Cluster Category Research Articles

Cluster structures for the A∞$A_\infty$ singularity

AbstractWe study a category of ‐graded maximal Cohen‐Macaulay (MCM) modules over the curve singularity and demonstrate that it has infinite type cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type cluster categories of Holm–Jørgensen, Fisher and Paquette–Yıldırım. As a consequence, has cluster tilting subcategories modelled by certain triangulations of the (completed) ‐gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategories, and show that these subcategories and their mutations exhibit the combinatorics of the completed ‐gon.

Spatial analysis, sources, and categories of e-waste clusters in developing countries: kano metropolis case study

Spatial analysis, sources, and categories of e-waste clusters in developing countries: kano metropolis case study

Classification and study of glass based on cluster analysis

As one of the earliest human materials invented by mankind, glass products play a great role in the study of history. Because the ancient glass is easily affected by the buried environment, resulting in the weathering of the surface of the cultural relics, this paper classifies the cultural relics in order to better protect and study the ancient glass. In this paper, some data of weathered cultural relics are collected to establish a model for subclassification of cultural relics.This paper first conducted principal component analysis of two different types of glass and screened out different principal components of two types of glass. Then, according to the number of cluster categories (K value) obtained by the contour algorithm, combined with the obtained principal components, the cluster analysis is used to divide the subclasses, and the specific subclass division method and division results are obtained. The subclass characteristics are obtained by analyzing for each subclass data. For the established subclass classification, multiple cluster analysis was performed using changed K values to perform the sensitivity and rationality analysis of the model. The results show that the model established in this paper finds a good classification rule for some chemical substances of weathered cultural relics, gives a logical division method, and explores and compares the similarities and differences between different chemical components.

Short-range ordering alters the dislocation nucleation and propagation in refractory high-entropy alloys

The role of short-range ordering (SRO) in the dislocation kinetics in refractory high-entropy alloys (RHEAs) remains controversial. On one hand, it was shown by simulations that the mobility of edge dislocations was enhanced while that of screw dislocations was reduced, leading to the conclusion that screw dislocations should be dominant. On the other hand, experiments exclusively showed the dominance of edge dislocations. Here, we investigate the impact of SRO in the grain interior and grain boundary on dislocation nucleation and propagation in a BCC MoTaTiWZr RHEA, using a combination of the density-functional theory calculations, Monte Carlo method, and molecular dynamic simulation. Our results show that this RHEA is energetically favorable to undergo SRO, thus forming a pseudo-composite microstructure. This microstructure consists of three categories of clusters: high energy clusters (HECs), medium energy clusters (MECs), and low energy clusters (LECs), with the HECs in grain boundaries acting as weak fillers to induce dislocation nucleation while the MECs/LECs serving as a strong matrix to stabilize the weak HECs. Importantly, SRO is found to enhance the energy barriers for both edge and screw dislocation motion and make the mobility of edge dislocations comparable to or even lower than screw dislocations, contributing to the dominance of edge dislocations in the BCC RHEA. Our work highlights the importance of SRO in influencing the dislocation activity of RHEAs and presents a fascinating route for designing RHEAs to achieve superior mechanical properties.

Exploring Public Relations Research Topics and Inter-Cluster Dynamics Through Computational Modeling (2010-2020): A Study Based on Two SSCI Journals

ABSTRACT This project addresses the evolution of public relations research over the past decade by examining its two SSCI-indexed journals with methods that can reveal the influence of multiple categories of research clusters. Modeling the full text of all 1,293 published articles in Public Relations Review (PRR) and the Journal of Public Relations Research (JPRR) from 2010 to 2020 (7,400,685 words), we identified nine non-discrete clusters in public relations research. Using three computational methods – structural topic modeling, inter-cluster network analysis, and network simulation – we found that (1) the strategic management cluster emerged as the most central for the past decade, followed by public relations professionalism, digital media, crisis communication, internal communication, global public relations, rhetoric and philosophy, media relations, and critical studies, ranked by their proportions in the scholarship; (2) JPRR had greater emphasis on the strategic management cluster relative to PRR, which offered a more diverse representation; (3) little longitudinal change occurred throughout the decade, although internal communication gained traction and public relations professionalism and media relations lost ground as the decade progressed; and 4) the last ten years of public relations research did not see intersection among theoretical traditions from different clusters as much as expected, leaving opportunity for more inter-cluster knowledge production. Theoretical and practical implications for the public relations research community are discussed.

Categories for Grassmannian Cluster Algebras of Infinite Rank

Abstract We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian category of infinite rank is given as the category of graded maximal Cohen–Macaulay modules over a certain hypersurface singularity. We show that generically free modules of rank $1$ in a Grassmannian category of infinite rank are in bijection with the Plücker coordinates in an appropriate Grassmannian cluster algebra of infinite rank. Moreover, this bijection is structure preserving, as it relates rigidity in the category to compatibility of Plücker coordinates. Along the way, we develop a combinatorial formula to compute the dimension of the $\textrm {Ext}^{1}$-spaces between any two generically free modules of rank $1$ in the Grassmannian category of infinite rank.

Composition Analysis and Identification of Glass Products Based on Hierarchical Clustering

Ancient glass is an important carrier of the development of Chinese civilization. Affected by the buried environment of cultural relics, ancient glass is very easy to weather. A large number of internal elements of glass exchange with environmental elements, resulting in changes in its composition and appearance, thus affecting the judgment of its correct classification. In this paper, a comprehensive evaluation model was established to analyze the chemical composition of glass. First of all, the chi-square test is used to determine the factors related to surface weathering. Then the chemical composition of different glass was analyzed by mathematical statistics, and the number of clustering categories was determined by the method of system clustering, combined with the determination of square Euclidean distance and elbow rule. Finally, the final classification result is obtained by judging the size of the grey correlation degree of the type classification law and the sub-classification division method obtained in the model. The results show that the comprehensive model can be used to analyze and identify the composition of glass products.

A geometric realization of silting theory for gentle algebras

A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category of the gentle algebra has a geometric interpretation in terms of this surface. In this paper we study silting theory in the bounded derived category of a gentle algebra in terms of its underlying surface. In particular, we show how silting mutation corresponds to the changing of graded arcs and that in some cases silting mutation results in the interpretation of the octahedral axioms in terms of the flipping of diagonals in a quadrilateral as in the work of Dyckerhoff and Kapranov (J Eur Math Soc 20(6):1473–1524, 2018) in the context of triangulated surfaces. We also show that the cutting of the underlying surface along a curve without self-intersections corresponds to silting reduction. This is analogous to the Calabi–Yau reduction of surface cluster categories as shown by Marsh and Palu (Proc Lond Math Soc (3) 108(2):411–440, 2014) and Qiu and Zhou (Compos Math 153(9):1779–1819, 2017).

Computation of extension spaces for the path algebra of type Ã(n - 1,1) using planar curves

Q is a quiver of type if its graph is of affine type and if its arrows have a certain orientation. We develop a bijection between the set of indecomposable kQ-modules whose dimension vectors are positive real roots of the root system associated to Q and a certain set of planar curves. We prove that the number of self-intersections of the curve which corresponds to the module M is equal to the dimension of . We also prove that, for many pairs of modules (M, N), the number of intersections between the corresponding two curves is equal to the dimension of , where C is the cluster category of kQ-mod.

Lattices of t‐structures and thick subcategories for discrete cluster categories

We classify t-structures and thick subcategories in any discrete cluster category C ( Z ) $\mathcal {C}(\mathcal {Z})$ of Dynkin type A $A$ , and show that the set of all t-structures on C ( Z ) $\mathcal {C}(\mathcal {Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on C ( Z ) $\mathcal {C}(\mathcal {Z})$ obtained in this way and the lattice of thick subcategories of C ( Z ) $\mathcal {C}(\mathcal {Z})$ are intimately related to the lattice of non-crossing partitions of type A $A$ . In particular, the lattice of equivalence classes of non-degenerate t-structures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.

STUDY OF THE COMPETITIVENESS AND SUSTAINABILITY OF THE MSME CLUSTER IN THE CITY OF SEMARANG

Development of MSME Clusters in Semarang City is carried out to support the activities of MSME actors who are grouped into various types. This research was conducted by taking a sample of 70 MSME actors in various clusters. The competitiveness and sustainability of the clusters are determined using the AHP (Analytic Hierarchy Process) Method. From the results of the analysis it was found that Clusters in Semarang City, it can be seen that based on the HR variable, all clusters in Semarang City fall into the criteria/category of Sustainable Clusters. However, when viewed from the competitiveness variable, there are 3 (three) clusters that fall into the less sustainable category, namely Metals, Tourism, and Furniture. So, in general, the results of the cluster categories in the city of Semarang show that the problems facing cluster sustainability are more like an inability to compete

Harnessing on Genetic Variability and Diversity of Rice (Oryza sativa L.) Genotypes Based on Quantitative and Qualitative Traits for Desirable Crossing Materials.

Yield is a complex parameter of rice due to its polygonal nature, sometimes making it difficult to coat the selection process in the breeding program. In the current study, 34 elite rice genotypes were assessed to evaluate 3 locations for the selection of desirable rice cultivars suitable for multiple environments based on genetic diversity. In variance analysis, all genotypes have revealed significant variations (p ≤ 0.001) for all studied characters, signifying a broader sense of genetic variability for selection purposes. The higher phenotypic coefficient of variation (PCV) and genotypic coefficient of variation (GCV) were found for yield-associated characteristics such as the number of grains panicle-1 (GP), panicles hill-1 (PPH), and tillers hill-1 (TILL). All of the characters had higher heritability (greater than 60%) and higher genetic advance (greater than 20%), which pointed out non-additive gene action and suggested that selection would be effective. The most significant traits causing the genotype variants were identified via principal component analysis. In the findings of the cluster analysis, 34 elite lines were separated into 3 categories of clusters, with cluster II being chosen as the best one. The relationship matrix between each elite cultivar and traits was also determined utilizing a heatmap. Based on multi-trait genotype-ideotype distance index (MGIDI), genotypes Gen2, Gen4, Gen14, Gen22, and Gen30 in Satkhira; Gen2, Gen6, Gen7, Gen15, and Gen30 in Kushtia; and Gen10, Gen12, Gen26, Gen30, and Gen34 in Barishal were found to be the most promising genotypes. Upon validation, these genotypes can be suggested for commercial release or used as potential breeding material in crossing programs for the development of cultivars suitable for multiple environments under the future changing climate.

Residential Environment Assessment by Older Adults in Nursing Homes during COVID-19 Outbreak.

The most vulnerable residential settings during the COVID-19 pandemic were older adult's nursing homes, which experienced high rates of incidence and death from this cause. This paper aims to ascertain how institutionalized older people assessed their residential environment during the pandemic and to examine the differences according to personal and contextual characteristics. The COVID-19 Nursing Homes Survey (Madrid region, Spain) was used. The residential environment assessment scale (EVAER) and personal and contextual characteristics were selected. Descriptive and multivariate statistical analysis were applied. The sample consisted of 447 people (mean age = 83.8, 63.1% = women, 50.8% = widowed, 40% = less than primary studies). Four residential assessment subscales (relationships, mobility, residential aspects, privacy space) and three clusters according to residential rating (medium-high with everything = 71.5% of cases, low with mobility = 15.4%, low with everything = 13.1%) were obtained. The logistic regression models for each cluster category showed to be statistically significant. Showing a positive affect (OR = 1.08), fear of COVID-19 (OR = 1.06), high quality of life (OR = 1.05), not having suspicion of depression (OR = 0.75) and performing volunteer activities (OR = 3.67) were associated with the largest cluster. It is concluded that a better residential evaluation was related to more favourable personal and contextual conditions. These results can help in the design of nursing homes for older adults in need of accommodation and care to facilitate an age-friendly environment.

Long-lasting sequences of BGP updates

The Border Gateway Protocol (BGP) is the protocol that makes the various networks composing the Internet communicate to each other. Routers speaking BGP exchange updates to keep the routing up-to-date and allow such communication. This usually is done to reflect changes in the routing configurations or as a consequence of link failures. In the Internet as a whole it is normal that BGP updates are continuously exchanged, but for any specific IP prefix, these updates are supposed to be concentrated in a short time interval that is needed to react to a network change. On the contrary, in this paper we show that there are many IP prefixes involved in quite long sequences consisting of a large number of BGP updates. Namely, examining ∼30 billion updates collected by 172 observation points distributed worldwide, we estimate that almost 30% of them belong to sequences lasting more than one week. Such sequences involve 222285 distinct IP prefixes, approximately one fourth of the number of announced prefixes. We detect such sequences using a method based on the Discrete Wavelet Transform. We publish an online tool for the exploration and visualization of such sequences, which is open to the scientific community for further research. We group together sequences that exhibit common behaviours. For this purpose, we devise a clusterization algorithm able to group the sequences based on their similarity in time. We highlight four categories of clusters, which are attributable to different types of Internet events. Our online tool allows also to explore and to visualize the computed clusters.

The characteristics of postprandial glycemic response patterns to white rice and glucose in healthy adults: Identifying subgroups by clustering analysis.

Large interpersonal variability in postprandial glycemic response (PGR) to white rice has been reported, and differences in the PGR patterns during the oral glucose tolerance test (OGTT) have been documented. However, there is scant study on the PGR patterns of white rice. We examined the typical PGR patterns of white rice and glucose and the association between them. We analyzed the data of 3-h PGRs to white rice (WR) and glucose (G) of 114 normoglycemic female subjects of similar age, weight status, and same ethnic group. Diverse glycemic parameters, based on the discrete blood glucose values, were calculated over 120 and 180 min. K-means clustering based on glycemic parameters calculated over 180 min was applied to identify subgroups and representative PGR patterns. Principal factor analysis based on the parameters used in the cluster analysis was applied to characterize PGR patterns. Simple correspondence analysis was performed on the clustering categories of WR and G. More distinct differences were found in glycemic parameters calculated over 180 min compared with that calculated over 120 min, especially in the negative area under the curve and Nadir. We identified four distinct PGR patterns to WR (WR1, WR2, WR3, and WR4) and G (G1, G2, G3, and G4), respectively. There were significant differences among the patterns regard to postprandial hyperglycemia, hypoglycemic, and glycemic variability. The WR1 clusters had significantly lower glycemic index (59 ± 19), while no difference was found among the glycemic index based on the other three clusters. Each given G subgroup presented multiple patterns of PGR to WR, especially in the largest G subgroup (G1), and in subgroup with the greatest glycemic variability (G3). Multiple subgroups could be classified based on the PGR patterns to white rice and glucose even in seemingly homogeneous subjects. Extending the monitoring time to 180 min was conducive to more effective discrimination of PGR patterns. It may not be reliable to extrapolate the patterns of PGR to rice from that to glucose, suggesting a need of combining OGTT and meal tolerance test for individualized glycemic management.

Policies of Misconduct: A Content Analysis of Codes of Conduct for Online Multiplayer Games

In this paper we searched the websites of 60 popular online multiplayer games to locate their codes of conduct and then performed a content analysis on 32 unique codes of conduct. Our analysis consisted of a two-cycle coding process including initial coding, and then pattern coding for clustering categories and themes together. Our aim was to better understand how game companies include codes of conduct on their websites and what content they include in the codes of conduct. The two-cycle coding process identified five main themes: (1) game company values, (2) expectations of players, (3) bad behaviors and rules, (4) moderation practices, and finally (5) document structure. Our findings suggest that codes of conduct are routinely inaccessible, if present at all, and that codes of conduct are often framed around punitive legal language that reflect policies of misconduct rather than expressing communal values and expectations. Our findings can help contribute towards community management in online games and make codes of conduct more accessible for all stakeholders in online gaming communities. We have also provided design recommendations and a design process that should help guide game companies looking to create value focused codes of conduct.

Tilting modules arising from knot invariants

We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot L [ a 1 , … , a n ] , we associate a quiver Q with potential and its Jacobian algebra A . We construct a family of canonical indecomposable A -modules M ( i ) , each supported on a different specific subquiver Q ( i ) of Q . Each of the M ( i ) is expected to parametrize the Jones polynomial of the knot. We study the direct sum M = ⊕ i M ( i ) of these indecomposables inside the module category of A as well as in the cluster category. In this paper we consider the special case where the two-bridge knot is given by two parameters a 1 , a 2 . We show that the module M is rigid and τ -rigid, and we construct a completion of M to a tilting (and τ -tilting) A -module T . We show that the endomorphism algebra End A T of T is isomorphic to A , and that the mapping T ↦ A [ 1 ] induces a cluster automorphism of the cluster algebra A ( Q ) . This automorphism is of order two. Moreover, we give a mutation sequence that realizes the cluster automorphism. In particular, we show that the quiver Q is mutation equivalent to an acyclic quiver of type T p , q , r (a tree with three branches). This quiver is of finite type if ( a 1 , a 2 ) = ( a 1 , 2 ) , ( 1 , a 2 ) , or ( 2 , 3 ) , it is tame for ( a 1 , a 2 ) = ( 2 , 4 ) or ( 3 , 3 ) , and wild otherwise.

Ptolemy diagrams and cotorsion pairs in m-cluster categories of type A

In this paper, we give a complete classification of cotorsion pairs in [Formula: see text]-cluster categories of type [Formula: see text], denoted by [Formula: see text], via certain configurations of [Formula: see text]-diagonals, called Ptolemy diagrams. As applications, we classify [Formula: see text]-rigid subcategories of [Formula: see text], which gives Jacquet–Malo’s classification of [Formula: see text]-cluster tilting subcategories of [Formula: see text]. When [Formula: see text], this generalizes the work of Holm et al. [Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type [Formula: see text], J. Algebraic Combin. 34 (3) (2011) 507–523] for the classification of torsion pairs in cluster categories of type [Formula: see text].

Quantifying Subnational Economic Complexity: Evidence from Romania

Over the last two decades, Romania has undergone strong economic growth, catching up to advanced economies and producing one of the best economic performances in the world. Along with these positive changes, industrial product diversification has increased through expanded foreign economic relations, with all of these supporting the complexity of economic activities. Even though there is a world ranking of countries showing the highest level of economic complexity, there is no information about regional contributions to the overall score in Romania. This paper fills this gap by measuring the economic complexity of Romania’s subnational areas (counties) in the last ten years. To calculate the Economic Complexity Index (ECI) at a regional level, 615 economic activities (four-digit classes according to the NACE classification) were taken into consideration, grouped into 68 cluster categories. The results show that significant changes in economic complexity have mainly occurred in less developed areas, the upper- and middle-ranked counties’ positions being relatively stable. Furthermore, we examined the impact of complexity on growth and convergence, finding that the ECI index is a good predictor both for future economic growth as well as for the evolution of income inequalities.

$$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras: triangulated surfaces and friezes

By viewing $$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras as triangulated surfaces, we find all cluster variables in terms of either (i) the frieze pattern (or bipartite belt) or (ii) the periodic quantities previously found for the cluster map associated with these frieze patterns. We show that these cluster variables form friezes which are precisely the ones found by Assem–Dupont by applying the cluster character to the associated cluster category.