. Low reliability and credibility of preprints, sharing results before peer review and premature media coverage are the most significant concerns about preprinting, emphasized in particular by respondents in the life and health sciences. According to respondents, the most crucial strategies to encourage preprinting are integrating preprinting into journal submission workflows and providing recognition for posting preprints. [ABSTRACT FROM AUTHOR]

The misalignment between recorded in-focus and out-of-focus images using the Phase Diversity (PD) algorithm leads to a dramatic decline in wavefront detection accuracy and image recovery quality for segmented active optics systems. This paper demonstrates the theoretical relationship between the image misalignment and tip-tilt terms in Zernike polynomials of the wavefront phase for the first time, and an efficient two-step alignment correction algorithm is proposed to eliminate these misalignment effects. This algorithm processes a spatial 2-D cross-correlation of the misaligned images, revising the offset to 1 or 2 pixels and narrowing the search range for alignment. Then, it eliminates the need for subpixel fine alignment to achieve adaptive correction by adding additional tip-tilt terms to the Optical Transfer Function (OTF) of the out-of-focus channel. The experimental results demonstrate the feasibility and validity of the proposed correction algorithm to improve the measurement accuracy during the co-phasing of segmented mirrors. With this alignment correction, the reconstructed wavefront is more accurate, and the recovered image is of higher quality. [ABSTRACT FROM AUTHOR]

This paper considers the role of mathematics in the process of acquiring new knowledge in physics and astronomy. The defining of the notions of continuum and discreteness in mathematics and the natural sciences is examined. The basic forms of representing the heuristic function of mathematics at theoretical and empirical levels of knowledge are studied: deducing consequences from the axiomatic system of theory, the method of generating mathematical hypotheses, “pure” proofs for the existence of objects and processes, mathematical modelling, the formation of mathematics on the basis of internal mathematical principles and the mathematical theory of experiment. [ABSTRACT FROM AUTHOR]

This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17-21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chaos detection and predictability, as well as to report recent applications of these techniques to different scientific fields. The collection of twelve papers in this Focus Issue represents the wide range of applications, spanning mathematics, physics, astronomy, particle accelerator physics, meteorology and medical research. This Preface surveys the papers of this Issue. [ABSTRACT FROM AUTHOR]