Set Of Pairs Research Articles

On Some Characteristics of Generalized γ-Closure Spaces

In this paper, we study that a pointwise symmetric γ-isotonic (γIso), γ-closure (γCl) mapping is uniquely specified by the pairs of sets it separates. Then, we demonstrate that when the γCl mapping of the domain is -γIso and the γCl mapping of the co-domain is γIso and pointwise γ-symmetric (γsym), mappings that only separate already separated pairs of sets are γ -continuous.

A Novel Sulfatase for Acesulfame Degradation in Wastewater Treatment Plants as Evidenced from Shinella Strains.

The artificial sweetener acesulfame is a persistent pollutant in wastewater worldwide. So far, only a few bacterial isolates were recently found to degrade acesulfame efficiently. In Bosea and Chelatococcus strains, a Mn2+-dependent metallo-β-lactamase-type sulfatase and an amidase signature family enzyme catalyze acesulfame hydrolysis via acetoacetamide-N-sulfonate to acetoacetate. Here, we describe a new acesulfame sulfatase in Shinella strains isolated from wastewater treatment plants in Germany. Their genomes do not encode the Mn2+-dependent sulfatase. Instead, a formylglycine-dependent sulfatase gene was found, together with the acetoacetamide-N-sulfonate amidase gene on a plasmid shared by all known acesulfame-degrading Shinella strains. Heterologous expression, proteomics, and size exclusion chromatography corroborated the physiological function of the Shinella sulfatase in acesulfame hydrolysis. Since both acesulfame sulfatase types are absent in other bacterial genomes or metagenome-assembled genomes, we surveyed 73 tera base pairs of wastewater-associated metagenome raw data sets. Bosea/Chelatococcus sulfatase gene signatures were regularly found from 2013, particularly in North America, Europe, and East Asia, whereas Shinella sulfatase gene signatures were first detected in 2020. Moreover, signatures for the Shinella sulfatase and amidase genes co-occur only in six data sets from China, Finland, and Mexico, suggesting that the Shinella genes were enriched or introduced quite recently in wastewater treatment facilities.

Multilevel Proteomics Reveals Epigenetic Signatures in BCG-Mediated Macrophage Activation

The bacillus Calmette-Guérin BCG vaccine (Mycobacterium bovis) is primarily used to prevent tuberculosis (TB) infections but has wide-ranging immunogenic effects. One of its most notable properties is its ability to induce trained immunity, a memory-like response in innate immune cells such as macrophages. Through targeted analyses of well-established histone marks, prior research has shown that these changes are generated through epigenetic modification. Mass spectrometry-based proteomic approaches provide a way to globally profile various aspects of the proteome, providing data to further identify unexplored mechanisms of BCG-mediated immunomodulation. Here we use multi-level proteomics (total, histone, and phospho to identify networks and potential mechanisms that mediate BCG induced immunomodulation in macrophages. Histone-focused proteomics and total proteomics were performed at the University of Cape Town (data available via ProteomeXchange with identifier PXD051187), while phosphoproteomics data was retrieved from the ProteomeXchange Repository (identifier PXD013171). We identify several epigenetic mechanisms that may drive BCG-induced training phenotypes. Evidence across the proteomics and histone-focused proteomics data sets pair 6 epigenetic effectors (NuA4, NuRD, NSL, Sin3A, SIRT2, SIRT6) and their substrates.

Spatial difference analysis and driving factor diagnosis for regional water resources carrying capacity based on set pair analysis

Studying regional water resources carrying capacity (WRCC) is an important way to find out and solve regional water resources problems. Analyzing the spatial difference of WRCC and diagnosing its driving factors is the basis for the implementation of the water control policy named "spatial balance". This study selects evaluation indicators for WRCC from three aspects: water resources, social economy, and ecological environment. The weights of indicators were determined by fuzzy analytic hierarchy process based on accelerated genetic algorithm (FAHP-AGA), and an evaluation method for WRCC was constructed based on set pair analysis (SPA). On this basis, the spatial difference analysis of regional WRCC and its key driving factor diagnosis model was established, and the empirical study was carried out in Anhui Province as an example. The results show that from 2011 to 2020, the WRCC of Anhui Province was increasing, with the average increase of each city reaching more than 0.3. The spatial difference of WRCC decreased, and the Gini coefficient decreased from 0.16 to 0.08. The key driving factors leading to the spatial difference of WRCC in Anhui Province include water resources module, water consumption per 10,000 yuan of GDP, equilibrium degree of water use structure, per capita GDP, population density, percentage of forest cover, and amount of chemical fertilizer applied per unit of effective irrigated area. Compared with common WRCC evaluation models, this model improves the comparability of the evaluation results. In addition, this model can further analyze the influence of multiple factor interactions on the evaluation results based on the common single factor analysis. The driving factor diagnosis results can provide theoretical guidance for the formulation of regulation measures for regional WRCC and the implementation of the "spatial equilibrium" water control policy.

Decision-making techniques based on aggregation operators and similarity measures under q-rung orthopair hesitant fuzzy connection numbers and their application

The concept of q-rung orthopair hesitant fuzzy set represents an advancement and extension of hesitant fuzzy sets, encompassing both fuzzy sets and q-rung orthopair fuzzy sets. q-rung orthopair hesitant fuzzy set characterizes a set of membership and non-membership grades within the interval [0, 1], which enhances its adaptability compared to existing methods. This flexibility proves invaluable in providing more insightful data about various objects. The primary objective of this research is to introduce a decision-making technique in the context of q-RHF using the theory of set pair analysis (SPA). q-RHFS effectively handles ambiguous data by incorporating membership and non-membership grades, while the connection number (CN) based on SPA theory manages the intricacies of uncertainty and certainty structures by relying on "identity", "discrepancy" and "contrary" grades. Building on the relationship between q-RHFS and the connection number of set pair analysis, a comprehensive framework known as q-rung hesitant fuzzy connection number set (qHCNs) is developed. This model not only addresses uncertainty, but also offers valuable insights. Furthermore, this research introduces similarity measures derived from qHCN and examines their advantages through illustrative examples. Additionally, a novel approach to decision modeling utilizing these measures applied to medical diagnosis is also introduced. The application of this established model contributes to an effective approach and demonstrated its soundness and efficiency. In addition, a detailed comparative study is conducted with the existing models and advantages of proposed model. The research concludes with a summary of the authors' findings, highlighting the consistency and effectiveness of their work.

On the Ramsey numbers of daisies I

Abstract Daisies are a special type of hypergraph introduced by Bollobás, Leader and Malvenuto. An $r$ -daisy determined by a pair of disjoint sets $K$ and $M$ is the $(r+|K|)$ -uniform hypergraph $\{K\cup P\,{:}\, P\in M^{(r)}\}$ . Bollobás, Leader and Malvenuto initiated the study of Turán type density problems for daisies. This paper deals with Ramsey numbers of daisies, which are natural generalisations of classical Ramsey numbers. We discuss upper and lower bounds for the Ramsey number of $r$ -daisies and also for special cases where the size of the kernel is bounded.

Planar #CSP Equality Corresponds to Quantum Isomorphism – A Holant Viewpoint

Recently, Mančinska and Roberson proved that two graphs G and \(G^{\prime }\) are quantum isomorphic if and only if they admit the same number of homomorphisms from all planar graphs. We extend this result to planar #CSP with any pair of sets \(\mathcal {F}\) and \(\mathcal {F}^{\prime }\) of real-valued, arbitrary-arity constraint functions. Graph homomorphism is the special case, in which each of \(\mathcal {F}\) and \(\mathcal {F}^{\prime }\) contains a single symmetric 0-1-valued binary constraint function. Our treatment uses the framework of planar Holant problems. To prove that quantum isomorphic constraint function sets give the same value on any planar #CSP instance, we apply a novel form of holographic transformation of Valiant, using the quantum permutation matrix \(\mathcal {U}\) defining the quantum isomorphism. Due to the noncommutativity of \(\mathcal {U}\) ’s entries, it turns out that this form of holographic transformation is only applicable to planar Holant. To prove the converse, we introduce the quantum automorphism group \(Qut(\mathcal {F})\) of a set \(\mathcal {F}\) of constraint functions/tensors and characterize the intertwiners of \(Qut(\mathcal {F})\) as the signature matrices of planar \(\text{Holant}{\mathcal {F}\,|\,\mathcal {EQ})\) quantum gadgets. Then, we define a new notion of (projective) connectivity for constraint functions and reduce their arity while preserving their inclusion in the original intertwiner space. Finally, to address the challenges posed by generalizing from 0-1 valued to real-valued constraint functions, we adapt a technique of Lovász in the classical setting for isomorphisms of real-weighted graphs to the setting of quantum isomorphisms.

Research on the Socio-Spatial Resilience Evaluation and Evolution of the Central Area of Beijing in Transitional China

In recent decades, the increasing threats of global climate change, natural disasters, and epidemics have brought extensive attention to resilience theory. However, most studies focus on the physical aspects of cities, overlooking the significance of the social perspective. This study addresses this gap by using social areas as the core spatial unit for analysis. By constructing a scientific indicator system and employing the set pair analysis method, this study comprehensively evaluates the multidimensional resilience levels of Beijing’s central area during its transitional period (1990–2020). The findings reveal that socio-spatial divisions, which emphasize the network structure of social relations and the dynamic changes in social spaces, are more suitable than traditional administrative divisions as fundamental units for resilience assessment. During Beijing’s transitional period, the comprehensive resilience of the central area and all social areas steadily increased, although social capital resilience faced the challenges of loss and slow recovery. Social areas with a unique internal connection, such as those based on ethnicity, exhibited more positive social capital resilience development. Additionally, social areas with lower population diversity and greater homogeneity tended to have higher comprehensive resilience and a more positive trend in social capital resilience development, whereas highly heterogeneous social areas faced significant constraints in resilience development. These findings may provide valuable insights for cities and communities to enhance their capacity to address future uncertainties and assist policymakers in making informed governance decisions.

Vertical Spatial Differentiation and Influencing Factors of Rural Livelihood Resilience: Evidence from the Mountainous Areas of Southwest China

Rural livelihood resilience (RLR) is significant for the sustainability of rural areas, farmers and agriculture. This research takes the mountainous areas of Southwest China as the study areas and integrates the buffer, adjustment and renewal capabilities to construct a RLR analysis framework and evaluation indicator system. The RLR of 234 sample counties was evaluated using set pair analysis, and the influencing factors of RLR were investigated using Geodetector. The aim is to scientifically analyze the vertical spatial differentiation and influencing factors of RLR and fully explore the risk-resistant potential of rural livelihood systems in mountainous areas. The results show that (1) From 2000 to 2020, RLR increases significantly, but the level is still low, and its structure shows a primary pattern of “buffer capability > adjustment capability > renewal capability”. (2) There is no significant negative correlation between RLR and terrain gradients, especially in the middle and low mountains. RLR in high mountainous areas is significantly lower than in low and medium mountainous areas, but the gap is narrowing. There are no significant gaps in RLR and various capabilities between low and medium mountain areas. (3) Economic development, non-agricultural industries and grassroots autonomous organizations are essential determinants for RLR. Economic development, grassroots autonomous organizations and transportation conditions are more important in low and medium mountain areas, while non-agricultural industries and medical conditions contribute more to high mountainous areas. (4) To enhance the RLR, policy recommendations should place a strong emphasis on extending the agricultural industry chain, improving rural production and living infrastructure and strengthening the supply of high-quality social public services. The findings can provide a scientific basis for governments to implement rural revitalization strategies and improve farmers’ well-being, as well as practical guidance for enhancing the risk resistance ability of underdeveloped mountainous rural areas.

Semi‐partial Quadratic Subtraction Set Pair Potential (SQSSPP) method for regional drought risk assessment: A case study in Suzhou City, China

AbstractDrought risk assessment plays a crucial role in effective drought management. However, it is often challenging due to the intricate relationships among various indicators and the lack of practical guidance. This study presents a drought risk assessment model developed using the Semi‐partial Quadratic Subtraction Set Pair Potential (SQSSPP) method, which is derived from the theory of set pair analysis. The indicator system comprises 21 indicators divided into four subsystems. The SQSSPP method utilizes uncertainty information in the overall development trend of regional drought risk states by extracting connection numbers from the Subtraction Set Pair Potential (SSPP), improving the reliability of evaluation results. The SQSSPP method is validated through a case study of Suzhou City, China, from 2007 to 2017. Three grades are used to evaluate comprehensive drought risk. The result shows an overall decreasing trend over time, with a level III risk in 2010 and consistently at level II from 2011 to 2017. Indicators in the hazard and resilience subsystems are the primary factors influencing drought risk in the Suzhou City. Specific indicators requiring emphasis for improvement are identified, including arable land rate, agricultural population ratio, reservoir regulation rate, current water supply capacity, and irrigation index. The SQSSPP method not only provides targeted drought risk assessment but also provides valuable guidance for future water resource management. While the study focuses on Suzhou City, the proposed approach is applicable to broader‐scale risk management evaluations and practices.

Best Scanline Determination of Pushbroom Images for a Direct Object to Image Space Transformation Using Multilayer Perceptron

Working with pushbroom imagery in photogrammetry and remote sensing presents a fundamental challenge in object-to-image space transformation. For this transformation, accurate estimation of Exterior Orientation Parameters (EOPs) for each scanline is required. To tackle this challenge, Best Scanline Search or Determination (BSS/BSD) methods have been developed. However, the current BSS/BSD methods are not efficient for real-time applications due to their complex procedures and interpolations. This paper introduces a new non-iterative BSD method specifically designed for line-type pushbroom images. The method involves simulating a pair of sets of points, Simulated Control Points (SCOPs), and Simulated Check Points (SCPs), to train and test a Multilayer Perceptron (MLP) model. The model establishes a strong relationship between object and image spaces, enabling a direct transformation and determination of best scanlines. This proposed method does not rely on the Collinearity Equation (CE) or iterative search. After training, the MLP model is applied to the SCPs for accuracy assessment. The proposed method is tested on ten images with diverse landscapes captured by eight sensors, exploiting five million SCPs per image for statistical assessments. The Root Mean Square Error (RMSE) values range between 0.001 and 0.015 pixels across ten images, demonstrating the capability of achieving the desired sub-pixel accuracy within a few seconds. The proposed method is compared with conventional and state-of-the-art BSS/BSD methods, indicating its higher applicability regarding accuracy and computational efficiency. These results position the proposed BSD method as a practical solution for transforming object-to-image space, especially for real-time applications.

Comprehensive evaluation and optimal management of extreme disaster risk in Chinese urban agglomerations by integrating resilience risk elements and set pair analysis

This study comprehensively assesses the extreme disaster risk faced by Chinese urban agglomerations and optimizes disaster risk management strategies to enhance their disaster resilience and sustainable development. The focus is specifically on droughts, floods, and earthquakes. The integration of resilience risk elements and set pair analysis (SPA) is employed to obtain risk assessment results for different urban agglomerations, including hazard, exposure, vulnerability, and disaster prevention and mitigation capabilities. The study explores the contributions of important indicators, such as exposure, vulnerability, and disaster prevention and mitigation capabilities, in disaster risk assessment, as well as their performance in various risk-prone urban areas. Comparative analysis of the assessment results for different urban agglomerations under various disaster types reveals varying levels of risk in droughts, floods, and earthquakes across different regions. Some areas exhibit higher hazard, exposure, or vulnerability levels, necessitating strengthened disaster prevention and mitigation measures. Regions with high exposure, low vulnerability, and strong disaster prevention and mitigation capabilities may face lower earthquake disaster risk, while regions with low exposure, high vulnerability, and weak disaster prevention and mitigation capabilities may face higher earthquake disaster risk. Moreover, the Comprehensive SPA model and Interval-valued SPA model outperform traditional SPA methods in assessing the existing flood risk level in Chinese urban agglomerations. The integrated model plays a significant role in predicting earthquake disasters, demonstrating the best predictive performance. This study provides essential reference data for urban disaster prevention and mitigation efforts, aiming to enhance urban resilience and disaster resilience capabilities.

An Improved Algorithm of Image Edge Detection Based on the Degree Connection Situation

Aiming at the defect of the poor ability to suppress the noise of the algorithm of image edge detection, as well as too much sensitive to the noise, an improved algorithm of image edge detection based on SPA (set pair analysis) by combining trend relationship of the degree connection situation with the algorithm of half-neighborhood adaptive image edge pick-up is presented in this paper. The core of the algorithm is first to detect the most possible direction of the edge by using the biggest value of Degree Connection Situation--c/a, and then calculate absolute value of the D-value between the average value of three points and the average value of five points and the standard deviation value of all the points value in the 8-neighborhood, at last, decide whether the center-point is on the edge according to the threshold value of the standard deviation value. The result of simulation indicates that, without any processing to the image, the improved algorithm is not only accurate but also legible in object brim pick-up, compared with the algorithm in literature; furthermore, the noise is greatly suppressed by using it.

Dissimilarity measures based on the application of Hamming distance to generate controlled probabilistic tests

Objectives. The problem of constructing dissimilarity measures based on the application of the Hamming distance to generate controlled random binary test sets is solved. The main goal of this article is to develop methods for determining the Hamming distance for the achievability of finding the difference between test sets when they coincide according to estimates of other difference measures.Methods. Based on the Hamming distance used in the theory and practice of generating controlled random tests, new dissimilarity measures are proposed for two binary test n-bit patterns. The basis of the proposed dissimilarity measures is the formation of sets of Hamming distances for initial sets, represented as sequences of characters from different alphabets.Results. The indistinguishability of pairs of binary test sets Ti and Tk is shown using a dissimilarity measure based on the application of the Hamming distance. In this case, different pairs of sets may have identical Hamming distance values. To construct new measures of difference, the original binary test sequences are represented as sequences consisting of characters belonging to different alphabets. Various strategies are proposed for applying new measures of difference based on the use of one of three rules in generating controlled probability tests. It is shown that in all three cases of dissimilarity measures, only the first few of their components areinformative, as a rule, no more than two or three. Accordingly, the computational complexity for all three options is comparable and does not exceed 3n comparison operations. The experimental studies carried out confirm the effectiveness of the proposed dissimilarity measures and their low computational complexity.Conclusion. The proposed dissimilarity measures expand the possibilities of generating test sets when forming controlled random tests. It is shown that test sets that are indistinguishable when using the Hamming distance as a dissimilarity measure have different values of the proposed dissimilarity measures, which makes it possible to more accurately classify randomly generated sets that are candidate test cases

Shadowed set approximations of L-fuzzy sets

Pedrycz shadowed sets are three-way approximations of fuzzy sets by transforming the infinite levels of fuzzy set membership grades in the unit interval [0,1] into three levels. The three levels represent qualitatively the sets of the white, grey, and black members of a shadowed set. In this paper, we generalize the notion of shadowed sets to the case of L-fuzzy sets by making three new contributions. First, we consider two representations of a shadowed set. One is a three-valued L-fuzzy set and the other is three pairwise disjoint sets. Second, we introduce two methods for constructing a shadowed set. One divides a finite lattice based on the notion of a pair of a set of designated core membership grades and a set of designated null membership grades. The other uses a pair of threshold sets, which generalizes the method that uses a pair of thresholds. We study formal properties of the two methods and show that they are equivalent. Finally, based on a distance function on a lattice, we present a simple method to build the sets of designated core and null membership grades.

A novel ranking approach for identifying crucial spreaders in complex networks based on Tanimoto Correlation

The identification and rank of crucial spreaders aim to survey the diffusion capability, which has a significant impact on controlling information spread in networks. However, most of the findings neglect the fused information of the structural hole and neighbors within two orders. In addition, they fail to focus on the effect brought by the association strength between a pair of different neighborhood sets. To solve these issues, in this work, we design a novel semi-local ranking algorithm for achieving better recognition effects, referred to as the Extended Tanimoto Correlation (ETC). We first construct a topological structure of neighborhood sets Cluster, and define HierarchyVectorofCluster based on a novel layered approach IKsD. Considering the structural hole, Tanimoto Correlation (TC) is presented to contribute to measuring the association strength between different clusters. Additionally, we explicitly extend the Tanimoto Correlation metric on semi-local information to calculate each spreader’s influence score. Simulation experiments employ capability indicators and correctness metrics to apply in various networks. Results demonstrate that our method outperforms state-of-the-art algorithms in identifying and ranking effects for good spreading influence.

Multiple attribute decision making based on score function of q-connection numbers, q-CNPWG aggregation operator of q-connection numbers, and set pair analysis theory in the environments of q-rung orthopair fuzzy numbers

This paper proposes a new multiple attribute decision making (MADM) method in the environments of q-rung orthopair fuzzy numbers (q-ROFNs) based on the proposed score function of q-connection numbers (q-CNs), the proposed q-connection number power weighted geometric (q-CNPWG) aggregation operator (AO) of q-CNs, and the set pair analysis (SPA) theory. Firstly, we propose a score function of q-CNs based on the SPA theory, where we also present some properties of the proposed score function of q-CNs. Then, we propose the q-CNPWG AO for aggregating q-CNs, where we also present some properties of the proposed q-CNPWG AO of q-CNs. Finally, we propose a new MADM method in the environments of q-ROFNs based on the proposed score function of q-CNs, the proposed q-CNPWG AO of q-CNs, and the SPA theory. The proposed MADM method can overcome the drawbacks of existing MADM methods in the environments of q-ROFNs, where they cannot distinguish preference orders of alternatives in some situations. The proposed MADM method is very useful for MADM in the environments of q-ROFNs.

Regret-based three-way decisions with set pair analysis in incomplete information systems

Set pair analysis is a valuable tool for managing uncertain systems and can effectively handle missing information in the decision-making process. In addition, regret theory can objectively describe the impact of decision-maker psychology on decision-making. However, traditional decision-making methods rarely combine set pair analysis and regret theory to discuss decision problems. Thus, this article aims to integrate regret theory into the three-way decision theory based on set pair analysis, presenting a novel approach to address multi-attribute decision-making problems in real life. Specifically, we first propose a data-driven approach based on set pair analysis to determine attribute weights. Then, a similarity relationship is established based on the weighted distance to calculate conditional probability. Meanwhile, the average value of regret and joy under each attribute is selected as a reference point to determine the relative utility function using regret theory. Subsequently, we develop a new three-way decision method in incomplete information systems and apply it to solve practical problems. Finally, the effectiveness and superiority of our method are demonstrated by case analysis and comparison. We also conduct sensitivity analysis to examine the stability of the new method.

Multi-apodization with cross-correlation combined with generalized sidelobe canceller applied to ultrasound imaging.

Beamforming is vital for medical ultrasound imaging systems. The generalized sidelobe canceller (GSC) beamforming can improve the image quality of lateral resolution, but its performance improvement in contrast and robustness is limited. This paper proposes an improved generalized sidelobe canceller algorithm based on multi-apodization with cross-correlation (MAXB-IGSC), which aims to improve the contrast and robustness of ultrasound imaging while maintaining the high image resolution and background speckle quality of GSC. The proposed MAXB-IGSC uses multiple pairs of complementary received apodization functions to process the echo data individually to obtain multiple pairs of data sets. The average of their normalized cross-correlation coefficients is then calculated and utilized to determine the adaptive subarray length of the GSC covariance matrix and weights the output of the improved GSC. The MAXB-IGSC improves the contrast ratio (CR) by 171.18% in anechoic cyst simulation and by 91.23%/130.97%/171.76% in geabr_0 (a dataset from the University of Michigan) experiment compared with GSC, respectively. Furthermore, MAXB-IGSC exhibits significant noise immunity, which greatly improves the robustness of the imaging. The technology also maintains the brightness and uniformity of the background speckle. The proposed MAXB-IGSC has potential for obtaining high-quality ultrasound images in clinical applications.

On the lattice of fuzzy rough sets

By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize the pairs of fuzzy sets that form fuzzy rough sets w.r.t. a t-similarity relation θ on U, for certain t-norms and implicators. If U is finite or the range of θ and of the fuzzy sets is a fixed finite chain, we establish conditions under which fuzzy rough sets form lattices. We show that this is the case for the min t-norm and any S-implicator defined by an involutive negator and the max co-norm.