Constructing physician group profiles within online medical consultation platforms enables the precise characterization of multi-dimensional features of physician cohorts. This approach facilitates a better understanding of physicians’ behavioral patterns and service quality on these platforms, thereby providing support for service optimization. Drawing upon existing research on factors influencing patients’ physician selection behavior, a conceptual model for physician profiling was established from three dimensions: physician, patient, and platform. Using the concept lattice method, profiles for dermatology and venereology physicians on the Haodf.com platform were constructed. Based on the Hasse diagram, the physician cohort was categorized into four distinct types: high-value elite, multi-domain active, high-efficiency interaction, and potential-to-be-explored. Furthermore, implicit dependencies among attribute tags were uncovered through association rule mining. Adopting a tripartite “physician-patient-platform” perspective, we developed a group profile for physicians on online consultation platforms, which validates the efficacy of the concept lattice method for such profiling. The mined association rules further reveal the interrelationships within the “physician-patient-platform” data, offering data-driven support for optimizing physician management, enhancing service quality, and enabling precise recommendations on these platforms.

A graph is considered to admit a covering if every edge of lies in a subgraph isomorphic to . We refer to as super antimagic total when there exists a bijection with such that the weights of all subgraphs isomorphic to , defined by , form an arithmetic sequence for integers and , where is the number of such subgraphs. In this work, we establish super antimagic total labelings for the classical book graph and for a generalized book graph constructed by extending the cycle-based structure of the standard model. We further show that the classical book graph appears as a special case of this generalized structure and that both graphs satisfy the super antimagic total property. Keywords: Super (a,d)-antimagic total labeling, C_m-antimagic, Book graph, generalized book graph, Graph coverings

Abstract The diverse dialects of Kurdish have long been the subject of scholarly debate on syllable structure, and this study examines the syllabification of Central Kurdish within the Optimality Theory framework. Data from a mini-corpus, drawn from native Central Kurdish speakers and enriched with findings from studies on Northern and Southern Kurdish dialects, provide the foundation for this investigation. The methodology involves extracting the constraints governing Central Kurdish’s syllable formation, where the nucleus consistently requires a single vowel and the onset is obligatory in a CV pattern that may extend to include a glide (forming CGV) at word-initial positions. The permissible coda appears either as a singleton or as part of a consonant cluster. Findings indicate that Central Kurdish and Southern Kurdish converge on a shared constraint ranking, producing the canonical C(G)V(C)(C) structure. Northern Kurdish dialects, however, display greater variation, with some allowing an unrestricted second consonant (C(C)V(C)(C)) and others restricting cluster composition. A Hasse diagram is employed to visualize these constraint relationships, highlighting Optimality Theory’s capacity to model both a core, maximally constrained syllable structure and peripheral trends. These results provide crucial insights into the dynamic interplay of phonological constraints that shape syllable structure across Kurdish dialects, advancing a unified typological understanding of the language.

Gas disasters in coal mines are the principal constraint on safe operations; accordingly, accurate gas time-series forecasting and real-time fluctuation monitoring are essential for prevention and early warning. A method termed Decomposition-Enhanced Cross-Graph Forecasting and Anomaly Finding is proposed. The Multi-Variate Variational Mode Decomposition (MVMD) algorithm is refined by integrating wavelet denoising with an Entropy Weight Method (EWM) multi-index scheme (seven indicators, including SNR and PSNR; weight-solver error ≤ 0.001, defined as the maximum absolute change between successive weight vectors in the entropy-weight iteration). Through this optimisation, the decomposition parameters are selected as K = 4 (modes) and = 1000, yielding effective noise reduction on 83,970 multi-channel records from longwall faces; after joint denoising, SSIM reaches 0.9849, representing an improvement of 0.5%–18.7% over standalone wavelet denoising. An interpretable Cross Interaction Refinement Graph Neural Network (CrossGNN) is then constructed. Shapley analysis is employed to quantify feature contributions; the m1t2 gas component attains a SHAP value of 0.025, which is 5.8× that of the wind-speed sensor. For multi-timestep prediction (T0–T2), the model achieves MAE = 0.008705754 and MSE = 0.000242083, which are 8.7% and 12.7% lower, respectively, than those of STGNN and MTGNN. For fluctuation detection, Pruned Exact Linear Time (PELT) with minimum segment length L_min = 58 is combined with a circular block bootstrap test to identify sudden-growth and high-fluctuation segments while controlling FDR = 0.10. Hasse diagrams are further used to elucidate dominance relations among components (e.g., m3t3, the third decomposed component of the T2 gas sensor). Field data analyses substantiate the effectiveness of the approach and provide technical guidance for the intellectualisation of coal-mine safety management.

We discuss (1+1)d gapless phases with non-invertible global symmetries, also referred to as categorical symmetries. This includes gapless phases showing properties analogous to gapped symmetry protected topological (SPT) phases, known as gapless SPT (or gSPT) phases; and gapless phases showing properties analogous to gapped spontaneous symmetry broken (SSB) phases, that we refer to as gapless SSB (or gSSB) phases. We fit these gapless phases, along with gapped SPT and SSB phases, into a phase diagram describing possible deformations connecting them. This phase diagram is partially ordered and defines a so-called Hasse diagram. Based on these deformations, we identify gapless phases exhibiting symmetry protected criticality, that we refer to as intrinsically gapless SPT (igSPT) and intrinsically gapless SSB (igSSB) phases. This includes the first examples of igSPT and igSSB phases with non-invertible symmetries. Central to this analysis is the Symmetry Topological Field Theory (SymTFT), where each phase corresponds to a condensable algebra in the Drinfeld center of the symmetry category. On a mathematical note, gSPT phases are classified by functors between fusion categories, generalizing the fact that gapped SPT phases are classified by fiber functors; and gSSB phases are classified by functors from fusion to multi-fusion categories. Finally, our framework can be applied to understand gauging of trivially acting non-invertible symmetries, including possible patterns of decomposition arising due to such gaugings.

Let R be a 2-torsion-free and n!-torsion-free commutative ring with unity, and let X be a locally finite preordered set. We endow the incidence algebra I(X,R) with a superalgebra structure via a nontrivial idempotent, which decomposes I(X,R) into even and odd parts A0⊕A1. Our main result shows that if any two directed edges in each connected component of the complete Hasse diagram (X,D) lie in one cycle, then every supercommuting map on I(X,R) is proper. A supercommuting map θ:I(X,R)→I(X,R) is defined by the condition [θ(x),x]s=0 for all x∈I(X,R), where [a,b]s=ab−(−1)|a||b|ba is the supercommutator. We prove that such maps must take the form θ(x)=λx+μ(x), where λ∈Zs(I(X,R)) (the supercenter) and μ:I(X,R)→Zs(I(X,R)) is an R-linear map. This generalizes the known results on commuting maps of incidence algebras and other associative algebras.

Abstract Brick polytopes constitute a remarkable family of polytopes associated to the spherical subword complexes of Knutson and Miller. They were introduced for finite Coxeter groups by Pilaud and Stump, who used them to produce geometric realizations of generalized associahedra arising from the theory of cluster algebras of finite types. In this paper, we present an application of the vast generalization of brick polyhedra for general subword complexes (not necessarily spherical) recently introduced by Jahn and Stump. More precisely, we show that the $$\nu $$ ν -associahedron, a polytopal complex whose edge graph is the Hasse diagram of the $$\nu $$ ν -Tamari lattice introduced by Préville-Ratelle and Viennot, can be geometrically realized as the complex of bounded faces of the brick polyhedron of a well chosen subword complex. We also present a suitable projection to the appropriate dimension, which leads to an elegant vertex-coordinate description.

In 2020, Bhavale and Waphare introduced the concepts of fundamental basic block and basic block. Further, Bhavale and Waphare have provided the recursive formulae of the number of non-isomorphic fundamental basic blocks as well as basic blocks, containing r comparable reducible elements and having nullity l. With the help of those formulae, Bhavale et al. obtained the Hasse diagrams of all non-isomorphic basic blocks containing up to four comparable reducible elements and having nullity up to five. In this paper, we actually obtain the Hasse diagrams of the basic blocks containing four comparable reducible elements and having nullity six.

Abstract Let G be a graph and let $$J=I_c(G)$$ J = I c ( G ) be its ideal of covers. The aims of this work are to study the v-number $$\textrm{v}(J)$$ v ( J ) of J and to study when J is linearly presented using combinatorics and commutative algebra. We classify when $$\textrm{v}(J)$$ v ( J ) attains its minimum and maximum possible values in terms of the vertex covers of the graph that satisfy the exchange property. If the cover ideal of a graph has a linear presentation, we express its v-number in terms of the covering number of the graph. If G is unmixed, the graph $$\mathcal {G}_J$$ G J of J is the graph whose vertices are the minimal vertex covers of G and whose edges are the pairs $$\{C,C'\}$$ { C , C ′ } such that $$|C\cup C'|=|C|+1$$ | C ∪ C ′ | = | C | + 1 . We show necessary and sufficient conditions for the graph $$\mathcal {G}_J$$ G J of J to be connected. Then, for unmixed König graphs, we classify when J is linearly presented using graph theory, and show some results on Cohen–Macaulay König graphs. If G is unmixed, it is shown that the columns of the linear syzygy matrix of J are linearly independent if and only if $$\mathcal {G}_J$$ G J has no strong 3-cycles. One of our main theorems shows that if G is unmixed and has no induced 4-cycles, then J is linearly presented. For unmixed graphs without 3- and 5-cycles, we classify combinatorially when J is linearly presented.

This paper analyzes the Hasse diagram, or family tree, of the 3D crystal classes, also called geometric crystal classes. The 32 point-group classes are partitioned into seven crystal systems. In this paper, the structures of these systems are analyzed, leading to a new understanding of the relationships among and within them. The point groups, including their subgroups up to conjugacy, appear in six structural motifs in the Hasse diagram or family tree. Each motif has a parity - even or odd - that determines its structure. In three dimensions, the odd motifs are called monads, trigonals and cubics, and the even motifs are called dyads, tetragonals and hexagonals. Of the 32 classes of 3D point groups, 29 have a well defined parity, in that they appear in either an even or an odd motif. In contrast, the three monoclinic point groups are 'ambidextrous', in that they appear in two motifs, one of each parity. An analysis of the ten 2D point groups reveals an analogous structure, except for the presence of an ambidextrous crystal system. The striking structural uniformity of the motifs across the Hasse diagram confirms that they are essential building blocks of the crystallographic point groups.

We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic three-dimensional (3D) N=4 quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby detailing the stratification of the symplectic singularity defined by the initial Coulomb branch. Leveraging the Lie algebra isomorphism su(4)≅so(6), we validate our algorithm via the 3D mirror of the 4D theories of class S of such type. This comparison involves moduli spaces that admit both orthosymplectic and unitary quiver realizations, the latter being well understood via standard techniques such as decay and fission. Higgsing on the Coulomb branch of the 3D mirror or the magnetic quiver translates to Higgs branch renormalization group flows of the corresponding higher-dimensional superconformal field theories. Thus, we benchmark our method via Higgsing 6D N=(1,0) D-type orbi-instanton theories, predicting novel Higgsing patterns involving products of interacting fixed points, and class S theories of type so(2N), demonstrating Higgsing to products of theories of types specified by Levi subalgebras of so(2N).

Protein-protein interactions (PPIs) are central to virtually all biological processes, and their disruption can lead to a wide spectrum of human diseases. Cross-linking mass spectrometry (XL-MS) enables proteome-scale detection of interacting peptide pairs, from which PPIs can be inferred. However, interpretating XL-MS data to assign homologous cross-linked peptide pairs to specific protein interactions can be challenging. A major hurdle arises when a single peptide can map to multiple proteins, and when two such peptides are paired, the number of possible protein-protein interactions increases combinatorially. This mapping ambiguity can lead to inflated interaction networks that could compromise downstream analysis and biological interpretation. However, this problem has often been overlooked or addressed using heuristic approaches in previous XL-MS studies. To tackle this challenge, we developed XL-Ranker, a computational framework that combines a set cover graph algorithm and machine learning to systematically resolve peptide-mapping ambiguity and infer high-confidence PPIs from XL-MS data. Applied to an XL-MS dataset from HEK293 cells, XL-Ranker identified a high-confidence network with 880 PPIs involving 964 unique genes. Among all possible PPIs, the ones selected by XL-Ranker for inclusion in the final network had significantly higher interaction scores in the STRING database than the excluded ones. Network analysis further demonstrated that these interactions form biologically meaningful clusters, supporting the accuracy of our approach. In summary, XL-Ranker provides a practical solution to a key analytical challenge in XL-MS data interpretation, enhancing the reliability of PPI discovery.

We reduce the problem of proving deterministic and nondeterministic Boolean circuit size lower bounds to the analysis of certain two-dimensional combinatorial cover problems. This is obtained by combining results of Razborov (1989), Karchmer (1993), and Wigderson (1993) in the context of the fusion method for circuit lower bounds with the graph complexity framework of Pudlák, Rödl, and Savický (1988). For convenience, we formalize these ideas in the more general setting of “discrete complexity”, i.e., the natural set-theoretic formulation of circuit complexity, variants of communication complexity, graph complexity, and other measures. We show that random graphs have linear graph cover complexity, and that explicit super-logarithmic graph cover complexity lower bounds would have significant consequences in circuit complexity. We then use discrete complexity, the fusion method, and a result of Karchmer and Wigderson (1993) to introduce nondeterministic graph complexity. This allows us to establish a connection between graph complexity and nondeterministic circuit complexity. Finally, complementing these results, we describe an exact characterization of the power of the fusion method in discrete complexity. This is obtained via an adaptation of a result of Nakayama and Maruoka (1995) that connects the fusion method to the complexity of “cyclic” Boolean circuits, which gneralize the computation of a circuit by allowing cycles in its specification.

Three-dimensional supersymmetric Chern–Simons matter (CSM) theories typically preserve \mathcal{N}=3𝒩=3 supersymmetry but can exhibit enhanced \mathcal{N}=4𝒩=4 supersymmetry under special conditions. A detailed understanding of the moduli space of CSM theories, however, has remained elusive. This paper addresses this gap by systematically analysing the maximal branches of the moduli space of \mathcal{N}=3𝒩=3 and \mathcal{N}=4𝒩=4 CSM realised via Type IIB brane constructions. Firstly, for \mathcal{N}=4𝒩=4 theories with Chern–Simons levels equal 11, the SL(2,\mathbb{Z})SL(2,ℤ) dualisation algorithm is employed to construct dual Lagrangian 3d \mathcal{N}=4𝒩=4 theories without CS terms. This allows the full moduli space to be determined using quiver algorithms that compute Higgs and Coulomb branch Hasse diagrams and associated RG flows. Secondly, for \mathcal{N}=4𝒩=4 theories with CS-levels greater 11, where SL(2,\mathbb{Z})SL(2,ℤ) dualisation does not yield CS-free Lagrangians, a new prescription is introduced to derive two magnetic quivers, MQ_AMQA and MQ_BMQB, whose Coulomb branches capture the maximal A and B branches of the original \mathcal{N}=4𝒩=4 CSM theory. Applying the decay and fission algorithm to MQ_{A/B}MQA/B then enables the systematic analysis of A/B branch RG flows and their geometric structures. Thirdly, for \mathcal{N}=3𝒩=3 CSM theories, one magnetic quiver for each maximal (hyper-Kähler) branch is derived from the brane system. This provides an efficient and comprehensive characterisation of these previously scarcely studied features.

In <span class="math inline">2020</span> Bhavale and Waphare introduced the concept of a nullity of a poset as nullity of its cover graph. According to Bhavale and Waphare, if a dismantlable lattice of nullity <span class="math inline"><em>k</em></span> contains <span class="math inline"><em>r</em></span> reducible elements then <span class="math inline">2 ≤ <em>r</em> ≤ 2<em>k</em></span>. In <span class="math inline">2003</span> Pawar and Waphare counted all non-isomorphic lattices on <span class="math inline"><em>n </em></span>elements having nullity one, containing exactly two reducible elements. Recently, Bhavale and Aware counted all non-isomorphic lattices on <span class="math inline"><em>n</em></span> elements having nullity two, containing up to three reducible elements. In this paper, we count up to isomorphism the class of all lattices on <span class="math inline"><em>n</em></span> elements having nullity two, containing exactly four reducible elements.

Identifying and ranking the key drivers of grassland conversion at the county level is crucial for developing targeted policies and improving protection efficiency. However, this process faces methodological challenges because of spatial and temporal variability. Partial order theory offers a robust framework for addressing these complexities. This study applies partial order theory (POT) combined with the Hasse diagram technique (HDT) to analyze grassland conversion in the Hohhot–Baotou–Ordos region during two time periods (2000–2010 and 2010–2020). First, patterns of grassland transformation are quantified, and the dominant driving factors of grassland conversion out (GCO) are identified and ranked, highlighting regional differences and temporal shifts. By integrating POT and HDT, this study offers a novel approach to handling complex, nonlinear, and hierarchical relationships among multiple drivers. The results provide scientific insight and policy recommendations for region-specific grassland management and sustainable land-use planning. The results show that (1) transitions between grasslands and other land-use types became more frequent across the two periods. Specifically, the rates of grassland conversion out and conversion increased from 2.1% and 3.5% during the period 2000–2010 to 4.7% and 4.8% during the period 2010–2020, respectively. (2) Urbanization was the primary driver of grassland conversion in 11 and 10 of the 18 counties during the first and second periods, respectively, followed by factors related to weather variables. (3) In the future, the eastern region of the study area needs to prioritize mitigating the impacts of urban development, while the western region should focus on enhancing ecological construction projects. This study recommends adopting region-specific ecological protection and economic strategies for balanced outcomes in conservation and development.

In this paper, we have introduced a novel color image encryption technique that relies on repairing a secret encryption key using algebraic lattices represented as Hasse diagrams and cryptography based on the matrices. The color images are converted into its RGB components ( Red, Green and Blue ) and each color is converted into a matrix of integers between 0 and 255. In this encryption process we proposed tow color images Lena of type JPEG and Baboon of type BMP with similar size, and we have involved the mathematical operations: addition, multiplication, and binary calculations, also be carried out a comparative study between certain encryption algorithms on this proposed color images. The experimental results reveal that the presented methods of image encryption has the advantages of large key space, strong robustness and good encryption and decryption performance. In addition, the product method has the merits of excellent performance of encryption.

This paper introduces the concept of the extended \(H\)-cover of a graph \(G\), denoted as \(G^*_H\) , as a generalization inspired by the extended double cover graphs discussed in Chen [1]. We explore the spectral properties and energy characteristics of \(G^*_H\), deriving formulae for the number of spanning trees in cases where both \(G\) and \(H\) are regular. Our investigation identifies several infinite families of equienergetic graphs and highlights instances of cospectral graphs within \(G^*_H\) . Additionally, we analyze various graph parameters related to the Indu-Bala product of graphs and the partial complement of the subdivision graph (PCSD) of \(G\).

In this paper, we study the full Higgs branch Hasse diagrams for any given 6d N = (1, 0) SCFTs constructed via F-theory. This can be done by a procedure of determining all the minimal Higgsings on the generalized quivers of the 6d SCFTs. We call this procedure the atomic Higgsing, which can be implemented iteratively. We present our general algorithm with many concrete examples of Hasse diagrams. We also compare our algorithm with the Higgsings determined by the 3d N = 4 magnetic quivers. For the cases where the magnetic quivers are unitary, we can reproduce the full Hasse diagrams. We also construct the orthosymplectic magnetic quivers from the Type IIA brane systems for some new examples. Our approach, based on F-theory, applies to the known and new orthosymplectic cases, as well as theories that do not have known descriptions in terms of magnetic quivers. We expect our geometry-based approach to help extend the horizon of the RG flows of the 6d SCFTs.

In today's digital age, many operational decisions in businesses rely on data sources, enabling organizations to enhance productivity, make informed decisions, and gain competitive advantages. However, businesses also face data breaches involving sensitive information—such as financial records, intellectual property, and customer personal data—which may be compromised inadvertently. These threats can often be mitigated by implementing robust cybersecurity measures, such as Data Loss Prevention (DLP), to ensure proper monitoring and control of all organizational data, enforce policies without exceptions, and prevent unauthorized data transfers or rule violations. Despite these measures, uncertainties remain regarding the efficacy of identifying threats at various stages of data loss to mitigate their adverse effects through effective cybersecurity. To address this, this paper introduces Complex Linear Diophantine Fuzzy Relations (CLDFRs). For the first time in fuzzy set theory, we analysed the relationships between various threats and components of DLP-based data loss solutions. Additionally, we present the concept of Hasse diagrams for Complex Linear Diophantine Fuzzy Sets and Relations to examine different cybersecurity methods and procedures. This approach helps determine the most effective strategy based on Hasse diagram analysis. Furthermore, after applying specific constraints to the decision-making process, the optimal cybersecurity approach is selected. Finally, a comparative analysis demonstrates the advantages of the proposed methods.