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Prior clustering approaches of soccer players have employed a variety of methods based on various data categories, but none of them have focused on clustering by career paths characterized through a time series analysis of yearly performance quality. Therefore, this study aims to propose a methodology how a career path can be represented as a time series of a player's seasonal qualities and then be clustered with players that have a similar career path. The underlying data focuses on soccer players from the five largest European soccer nations (Big-5). This allows for the identification of different types of career paths of players and the investigation of significant disparities between career paths among the Big-5 nations. In line with our proposed methodological approach, we identified and interpreted 13 different clusters of player career paths. These range from the cluster with the highest player quality scores to the pattern comprising players with the weakest scores. Further, the detected clusters show significant differences regarding variables of soccer players' early career phase in adolescence (e.g., age of debut in professional soccer, years spent in a youth academy). The presented approach might represent a first step for stakeholders in soccer to get an objective insight in players' career by utilizing mainly freely available data sources. [ABSTRACT FROM AUTHOR]

Advanced footwear technology featuring stack heights higher than 30 mm has been proven to improve running economy in elite and recreational runners. While it is understood that the physiological benefit is highly individual, the individual biomechanical response to different stack heights remains unclear. Thirty-one runners performed running trials with three different shoe conditions of 25 mm, 35 mm, and 45 mm stack height on an outdoor running course wearing a STRYD sensor. The STRYD running variables for each participant were normalized to the 25 mm shoe condition and used to cluster participants into three distinct groups. Each cluster showed unique running patterns, with leg spring stiffness and vertical oscillation contributing most to the variance. No significant differences were found between clusters in terms of body height, body weight, leg length, and running speed. This study indicates that runners change running patterns individually when running with footwear featuring different stack heights. Clustering these patterns can help understand subgroups of runners and potentially support running shoe recommendations. [ABSTRACT FROM AUTHOR]

We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type. This completes the classification of all mutation-finite cluster algebras started in [Felikson, Shapiro, and Tumarkin, J. Eur. Math. Soc. 14 (2012)]. [ABSTRACT FROM AUTHOR]

Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group of the cluster integrable system. This cluster modular group was recently characterized by the first author and Inchiostro. There exist some discrete integrable dynamics that make use of non-local transformations associated with geometric \(R\)-matrices. In this article we characterize the generalized cluster modular group - which includes both local and non-local transformations - in terms of extended affine symmetric groups. We also describe the action of the generalized cluster modular group on the spectral data associated with cluster integrable systems.Mathematics Subject Classifications: 82B23, 13F60, 14H70, 20B35Keywords: Bipartite dimer model, cluster algebras, geometric \(R\)-matrices, discrete integrable systems, extended affine symmetric group

Deep clustering is an approach that uses deep learning to cluster data, since it involves training a neural network model to become familiar with a data representation that is suitable for clustering. Deep clustering has been applied to a wide range of data types, including images, texts, time series and has the advantage of being able to automatically learn features from the data, which can be more effective than using hand-crafted features. It is also able to handle high-dimensional data, such as time series with many variables, which can be challenging for traditional clustering techniques. In this paper, we introduce a novel deep neural network type to improve the performance of the auto-encoder part by ignoring the unnecessary extra-noises and labelling the input data. Our approach is helpful when just a limited amount of labelled data is available, but labelling a big amount of data would be costly or time-consuming. It also applies for the data in high-dimensional and difficult to define a good set of features for clustering. [ABSTRACT FROM AUTHOR]

We study the reflections of locally free Caldero–Chapoton functions associated to representations of Geiß–Leclerc–Schröer’s quivers with relations for symmetrizable Cartan matrices. We prove that for rank 2 cluster algebras, non-initial cluster variables are expressed as locally free Caldero–Chapoton functions of locally free indecomposable rigid representations. Our method gives rise to a new proof of the locally free Caldero–Chapoton formulas obtained by Geiß–Leclerc–Schröer in Dynkin cases. For general acyclic skew-symmetrizable cluster algebras, we prove the formula for any non-initial cluster variable obtained by almost sink and source mutations. [ABSTRACT FROM AUTHOR]

It is known that many (upper) cluster algebras possess different kinds of good bases which contain the cluster monomials and are parametrized by the tropical points of cluster Poisson varieties. For a large class of upper cluster algebras (injective-reachable ones with full rank coefficients), we describe all of their bases with these properties. Moreover, we show the existence of the generic basis for them. In addition, we prove that Bridgeland's representation-theoretic formula is effective for their theta functions (weak genteelness). Our results apply to (almost) all known cluster algebras arising from representation theory or higher Teichmüller theory, including quantum affine algebras, unipotent cells, double Bruhat cells, skein algebras over surfaces, where we change the coefficients if necessary so that the full rank assumption holds. [ABSTRACT FROM AUTHOR]

The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra. [ABSTRACT FROM AUTHOR]

Associated to a convex integral polygon N is a cluster integrable system XN constructed from the dimer model. We compute the group GN of symmetries of XN , called the (2-2) cluster modular group, showing that it is a certain abelian group conjectured by Fock and Marshakov. Combinatorially, non-torsion elements of GN are ways of shuffling the underlying bipartite graph, generalizing domino-shuffling. Algebro-geometrically, GN is a subgroup of the Picard group of a certain algebraic surface associated to N. [ABSTRACT FROM AUTHOR]

We study Newton polytopes for cluster variables in cluster algebras $\mathcal{A}(\Sigma)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster variable can be written as a Laurent polynomial in the cluster variables of the initial seed $\Sigma$. The cluster variable Newton polytopes are the Newton polytopes of these Laurent polynomials. We show that if $\Sigma$ has principal coefficients or boundary frozen variables, then all cluster variable Newton polytopes are saturated. We also characterize when these Newton polytopes are empty; that is, when they have no non-vertex lattice points.Mathematics Subject Classifications: 13F60, 52B20Keywords: Cluster algebras, Newton polytopes, snake graphs

The task of remote sensing image object detection in low latency scenes is of great research significance. To address the problem that the current high‐precision object detection algorithm based on a feature pyramid network is slow due to a large number of parameters and complicated computation, a fast remote sensing image object detection method based on a Single‐scale Feature Transformation Network (SFTN) is proposed. Firstly, based on the single‐scale remote sensing image features, the new channel features are quickly generated by a linear transformation of the original features and convolution kernel clustering optimization using cosine similarity; secondly, in order to obtain multi‐scale receptive fields, a parallel residual hole convolution module is designed to cover multi‐category remote sensing object scales on the feature map; finally, angle variables are introduced and optimized using angle similarity to effectively improve the object orientation accuracy. The experimental results on different datasets show that the method in this paper improves the detection speed rapidly while ensuring the accuracy of remote sensing image object detection, which is better than many remote sensing image object detection methods. The results demonstrate the reliability and robustness of the method. [ABSTRACT FROM AUTHOR]

India has targeted elimination of lymphatic filariasis (LF) through mass drug administration (MDA) by 2027. Mapping of LF endemic areas is a priority for implementation of MDA. Current national LF remapping tool for unsurveyed/uncertain districts, have many limitations. The WHO has recommended a sensitive and rapid remapping protocol (Mini-TAS), that needs validation in Indian setting. Hence, in the present study a comparative assessment of these two protocols (national protocol vs Mini-TAS) was undertaken in two non-MDA districts of Odisha, with unknown filarial endemicity but reporting chronic cases. Purposive sampling was done in five top sites based on filarial case count as per the national protocol. Random 30 cluster survey was done by conducting school based Mini-TAS, Microfilariae (Mf) survey among adults (>10 years) in villages/wards with schools and Molecular Xenomonitoring (MX) of infection in vectors. Costing by activity and items of the surveys was acomplished using itemized cost menu. In Kalahandi, one of the five purposive sampling sites showed Mf prevalence above threshold (> 1%). But except Mini-TAS neither MX nor house-hold Mf survey among adults could detect the infection above the threshold. While in Balangir, Mf prevalence in all purposive sampling sites,Mini-TAS, Mf prevalence among adult and MX were above the respective thresholds confirming endemicity of LF in the district. The per sample cost of purposive sampling for Mf was the lowest INR 41, followed by adult Mf sampling INR 93. Mini-TAS and MX were expensive with INR 659 and 812 respectively. The study demonstrates that though all the sampling methods could detect filarial infection above the threshold in high-risk areas, Mini-TAS could only detect infection in low-risk areas. Therefore, in the national programme Mini-TAS can be used as a decision-making tool to determine whether to exclude/ include a district having uncertain endemicity for MDA. [ABSTRACT FROM AUTHOR]

Scattering amplitudes in planar N = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras. Starting from the Plücker ideal, we describe how the polynomial cluster variables are encoded in non-prime initial ideals associated to certain maximal cones of the positive tropical fan. Following [1] we show that extending the Plücker ideal by such variables leads to a Gröbner fan with a single maximal Gröbner cone spanned by the positive tropical rays. The associated initial ideal encodes the compatibility relations among the full set of cluster variables. Thus we find that the Gröbner structure naturally encodes both the symbol alphabet and the cluster adjacency relations exhibited by scattering amplitudes without invoking the cluster algebra at all. As a potential application of these ideas we then examine the kinematic ideal associated to non-dual conformal massless scattering written in terms of spinor helicity variables. For five-particle scattering we find that the ideal can be identified with the Plücker ideal for Gr(3, 6) and the corresponding tropical fan contains a number of non-prime ideals which encode all additional letters of the two-loop pentagon function alphabet present in various calculations of massless five-point finite remainders. [ABSTRACT FROM AUTHOR]

The HIV-1 entry inhibitor temsavir prevents the viral receptor CD4 (cluster of differentiation 4) from interacting with the envelope glycoprotein (Env) and blocks its conformational changes. To do this, temsavir relies on the presence of a residue with small side chain at position 375 in Env and is unable to neutralize viral strains like CRF01_AE carrying His375. Here we investigate the mechanism of temsavir resistance and show that residue 375 is not the sole determinant of resistance. At least six additional residues within the gp120 inner domain layers, including five distant from the drug-binding pocket, contribute to resistance. A detailed structure-function analysis using engineered viruses and soluble trimer variants reveals that the molecular basis of resistance is mediated by crosstalk between His375 and the inner domain layers. Furthermore, our data confirm that temsavir can adjust its binding mode to accommodate changes in Env conformation, a property that likely contributes to its broad antiviral activity. The HIV-1 entry inhibitor temsavir prevents the interaction of the envelope glycoprotein with its cellular receptor. Here, authors apply CryoEM to show that HIV-1 clade AE resistance to temsavir is a combination of the residue at position 375 (His) and mutations in the gp120 mobile layers. Mutation of His375 to Ser/Thr and reversion of the layer mutations are required to restore temsavir sensitivity. [ABSTRACT FROM AUTHOR]

The field of qualitative research is robust and nuanced. While there are foundational standards to which all researchers hold, many intricacies regarding theory, methods, and analysis are influenced by differing training and expectations. These latter components are themselves often influenced by the norms of culture and geographic location. Researchers can learn much from international inquiry. In this introduction to the special issue of The Qualitative Report, “International Scholarship for Qualitative Theory, Methods, and Analysis,” we briefly consider the benefits and challenges that come from international scholarship. We then introduce the articles in the issue and their connection with the 2023 World Conference on Qualitative Research. [ABSTRACT FROM AUTHOR]

In the Categorical Clustering problem, we are given a set of vectors (matrix) A = { a 1 , ... , a n } over Σ m , where Σ is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. Fomin, Golovach, and Panolan [ICALP 2018] proved that the problem is fixed-parameter tractable for the binary case Σ = { 0 , 1 }. We extend this algorithmic result to a popular capacitated clustering model, where in addition the sizes of the clusters are lower and upper bounded by integer parameters p and q , respectively. Our main theorem is that the problem is solvable in time 2 O (B log ⁡ B) | Σ | B ⋅ (m n) O (1). [ABSTRACT FROM AUTHOR]

In 1975, Symons [[5]] introduced a subsemigroup of HT ht , defined as HT ht , for a nonempty subset I Y i of I X i , determining all its automorphisms. The first paper [[21]] introduces a construction of a new graph associated with a semihypergroup, using the fundamental relation HT ht . In particular, it is shown that the Cayley graphs generated by transposition trees on the set HT ht are HT ht -extendable and their extendability number is HT ht for any integer HT ht . Connections between algebraic structure theory and graph theory have been established in order to solve open problems in one theory with the help of the tools existing in the other, emphasizing the remarkable properties of one theory with techniques involving the second. [Extracted from the article]

Few-shot Relation Classification identifies the relation between target entity pairs in unstructured natural language texts by training on a small number of labeled samples. Recent prototype network-based studies have focused on enhancing the prototype representation capability of models by incorporating external knowledge. However, the majority of these works constrain the representation of class prototypes implicitly through complex network structures, such as multi-attention mechanisms, graph neural networks, and contrastive learning, which constrict the model's ability to generalize. In addition, most models with triplet loss disregard intra-class compactness during model training, thereby limiting the model's ability to handle outlier samples with low semantic similarity. Therefore, this paper proposes a non-weighted prototype enhancement module that uses the feature-level similarity between prototypes and relation information as a gate to filter and complete features. Meanwhile, we design a class cluster loss that samples difficult positive and negative samples and explicitly constrains both intra-class compactness and inter-class separability to learn a metric space with high discriminability. Extensive experiments were done on the publicly available dataset FewRel 1.0 and 2.0, and the results show the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Since the late 20th century, Engineering Education Research (EER) has been expanding globally as a field, although its identity varies across institutions and countries around the world. This diversity in how EER is experienced across contexts impacts how capability is developed, including identities, knowledge, practices, agendas, funding, and pathways. The theme of 'Engineering Education Research Capability Development' was explored in papers, presentations, and workshops throughout the jointly held 2021 Research in Engineering Education Symposium and Australasian Association for Engineering Education conference. This special issue presents a continuation of that theme. The papers collectively contribute to expanding global understanding of the field, with implications for future capacity building efforts in engineering education practice and research. [ABSTRACT FROM AUTHOR]

The batch clustering algorithm for classification application requires the initial parameters and also has a drifting phenomenon for the stochastic process. The initial parameters are critical for the clustering to converge to the partial optimum. The drifting phenomenon in original batch clustering still has space to be improved thus to speed up the convergence based on the initial parameters. This paper proposes an unsupervised clustering method by addressing these two issues. Firstly, the estimation method for the initial parameters has been given in preliminary with a hierarchical manner of principal component analysis (PCA). The nonlinear parameters have been estimated based on a mathematical connection between PCA and clusters membership. With initial parameters, the drifting issue is addressed by combing the gradient descent and the batch clustering on an auxiliary objective to refine the initial parameters. The efficiency of the clustering process is proved based on the relationship between two quadratic functions followed by a justification. In addition, the effectiveness of the proposed method has been validated with the statistical F measure in classification application. The validation results show that the efficiency of the proposed gradient descent batch clustering has been improved significantly with trade-off to the accuracy in comparison of the original algorithms under the mean squared error (MSE) criterion. [ABSTRACT FROM AUTHOR]

Ulam's spiral reveals patterns in the prime numbers by presenting positive integers in a right-angled whorl. The classic spatial prisoner's dilemma (PD) reveals pathways to cooperation by presenting a model of agents interacting on a grid. This paper brings these tools together via a deterministic spatial PD model that distributes cooperators at the prime-numbered locations of Ulam's spiral. The model focuses on a narrow boundary game variant of the PD for ease of comparison with early studies of the spatial PD. Despite constituting an initially small portion of the population, cooperators arranged in Ulam's spiral always grow to dominance when (i) the payoff to free-riding is less than or equal to 8/6 (≈1.33) times the payoff to mutual cooperation and (ii) grid size equals or exceeds 23 × 23. As in any spatial PD model, particular formations of cooperators spur this growth and here these formations draw attention to rare configurations in Ulam's spiral. [ABSTRACT FROM AUTHOR]

We notice that the famous pentagon identity for quantum dilogarithm functions and the five-term relation for certain operators related to Macdonald polynomials discovered by Garsia and Mellit can both be understood as specific cases of a general "master pentagon identity" for group-like elements in the Ding-Iohara-Miki (or quantum toroidal, or elliptic Hall) algebra. We prove this curious identity and discuss its implications. [ABSTRACT FROM AUTHOR]

We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in N = 4 super Yang-Mills theory. In particular, we conjecture that, given a maximal cut of a loop amplitude, Landau singularities and poles of each Yangian invariant appearing in any representation of the corresponding leading singularities can be found together in a cluster. We check these adjacencies for all one-loop amplitudes up to 9 points. Along the way, we also prove that all (rational) N²MHV Yangian invariants are cluster adjacent, confirming original conjectures. [ABSTRACT FROM AUTHOR]

The field of computer science, like its sub-field of cyber threat modelling, is rapidly evolving. The prerequisites for key changes can be summarized as follows: cyber threats are evolving; there are leaks of special services tools; agile development methodology is being introduced everywhere; the boundaries of the object of protection are blurred; the scope of application of artificial intelligence is expanding; potentially vulnerable API integrations are increasingly being used. These factors lead to the fact that the processes of analysis of cyber threats, analysis of protective measures, generalization of data, and development of protective tools should now be considered continuous, not discrete. At the same time, the cost of cybersecurity increases like an avalanche in an attempt to avoid reputational and information losses. The only way to avoid this tendency is to apply a rational, scientific, accurate method of cognition to these processes. Thus, the creation of mathematical models of processes in the field of cybersecurity is now more relevant than ever. The article is devoted to the investigation of the process of the influence of an active viral cyber threat on a high-availability cluster in the paradigm of the provisions of the theory of Markov processes, graph theory and the theory of mathematical analysis. The main contribution of the research is a formalized computationally efficient method of approximate estimation of the average number of affected elements of the target high-availability cluster under the influence of an active viral cyber threat. Also, a criterion that allows estimating the trend of the quantitative parameter of the metric of the model of the studied process at medium and long time intervals is proposed. To obtain the declared scientific result, the authors: - formulated a Markov model of the process of the influence of an active viral cyber threat on a high availability cluster; - substantiated a compact metric for accurate assessment of the average number of cluster elements affected by an active viral cyber threat at any time; - formulated a computationally efficient method of approximate estimation of the parameter of the mentioned metric for the model of the target studied process; - proposed a criterion that allows researchers to evaluate the trend of the parameter of the mentioned metric for the model of the target researched process at medium and long intervals of time. The adequacy of the formulated method has been proven empirically. [ABSTRACT FROM AUTHOR]

We extend recent work by Howie, Mathews and Purcell to simplify the calculation of A-polynomials for any family of hyperbolic knots related by twisting. The main result follows from the observation that equations defining the deformation variety that correspond to the twisting are reminiscent of exchange relations in a cluster algebra. We prove two additional results with analogues in the context of cluster algebras: the Laurent phenomenon, and intersection numbers appearing as exponents in the denominator. We demonstrate our results on the twist knots, and on a family of twisted torus knots for which A-polynomials have not previously been calculated. [ABSTRACT FROM AUTHOR]

We introduce an analogue of the classical Markov equation that involves dual numbers a +αε with ε² = 0. This equation characterizes the "shadow Markov numbers" recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra mutations. [ABSTRACT FROM AUTHOR]

In (2019), Rietsch and Williams relate cluster structures and mirror symmetry for type A Grassmannians Gr (k , n) , and use this interaction to construct Newton-Okounkov bodies and associated toric degenerations. In this article we define a cluster seed for the Lagrangian Grassmannian, and prove that the associated Newton-Okounkov body agrees up to unimodular equivalence with a polytope obtained from the superpotential defined by Pech and Rietsch on the mirror Orthogonal Grassmannian in Pech and Rietsch (2013). [ABSTRACT FROM AUTHOR]

We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrisable matrix has a geometric realisation by reflections. We also explore the structure of acyclic representatives in finite mutation classes and their relations to acute-angled simplicial domains in the corresponding reflection groups. [ABSTRACT FROM AUTHOR]

• Cluster energy-saving optimization is described as two MILP problems by two different variable definitions. • The switching cost of servers is considered in the two MILP problems to prevent server switching jitter. • A variable division method is proposed to transform the MINLP problem into an MILP problem. • We present the detailed experimental results from several perspectives. The issue of how to dynamically optimize the deployment of an application server cluster according to the changing load to reduce energy consumption is an important problem that must be urgently solved. In this paper, we propose an energy-saving optimization strategy for application server clusters, whose optimization content includes the on/off state, CPU frequency, and load size of each server. Compared with existing research, our strategy is not only more accurate in power and load models but also considers the switching cost of servers to avoid server switching jitter. The strategy includes two schemes, which both formulate the cluster energy-saving optimization as a mixed integer linear programming (MILP) problem and then adopt a toolkit to solve the problem. One scheme defines variables for each server, and the resulting programming problem is called the MILP4PH problem. The other scheme defines variables for each server type, resulting in a programming problem called the MILP4GH problem. The experimental results reveal that for clusters with poor homogeneity, the MILP4PH problem has fewer variables and can be solved in real time, while for clusters with good homogeneity, the MILP4GH problem has fewer variables and can be solved in real time. [ABSTRACT FROM AUTHOR]

We describe an iterative construction of Lagrangian tori in the complex Grassmannian Gr(k, n), based on the cluster algebra structure of the coordinate ring of a mirror Landau-Ginzburg model proposed by Marsh and Rietsch (2020). Each torus comes with a Laurent polynomial, and local systems controlled by the k-variables Schur polynomials at the n-th roots of unity. We use this data to give examples of monotone Lagrangian tori that are neither displaceable nor Hamiltonian isotopic to each other, and that support nonzero objects in different summands of the spectral decomposition of the Fukaya category over C. [ABSTRACT FROM AUTHOR]

The fusion of two Mirković--Vilonen cycles is a degeneration of their product, defined using the Beilinson--Drinfeld Grassmannian. In this paper, we put in place a conceptually elementary approach to computing this product in type A.We do so by transferring the problem to a fusion of generalized orbital varieties using the Mirković--Vybornov isomorphism. As an application, we explicitly compute all cluster exchange relations in the coordinate ring of the upper-triangular subgroup of GL4, confirming that all the cluster variables are contained in the Mirković--Vilonen basis. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms have been hybridized with the standard K-means to address the latter's challenges in finding a solution to automatic clustering problems. However, the distance calculations required in the standard K-means phase of the hybrid clustering algorithms increase as the number of clusters increases, and the associated computational cost rises in proportion to the dataset dimensionality. The use of the standard K-means algorithm in the metaheuristic-based K-means hybrid algorithm for the automatic clustering of high-dimensional real-world datasets poses a great challenge to the clustering performance of the resultant hybrid algorithms in terms of computational cost. Reducing the computation time required in the K-means phase of the hybrid algorithm for the automatic clustering of high-dimensional datasets will inevitably reduce the algorithm's complexity. In this paper, a preprocessing phase is introduced into the K-means phase of an improved firefly-based K-means hybrid algorithm using the concept of the central limit theorem to partition the high-dimensional dataset into subgroups of randomly formed subsets on which the K-means algorithm is applied to obtain representative cluster centers for the final clustering procedure. The enhanced firefly algorithm (FA) is hybridized with the CLT-based K-means algorithm to automatically determine the optimum number of cluster centroids and generate corresponding optimum initial cluster centroids for the K-means algorithm to achieve optimal global convergence. Twenty high-dimensional datasets from the UCI machine learning repository are used to investigate the performance of the proposed algorithm. The empirical results indicate that the hybrid FA-K-means clustering method demonstrates statistically significant superiority in the employed performance measures and reducing computation time cost for clustering high-dimensional dataset problems, compared to other advanced hybrid search variants. [ABSTRACT FROM AUTHOR]

Atmospheric new particle formation (NPF) events are regularly observed in urban Beijing, despite high concentrations of background particles which, based on theory, should inhibit NPF due to high values of coagulation sink (CoagS). The survival probability, which depends on both CoagS and particle growth rate (GR), is a key parameter in determining the occurrence of NPF events as it describes the fraction of newly formed particles that survive from a smaller diameter to a larger diameter. In this study, we investigate and compare survival probabilities from 1.5 to 3 nm (J3/J1.5), from 3 to 6 nm (J6/J3), and from 6 to 10 nm (J10/J6) based on analytical formulae, cluster population simulations, and atmospheric observations from Beijing. We find that survival probabilities based on the cluster population simulations and one of the analytical formulae are in a good agreement. However, at low ratios between the background condensation sink (CS) and GR, and at high concentrations of sub-3 nm clusters, cluster–cluster collisions efficiently lower survival probabilities in the cluster population simulations. Due to the large concentrations of clusters and small particles required to considerably affect the survival probabilities, we consider it unlikely that cluster–cluster collisions significantly affect atmospheric survival probabilities. The values of J10/J6 observed in Beijing show high variability, most likely due to influences of primary particle emissions, but are on average in relatively good agreement with the values based on the simulations and the analytical formulae. The observed values of J6/J3 are mostly lower than those predicted based on the simulations and the analytical formulae, which could be explained by uncertainties in CS and GR. The observed values of J3/J1.5 at high CS / GR are much higher than predicted based on the simulations and the analytical formulae. We argue that uncertainties in GR or CS are unlikely to solely explain the observed values of J3/J1.5 under high CS conditions. Thus, further work is needed to better understand the factors influencing survival probabilities of sub-3 nm atmospheric particles in polluted environments. [ABSTRACT FROM AUTHOR]

We describe several aspects of the theory of strongly F-regular rings, including how they should be defined without the hypothesis of F-finiteness, and its relationship to tight closure theory, to F-signature, and to cluster algebras. As a necessary prerequisite, we give a quick introduction to tight closure theory, without proofs, but with discussion of underlying ideas. This treatment includes characterizations, important applications, and material concerning the existence of various kinds of test elements, since test elements play a considerable role in the theory of strongly F-regular rings. We introduce both weakly F-regular and strongly F-regular rings. We give a number of characterizations of strong F-regularity. We discuss techniques for proving strong F-regularity, including Glassbrenner's criterion and several methods that have been used in the literature. Many open questions are raised. [ABSTRACT FROM AUTHOR]

Distances to the k -nearest-neighbor (k NN) data points from volume-filling query points are a sensitive probe of spatial clustering. Here, we present the first application of k NN summary statistics to observational clustering measurement, using the 1000 richest redMaPPer clusters (0.1 ≤ z ≤ 0.3) from the SDSS DR8 catalog. A clustering signal is defined as a difference in the cumulative distribution functions (CDFs) of k NN distances from fixed query points to the observed clusters versus a set of unclustered random points. We find that the k  = 1, 2-NN CDFs of redMaPPer deviate significantly from the randoms' across scales of 35 to 155 Mpc, which is a robust signature of clustering. In addition to k NN, we also measure the two-point correlation function for the same set of redMaPPer clusters versus random points, which shows a noisier and less significant clustering signal within the same radial scales. Quantitatively, the χ2 distribution for both the k NN-CDFs and the two-point correlation function measured on the randoms peak at χ2 ∼ 50 (null hypothesis), whereas the k NN-CDFs (χ2 ∼ 300, p  = 1.54 × 10−36) pick up a much more significant clustering signal than the two-point function (χ2 ∼ 100, p  = 1.16 × 10−6) when measured on redMaPPer. Finally, the measured 3NN and 4NN CDFs deviate from the predicted k  = 3, 4-NN CDFs assuming an ideal Gaussian field, indicating a non-Gaussian clustering signal for redMaPPer clusters, although its origin might not be cosmological due to observational systematics. Therefore, k NN serves as a more sensitive probe of clustering complementary to the two point correlation function, providing a novel approach for constraining cosmology and galaxy–halo connection. [ABSTRACT FROM AUTHOR]

The tourism industry has experienced fast and sustainable growth over the years in the economic sector. The data available online on the ever-growing tourism sector must be given importance as it provides crucial economic insights, which can be helpful for consumers and governments. Natural language processing (NLP) techniques have traditionally been used to tackle the issues of structuring of unprocessed data, and the representation of the data in a knowledge-based system. NLP is able to capture the full richness of the text by extracting the entity and relationship from the processed data, which is gathered from various social media platforms, webpages, blogs, and other online sources, while successfully taking into consideration the semantics of the text. With the purpose of detecting connections between tourism and economy, the research aims to present a visual representation of the refined data using knowledge graphs. In this research, the data has been gathered from Twitter using keyword extraction techniques with an emphasis on tourism and economy. The research uses TextBlob to convert the tweets to numeric vector representations and further uses clustering techniques to group similar entities. A cluster-wise knowledge graph has been constructed, which comprises a large number of relationships among various factors, that visualize entities and their relationships connecting tourism and economy. [ABSTRACT FROM AUTHOR]

The terahertz (THz) waves with enormous bandwidth can be used along with the existing sub-6GHz and millimeter wave (mmWave) bands to achieve the ever evolving ecosystem of applications that need to be supported by the modern wireless networks. This paper investigates a user-centric dynamic base station (BS) clustering design for a hybrid network where THz, mmWave, and sub-6GHz BSs coexist. Invoking the proposed clustering model, the BS cooperation within each band is made possible by considering long term channel variations and all the surrounding BSs within a cluster with tunable size. A typical user is associated with the best BS cluster, from either a sub-6GHz, mmWave or THz tier based on the maximum signal-to-interference-plus-noise-ratio (SINR) criterion or the maximum rate criterion. Using tools from stochastic geometry, we assess the performance of the proposed user-centric hybrid system in terms of SINR and rate coverage performances, while accounting for: band specific propagation models, directional beamfroming, and BSs random locations. The accuracy of the analytical results is validated with Monte-Carlo simulations. The obtained results recognize a clear coverage/rate trade-off where a high fraction of THz BSs improves the rate significantly but may degrade the coverage performance. Thus, with carefully planned networks, enabling user-centric BS cooperation for hybrid wireless systems can achieve ultra-high rates while maintaining sufficient coverage in sixth-generation (6G) networks. [ABSTRACT FROM AUTHOR]

Rank 1 modules are the building blocks of the category CM(Bk,n) of Cohen-Macaulay modules over a quotient Bk,n of a preprojective algebra of affine type A. Jensen, King and Su showed in [8] that the category CM(Bk,n) provides an additive categorification of the cluster algebra structure on the coordinate ring C[Gr(k,n)] of the Grassmannian variety of k-dimensional subspaces in Cn. Rank 1 modules are indecomposable, they are known to be in bijection with k-subsets of {1,2, . . .,n}, and their explicit construction has been given in [8]. In this paper, we give necessary and sufficient conditions for indecomposability of an arbitrary rank 2 module in CM(Bk,n) whose filtration layers are tightly interlacing. We give an explicit construction of all rank 2 decomposable modules that appear as extensions between rank 1 modules corresponding to tightly interlacing k-subsets I and J. [ABSTRACT FROM AUTHOR]

Snake graphs are connected planar graphs consisting of a finite sequence of adjacent tiles (squares) T 1 , T 2 , ... , T n . In this case, for 1 ≤ j ≤ n − 1 , two consecutive tiles T j and T j + 1 share exactly one edge, either the edge at the east (west) of T j ( T j + 1 ) or the edge at the north (south) of T j ( T j + 1 ). Finding the number of perfect matchings associated with a given snake graph is one of the most remarkable problems regarding these graphs. It is worth noting that such a number of perfect matchings allows a bijection between the set of snake graphs and the positive continued fractions. Furthermore, perfect matchings of snake graphs have also been used to find closed formulas for cluster variables of some cluster algebras and solutions of the Markov equation, which is a well-known Diophantine equation. Recent results prove that snake graphs give rise to some string modules over some path algebras, connecting snake graph research with the theory of representation of algebras. This paper uses this interaction to define Brauer configuration algebras induced by schemes associated with some multisets called polygons. Such schemes are named Brauer configurations. In this work, polygons are given by some admissible words, which, after appropriate transformations, permit us to define sets of binary trees called groves. Admissible words generate codes whose energy values are given by snake graphs. Such energy values can be estimated by using Catalan numbers. We include in this paper Python routines to compute admissible words (i.e., codewords), energy values of the generated codes, Catalan numbers and dimensions of the obtained Brauer configuration algebras. [ABSTRACT FROM AUTHOR]

To build devices offering users comfortable experience, it is important to focus on form factor and multifunctionality. In this study, for the first time, multifunctional Zn clusters with shape memory, self‐healing, triboelectricity, and optical sensing synergized with rollable form factor are designed and fabricated by coordinating COO− and Zn2+. As pore forming agent, Zn clusters produce hierarchical porous structure depending on Zn amount. Zn clusters are applied as message transmitters and charge containers in optical sensing and corona charge injection, respectively. Moreover, Zn clusters in PVB‐COO‐Zn serve as positive tribomaterial due to Zn ion doping effect, increasing the output performance as the Zn amount reaches 20 wt%. In addition, injecting positive charge into PVB‐COO‐Zn 20 lead to more than 24 times increase in output performance compared to those of non‐porous structures. The reversibility of Zn clusters endows shape memory and self‐healing, synergized with the rollable form factor. The rollability is implemented using the long alkyl chain and the energy absorption of porous structure, providing damage resistance. The advancements in this work provide opportunities for multifunctional and unique applications (shape memory rotating‐triboelectric nanogenerator, rollable self‐healing touchpad, hidden tag) synergized with rollability that accomplishes working in broadened condition in near future. [ABSTRACT FROM AUTHOR]

An algorithm widely used in hotel companies for demand analysis is the so-called K-means. The aforementioned algorithm is based on the use of the Euclidean distance as a dissimilarity measure and this fact can cause a main handicap. Concretely, the Euclidean distance provides a global difference measure between the values of the descriptive variables that can blur the relative differences in each component separately and, hence, the cluster algorithm can assign a custom to an incorrect cluster. In order to avoid this drawback, this paper proposes an application of the use of Ordered Weighted Averaging (OWA) operators and an OWA-based K-means for clustering customers staying at a real five-star hotel, located in a mature sun-and-beach area, according to their propensity to spend. It must be pointed out that OWA-based distance calculates relative distances and it is sensitive to the differences in each component separately. All experiments show that the use of the OWA operator improves the performance of the classical K-means up to 21.6 % and reduces the number of convergence iterations up to 48.46 % . Such an improvement has been tested through a ground truth, designed by the marketing department of the firm, which states the cluster to which each tourist belongs. Moreover, the customer classification is achieved regardless of the season in which the customer stays at the hotel. All these facts confirm that the OWA-based K-means could be used as an appropriate tool for classifying tourists in purely exploratory and predictive stages. Furthermore, the new methodology can be implemented without requiring radical changes in the implementation of the classical methodology and in data processing which is crucial so that it can be incorporated into the control panel of a real hotel without additional implementation costs. [ABSTRACT FROM AUTHOR]

Federated Learning (FL) over wireless network enables data-conscious services by leveraging the ubiquitous intelligence at network edge for privacy-preserving model training. As the proliferation of context-aware services, the diversified personal preferences cause disagreeing conditional distributions among user data, which leads to poor inference performance. In this sense, clustered federated learning is proposed to group user devices with similar preference and provide each cluster with a personalized model. This calls for innovative design in edge association that involves user clustering and also resource management optimization. We formulate an accuracy-cost trade-off optimization problem by jointly considering model accuracy, communication resource allocation and energy consumption. To comply with parameter encryption techniques in FL, we propose an iterative solution procedure which employs deep reinforcement learning based approach at cloud server for edge association. The reward function consists of minimized energy consumption at each base station and the averaged model accuracy of all users. Under our proposed solution, multiple edge base station are fully exploited to realize cost efficient personalized federated learning without any prior knowledge on model parameters. Simulation results show that our proposed strategy outperforms existing strategies in achieving accurate learning at low energy cost. [ABSTRACT FROM AUTHOR]

Individuals differ in average phenotypes and in sensitivity to environmental variation. Such context sensitivity can be modelled as random slope variation. Random slope variation implies that the proportion of between‐individual variation varies across the range of a covariate (environment/context/time/age) and has thus been called 'conditional' repeatability.We propose to put conditional repeatabilities in perspective of the total phenotypic variance and suggest a way of standardization using the random slope coefficient of determination RS2. Furthermore, we illustrate that the marginalized repeatability Rmar averaged across an environmental gradient offers a biologically relevant description of between‐individual variation.We provide simple equations for calculating key descriptors of conditional repeatabilities, clarify the difference between random intercept variation and average between‐individual variation and make recommendations for comprehensive reporting.While we introduce the concept with individual variation in mind, the framework is equally applicable to other type of between‐group/cluster variation that varies across some (environmental) gradient. [ABSTRACT FROM AUTHOR]

Single-cell measurements incorporate invaluable information regarding the state of each cell and its underlying regulatory mechanisms. The popularity and use of single-cell measurements are constantly growing. Despite the typically large number of collected data, the under-representation of important cell (sub-)populations negatively affects down-stream analysis and its robustness. Therefore, the enrichment of biological datasets with samples that belong to a rare state or manifold is overall advantageous. In this work, we train families of generative models via the minimization of Rényi divergence resulting in an adversarial training framework. Apart from the standard neural network-based models, we propose families of semi-interpretable generative models. The proposed models are further tailored to generate realistic gene expression measurements, whose characteristics include zero-inflation and sparsity, without the need of any data pre-processing. Explicit factors of the data such as measurement time, state or cluster are taken into account by our generative models as conditional variables. We train the proposed conditional models and compare them against the state-of-the-art on a range of synthetic and real datasets and demonstrate their ability to accurately perform data interpolation and augmentation. [ABSTRACT FROM AUTHOR]

Density-based clustering is a widely explored domain in the field of machine learning, with numerous methods proposed to address challenges in clustering under varying density conditions. These methods primarily categorize samples based on their local density. However, challenges arise when dealing with boundary samples. The density of certain boundary samples is typically lower, which can lead to misclassification as noise. Moreover, in situations where two clusters have similar densities and are in close proximity, accurately classifying the boundary points between them becomes a challenging task. In this paper, we introduce an enhanced approach based on k -nearest neighbors to address this challenge within density-based clustering. In our method, upon the formation of a new cluster, we identify boundary samples by examining the spatial relationships between each sample and its k -nearest neighbors, as well as their connections to the newly established cluster. Once all clusters are formed, we refine the classification of these boundary samples by adjusting or retaining their assigned labels based on their k -nearest neighbors. Experimental evaluations on synthetic and real-world datasets demonstrate the effectiveness of our proposed method. • A new density clustering method based on boundary samples verification is proposed. • The method can handle datasets with different densities and shapes. • The method only requires one integer parameter, easy to use. • Outperforms existing methods on various benchmark datasets. [ABSTRACT FROM AUTHOR]

We study the Coulomb branches of four-dimensional supersymmetric quantum field theories with N = 2 supersymmetry, including the KK theories obtained from the circle compactification of the 5d N = 1 En Seiberg theories, with particular focus on the relation between their Seiberg-Witten geometries and rational elliptic surfaces. More attention is given to the modular surfaces, which we completely classify using the classification of subgroups of the modular group PSL(2, ℤ), deriving closed-form expressions for the modular functions for all congruence and some of the non-congruence subgroups. Moreover, in such cases, we give a prescription for determining the BPS quivers from the fundamental domains of the monodromy groups and study how changes of these domains can be interpreted as quiver mutations. This prescription can be also generalized to theories whose Coulomb branches contain 'undeformable' singularities, leading to known quivers of such theories. [ABSTRACT FROM AUTHOR]

The enumeration of Dyck paths is one of the most remarkable problems in Catalan combinatorics. Recently introduced categories of Dyck paths have allowed interactions between the theory of representation of algebras and cluster algebras theory. As another application of Dyck paths theory, we present Brauer configurations, whose polygons are defined by these types of paths. It is also proved that dimensions of the induced Brauer configuration algebras and the corresponding centers are given via some integer sequences related to Catalan triangle entries. [ABSTRACT FROM AUTHOR]

Wild ornamental plants are beneficial as well as dangerous for the environment. Because the introduction of attractive plants that are not suited to the local ecosystem can result in significant environmental damage, a quick integration strategy based on an enhanced clustering algorithm is proposed for wild ornamental plant resources. The technique is enhanced with density stratification by integrating the k-means distance measurement formula and establishing the objective function of clustering optimization. The cluster termination condition is controlled by the number of clusters k, and the wild plant data categories are continually merged. Uneven density distribution is used to deal with the wild plant distribution dataset. To obtain the distribution of wild ornamental plants in different regions, to estimate the optimal parameters of wild plant samples, to combine with maximum likelihood classification to obtain the plant flora differentiation degree, and to complete the resource integration, remote sensing images were used. Comprehensive survey and systematic sampling were used to conduct a complete survey of the protected area. The heat map of the plant size distribution shows that there is a clear negative correlation between the spatial scale difference and the overall density difference of the plant distribution, that is, it appears spatially. From the experimental analysis, it is observed that the high-density small-scale and low-density large-scale agglomeration distribution characteristics delay is 1.96 s. [ABSTRACT FROM AUTHOR]

Dense time-series remote sensing images have transformed the traditional bitemporal land-cover change detection to continuous monitoring. Previous work mostly employs linear fitting, prediction, or decomposition methods, and the detection accuracy is not high. The latest progress of deep learning (DL) shows its advantages in time-series change monitoring. However, DL models are computationally expensive and require lots of labeled samples, resulting in often employed prediction-threshold-based unsupervised change detection method. However, the determination of a reasonable threshold has always been a big problem. Therefore, we proposed the similarity-measurement-based deep transfer learning for time-series adaptive change detection (SDTL-TSACD) model. First, a standard dynamic time warping (SDTW) distance was proposed and used to cluster large-scale time series into multiple subcategories with high time-series similarity. Second, a time convolutional network (TCN) was used for nonlinear time-series fitting and prediction, and an early stop strategy was used to prevent overfitting. Then, the trained TCN model would be transferred and performed pixel-by-pixel time-series prediction within the same category, and the SDTW was also used to evaluate the prediction accuracy. Finally, the Otsu adaptive threshold was used to detect change points, and the spatial neighbor relationship was used to eliminate the pseudo-change points. Change detection results using 132 benchmark datasets showed that the SDTL-TSACD performed well in both accuracy and efficiency. In addition, the MOD13Q1-EVI images from 2001 to 2020 were used to study the land-cover change of the Loess Plateau, and the SDTL-TSACD also showed a good ability to solve practical problems. [ABSTRACT FROM AUTHOR]