Projectional Coderivatives and Calculus Rules

This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a smooth manifold, the projectional coderivative can be refined as a fixed-point expression. We will also improve the generalized Mordukhovich criterion to give a complete characterization of the relative Lipschitz-like property under such a setting. Chain rules and sum rules are obtained to facilitate the application of the tool to a wider range of problems

Spatio-Temporal Patterns and Climate Variables Controlling of Biomass Carbon Stock of Global Grassland Ecosystems from 1982 to 2006

Grassland ecosystems play an important role in subsistence agriculture and the global carbon cycle. However, the global spatio-temporal patterns and environmental controls of grassland biomass are not well quantified and understood. The goal of this study was to estimate the spatial and temporal patterns of the global grassland biomass and analyze their driving forces using field measurements, Normalized Difference Vegetation Index (NDVI) time series from satellite data, climate reanalysis data, and a satellite-based statistical model. Results showed that the NDVI-based biomass carbon model developed from this study explained 60% of the variance across 38 sites globally. The global carbon stock in grassland aboveground live biomass was 1.05 Pg·C, averaged from 1982 to 2006, and increased at a rate of 2.43 Tg·C·y−1 during this period. Temporal change of the global biomass was significantly and positively correlated with temperature and precipitation. The distribution of biomass carbon density followed the precipitation gradient. The dynamics of regional grassland biomass showed various trends largely determined by regional climate variability, disturbances, and management practices (such as grazing for meat production). The methods and results from this study can be used to monitor the dynamics of grassland aboveground biomass and evaluate grassland susceptibility to climate variability and change, disturbances, and management

Adaptive Waveform Design for Multiple Radar Tasks Based on Constant Modulus Constraint

Cognitive radar is an intelligent system, and it can adaptively transmit waveforms to the complex environment. The intelligent radar system should be able to provide different trade-offs among a variety of performance objectives. In this paper, we investigate the mutual information (MI) in signal-dependent interference and channel noise. We propose a waveform design method which can efficiently synthesize waveforms and provide a trade-off between estimation performance and detection performance. After obtaining a local optimal waveform, we apply the technique of generating a constant modulus signal with the given Fourier transform magnitude to the waveform. Finally we obtain a waveform that has constant modulus property

MM-BigBench: Evaluating Multimodal Models on Multimodal Content Comprehension Tasks

The popularity of multimodal large language models (MLLMs) has triggered a recent surge in research efforts dedicated to evaluating these models. Nevertheless, existing evaluation studies of MLLMs primarily focus on the comprehension and reasoning of unimodal (vision) content, neglecting performance evaluations in the domain of multimodal (vision-language) content understanding. Beyond multimodal reasoning, tasks related to multimodal content comprehension necessitate a profound understanding of multimodal contexts, achieved through the multimodal interaction to obtain a final answer. In this paper, we introduce a comprehensive assessment framework called MM-BigBench, which incorporates a diverse range of metrics to offer an extensive evaluation of the performance of various models and instructions across a wide spectrum of diverse multimodal content comprehension tasks. Consequently, our work complements research on the performance of MLLMs in multimodal comprehension tasks, achieving a more comprehensive and holistic evaluation of MLLMs. To begin, we employ the Best Performance metric to ascertain each model's performance upper bound on different datasets. Subsequently, the Mean Relative Gain metric offers an assessment of the overall performance of various models and instructions, while the Stability metric measures their sensitivity. Furthermore, previous research centers on evaluating models independently or solely assessing instructions, neglecting the adaptability between models and instructions. We propose the Adaptability metric to quantify the adaptability between models and instructions. Our paper evaluates a total of 20 language models (14 MLLMs) on 14 multimodal datasets spanning 6 tasks, with 10 instructions for each task, and derives novel insights. Our code will be released at https://github.com/declare-lab/MM-BigBench.Comment: Undervie

Quality analysis and function prediction of soil microbial communities of Polygonatum cyrtonema in two indigenous-origins

Polygonatum cyrtonema Hua (PCH), as an important economic crop, is used as raw industrial materials and traditional Chinese medicine. There are significant variations in the quality of PCH from different geographical origins. It can be due to the change of the endophytic fungi and soil microbial communities of PCH. Therefore, the aim of this study is to investigate the composition and functional prediction of the main microbial communities in the rhizomes and soil of PCH and explore their impact on medicinal quality. High-throughput sequencing techniques targeting ITS and 16S rDNA were employed to compare the structure and biodiversity differences of endophytic fungi in the rhizomes and soil microbial communities of PCH from 12 different locations in Sichuan and Guangxi province. Heatmap analysis was used for comprehensive statistics and visualization of the richness of rhizome and soil microbial communities from all locations. Venn analysis was conducted to determine the total number of shared fungi between rhizomes and soil, and GraphPad Prism analysis was employed to predict and compare the microbial communities related to phenotypes at the genus level in Sichuan and Guangxi. Tax4Fun and Fungild were used for metabolic function prediction of microbial communities in the rhizomes and soil of PCH. The results revealed the identification of 19,387 bacterial amplicon sequence variants (ASVs) in the rhizomes and 37,990 bacterial ASVs in the soil, with 6,889 shared bacterial ASVs. In addition, 2,948 fungal ASVs were identified in the rhizomes and 8,868 in the soil, with 1,893 shared fungal ASVs. Microbial sequencing results indicated that the fungal communities between soil and rhizomes were mainly composed of Ascomycota and Basidiomycota, while bacterial communities included Proteobacteria, Acidobacteria, Bacteroidota, Gammatimonadota, and Firmicutes. Dominant bacterial groups such as Nitrospira, Acidibacter, and fungal groups including Mortierella, Ceratobasidium, and Fusarium were identified as potential contributors to the observed traits. In the top 15 microbial genera, both Sichuan and Guangxi contain 15 bacterial genera, but there are differences in their abundance. Guangxi has three unique fungal genera, including the genera Scleroderma, Russula, and Gliocladiopsis. On the other hand, Sichuan has the unique fungal genus Chamaeota. The correlation analysis between the microbiota and the chemical content from 12 different collecting spots was performed by GraphPad Prism. Burkholderia-Caballeronia-Paraburkholderia, Acidibacter, and Amycolatopsis show an inverse proportionality to total polysaccharides and saponins, while Enterobacter shows a direct proportionality to total polysaccharides and inverse proportionality to saponins. The metabolism pathways show a significant positive correlation with PCH polysaccharides and saponins. This study provide new insights into the mechanisms underlying the quality differences between the two major indigenous areas

Famine exposure in early life increases risk of cataracts in elderly stage

BackgroundEpidemiological studies have shown that early-life nutritional deficiencies are associated with an increased risk of diseases later in life. This study aimed to explore the correlation between famine exposure during the early stages of life and cataracts.MethodsWe included 5,931 participants from the Chinese Longitudinal Healthy Longevity Survey (CLHLS) 2018 cross-sectional data in our study. Subjects were categorized into three groups by their age during the famine: adulthood group, school age famine exposure group, and teenage famine exposure group. Utilizing binary logistic regression models, we investigated the relationship between early-life famine exposure and cataracts.ResultsCompared to the adulthood group, both the school age exposure group (OR = 2.49, 95%CI = 1.89–3.27) and teenage exposure group (OR = 1.45, 95%CI = 1.20–1.76) had a heightened risk of developing cataracts in elderly stage. And the sex differences in the impact of famine during early years on elderly cataract risk were observed, particularly indicating a higher risk among women who experienced childhood famine compared to men with similar exposure.ConclusionFamine exposure during the early stages of life is associated with a heightened risk of developing cataracts in old age. To prevent cataracts in elderly individuals, particularly in females, measures should be taken to address nutritional deficiencies in these specific periods