Linear Mixture Research Articles

Unsupervised object-based spectral unmixing for subpixel mapping

Subpixel mapping (SPM) addresses the widespread mixed pixel problem in remote sensing images by predicting the spatial distribution of land cover within mixed pixels. However, conventional pixel-based spectral unmixing, a key pre-processing step for SPM, neglects valuable spatial contextual information and struggles with spectral variability, ultimately undermining SPM accuracy. Additionally, while extensively utilized, supervised spectral unmixing is labor-intensive and user-unfriendly. To address these issues, this paper proposes a fully automatic, unsupervised object-based SPM (UO-SPM) model that exploits object-scale information to reduce spectral unmixing errors and subsequently enhance SPM. Given that mixed pixels are typically located at the edges of objects (i.e., the inner part of objects is characterized by pure pixels), segmentation and morphological erosion are employed to identify pure pixels within objects and mixed pixels at the edges. More accurate endmembers are extracted from the identified pure pixels for the secondary spectral unmixing of the remaining mixed pixels. Experimental results on 10 study sites demonstrate that the proposed unsupervised object (UO)-based analysis is an effective model for enhancing both spectral unmixing and SPM. Specifically, the spectral unmixing results of UO show an average increase of 3.65 % and 1.09 % in correlation coefficient (R) compared to Fuzzy-C means (FCM) and linear spectral mixture model (LSMM)-derived coarse proportions, respectively. Moreover, the UO-derived results of four SPM methods (i.e., Hopfield neural network (HNN), Markov random field (MRF), pixel swapping (PSA) and radial basis function interpolation (RBF)) exhibit an average increase of 5.89 % and 3.04 % in overall accuracy (OA) across the four SPM methods and 10 study sites compared to the FCM and LSMM-based results, respectively. Moreover, the proportions of both mixed and pure pixels are more accurately predicted. The advantage of UO-SPM is more evident when the size of land cover objects is larger, benefiting from more accurate identification of objects.

Multivariate simulation using a locally varying coregionalization model

Understanding the response of materials in downstream processes of mining operations relies heavily on proper multivariate spatial modeling of relevant properties of such materials. Ore recovery and the behavior of tailings and waste are examples where capturing the mineralogical composition is a key component: in the first case, to ensure reliable revenues, and in the second one, to avoid environmental risks involved in their disposal. However, multivariate spatial modeling can be difficult when variables exhibit intricate relationships, such as non-linear correlation, heteroscedastic behavior, or spatial trends. This work demonstrates that the complex multivariate behavior among variables can be reproduced by disaggregating the global non-linear behavior through the spatial domain and looking instead at the local correlations between Gaussianized variables. Local linear dependencies are first inferred from a local neighborhood and then interpolated through the domain using Riemannian geometry tools that allow us to handle correlation matrices and their spatial interpolation. By employing a non-stationary modification of the linear model of coregionalization, it is possible to independently simulate variables and then combine them as a linear mixture that locally varies according to the inferred correlation, reproducing the global multivariate behavior seen on input variables. A real case study is presented, showing the reproduction of the reference multivariate distributions, as well as direct and cross semi-variograms.

Excess Mortality and its Determinants During the COVID-19 Pandemic in 21 Countries: An Ecological Study from the C-MOR Project, 2020 and 2021.

The COVID-19 pandemic overwhelmed health systems, resulting in a surge in excess deaths. This study clustered countries based on excess mortality to understand their response to the pandemic and the influence of various factors on excess mortality within each cluster. This ecological study is part of the COVID-19 MORtality (C-MOR) Consortium. Mortality data were gathered from 21 countries and were previously used to calculate weekly all-cause excess mortality. Thirty exposure variables were considered in five categories as factors potentially associated with excess mortality: population factors, health care resources, socioeconomic factors, air pollution, and COVID-19 policy. Estimation of Latent Class Linear Mixed Model (LCMM) was used to cluster countries based on response trajectory and Generalized Linear Mixture Model (GLMM) for each cluster was run separately. Using LCMM, two clusters were reached. Among 21 countries, Brazil, the USA, Georgia, and Poland were assigned to a separate cluster, with the mean of excess mortality z-score in 2020 and 2021 around 4.4, compared to 1.5 for all other countries assigned to the second cluster. In both clusters the population incidence of COVID-19 had the greatest positive relationship with excess mortality while interactions between the incidence of COVID-19, fully vaccinated people, and stringency index were negatively associated with excess mortality. Moreover, governmental variables (government revenue and government effectiveness) were the most protective against excess mortality. This study highlighted that clustering countries based on excess mortality can provide insights to gain a broader understanding of countries' responses to the pandemic and their effectiveness.

Global and local endmembers spectral patterns to estimate the urban structure in Porto Alegre (Brazil) in Landsat images using the Linear Spectral Mixture Model procedure

Global and local endmembers spectral patterns to estimate the urban structure in Porto Alegre (Brazil) in Landsat images using the Linear Spectral Mixture Model procedure

An Adaptive Unmixing Method Based on Iterative Multi-Objective Optimization for Surface Water Fraction Mapping (IMOSWFM) Using Zhuhai-1 Hyperspectral Images

Surface water fraction mapping is an essential preprocessing step for the subpixel mapping (SPM) of surface water, providing valuable prior knowledge about surface water distribution at the subpixel level. In recent years, spectral mixture analysis (SMA) has been extensively applied to estimate surface water fractions in multispectral images by decomposing each mixed pixel into endmembers and their corresponding fractions using linear or nonlinear spectral mixture models. However, challenges emerge when introducing existing surface water fraction mapping methods to hyperspectral images (HSIs) due to insufficient exploration of spectral information. Additionally, inaccurate extraction of endmembers can result in unsatisfactory water fraction estimations. To address these issues, this paper proposes an adaptive unmixing method based on iterative multi-objective optimization for surface water fraction mapping (IMOSWFM) using Zhuhai-1 HSIs. In IMOSWFM, a modified normalized difference water fraction index (MNDWFI) was developed to fully exploit the spectral information. Furthermore, an iterative unmixing framework was adopted to dynamically extract high-quality endmembers and estimate their corresponding water fractions. Experimental results on the Zhuhai-1 HSIs from three test sites around Nanyi Lake indicate that water fraction maps obtained by IMOSWFM are closest to the reference maps compared with the other three SMA-based surface water fraction estimation methods, with the highest overall accuracy (OA) of 91.74%, 93.12%, and 89.73% in terms of pure water extraction and the lowest root-mean-square errors (RMSE) of 0.2506, 0.2403, and 0.2265 in terms of water fraction estimation. This research provides a reference for adapting existing surface water fraction mapping methods to HSIs.

Exposure to PM2.5 and its constituents in relation to thyroid function of pregnant women: Separate and mixture analyses

The relationships between exposure to PM2.5 and its constituents and thyroid hormone (TH) levels in pregnant women are still uncertain, particularly regarding the impact of mixed exposure to PM2.5 constituents on thyroid function during pregnancy. This study aimed to investigate the individual and mixed effect of PM2.5 and its constituents on TH levels during pregnancy. Fluorescence and chemiluminescence immunoassays were utilized to measure serum concentrations of free thyroxine (FT4) and thyroid-stimulating hormone (TSH) in pregnant women participating in the Fujian Birth Cohort Study (FJBCS). PM2.5 and its constituents were obtained from the ChinaHighAirPollutants dataset. Generalized linear regression model and mixture analysis were applied to explore the individual and mixed effect of PM2.5 and its constituents on TH levels. 13711 participants from the FJBCS were taken into the final analysis. In the context of separate exposure, an increase of one interquartile range (IQR) in PM2.5 exposure during the 1st trimester, 2nd trimester, and entire pregnancy was associated with a decrease of −0.042 (−0.050, −0.034), −0.017 (−0.026, −0.009), and −0.011 (−0.017, −0.004) in FT4 level, respectively. As well, significant negative associations were observed between FT4 level and PM2.5 constituents. Additionally, PM2.5 and its constituents were in relation to an increased risk of hypothyroxinemia in pregnant women. It is noteworthy that, in the context of mixed exposure, the weighted quantile sum regression (WQS) indices were significantly associated with both FT4 level (1st trimester: −0.031 (−0.036, −0.026); 2nd trimester: −0.026 (−0.030, −0.023); whole pregnancy: −0.024 (−0.028, −0.020)) and hypothyroxinemia risk (1st trimester: 1.552 (1.312, 1.821); 2nd trimester: 1.453 (1.194, 1.691); whole pregnancy: 1.402 (1.152, 1.713)). PM2.5 and its chemical constituents may affect thyroid function in pregnant women individually and in combination, with the effect observed during early gestational exposure being most pronounced.

The Standardized Spectroscopic Mixture Model

The standardized spectral mixture model combines the specificity of a physically based representation of a spectrally mixed pixel with the generality and portability of a spectral index. Earlier studies have used spectrally and geographically diverse collections of broadband and spectroscopic imagery to show that the reflectance of the majority of ice-free landscapes on Earth can be represented as linear mixtures of rock and soil substrates (S), photosynthetic vegetation (V) and dark targets (D) composed of shadow and spectrally absorptive/transmissive materials. However, both broadband and spectroscopic studies of the topology of spectral mixing spaces raise questions about the completeness and generality of the Substrate, Vegetation, Dark (SVD) model for imaging spectrometer data. This study uses a spectrally diverse collection of 40 granules from the EMIT imaging spectrometer to verify the generality and stability of the spectroscopic SVD model and characterize the SVD topology and plane of substrates to assess linearity of spectral mixing. New endmembers for soil and non-photosynthetic vegetation (NPV; N) allow the planar SVD model to be extended to a tetrahedral SVDN model to better accommodate the 3D topology of the mixing space. The SVDN model achieves smaller misfit than the SVD, but does so at the expense of implausible fractions beyond [0, 1]. However, a refined spectroscopic SVD model still achieves small (<0.03) RMS misfit, negligible sensitivity to endmember variability and strongly linear scaling over more than an order of magnitude range of spatial resolution.

A Bayesian beta-binomial piecewise growth mixture model for longitudinal overdispersed binomial data.

In a recent 12-week smoking cessation trial, varenicline tartrate failed to show significant improvements in enhancing end-of-treatment abstinence when compared with placebo among adolescents and young adults. The original analysis aimed to assess the average effect across the entire population using timeline followback methods, which typically involve overdispersed binomial counts. We instead propose to investigate treatment effect heterogeneity among latent classes of participants using a Bayesian beta-binomial piecewise linear growth mixture model specifically designed to address longitudinal overdispersed binomial responses. Within each class, we fit a piecewise linear beta-binomial mixed model with random changepoints for each study group to detect critical windows of treatment efficacy. Using this model, we can cluster subjects who share similar characteristics, estimate the class-specific mean abstinence trends for each study group, and quantify the treatment effect over time within each class. Our analysis identified two classes of subjects: one comprising high-abstinent individuals, typically young adults and light smokers, in which varenicline led to improved abstinence; and another comprising low-abstinent individuals for whom varenicline showed no discernible effect. These findings highlight the importance of tailoring varenicline to specific participant subgroups, thereby advancing precision medicine in smoking cessation studies.

Enhancing eMSOT with nonlinear mixed model approaches for precise blood oxygenation imaging in tissues

Multispectral optoacoustic tomography (MSOT) utilizes multiple wavelengths to illuminate tissue, producing a series of optoacoustic images rich in spectral information. This approach offers a more comprehensive spectral profile compared to conventional optoacoustic techniques. Contrasted with single-wavelength optoacoustic images, the spectral information can be amalgamated with endogenous chromophores or exogenous dyes within biological organisms, thereby unveiling physiological, cellular, and subcellular functions. The development of eigenspectral optoacoustic tomography (eMSOT), grounded in the linear mixture model (LMM), along with its various derivative methods, facilitates label-free imaging of tissue oxygen saturation in deep-seated structures. However, the effectiveness of the LMM may diminish in the presence of multiple scattering effects or inter-substance interactions, thereby impairing the performance of the eMSOT method in heterogeneous tissues. To address this issue, we propose incorporating a nonlinear model to enhance the eMSOT technique, which we refer to as NL-eMSOT (non-linear eMSOT). This model employs the Hadamard product as a nonlinear component of the LMM, effectively characterizing the interactions between photons and both oxygenated and deoxygenated hemoglobin within the near-infrared spectral window. This innovation resolves the nonlinear unmixing problem inherent in optoacoustic imaging. Our approach, validated through numerical simulations, phantom experiments, and in vivo studies, improves the accuracy of quantitative oxygen saturation estimation in heterogeneous tissues by accounting for inter-substance interactions. Consequently, it necessitates the consideration of more complex mixing models to adequately address nonlinear interactions.

Data Privacy Preserving for Centralized Robotic Fault Diagnosis With Modified Dataset Distillation

Abstract Industrial robots generate monitoring data rich in sensitive information, often making enterprises reluctant to share, which impedes the use of data in fault diagnosis modeling. Dataset distillation (DD) is an effective approach to condense large dataset into smaller, synthesized forms, focusing solely on fault-related features, which facilitates secure and efficient data transfer for diagnostic purposes. However, the challenge of achieving satisfactory fault diagnosis accuracy with distilled data stems from the computational complexity in data distillation process. To address this problem, this article proposes a modified KernelWarehouse (MKW) network-based DD method to achieve accurate fault diagnosis with the distilled dataset. In this algorithm, DD first generates distilled training and testing dataset, followed by the training of an MKW-based network based on these distilled datasets. Specifically, MKW reduces network complexity through the division of static kernels into disjoint kernel cells, which are then computed as linear mixtures from a shared warehouse. An experimental study based on the real-world robotic dataset reveals the effectiveness of the proposed approach. The experimental results indicate that the proposed method can achieve a fault diagnosis accuracy of 86.3% when only trained with distilled data.

The Gibbs and Butler Equations and the Surface Activity of Dilute Aqueous Solutions of Strong and Weak Linear Polyelectrolyte-Surfactant Mixtures: The Roles of Surface Composition and Polydispersity.

In a previous paper, we applied a combination of direct measurements of both surface tension and surface excess in conjunction with the Gibbs equation to explain features of the adsorption and surface tension of mixtures of surfactants and strong linear polyelectrolytes at the air-water interface. This paper extends that model by including (i) the restrictions of the Butler equation for the behavior of the surface tension of mixed systems and (ii) the surface behavior of surfactant and linear weak polyelectrolyte mixtures, for which the inclusion of measurements of the surface excess and composition is shown to be particularly important. In addition, a closer examination of earlier data at higher concentrations provides evidence that the surface layering that is often observed in polyelectrolyte-surfactant systems is also an average equilibrium phenomenon and is driven by particular aggregation patterns that occur in some systems and not in others. Although the successful application of the Gibbs and Butler equations indicates that strong polyelectrolyte-surfactant systems can be described in terms of an average equilibrium over wide ranges of concentration, we have identified two concentration ranges where polydispersity in either polyelectrolyte molecular weight or composition results in significant time dependence of the surface behavior.

Evaluation of Multi-Valued Data Transmission in Two-Dimensional Symbol Mapping using Linear Mixture Model

Evaluation of Multi-Valued Data Transmission in Two-Dimensional Symbol Mapping using Linear Mixture Model

Broad-area-search of new construction using time series analysis of Landsat and Sentinel-2 data

New construction activities can alter surface albedo and structure, which then affect surface temperature and roughness, and hence have a significant impact on urban climate. Construction activity is also an important indicator of human development and movement and is of high interest to the intelligence community. A new approach for Broad-Area-Search of New Construction activities (BASC) by combining time series analysis and rule-based filters using Landsat data was developed and tested in five selected cities (Boston, Shanghai, São Paulo, Dubai, and Ho Chi Minh City). The algorithm transforms Landsat images into fractions of a set of four endmembers using Linear Spectral Mixture Analysis (LSMA) and then applies the Continuous Change Detection and Classification (CCDC) algorithm for change detection. A set of rule-based filters and spatial processing was then applied to narrow the search to changes related to construction activities. Overall, BASC reached a recall of 0.83, a precision of 0.58, and an F1-Score of 0.68. Among the five cities, Dubai had the highest recall of 1.0 and the highest F1-score of 0.75, while Boston had the highest precision of 0.63. BASC performed worst in Shanghai with an F1-Score of 0.6, mainly due to it having the lowest recall of 0.62, while São Paulo has the lowest precision of 0.5. Common sources of omission errors include low-density, redevelopment, and small sites, while common commission errors include roofing, land clearing, water level changes, and re-surfacing projects. For comparison, BASC using Sentinel-2 Top-of-Atmosphere (TOA) Reflectance data recorded an overall F1-Score of 0.63, but with higher recall and lower precision. Integration of Sentinel-2 Surface Reflectance and Sentinel-1 SAR data has the potential to further improve the performance of BASC. The new algorithm provided a method for routine monitoring of construction activities over large areas. The result of such monitoring can be used as a baseline to narrow down the candidate targets of construction activities, where very high-resolution imagery can then be requested to perform further examination.

Predicting soil nutrients with PRISMA hyperspectral data at the field scale: the Handan (south of Hebei Province) test cases

ABSTRACT This research investigates the suitability of PRISMA and Sentinel-2 satellite imagery for retrieving topsoil properties such as Organic Matter (OM), Nitrogen (N), Phosphorus (P), Potassium (K), and pH in croplands using different Machine Learning (ML) algorithms and signal pre-treatments. Ninety-five soil samples were collected in Quzhou County, Northeast China. Satellite images captured soil reflectance data when bare soil was visible. For PRISMA data, a Linear Mixture Model (LMM) was used to separate soil and Photosynthetic Vegetation (PV) endmembers, excluding Non-Photosynthetic Vegetation (NPV) using Band Depth values at the 2100 nm absorption peak of cellulose. Sentinel-2 bare soil reflectance spectra were obtained using thresholds based on NDVI and NBR2 indices. Results showed PRISMA data provided slightly better accuracy in retrieving topsoil nutrients than Sentinel-2. While no optimal predictive algorithm was best, absorbance data proved more effective than reflectance. PRISMA results demonstrated potential for predicting soil nutrients in real scenarios.

Fetal and Infancy Exposure to Phenols, Parabens, and Phthalates and Anthropometric Measurements up to 36 Months, in the Longitudinal SEPAGES Cohort.

Endocrine-disrupting chemicals may play a role in adiposity development during childhood. Until now literature in this scope suffers from methodologic limitations in exposure assessment using one or few urine samples and missing assessment during the infancy period. We investigated the associations between early-life exposure to quickly metabolized chemicals and post-natal growth, relying on repeated within-subject urine collections over pregnancy and infancy. We studied the associations of four phenols, four parabens, seven phthalates, and one nonphthalate plasticizer from weekly pooled urine samples collected from the mother during second and third trimesters (median 18 and 34 gestational weeks, respectively) and infant at 2 and 12 months of age, and child growth until 36 months. We relied on repeated measures of height, weight and head circumference from study visits and the child health booklet to predict growth outcomes at 3 and 36 months using the Jenss-Bayley nonlinear mixed model. We assessed associations with individual chemicals using adjusted linear regression and mixtures of chemicals using a Bayesian kernel machine regression model. The unipollutant analysis revealed few associations. Bisphenol S (BPS) at second trimester was positively associated with all infant growth parameters at 3 and 36 months, with similar patterns between exposure at third trimester and all infant growth parameters at 3 months. Mono-n-butyl phthalate (MnBP) at 12 months was positively associated with body mass index (BMI), weight, and head circumference at 36 months. Mixture analysis revealed positive associations between exposure at 12 months and BMI and weight at 36 months, with MnBP showing the highest effect size within the mixture. This study suggests that exposure in early infancy may be associated with increased weight and BMI in early childhood, which are risk factors of obesity in later life. Furthermore, this study highlighted the impact of BPS, a compound replacing bisphenol A, which has never been studied in this context. https://doi.org/10.1289/EHP13644.

Revolutionizing prostate cancer diagnosis: Unleashing the potential of an optimized deep belief network for accurate Gleason grading in histological images

PC (Prostate Cancer) is the second highest cause of death due to cancer in men globally. Proper detection and treatment are critical for halting or controlling the growth and spread of cancer cells within the human organism. However, evaluating these sorts of images is difficult and time-consuming, requiring histopathological image recognition as the most reliable method for treating PC because of its distinct visual characteristics. Risk evaluation and treatment planning rely heavily on histological image-based Gleason grading of prostate tumors. This work introduces an innovative approach to histological image analysis for prostate cancer diagnosis and Gleason grading. The Elephant Herding Optimization-based Hyper-parameter Convolutional Deep Belief Network (CDBN-EHO) is presented alongside a grading network head-optimized deep belief network technique for multi-task prediction. Leveraging an effective Bayesian inference method, fully linked Conditional Random Field (CRF) techniques are utilized for segmentation, with pairwise boundary capacities determined by a linear mixture of Gaussian kernels. The multi-task approach aims to enhance performance by incorporating contextual information, leading to breakthrough results in the identification of epithelial cells and the grading of Gleason scores. The objective of this study is to demonstrate the effectiveness of the optimized deep belief network technique in improving diagnostic accuracy and efficiency for prostate cancer diagnosis and Gleason grading in histological images.

Association between parabens exposure and neurodevelopment in children

ObjectiveParabens are a group of substances commonly employed as antimicrobial preservatives. The effect of parabens on the development of neurotoxicity in children is still controversial. This study aimed to explore the associations between parabens exposure and children's neurodevelopmental performance, emphasizing potential sex differences and the combined effects of parabens. MethodsWe used the long-term follow-up study of Taiwanese generation, Taiwan Birth Panel Study II (TBPS II). We recruited the group of children at 6–8 years old. And, we measured parabens in children urine, including methylparaben (MP), ethylparaben (EP), propylparaben (PP) and butylparaben (BP). Children's attention-related performance was evaluated using the Conners Kiddie Continuous Performance Test 2nd Edition (K-CPT 2). The study employed both linear regression and mixture analysis quantile g-computation (QGC) methods to discern associations. A stratified analysis by sex and QGC was implemented to delve deeper into the cumulative effects of parabens. ResultsA total of 446 subjects completed both the parabens analysis and the K-CPT 2 survey. The overall association between parabens and neurodevelopmental performance was not pronounced, but discernible sex differences emerged. In the single pollutant analysis, elevated PP concentrations were associated with higher K-CPT 2 scores particularly in detectability (d') (β = 0.92 [95 % CI = 0.15 to 1.69]) and commissions (β = 0.95 [95 % CI = 0.12 to 1.78]), among girls. Further, in the mixture analysis, a significant association between PP and detectability (d') was observed in girls (β = 1.68 [95 % CI = 0.11 to 3.26]). ConclusionsThis study identified sex-specific associations between parabens and attention performance. Consistent outcomes across single and mixture analysis methods. Further research is crucial to clarify these causal associations.

The orientation of CpG conjugation on aluminum oxyhydroxide nanoparticles determines the immunostimulatory effects of combination adjuvants

In subunit vaccines, aluminum salts (Alum) are commonly used as adjuvants, but with limited cellular immune responses. To overcome this limitation, CpG oligodeoxynucleotides (ODNs) have been used in combination with Alum. However, current combined usage of Alum and CpG is limited to linear mixtures, and the underlying interaction mechanism between CpG and Alum is not well understood. Thus, we propose to chemically conjugate Alum nanoparticles and CpG (with 5′ or 3′ end exposed) to design combination adjuvants. Our study demonstrates that compared to the 3′-end exposure, the 5′-end exposure of CpG in combination adjuvants (Al-CpG-5′) enhances the activation of bone-marrow derived dendritic cells (BMDCs) and promotes Th1 and Th2 cytokine secretion. We used the SARS-CoV-2 receptor binding domain (RBD) and hepatitis B surface antigen (HBsAg) as model antigens to demonstrate that Al-CpG-5′ enhanced antigen-specific antibody production and upregulated cytotoxic T lymphocyte markers. Additionally, Al-CpG-5′ allows for coordinated adaptive immune responses even at lower doses of both CpG ODNs and HBsAg antigens, and enhances lymph node transport of antigens and activation of dendritic cells, promoting Tfh cell differentiation and B cell activation. Our novel Alum-CPG strategy points the way towards broadening the use of nanoadjuvants for both prophylactic and therapeutic vaccines.

Dynamic Regret of Adversarial MDPs with Unknown Transition and Linear Function Approximation

We study reinforcement learning (RL) in episodic MDPs with adversarial full-information losses and the unknown transition. Instead of the classical static regret, we adopt dynamic regret as the performance measure which benchmarks the learner's performance with changing policies, making it more suitable for non-stationary environments. The primary challenge is to handle the uncertainties of unknown transition and unknown non-stationarity of environments simultaneously. We propose a general framework to decouple the two sources of uncertainties and show the dynamic regret bound naturally decomposes into two terms, one due to constructing confidence sets to handle the unknown transition and the other due to choosing sub-optimal policies under the unknown non-stationarity. To this end, we first employ the two-layer online ensemble structure to handle the adaptation error due to the unknown non-stationarity, which is model-agnostic. Subsequently, we instantiate the framework to three fundamental MDP models, including tabular MDPs, linear MDPs and linear mixture MDPs, and present corresponding approaches to control the exploration error due to the unknown transition. We provide dynamic regret guarantees respectively and show they are optimal in terms of the number of episodes K and the non-stationarity P̄ᴋ by establishing matching lower bounds. To the best of our knowledge, this is the first work that achieves the dynamic regret exhibiting optimal dependence on K and P̄ᴋ without prior knowledge about the non-stationarity for adversarial MDPs with unknown transition.

A global estimate of monthly vegetation and soil fractions from spatiotemporally adaptive spectral mixture analysis during 2001–2022

Abstract. Multifaceted regime shifts of Earth's surface are ongoing dramatically and – in turn – considerably alter the global carbon budget, energy balance and biogeochemical cycles. Sustainably managing terrestrial ecosystems necessitates a deeper comprehension of the diverse and dynamic nature of multicomponent information within these environments. However, comprehensive records of global-scale fractional vegetation and soil information that encompass these structural and functional complexities remain limited. Here, we provide a globally comprehensive record of monthly vegetation and soil fractions during the period 2001–2022 using a spatiotemporally adaptive spectral mixture analysis framework. This product is designed to continuously represent Earth's terrestrial surface as a percentage of five physically meaningful vegetation and soil endmembers, including photosynthetic vegetation (PV), nonphotosynthetic vegetation (NPV), bare soil (BS), ice or snow (IS) and dark surface (DA), with high accuracy and low uncertainty compared to the previous vegetation index and vegetation continuous-field product as well as traditional fully constrained linear spectral mixture models. We also adopt nonparametric seasonal Mann–Kendall tested fractional dynamics to identify shifts based on interactive changes in these fractions. Our results – superior to previous portrayals of the greening planet – not only report a +9.35 × 105 km2 change in photosynthetic vegetation, but also explore decreases in nonphotosynthetic vegetation (−2.19 × 105 km2), bare soil (−5.14 × 105 km2) and dark surfaces (−2.27 × 105 km2). In addition, interactive changes in these fractions yield multifaceted regime shifts with important implications, such as a simultaneous increase in PV and NPV in central and southwestern China during afforestation activities, an increase in PV in cropland of China and India due to intensive agricultural development, a decrease in PV and an increase in BS in tropical zones resulting from deforestation. These advantages emphasize that our dataset provides locally relevant information on multifaceted regime shifts at the required scale, enabling scalable modeling and effective governance of future terrestrial ecosystems. The data about five fractional surface vegetation and soil components are available in the Science Data Bank (https://doi.org/10.57760/sciencedb.13287, Sun and Sun, 2023).