In recent years, there has been extensive work on inequalities among partition functions. In particular, Nicolas, and independently DeSalvo–Pak, proved that the partition function $p(n)$ is eventually log-concave. Inspired by this and other results, Chern–Fu–Tang first conjectured the log-concavity of $k$-coloured partitions. Three of the authors and Tripp later proved this conjecture by introducing recursive sequences and a strict inequality for fractional partition functions, giving explicit errors. In this paper, we show that the log-concavity is, in fact, strict for $k\geq 2$. We shed further light on this phenomenon by utilizing Hardy–Littlewood–Pólya’s notion of majorizing. We prove that for partitions $\boldsymbol{a},\boldsymbol{b}$ of $n\in{\mathbb N}$, if $\boldsymbol b$ majorizes $\boldsymbol a$, then $p_k(\boldsymbol{a}) \gt p_k(\boldsymbol{b})$. Numerical calculations indicate that our result is sharp.

We present a detailed characterisation of radio frequency interference (RFI) in the 2.4 GHz band around Murriyang, CSIRO’s Parkes radio telescope. The dominant sources of interference are Wi-Fi and Bluetooth transmissions. We quantify how the intensity and directionality of this RFI vary with time of day and document its evolution over several years. Although most observers currently discard data within this band, our analysis shows that the interference is confined in both time and frequency and can be effectively mitigated. Using 10 seconds of 16-bit voltage data recorded during observations of the Vela Pulsar (PSR J0835—4510), we demonstrate that the majority of the channelised data remain unaffected by RFI. We compare three RFI detection and mitigation algorithms and evaluate their relative performance. All methods perform effectively, and any could be implemented in real time to enable productive use of this observing band. A real time implementation would allow the scientific use of this 128MHz observing band to increase, from almost 70% of the band being completely unusable all of the time, to over 90% of becoming accessible for science. Given its simplicity and efficiency, a basic power-threshold approach offers a relatively straightforward solution.

Data Coordinating Centers (DCCs) play essential roles in multisite clinical and translational research, ensuring consistent protocol implementation, data integrity, and regulatory compliance across geographically and organizationally diverse sites. As study design, regulatory, and technological complexity have evolved, DCC responsibilities have expanded beyond data coordination. This rapid scoping review maps published experiences from academic DCCs to address two questions: (i) What key organizational and operational challenges have been reported? (ii) What solutions and emerging technologies have been adopted in response? We conducted a rapid scoping review in accordance with the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews). We searched the peer-reviewed literature (2010–2025) using PubMed, Scopus, and the Web of Science Core Collection. Fifteen reports describing 16 DCCs were included in this review. DCCs faced recurring challenges related to infrastructure development, multisite coordination, regulatory governance, data heterogeneity, and workforce development. Reported adaptations include homegrown modular infrastructure solutions, standardized workflows, streamlined proactive regulatory processes, and workforce investments. By synthesizing evidence on DCC challenges and adaptations, this review provides practical guidance to help DCCs enhance operational feasibility and uphold scientific integrity in multisite clinical and translational research.

Recent advances in healthcare and rising life expectancy intensify longevity risk, motivating a deeper understanding of how cause-of-death (COD) rates interact. Using male COD data from 1978 to 2018 in the United States, we develop a copula-based hierarchical framework for seven major causes: cancer, diabetes, external causes, influenza, mental disorders, nephritis, and vascular disease. The framework integrates reconciliation, hierarchical dependence, and long-run equilibrium using a Lee–Carter (LC) setting. More specifically, the LC period indices are estimated under reconciliation penalties and are modeled through a sparse vector error correction model, with dependence captured by a hierarchical Archimedean copula. Two applications illustrate the value of our approach. In out-of-sample forecasting, the framework outperforms the standard LC model by improving the accuracy of aggregate mortality rates. In structural analysis, fitted connectedness reveals that diabetes and vascular disease act as net transmitters of mortality shocks, while cancer and external causes are net receivers. These insights help actuaries, demographers, clinicians, and policymakers enhance mortality forecasting to assess whether prioritizing government interventions for high-transmission causes could potentially maximize overall mortality improvements for society.

We study a nonlinear branching diffusion process in the sense of McKean, i.e. where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness result by using contraction arguments. Then we consider the notion of weak solution and its equivalent martingale problem formulation. In this setting, we provide a general weak existence result, as well as a propagation of chaos property, i.e. the McKean–Vlasov branching diffusion is the limit of a large-population branching diffusion process with mean-field interaction.

In this Opinion Paper, we argue that the absence of animal welfare in the United Nations’ sustainable development goals (SDGs) may not be as detrimental as some suggest. We put forward the view that the welfare of animals is an integral part of the concept of sustainability, that development which affects animals cannot be sustainable without due consideration to their welfare, and we give examples in support of this position. Put simply: no mention means animal welfare could be, and potentially should be, anywhere and everywhere in the goals. For livestock species, we submit that the synergies between the SDGs when animal welfare is included greatly outweigh the conflicts usually highlighted. Further, considering animal welfare as both an achievable goal and as a mechanism for sustainable development allows improvement of animal welfare to carry the weight it warrants: an animal with poor welfare is not a sustainable animal. By extension, products from animals with poor welfare cannot be considered sustainable, and animal welfare is necessarily included in a well-functioning ecosystem. Through the paper we argue that the challenge is not to add in animal welfare, but to think sustainability with animal welfare. We conclude by giving directions to where animal welfare can be integrated when developing sustainable actions.

This study examines how grassroots gender NGOs in China navigate online fundraising amid tightening regulations and declining external funding. Drawing on a longitudinal analysis of 463 crowdfunding projects by 124 gender NGOs on Tencent Charity, it shows how these organizations pursue gender equality under pressure from the state and the platform economy. The study identifies two interrelated strategies: (1) strategic conformity through issue reframing to ally with state agendas for algorithmic visibility and (2) strategic stealth in intersectional boundary-spanning, calibrating (in)visibility while leveraging cross-sectoral collaboration to sustain gender advocacy. These practices reflect how gender NGOs continually negotiate visibility, legitimacy, and autonomy. The findings suggest that digital philanthropy, rather than diversifying fundraising, often reproduces hierarchies of attention and access. Conceptualizing strategic stealth in intersectional boundary-spanning as adaptive, issue-expanding practices, this study deepens understanding of NGOs’ constrained agency and highlights platform governance as a key force channeling state priorities in civic fundraising.

The nosological status and psychopathology of delusional disorder have been a subject of debate since Kraepelin distinguished it from schizophrenia and affective psychoses. Contemporary diagnostic manuals define delusional disorder primarily by the presence of delusions, offering limited guidance for its differentiation from schizophrenia. Notably, DSM-5 introduced a major, seemingly unexplained change by allowing bizarre delusions in delusional disorder, contrary to ICD-11, prior DSM editions, and classical descriptions. This narrative review revisits the seminal works of six classical authors (Kraepelin, Jaspers, Kretschmer, Sérieux and Capgras, and De Clérambault), who shaped the concept of delusional disorder (paranoia), and their detailed clinical cases of the disorder. All considered delusional disorder to be an independent psychotic disorder, characterized by chronic, systematized, nonbizarre delusions, preservation of personality, and minimal hallucinations, with a largely intact experiential framework outside of the delusional theme. Additional features such as delusional misinterpretations, illusions, and false memories were also emphasized in the classical literature. We examined these authors’ clinical cases of delusional disorder for the presence of delusional features characteristic of schizophrenia (delusional mood, first-rank symptoms, autistic-solipsistic delusions, and double bookkeeping), which index alterations in the structure of experience rather than mere delusional content. Such delusions were rarely found in the classical clinical cases of delusional disorder. Our findings highlight psychopathological distinctions between delusional disorder and schizophrenia, suggesting that schizophrenia involves a qualitative alteration of the experiential framework that is absent in delusional disorder. These findings raise concerns about the validity of the DSM-5 change, allowing bizarre delusions in delusional disorder.

As Lucy Grace writes, “Our lives are a bundle of stories.”1 In fact, even the self, that seemingly solid and continuous “I” we carry through the world, is a story, a narrative we construct and reconstruct by piecing together memories and experiences into what feels like, as Guy Saunders writes, “a single unified self.”2 We are thus all storytellers at heart, and the story we are most often telling, retelling, and revising is ourselves. As cognitive scientist Daniel Dennett argues in Consciousness Explained, our selves are “magnificent fictions,” not “independently existing soul-pearls” but “artifacts of the social processes that create us.”3 We do not discover who we are; we narrate ourselves into being.

The present study addresses the question of whether an individual who does not understand a sentence might still be able to repeat it verbatim. To answer this question, we examined paraphrasing and repetition data from two previous studies: Pavlenko et al. (2019), which analyzed L1 and L2 participants’ paraphrasing of seven Miranda warning sentences, and Akbary et al. (2023), which compared L1 and L2 participants’ paraphrasing and elicited imitation (EI) performance on 30 commonly used EI sentences. We formulated our questions into four predictions, two of which directly addressed whether rote repetition without comprehension occurs at all. Our results confirmed both predictions, identifying 36 (5.6%) of the 646 instances of verbatim sentence repetition in the data as potential cases of repetition without comprehension. However, a broader analysis showed that the evidence for a lack of comprehension was relatively weak and ambiguous. We conclude with recommendations for overcoming the limitations of the present study and resolving the ambiguity of our findings.