Search Results (16)

This paper introduces a framework of hypercompositional algebra on fuzzy graphs by defining and analyzing fuzzy path-based hyperoperations. Building on the notion of strongest strong paths (paths that are both strength-optimal and composed exclusively of strong edges, where each edge achieves maximum connection strength between its endpoints), we define two operations: a vertex-based fuzzy path hyperoperation and an edge-based variant. These operations generalize classical graph hyperoperations to the fuzzy setting while maintaining compatibility with the underlying topology. We prove that the vertex fuzzy path hyperoperation is associative, forming a fuzzy hypersemigroup, and establish additional properties such as reflexivity and monotonicity with respect to $\alpha$-cuts. Structural features such as fuzzy strong cut vertices and edges are examined, and a fuzzy distance function is introduced to quantify directional connectivity strength. We define an equivalence relation based on mutual full-strength reachability and construct a quotient fuzzy graph that reflects maximal closed substructures under the vertex fuzzy path hyperoperation. Applications are discussed in domains such as trust networks, biological systems, and uncertainty-aware communications. This work aims to lay the algebraic foundations for further exploration of fuzzy hyperstructures that support modeling, analysis, and decision-making in systems governed by partial and asymmetric relationships. Full article

Symmetry in non-planar graphs is a fundamental concept that enhances understanding, simplifies analyses, and has practical implications in diverse fields such as science, engineering, and mathematics. A total $\kappa$-labeling for a graph $\check{G_{\nu }}$ is composed of two labeling: one is an edge labeling ${{\rm Y}}_e:E(\check{G_{\nu }})\to \{1,2,3,\dots ,{\kappa }_e\}$ and the other is a vertex labeling ${{\rm Y}}_v:V(\check{G_{\nu }})\to \{0,2,4,\dots ,2{\kappa }_v\}$, where $\kappa =max\{{\kappa }_e,2{\kappa }_v\}$. The weight of an edge under reflexive labeling is defined as $wt(pq)={{\rm Y}}_v(p)+{{\rm Y}}_e(pq)+{{\rm Y}}_v(q)\forall e=pq$. The total $\kappa -labeling$ is said to be an edge-irregular reflexive $\kappa -labeling$, if for every two edges $e_{\delta }$ and $e_j$, the weights are distinct. The lowest value of $\kappa$ for which the graph $\check{G_{\nu }}$ has an irregular reflexive edge $\kappa -labeling$ is called the reflexive edge strength of $\check{G_{\nu }}$, denoted as $res(\check{G_{\nu }})$. $res(\check{G_{\nu }})$ captures irregularity while preserving reflexivity by quantifying edge-weight variability in reflexive graphs. In this article, we are interested in determining the tight lower bound for non-planar prisms, cross prisms, cross-particle modified graphs, and cross-particle glowing graphs under reflexive labeling. Full article

Event causality identification (ECI) focuses on detecting causal relationships between events within a document. Existing approaches typically treat each event-mention pair independently, overlooking the relational dynamics and potential conflicts among event causalities. To tackle this challenge, we propose the Event-induced Graph with Constraints (EiGC), which models the complex event-level causal structures in a more realistic manner, facilitating comprehensive causal relation identification. To be more specific, we construct a graph based on diverse event-driven knowledge sources, such as coreference and co-occurrence relations. A graph convolutional network (GCN) is then employed to encode these structural features, effectively capturing both local and global dependencies between nodes. Additionally, we implement event-aware constraints through integer linear programming, incorporating the principles of uniqueness, non-reflexivity, and coreference consistency in event-causal relationships. This approach ensures logical consistency and prevents conflicts in the prediction outcomes. Experimental results on three widely used datasets illustrate that our proposed EiGC approach achieves excellent performance among all the baseline models. Full article

In this paper, we initiate a concept of graph-proximal functions. Furthermore, we give a notion of being generalized Geraghty dominating for a pair of mappings. This permits us to establish the existence of and unique results for a common best proximity point of complete metric space. Additionally, we give a concrete example and corollaries related to the main theorem. In particular, we apply our main results to the case of metric spaces equipped with a reflexive binary relation. Finally, we demonstrate the existence of a solution to boundary value problems of particular second-order differential equations. Full article

The use of knowledge graphs has grown significantly in recent years. However, entities and relationships must be transformed into forms that can be processed by computers before the construction and application of a knowledge graph. Due to its simplicity, effectiveness, and great interpretability, the translation model lead by TransE has garnered the most attention among the many knowledge representation models that have been presented. However, the performance of this model is poor when dealing with complex relations such as one-to-many, many-to-one, and reflexive relations. Therefore, a knowledge representation learning model based on a relational neighborhood and flexible translation (TransRFT) is proposed in this paper. Firstly, the triples are mapped to the relational hyperplane using the idea of TransH. Then, flexible translation is applied to relax the strict restriction h + r = t in TransE. Finally, the relational neighborhood information is added to further improve the performance of the model. The experimental results show that the model has good performance in triplet classification and link prediction. Full article

While surveying some internal categorical structures and their applications, it is shown that triangulations and internal groupoids can be unified as two different instances of the same common structure, namely a multi-link. A brief survey includes the categories of directed graphs, reflexive graphs, links, multi-links, triangulations, trigraphs, multiplicative graphs, groupoids, pregroupoids, internal categories, kites, directed kites and multiplicative kites. Most concepts are well-known, and all of them have appeared in print at least once. For example, a multiplicative directed kite has been used as a common generalization for an internal category and a pregroupoid. The scope of the notion of centralization for equivalence relations is widened into the context of digraphs while providing a new characterization of internal groupoids. Full article

A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let $\mathcal{R}$ be a commutative ring with identity, and $Z^{*}(\mathcal{R})$ is the set of all non-zero zero divisors of $\mathcal{R}$. Then, $\Gamma (\mathcal{R})$ is said to be a zero-divisor graph if and only if $a·b=0$, where $a,b\in V(\Gamma (\mathcal{R}))=Z^{*}(\mathcal{R})$ and $(a,b)\in E(\Gamma (\mathcal{R}))$. We define $a\sim b$ if $a·b=0$ or $a=b$. Then, ∼ is always reflexive and symmetric, but ∼ is usually not transitive. Then, $\Gamma (\mathcal{R})$ is a symmetric structure measured by the ∼ in commutative rings. Here, we will draw the zero-divisor graph from commutative rings and discuss topological indices for a zero-divisor graph by vertex eccentricity. In this paper, we will compute the total eccentricity index, eccentric connectivity index, connective eccentric index, eccentricity based on the first and second Zagreb indices, Ediz eccentric connectivity index, and augmented eccentric connectivity index for the zero-divisor graph associated with commutative rings. These will help us understand the characteristics of various symmetric physical structures of finite commutative rings. Full article

Due to the increasing complexity of analog circuits and their integration into System-on-Chips (SoC), the analog design and verification industry would greatly benefit from an expansion of system-level methodologies using SystemC AMS. These can provide a speed increase of over $\mathrm{100,000}$× in comparison to SPICE-level simulations and allow interoperability with digital tools at the system-level. However, a key barrier to the expansion of system-level tools for analog circuits is the lack of confidence in system-level models implemented in SystemC AMS. Functional equivalence of single Laplace Transfer Function (LTF) system-level models to respective SPICE-level models was successfully demonstrated recently. However, this is clearly not sufficient, as the complex systems comprise multiple LTF modules. In this article, we go beyond single LTF models, i.e., we develop a novel graph-based methodology to formally check equivalence between complex system-level and SPICE-level representations of Single-Input Single-Output (SISO) linear analog circuits, such as High-Pass Filters (HPF). To achieve this, first, we introduce a canonical representation in the form of a Signal-Flow Graph (SFG), which is used to functionally map the two representations from separate modeling levels. This canonical representation consists of the input and output nodes and a single edge between them with an LTF as its weight. Second, we create an SFG representation with linear graph modeling for SPICE-level models, whereas for system-level models we extract an SFG from the behavioral description. We then transform the SFG representations into the canonical representation by utilizing three graph manipulation techniques, namely node removal, parallel edge unification, and reflexive edge elimination. This allows us to establish functional equivalence between complex system-level models and SPICE-level models. We demonstrate the applicability of the proposed methodology by successfully applying it to complex circuits. Full article

Multiple representations, such as experimental data, schemas, tables, and graphs, are an essential resource in science teaching. However, their use in the classroom typically poses a challenge for preservice teachers. The aim of this research is to examine changes in the practices of a group of preservice teachers regarding the use of multiple representations in the teaching of kinetic energy to 9th grade students, when this training is included in their initial teacher education program. For this purpose, a collaborative, reflexive, and student-learning centered approach, namely, a lesson study with three cycles, was implemented. A descriptive and content analysis for qualitative data collected showed improvement in the practices of the preservice teachers, namely on the representations both of the event that represents the “real” world, as well as of the scientific concepts. The results obtained contribute to deepening the knowledge on the use of multiple representations by preservice teachers, as well as to increasing the knowledge on using lesson study to develop the ability to use multiple representations during initial teacher education. Full article

Models@runtime (models at runtime) are based on computation reflection. Runtime models can be regarded as a reflexive layer causally connected with the underlying system. Hence, every change in the runtime model involves a change in the reflected system, and vice versa. To the best of our knowledge, there are no runtime models for Python applications. Therefore, we propose a formal approach based on Petri Nets (PNs) to model, develop, and reconfigure Python applications at runtime. This framework is supported by a tool whose architecture consists of two modules connecting both the model and its execution. The proposed framework considers execution exceptions and allows users to monitor Python expressions at runtime. Additionally, the application behavior can be reconfigured by applying Graph Rewriting Rules (GRRs). A case study using Service-Level Agreement (SLA) violations is presented to illustrate our approach. Full article

The α₁-adrenoceptor agonist phenylephrine (PE) and Angiotensin II (Ang II) are both potent vasoconstrictors at peripheral resistance arteries. PE has pure vasoconstrictive properties. Ang II, additionally, modulates central nervous blood pressure (BP) control via sympathetic baroreflex resetting. However, it is unknown whether Ang II vs. PE mediated vasoconstriction at equipressor dose uniformly or specifically modifies arterial stiffness. We conducted a three-arm randomized placebo-controlled cross-over trial in 30 healthy volunteers (15 female) investigating the effects of Ang II compared to PE at equal systolic pressor dose on pulse wave velocity (PWV), pulse wave reflection (augmentation index normalized to heart rate 75/min, AIx) and non-invasive hemodynamics by Mobil-O-Graph™ and circulating core markers of endothelial (dys-)function. PE but not Ang II-mediated hypertension induced a strong reflex-decrease in cardiac output. Increases in PWV, AIx, total peripheral resistance and pulse pressure, in contrast, were stronger during PE compared to Ang II at equal mean aortic BP. This was accompanied by minute changes in circulating markers of endothelial function. Moreover, we observed differential hemodynamic changes after stopping either vasoactive infusion. Ang II- and PE-mediated BP increase specifically modifies arterial stiffness and hemodynamics with aftereffects lasting beyond mere vasoconstriction. This appears attributable in part to different interactions with central nervous BP control including modified baroreflex function. Full article

The line graph of a graph G is another graph of which the vertex set corresponds to the edge set of G, and two vertices of the line graph of G are adjacent if the corresponding edges in G share a common vertex. A graph is reflexive if the second-largest eigenvalue of its adjacency matrix is no greater than 2. Reflexive graphs give combinatorial ground to generate two classes of algebraic numbers, Salem and Pisot numbers. The difficult question of identifying those graphs whose line graphs are reflexive (called L-reflexive graphs) is naturally attacked by first answering this question for trees. Even then, however, an elegant full characterization of reflexive line graphs of trees has proved to be quite formidable. In this paper, we present an efficient algorithm for the exhaustive generation of maximal L-reflexive trees. Full article

A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph $G=(V,E)$ a vertex labeling is a capacity from V to an arrangement of integers. A graph with such a capacity characterized is known as a vertex-labeled graph. Similarly, an edge labeling is an element of E to an arrangement of labels. For this situation, the graph is called an edge-labeled graph. We examine an edge irregular reflexive k-labeling for the disjoint association of the cycle related graphs and decide the correct estimation of the reflexive edge strength for the disjoint association of s isomorphic duplicates of the cycle related graphs to be specific Generalized Peterson graphs. Full article

This study evaluated the effects of exergaming on college students’ energy expenditure (EE), moderate-to-vigorous physical activity (MVPA), light physical activity (LPA), rating of perceived exertion (RPE), and enjoyment compared to traditional treadmill exercise, and sex differences. Sixty college students (30 female; $\overline{\mathrm{X}}$ _age = 23.6 ± 4.1 years) completed three 20-min exercise sessions on Xbox 360 Kinect Just Dance (Microsoft, Redmond, WA, USA), Xbox 360 Kinect Reflex Ridge (Microsoft, Redmond, WA, USA), and treadmill walking. Their EE and PA were assessed by ActiGraph accelerometers (ActiGraph Co.; Pensacola, FL, USA); RPE every four min; enjoyment via an established scale. Significant exercise-type by sex interaction effects were observed for RPE (p < 0.01): females reported significantly lower RPE during exergaming sessions but significantly higher RPE during treadmill walking. Results revealed significant main effects for all outcomes between exercise sessions (all p < 0.01): treadmill walking resulted in significantly higher metabolic equivalents (METs), MVPA, and EE (p < 0 .01), yet lower LPA (p < 0.01), compared to the two exergaming sessions. Participants’ RPE was significantly higher during treadmill walking than during exergaming sessions, with exergaming eliciting significantly higher enjoyment (all p < 0.01). College students find exergaming more enjoyable and report lower RPE compared to traditional treadmill exercise, though not yet matching the moderate physiological intensity level. Full article

In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph $G=(V,E)$ , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a capacity characterized defined is known as a vertex-marked graph. Similarly, an edge naming is a mapping of an element of E to an arrangement of marks. In this case, the diagram is called an edge-marked graph. We consider an edge irregular reflexive k-labeling for the disjoint association of wheel-related diagrams and deduce the correct estimation of the reflexive edge strength for the disjoint association of m copies of some wheel-related graphs, specifically gear graphs and prism graphs. Full article