Path-Following Method to Determine the Field of Values of a Matrix with High Accuracy

We describe a novel and efficient algorithm for calculating the field of values boundary, $\partial\textrm{W}(\cdot)$, of an arbitrary complex square matrix: the boundary is described by a system of ordinary differential equations which are solved using Runge--Kutta (Dormand--Prince) numerical integration to obtain control points with derivatives then finally Hermite interpolation is applied to produce a dense output. The algorithm computes $\partial\textrm{W}(\cdot)$ both efficiently and with low error. Formal error bounds are proven for specific classes of matrix. Furthermore, we summarise the existing state of the art and make comparisons with the new algorithm. Finally, numerical experiments are performed to quantify the cost-error trade-off between the new algorithm and existing algorithms

Establishing a health CASCADE-curated open-access database to consolidate knowledge about co-creation: novel artificial intelligence-assisted methodology based on systematic reviews

BACKGROUND: Co-creation is an approach that aims to democratize research and bridge the gap between research and practice, but the potential fragmentation of knowledge about co-creation has hindered progress. A comprehensive database of published literature from multidisciplinary sources can address this fragmentation through the integration of diverse perspectives, identification and dissemination of best practices, and increase clarity about co-creation. However, two considerable challenges exist. First, there is uncertainty about co-creation terminology, making it difficult to identify relevant literature. Second, the exponential growth of scientific publications has led to an overwhelming amount of literature that surpasses the human capacity for a comprehensive review. These challenges hinder progress in co-creation research and underscore the need for a novel methodology to consolidate and investigate the literature. OBJECTIVE: This study aimed to synthesize knowledge about co-creation across various fields through the development and application of an artificial intelligence (AI)-assisted selection process. The ultimate goal of this database was to provide stakeholders interested in co-creation with relevant literature. METHODS: We created a novel methodology for establishing a curated database. To accommodate the variation in terminology, we used a broad definition of co-creation that encompassed the essence of existing definitions. To filter out irrelevant information, an AI-assisted selection process was used. In addition, we conducted bibliometric analyses and quality control procedures to assess content and accuracy. Overall, this approach allowed us to develop a robust and reliable database that serves as a valuable resource for stakeholders interested in co-creation. RESULTS: The final version of the database included 13,501 papers, which are indexed in Zenodo and accessible in an open-access downloadable format. The quality assessment revealed that 20.3% (140/688) of the database likely contained irrelevant material, whereas the methodology captured 91% (58/64) of the relevant literature. Participatory and variations of the term co-creation were the most frequent terms in the title and abstracts of included literature. The predominant source journals included health sciences, sustainability, environmental sciences, medical research, and health services research. CONCLUSIONS: This study produced a high-quality, open-access database about co-creation. The study demonstrates that it is possible to perform a systematic review selection process on a fragmented concept using human-AI collaboration. Our unified concept of co-creation includes the co-approaches (co-creation, co-design, and co-production), forms of participatory research, and user involvement. Our analysis of authorship, citations, and source landscape highlights the potential lack of collaboration among co-creation researchers and underscores the need for future investigation into the different research methodologies. The database provides a resource for relevant literature and can support rapid literature reviews about co-creation. It also offers clarity about the current co-creation landscape and helps to address barriers that researchers may face when seeking evidence about co-creation