It is well known that the distributivity of one aggregation function over another is a desirable interaction between aggregation functions and has been continuously studied in the literature both for theoretical and practical reasons. Among the many classes of aggregation functions introduced over the past decades, the classes of uninorms and nullnorms stand out because of their potential applications in a broad variety of fields. Similarly, the classes of overlap and grouping functions have received ample attention. In this paper, on the one hand, we focus on the class of S-uninorms, a common generalization of nullnorms and conjunctive uninorms. On the other hand, we consider other more general classes of general overlap and general grouping functions. We continue and wrap up the investigation of the distributivity equation for the above-mentioned classes. In particular, we discuss the distributivity of S-uninorms (with an underlying uninorm belonging to V-min) over general overlap or general grouping functions, and vice versa. In both cases, we fully characterize the solutions by providing necessary and sufficient conditions.

This paper examines the performance of regional innovation across 220 European regions. A poset-based approach is adopted to obtain a ranking of the European regions, which is then compared with the results described in the Regional Innovation Scoreboard 2019 (RIS 2019). The poset-based approach is based on the theory of partially ordered sets; it respects the ordinal nature of data, maintains a high standard of objectivity and avoids compensation effects caused by averaging indicators, possibly leading to different positions for some regions. The poset-based ranking indeed reveals a geographical map of innovation that differs from the RIS19. The results show that seven regions located in Italy, Austria and Romania have improved their position in the ranking, whereas six regions located in Denmark, United Kingdom, the Netherlands and Ireland have worsened their position in the ranking in comparison with the RIS19. The findings highlight the role of methodological choices in shaping regional innovation rankings and provide evidence useful for policymakers and regional stakeholders interested in understanding innovation performance without aggregation bias.

The Lilliefors normality test is a classical extension of the Kolmogorov-Smirnov goodness-of-fit test tailored to assessing normality. A recent modification improves its robustness to outliers by introducing a subsetting function. In this paper, we propose an alternative approach that replaces subsetting functions with Ordered Weighted Averaging (OWA) functions and further generalizes the test to any location-scale family, not only the normal distribution. We conduct extensive experiments on the power of the resulting test for three representative location-scale families-normal, uniform and shifted-exponential-using different weight vectors to define the OWA functions. The results indicate that the best trade-off between robustness and statistical power is achieved by a well-known special class of OWA functions: the order statistics.

A set of 2n candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next round until the nth round (the final one) in which the final winner is declared. The candidates are arranged on a board in a given order, which is maintained among the remaining candidates at all rounds. A study of the size of the commission is carried out in order to obtain the desired result of any candidate being a possible winner. For 2n candidates with n >= 3, we identify a voting profile with 4n-3 voters such that any candidate could win simply by choosing a proper initial order of the candidates. Moreover, in the setting of a random number of voters, we obtain the same results, with high probability, when the expected number of voters is large. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Elo rating and its variants are widely employed to characterize the social (dominance) hierarchies within animal groups. These ranking methods are considered the state-of-the-art for analysing sequential dyadic agonistic interaction data. However, they have been criticized for adapting slowly to rare but abrupt and important changes in the dominance hierarchy. In this paper, we show that this delayed response can be overcome by making the update parameter of the Elo rating time-dependent. By distinguishing between two types of interactions, i.e., low-impact and high-impact interactions each with an associated update parameter, a simple parametrization of a time-dependent update parameter can be obtained. We refer to this innovation as Dual Elo. Building on Optimized Elo, we propose a computationally efficient maximum-likelihood-based algorithm to fit Dual Elo to an observed sequence of interactions. The result is an extension of Elo rating that can handle a mix of gradual and sudden changes in the hierarchy, leading to a model that is more responsive with more robust estimates of the temporal evolution of the Elo scores. A systematic evaluation of the Dual Elo rating on both simulated and publicly available datasets demonstrates its robustness, even when the observations of the outcomes of interactions are noisy.

In this work, we propose a new family of aggregation functions inspired by the well-known Choquet integral. To build these functions, we replace the measure in the definition of the Choquet integral by an appropriate function. We study the properties of these aggregation functions and explore the relations with some other common aggregation functions such as order statistics and overlap and grouping functions.

Zero-shot indoor scene recognition has the ability to recognize new indoor images from an unseen scene class, which plays an important role in robot navigation and localization. However, different from traditional zero-shot object classification, expert-annotated semantic information is scarce for indoor scene images, which is crucial for zero-shot indoor scene recognition. For this reason, we propose a multi-modal semantic representation learning method (MMSRL). Specifically, benefiting from the powerful ability of the pre-trained BERT model, the word vector of an indoor scene class is first extracted as one modal semantic representation. Then, taking advantage of visual prototype learning, a visual-guided semantic feature learning method is proposed to extract another modal semantic representation. Subsequently, based on the self-attention mechanism, a shared-and-specific modality attention method is proposed to fuse the above two modal features, which helps to generate an effective multi-modal semantic representation. Finally, two encoder reconstruction loss functions are formulated to build the relation between the visual and the semantic features. In particular, considering the lack of label information in the testing phase, a revised visual-guided semantic feature learning method is devised to promote the zero-shot recognition performance. Comprehensive experimental results on three public indoor scene datasets demonstrate the effectiveness of the proposed method, achieving recognition accuracies of 61.91 %, 73.65 %, and 57.87 % on the MIT-67, SUN-300, and Scene-15 datasets, respectively.

Water scarcity in arid regions has promoted the widespread adoption of brackish water irrigation, which plays an essential role in ensuring regional food security and sustaining agricultural production. However, long-term use of brackish water inevitably reshapes groundwater hydrochemical characteristics and microbial community structure, while seasonal dynamics and ecological functions of groundwater microorganisms remain insufficiently studied. In this study, seasonal groundwater surveys were conducted in the Jinghuiqu Irrigation District, with a focus on the impacts of salinity and seasonal variability. By integrating hydrochemical analyses, isotope tracing, and 16S rRNA sequencing, we systematically investigated microbial community composition, nitrogen metabolism, and ecological functions. The results showed that salinity, as the primary environmental filter, did not lead to a significant decline in species abundance but instead promoted greater diversification and functional differentiation of microbial communities. Seasonal variation acted as a secondary factor interacting with salinity: in the dry season and under high salinity conditions, microbial co-occurrence networks were more compact and modular, indicating enhanced niche differentiation but reduced stability; in contrast, wet season networks were smaller and more diffuse, consistent with irrigation-induced environmental disturbances. Notably, microbial ecological functions remained relatively stable, with denitrification as the main driver of nitrogen-cycling, supplemented by assimilatory reduction and ammonification under different conditions. Nitrogen reduction processes were primarily regulated by electron donors/receptors, nitrogen source types, and organic carbon inputs, with organic carbon supply not only fueling nitrogen-cycling but also directly linking and regulating the carbon cycle. This study advances understanding of groundwater biogeochemical processes under long-term brackish water irrigation and provides new insights for research and management in similar irrigation districts.

Document set expansion is a fundamental problem in information retrieval, involving the augmentation of an initial document set with additional relevant documents from a larger corpus. Query reformulation techniques, such as query expansion and refinement, offer effective means to modify initial queries and retrieve supplementary documents, but they are inherently limited by dependence on an initial query and relevance feedback. In contrast, embedding techniques represent documents in a feature space, enabling expansion or contraction by exploiting document similarities. However, existing approaches often fail to reconcile the advantages of both strategies. To address this, we propose a novel method that integrates query reformulation and embedding techniques into a unified framework. Our method aims to augment document sets-allowing both expansion and contraction-while satisfying desirable properties, including high intra-set document embedding similarity, fidelity to the initial set, and simplicity through low-complexity queries. While we show that our proposal admits a Mixed Integer Quadratic Programming formulation, which can be globally optimized for small problem sizes, we also present a computationally efficient heuristic search algorithm for larger instances. We illustrate our method using a running toy example and demonstrate its efficacy through experimental evaluation on a benchmark corpus of newspaper articles.

Understanding the population dynamics of ecological systems is crucial for predicting shifts in biodiversity and ensuring the protection of these systems. Established models often focus on pairwise species interactions, yet recent studies have highlighted the importance of higher-order interactions (HOIs) in shaping community structure and function. In this study, we investigate the effects of HOIs in an agent-based model with three species engaged in intransitive competition. We introduce an HOI where one species modifies the competition between the other two. We explore the impact of the strength, radius of influence, and speed of this interaction modification on species abundances and oscillations thereof. Our results show that these abundances are not only greatly impacted by the strength, but also by the radius and speed of the interaction modification. A deeper investigation demonstrates that the changes in the oscillations are caused by the interaction modification itself, and not the change in pairwise interaction strength caused by the HOI. These results emphasise the importance of considering the spatio-temporal scales of higher-order interactions when assessing ecosystem stability, highlighting that such interactions can introduce complex dynamical behaviours that go beyond the predictions of traditional pairwise or simpler higher-order models.

In this paper, we investigate the lattice structure of the set of functions from a bounded lattice to a frame under the join- and meet-convolution operations. Unlike previous work, we do not assume distributivity of the bounded lattice. Instead, we restrict attention to the class of regular functions, which are constant on every interval spanned by a reducible couple. We show that this class forms a Birkhoff system. To clarify the role of convexity in the non-distributive setting, we refine the notion of convexity to the level of individual points. We prove that the set of regular functions that (i) share a supremum greater than or equal to that of a given regular function, (ii) are at least as convex as that function, and (iii) coincide with it on its non-convex elements, forms a lattice. As a consequence, the set of regular and convex functions with a common supremum itself constitutes a bounded lattice. These results show that the theory of convolution lattices in the distributive setting extends to the non-distributive case when idempotence is replaced by regularity.

Determining properties of an arbitrary binary sequence is a challenging task if only local processing is allowed. Among these properties, the determination of the parity of 1s by distributed consensus has been a recurring endeavour in the context of automata networks. In its most standard formulation, a one-dimensional cellular automaton rule should process any odd-sized cyclic configuration and lead the lattice to converge to the homogeneous fixed point of 0s if the parity of 1s is even and to the homogeneous fixed point of 1s, otherwise. The only known solution to this problem with a single rule was given by Betel, de Oliveira and Flocchini (coined BFO rule after the authors' initials). However, three years later the authors of the BFO rule realised that the rule would fail for some specific configuration and proposed a computationally sound fix, but a proof could not be worked out. Here we provide another fix to the BFO rule along with a full proof, therefore reassuring that a single-rule solution to the problem really does exist.

Recently, vision-language models, such as the well-known CLIP, have demonstrated remarkable generalization ability in various zero-shot recognition tasks. However, their performance on zero-shot fine-grained recognition, especially for indoor scenes, remains limited due to the high between-class semantic similarity. To address this challenge, we propose a Diverse Semantic Representation Learning (DSRL) method based on the pre-trained vision-language model for zero-shot indoor scene recognition. Specifically, we first design a meaningful prompt text for indoor scene images to extract semantic features based on the CLIP text encoder. Then, in order to explore diverse visual-related semantic features, we introduce a visual-guided semantic feature learning method based on the CLIP image encoder, which refines the diverse visual prototypes through contrastive learning. Next, these features are fused by a multi-head attention fusion strategy, generating the diverse semantic representations. Finally, a dual reconstruction loss and a cross-entropy loss are constructed to facilitate knowledge transfer for zero-shot learning. In the testing phase, inspired by the convergent evolution theory, we revise the visual-guided semantic feature learning method to obtain the diverse semantic representations for unseen images. Extensive experiments on three indoor scene datasets demonstrate that DSRL achieves the state-of-the-art performance in zero-shot indoor scene recognition.

Data-driven models have increasingly been used as useful tools for process simulation in urban wastewater treatment plants (WWTPs), but their lack of interpretability and limited generalization hinder their application in practical engineering scenarios. In this study, a hybrid neural network incorporating an attention-based encoder and a long short-term memory module was proposed for data-driven modeling of the anaerobic-anoxic-oxic (A2O) process in real WWTPs. Compared with several widely used baseline deep learning architectures for time-series prediction, the proposed method demonstrated improved accuracy and efficiency in predicting dissolved oxygen (DO) concentrations in the oxic zone. The model was further analyzed using a bidimensional interpretable deep learning framework, enabling global interpretability analysis across temporal and feature levels. This bidimensional perspective provided new insights for optimizing model architecture and feature selection. Three practical scenarios characterized by stepped water temperature distributions were defined, and local interpretability methods were employed to enhance understanding of the individual and interactive effects of aeration rate and water temperature on DO within each scenario. The results indicate that the interaction mechanisms among core variables affecting DO vary significantly across different seasonal conditions. Therefore, it is necessary to design scenario-specific aeration strategies to optimize real-time control operations in WWTPs. Additionally, the transfer learning method, incorporating dynamic system similarity, significantly enhanced the model's generalization capability. This suggests that transferring and retraining models across similar A2O systems may be an effective approach for improving model reuse and addressing the "cold start" challenge in newly constructed WWTPs.

The property of α -migrativity between binary operations is both interesting and mathematically challenging, and is of particular importance in the study of binary aggregation functions, both from a theoretical and a practical point of view. Here, we continue the investigation of this research direction by focusing on S-uninorms, general overlap and general grouping functions, where S-uninorms can be seen as a significant generalization of nullnorms and conjunctive uninorms. First, we discuss the α -migrativity of S-uninorms over general overlap or general grouping functions and identify the necessary and sufficient conditions for α -migrativity to hold. Next, we investigate the α -migrativity of overlap and grouping functions over S-uninorms and obtain that for overlap functions it cannot hold when α∈ ]0,1] , whereas for grouping functions it cannot hold when α∈ [0,ϱ ] , where ϱ is the IFC element of the S-uninorm. Finally, we study the α -migrativity of general overlap or general grouping functions over S-uninorms and obtain full characterizations.

The advancement of intelligent wastewater treatment urgently requires a high-accuracy digital-twin framework for real-world applications. However, the widespread prevalence of missing or corrupted sensor data, coupled with process non-linearity and dynamic variability, continues to hinder the reliability of conventional modeling and control approaches in industrial wastewater treatment. To overcome these challenges, this study proposes an end-to-end framework that integrates mechanistic-model-guided data preprocessing, multi-architecture deep learning prediction, and model predictive control for industrial wastewater treatment. Employing real-time sensor data from the Hongxing Pharmaceutical Industrial Park’s wastewater treatment plant (transmitted via the message queuing telemetry transport (MQTT) protocol), the proposed framework was rigorously validated using a complete workflow, which comprised data preprocessing, model prediction, predictive control, and transmitting feedback about the optimized control variables to the plant’s programmable logic controller. When compared with their conventional counterparts, the novel methods implemented in each module of the proposed framework deliver higher data quality and reliability, superior prediction accuracy, and quicker response times for control optimization. This end-to-end framework provides a foundation for future applications of digital-twin technology for intelligent industrial wastewater management.

Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that axiomatic properties of ternary fuzzy relations seem to be ideally suited to capture geometric characteristics of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as geometric properties. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.

This paper provides a brief summary of recent results on the number-conserving capabilities of cellular automata. We focus on studies that resulted in establishing complete lists of such CAs for a given dimension, state set, and neighborhood type. Moreover, we outline key, new questions arising from these results and point to obstacles hampering further progress.

This paper presents a new way of looking at state-conserving one-dimensional cellular automata. Such cellular automata preserve the distribution of states, i.e., the number of cells in each state, throughout the entire evolution of the system. The tools introduced make it possible to fully characterize and enumerate all such cellular automata with radius one, regardless of the number of states. Surprisingly, it turns out that the number of state-conserving one-dimensional cellular automata with radius one and k states is very closely related to the number of labeled directed graphs with k vertices and not containing a directed path of length two.

Mathematical modelling is increasingly used to improve the design, understanding, and operation of water systems. Mechanistic models are dominant in the water sector, but are limited by the knowledge on which they are based. Incorporating a data-driven component allows for capturing missing dynamics from data, an approach commonly known as hybrid modelling. Here, we go one step further and leverage this data-driven component for model analysis. By applying Shapley value analysis, we can identify the dynamics missing in the mechanistic component. We demonstrate the strength of this method on two simulation studies, a simple Lotka-Volterra case and a complex activated sludge model case, successfully interpreting the missing dynamics. Moreover, we apply the Shapley value analysis to real data from a settling system, comparing and identifying the missing dynamics of different settler models. In all cases, the method gives valuable insights into the deficiencies of the mechanistic model. Shapley value analysis is of great value during modelling campaigns: identifying model weaknesses, aiding in model selection, and guiding decisions on future data collection efforts. It well deserves a spot in the modeller's toolbox.