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We analyze the connection between two perspectives when defining fuzzy sets: the viewpoint of mappings and the viewpoint of families of level cuts. This analysis is mathematically supported by the framework of a categorical adjunction, which serves as a dictionary between these two perspectives. We prove that hesitant fuzzy sets and gradual sets are strongly related through this connection. This allows concepts and operations to be transferred from one class to the other, and vice versa. Concretely, as an application, we provide lattice operations on gradual sets, compatible with Zadeh’s max-min operations on fuzzy sets, when considering them as families of level cuts. We discuss the well-known representation theorem for fuzzy sets within this framework, and we show that the representation of fuzzy sets as gradual sets depends on the chosen embedding of fuzzy sets as hesitant fuzzy sets. Hence, distinct embeddings yield diverse representations of fuzzy sets as collections of subsets. Furthermore, we extend this methodology to include other classes of extended fuzzy sets. As a consequence, a representation theorem for interval-valued fuzzy sets is provided.

Global biodiversity is negatively affected by anthropogenic climate change. As species distributions shift due to increasing temperatures and precipitation fluctuations, many species face the risk of extinction. In this study, we explore the expected trend for plant species distributions in Central America and southern Mexico under two alternative Representative Concentration Pathways (RCPs) portraying moderate (RCP4.5) and severe (RCP8.5) increases in greenhouse gas emissions, combined with two species dispersal assumptions (limited and unlimited), for the 2061-2080 climate forecast. Using an ensemble approach employing three techniques to generate species distribution models, we classified 1924 plant species from the region's (sub)tropical forests according to IUCN Red List categories. To infer the spatial and taxonomic distribution of species' vulnerability under each scenario, we calculated the proportion of species in a threat category (Vulnerable, Endangered, Critically Endangered) at a pixel resolution of 30 arc seconds and by family. Our results show a high proportion (58-67%) of threatened species among the four experimental scenarios, with the highest proportion under RCP8.5 and limited dispersal. Threatened species were concentrated in montane areas and avoided lowland areas where conditions are likely to be increasingly inhospitable. Annual precipitation and diurnal temperature range were the main drivers of species' relative vulnerability. Our approach identifies strategic montane areas and taxa of conservation concern that merit urgent inclusion in management plans to improve climatic resilience in the Mesoamerican biodiversity hotspot. Such information is necessary to develop policies that prioritize vulnerable elements and mitigate threats to biodiversity under climate change.

Background and Objectives: Accurate diagnosis of cardiovascular diseases often relies on the electrocardiogram (ECG). Since the cardiac vector is located within a three-dimensional space and the standard ECG comprises 12 projections or leads derived from it, redundant information is inherently present. This study aims to quantify this redundancy and its impact on classification tasks using Convolutional Neural Networks (CNNs) in cardiovascular diseases. Methods: We employed signal theory and mutual information to introduce a novel redundancy metric and explored techniques for redundancy augmentation and reduction. This involved lead selection and transformation to evaluate the effects on neural network performance. Results: Our findings indicate that optimizing input configurations through redundancy reduction techniques can enhance the performance of deep learning models in cardiovascular diagnostics, provided that the information is preserved and minimally distorted. Conclusion: For the first time, this research has quantified the redundancy present in the input by validating various redundancy reduction techniques using a CNN. This discovery paves the way for advancing biomedical signal processing research, simplifying model complexity, and enhancing diagnostic performance in cardiovascular medicine within reduced lead systems, such as Holter monitors or wearables. [ABSTRACT FROM AUTHOR]

Background and ObjectivesAccurate diagnosis of cardiovascular diseases often relies on the electrocardiogram (ECG). Since the cardiac vector is located within a three-dimensional space and the standard ECG comprises 12 projections or leads derived from it, redundant information is inherently present. This study aims to quantify this redundancy and its impact on classification tasks using Convolutional Neural Networks (CNNs) in cardiovascular diseases.MethodsWe employed signal theory and mutual information to introduce a novel redundancy metric and explored techniques for redundancy augmentation and reduction. This involved lead selection and transformation to evaluate the effects on neural network performance.ResultsOur findings indicate that optimizing input configurations through redundancy reduction techniques can enhance the performance of deep learning models in cardiovascular diagnostics, provided that the information is preserved and minimally distorted.ConclusionFor the first time, this research has quantified the redundancy present in the input by validating various redundancy reduction techniques using a CNN. This discovery paves the way for advancing biomedical signal processing research, simplifying model complexity, and enhancing diagnostic performance in cardiovascular medicine within reduced lead systems, such as Holter monitors or wearables.