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Classical regression models, due to the limited computational expense and good performance, can be used for the attribution of interannual variability in flood peaks. However, these models capture the relation between predictand (i.e., flood peaks) and predictors (i.e., climate variables), suffering from the disconnect between correlation and causation. Here, we utilize a causal Bayesian Network model to establish causal relationships between flood peaks and basin‐ and season‐averaged precipitation and temperature, which were found to be useful predictors in previous regression‐based attribution studies. We develop these models for seasonal flood peaks for 3,884 gauges across the conterminous Unites States, achieving a median Spearman's rank correlation above 0.7. By performing do‐calculus intervention on the predictors, we found a strong causal relationship between seasonal maximum daily discharge and both concurrent and lagged season‐precipitation and temperature, consistent with underlying physical processes across different basins. The Bayesian Network model effectively predicts the interannual variability in seasonal and annual peak discharges and establishes a causal link between them. The model identifies key drivers across different seasons and regions in CONUS and highlights that antecedent catchment wetness is particularly relevant for high magnitude flows, while precipitation is the dominant driver of medium flows. This study significantly expands our current knowledge on causal flood drivers and presents a novel approach to flood prediction and attribution. Plain Language Summary Traditional regression models are found to be effective in modeling the year‐to‐year variability in flood peaks but fail to represent the causal relationship between flood and their drivers. To address this gap, we use a causal Bayesian Network model for modeling the interannual variability in flood peaks. We use basin‐ and season‐averaged precipitation and temperature, which are climate variables commonly used in regression models as predictors and develop Bayesian Network models to describe the changes in flood peaks for 3,884 gauges across the conterminous United States and found that they work well. We also establish the causal relationship between flood peaks and their drivers using the causal framework. The causal relationship established in the study is consistent with the underlying physical mechanisms. The study results enhance our understanding of the key drivers of flooding and improve our ability to predict floods. Key Points The Bayesian network models can well reproduce the interannual variability in seasonal and annual flow peaks Precipitation drives floods in the eastern and southern US, while temperature influences peak flows in the western and northeastern US The causal link derived by the Bayesian Network models is consistent with the underlying physical mechanisms

Multivariate time series data collected extensively from the real world allows us to observe urban phenomena on an unprecedented scale. However, recovering the underlying causal relations from these observations remains a challenging task, as these causal relations tend to be time-varying. Previous methods have extracted a causal graph over a long period of observation, but cannot be directly applied to capture, interpret, and verify dynamic causal relations. In this paper, we propose a novel visual analysis method for in-depth analysis of dynamic causal relations in multivariate time series. To address the following three challenges: detecting causality, explaining dynamic causality, and uncovering questionable causality, we design and develop the interactive visual analysis system MTCausal. First, a causal detection framework based on Granger causality test is used to obtain the time-varying causal relations in multivariate time series. Then, a dynamic causal graph visualization is designed to explore and interpret these causal graphs over time. Finally, a set of novel visualizations and interactions are designed to support the validation and comparison of causal relations to improve the results of causal analysis. The effectiveness of MTCausal is evaluated through the case studies on the real-world air pollution dataset, which demonstrate that users can effectively explore and analyze dynamic causal relationships. Graphic Abstract

Depression is increasingly recognized as a disorder not only of the brain but also of systemic metabolic dysfunction, particularly involving the gut microbiota. Integrating multi-cohort gut microbiome data with constraint-based metabolic modeling, this study investigates how microbial metabolic fluxes mediate depressive symptoms. Significant alterations in microbial pathways, notably those related to amino acid metabolism and neurotransmitter precursors, were identified. Causal mediation analysis showed that gut microbial composition influenced depressive symptoms, significantly mediated by specific metabolites including butyrate, Cu 2+ , and tryptophan-derived compounds. This study, employing systems biology and mediation analysis, suggests that microbial metabolic activity mediates the gut-brain axis’s role in depression development and severity. These results enhance our understanding of microbiota-related mechanisms in mental health and highlight potential metabolic targets for depression treatment. Key points • Gut Microbiome Diversity and Depression: This study demonstrates that individuals with depression exhibit significantly reduced gut microbial diversity compared to healthy controls. The decline is most pronounced in measures of species richness and evenness, as indicated by lower Observed, Shannon, and Chao1 indices. Notably, taxa such as the Micrococcaceae family are enriched in the depression group, while Firmicutes are more prevalent in healthy individuals. These shifts suggest that a less diverse gut microbiome may be associated with depression, potentially influencing host metabolic functions and mental health. • Metabolic Pathway Alterations in Depression: The study identified significant alterations in several key metabolic pathways between individuals with depression and healthy controls. These include disruptions in fatty acid synthesis, pentose and glucuronate interconversions, thiamine metabolism, and primary amine metabolism. Such metabolic dysfunctions in the gut microbiota may interfere with nutrient processing, neurotransmitter production, and redox balance, potentially contributing to the development and progression of depressive symptoms. These pathway-level differences emphasize the functional role of the gut microbiome in mental health beyond taxonomic shifts alone. • Potential Biomarkers and Therapeutic Targets: The study identified 21 metabolites with significantly different fluxes between depression patients and healthy individuals, highlighting key disruptions in L-Dopa metabolism and copper (Cu ) metabolism. These findings suggest that gut microbial modulation of neurotransmitter precursors and metal ion homeostasis may play a pivotal role in depression pathophysiology. Specifically, altered L-Dopa metabolism may reduce dopamine availability in the brain, while reduced Cu consumption by gut microbes could elevate systemic copper levels, enhancing oxidative stress. These metabolite-level differences offer promising biomarkers for depression diagnosis and open up novel therapeutic avenues, such as targeting microbial metabolism to restore neurochemical balance.

Recent discussions of model selection and multimodel inference highlight a general challenge for researchers: how to convey the explanatory content of a hypothesized model or set of competing models clearly. The advice from statisticians for scientists employing multimodel inference is to develop a well-thought-out set of candidate models for comparison, though precise instructions for how to do that are typically not given. A coherent body of knowledge, which falls under the general term causal analysis, now exists for examining the explanatory scientific content of candidate models. Much of the literature on causal analysis has been recently developed, and we suspect may not be familiar to many ecologists. This body of knowledge comprises a set of graphical tools and axiomatic principles to support scientists in their endeavors to create “well-formed hypotheses,” as statisticians are asking them to do. Causal analysis is complementary to methods such as structural equation modeling, which provides the means for evaluation of proposed hypotheses against data. In this paper, we summarize and illustrate a set of principles that can guide scientists in their quest to develop explanatory hypotheses for evaluation. The principles presented in this paper have the capacity to close the communication gap between statisticians, who urge scientists to develop well-thought-out coherent models, and scientists, who would like some practical advice for exactly how to do that.

Independent component analysis is a probabilistic method for learning a linear transform of a random vector. The goal is to find components that are maximally independent and non-Gaussian (non-normal). Its fundamental difference to classical multi-variate statistical methods is in the assumption of non-Gaussianity, which enables the identification of original, underlying components, in contrast to classical methods. The basic theory of independent component analysis was mainly developed in the 1990s and summarized, for example, in our monograph in 2001. Here, we provide an overview of some recent developments in the theory since the year 2000. The main topics are: analysis of causal relations, testing independent components, analysing multiple datasets (three-way data), modelling dependencies between the components and improved methods for estimating the basic model.

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have proposed 'SAFE' rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into the optimization. We propose strong rules that are very simple and yet screen out far more predictors than the SAFE rules. This great practical improvement comes at a price: the strong rules are not foolproof and can mistakenly discard active predictors, i.e. predictors that have non-zero coefficients in the solution. We therefore combine them with simple checks of the Karush-Kuhn-Tucker conditions to ensure that the exact solution to the convex problem is delivered. Of course, any (approximate) screening method can be combined with the Karush-Kuhn-Tucker conditions to ensure the exact solution; the strength of the strong rules lies in the fact that, in practice, they discard a very large number of the inactive predictors and almost never commit mistakes. We also derive conditions under which they are foolproof. Strong rules provide substantial savings in computational time for a variety of statistical optimization problems.

The realization of digital intelligence is inseparable from the collection and effective application of knowledge. However, in the production process of enterprises, there is a type of “Third Data” which is rich in empirical knowledge but has not been paid attention to. This kind of data is generated from the records of the process in which enterprise employees solve quality problems and is the externalization of empirical knowledge. Because causal analysis is the key to solving quality problems, and there are many factors affecting the cause analysis and the analysis process is complex, this paper makes full use of the causal knowledge and problem contexts contained in the “Third Data”, and systematically considered the duality of cause analysis, the situation dependence of quality problems, the diversity of situations, the similarity among actual quality problems, the differences between short-term solutions and long-term solutions, then proposed the concept of Multi-layer Causal Knowledge Network(MCKN). Next, this paper analyzes the composition and expression of MCKN, and the corresponding construction process and steps are given. Finally, through the case study, the scientificity, rationality, and effectiveness of MCKN are verified. MCKN proposed in this paper provides new ideas and methods for comprehensive and in-depth analysis of the causality of quality problems and helps to improve the level of knowledge and intelligence of quality management.

Precise apple counting in complex orchards is vital for efficient management, yield estimation, and automated picking. Traditional YOLO-based models suffer from fixed convolutional weights, ineffective feature screening, and interference from branch/leaf shadows and film bagging, leading to poor robustness. They also can't fully utilize multi-scale feature complementarity, causing detail loss and inaccuracy in counting dense or small apples. To address these, we propose the YOLO11-SBS model. It introduces the C3k2_SAC module for intelligent feature extraction, the C2PSA_BIF module to optimize feature interactions, and adds SSFF and TFE modules to boost feature representation. Furthermore, to comprehensively evaluate model robustness and counting quality, this study applies the ACE metric and constructs a task-oriented Overall Robustness and Counting Metric (ORCM). The ACE metric is used to assess robustness under illumination perturbation, whereas ORCM is designed to jointly characterize false-detection and missed-detection errors under different occlusion levels. The improved model shows marked advantages, reducing missed and false detections. It maintains high accuracy and recall, especially for green apples similar to the background, providing an efficient and accurate solution for apple counting in complex orchards with high practical value.

Atmospheric aridity (vapor pressure deficit, VPD) and soil moisture (SM) deficit limit plant photosynthesis and, thus, affect vegetation carbon uptake. The strong correlation between SM and VPD makes it challenging to delineate their relative contributions to regional vegetation productivity. Addressing this gap is vital to understand the future trajectory of plant productivity in India—the second-highest contributor to global greening. Here, we separate the controls of SM and VPD on the Indian vegetation using statistical and causal analysis. We found that vegetation productivity in India is primarily controlled by SM limitation (87.66% of grids) than VPD limitation (12.34% of grids). Vegetation has a varying association with SM and VPD across different agroecological regions in India. The negative impact of VPD on vegetation carbon uptake is not visible in high-rainfall areas of India. These findings advance our understanding of vegetation dynamics under regional dryness stress and can enhance dynamic vegetation model estimates for India under changing climate scenarios.