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1. Existence and analyticity of solutions of the Kuramoto–Sivashinsky equation with singular data

   https://doi.org/10.1017/prm.2024.106  

   Ambrose, David M; Lopes_Filho, Milton C; Nussenzveig_Lopes, Helena J (November 2024, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)

   We prove the existence of solutions to the Kuramoto–Sivashinsky equation with low regularity data in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any spatial dimension, we allow the data to have its antiderivative in the Wiener algebra. In one spatial dimension, we also allow data that are in a pseudomeasure space of negative order. In two spatial dimensions, we also allow data that are in a pseudomeasure space one derivative more regular than in the one-dimensional case. In the course of carrying out the existence arguments, we show a parabolic gain of regularity of the solutions as compared to the data. Subsequently, we show that the solutions are in fact analytic at any positive time in the interval of existence. 

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2. Long-time behaviour for a nonlocal model from directed polymers

   https://doi.org/10.1088/1361-6544/aca9b3  

   Gu, Yu; Henderson, Christopher (December 2022, Nonlinearity)

   Abstract We consider the long time behaviour of solutions to a nonlocal reaction diffusion equation that arises in the study of directed polymers in a random environment. The model is characterized by convolution with a kernel R and an L 2 inner product. In one spatial dimension, we extend a previous result of the authors (arXiv: 2002.02799 ), where only the case R = δ was considered; in particular, we show that solutions spread according to a 2 / 3 power law consistent with the KPZ scaling conjectured for directed polymers. In the special case when R = δ , we find the exact profile of the solution in the rescaled coordinates. We also consider the behaviour in higher dimensions. When the dimension is three or larger, we show that the long-time behaviour is the same as the heat equation in the sense that the solution converges to a standard Gaussian. In contrast, when the dimension is two, we construct a non-Gaussian self-similar solution. 

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3. An Inquiry into the Use of Intercoder Reliability Measures in Qualitative Research

   Wilson-Lopez, A.; Minichiello, A.; Green, T. (July 2019, ASEE Annual Conference proceedings)

   In this theory paper, we set out to consider, as a matter of methodological interest, the use of quantitative measures of inter-coder reliability (e.g., percentage agreement, correlation, Cohen’s Kappa, etc.) as necessary and/or sufficient correlates for quality within qualitative research in engineering education. It is well known that the phrase qualitative research represents a diverse body of scholarship conducted across a range of epistemological viewpoints and methodologies. Given this diversity, we concur with those who state that it is ill advised to propose recipes or stipulate requirements for achieving qualitative research validity and reliability. Yet, as qualitative researchers ourselves, we repeatedly find the need to communicate the validity and reliability—or quality—of our work to different stakeholders, including funding agencies and the public. One method for demonstrating quality, which is increasingly used in qualitative research in engineering education, is the practice of reporting quantitative measures of agreement between two or more people who code the same qualitative dataset. In this theory paper, we address this common practice in two ways. First, we identify instances in which inter-coder reliability measures may not be appropriate or adequate for establishing quality in qualitative research. We query research that suggests that the numerical measure itself is the goal of qualitative analysis, rather than the depth and texture of the interpretations that are revealed. Second, we identify complexities or methodological questions that may arise during the process of establishing inter-coder reliability, which are not often addressed in empirical publications. To achieve this purposes, in this paper we will ground our work in a review of qualitative articles, published in the Journal of Engineering Education, that have employed inter-rater or inter-coder reliability as evidence of research validity. In our review, we will examine the disparate measures and scores (from 40% agreement to 97% agreement) used as evidence of quality, as well as the theoretical perspectives within which these measures have been employed. Then, using our own comparative case study research as an example, we will highlight the questions and the challenges that we faced as we worked to meet rigorous standards of evidence in our qualitative coding analysis, We will explain the processes we undertook and the challenges we faced as we assigned codes to a large qualitative data set approached from a post positivist perspective. We will situate these coding processes within the larger methodological literature and, in light of contrasting literature, we will describe the principled decisions we made while coding our own data. We will use this review of qualitative research and our own qualitative research experiences to elucidate inconsistencies and unarticulated issues related to evidence for qualitative validity as a means to generate further discussion regarding quality in qualitative coding processes. 

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4. Category X: What does the Visibility of People who Reject the Gender Binary Mean for the Gender Structure?

   Risman, Barbara J.; Travers; Fleming, Colby (June 2022, International journal of gender studies)

   In this paper, we address the growing visibility of people who reject gender categories and identify as neither women nor men. We begin with a brief overview of how we conceptualize gender as a social structure. We use this theoretical framework to theorize how the increased visibility of people who reject the gender binary influence how we understand the gender structure, social change, and social justice. While we offer no empirical analysis in this article, we do draw upon interviews with 120 non-binary people in three metropolitan areas in the United States and interviews that are in process in Italy and Spain. We discuss the possibility that those who reject gender categories may increase freedom from gendered expectations for everyone, but also the possibility of backlash to increased visibility of gender non-conformity. We conclude the paper with an argument that the future of feminism as a social movement should be aimed at liberation from gender itself. 

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5. Two-point Correlation Function Studies for the Milky Way: Discovery of Spatial Clustering from Disk Excitations and Substructure

   https://doi.org/10.3847/1538-4357/ac9ccc  

   Hinkel, Austin; Gardner, Susan; Yanny, Brian (January 2023, The Astrophysical Journal)

   Abstract We introduce a two-particle correlation function (2PCF) for the Milky Way, constructed to probe spatial correlations in the orthogonal directions of the stellar disk in the Galactic cylindrical coordinates of R , ϕ , and z . We use this new tool to probe the structure and dynamics of the Galaxy using the carefully selected set of solar neighborhood stars ( d ≲ 3 kpc) from Gaia Data Release 2 that we previously employed for studies of axial symmetry breaking in stellar number counts. We make additional, extensive tests, comparing to reference numerical simulations, to ensure our control over possibly confounding systematic effects. Supposing either axial or north–south symmetry, we divide this data set into two nominally symmetric sectors and construct the 2PCF, in the manner of the Landy–Szalay estimator, from the Gaia data. In so doing, working well away from the midplane region in which the spiral arms appear, we have discovered distinct symmetry-breaking patterns in the 2PCF in its orthogonal directions, thus establishing the existence of correlations in stellar number counts alone at subkiloparsec length scales for the very first time. In particular, we observe extensive wavelike structures of amplitude greatly in excess of what we would estimate if the system were in a steady state. We study the variations in these patterns across the Galactic disk, and with increasing ∣ z ∣, and we show how our results complement other observations of non-steady-state effects near the Sun, such as vertical asymmetries in stellar number counts and the Gaia snail. 

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