Shinjuku College of Information Technology

Graph-structured data often exhibit complex edge semantics beyond simple undirected links—such as one‐way flows, independent endpoint orientations, or multiple parallel arcs. While standard Graph Neural Networks (GNNs) handle undirected and directed graphs, they cannot fully exploit richer topologies like bidirected or multidirected graphs. We introduce two novel GNN variants: Bidirected GNNs, which separately aggregate messages according to endpoint‐specific arrow assignments, and Multidirected GNNs, which incorporate parallel‐edge counts into feature updates. We present formal definitions, derive update rules, and showcase illustrative examples to demonstrate each model’s ability to encode complex orientation and multiplicity patterns. Our frameworks pave the way for more expressive graph representation learning in domains requiring fine‐grained edge semantics.

Endocrine surgery encompasses various organ systems, but thyroid surgery represents the major component. The Japanese Association of Thyroid Surgeons published nationwide data on thyroid cancer surgery until 2005, since when no further reports have been published. Thus, we analyzed thyroid surgery trends using data from the National Clinical Database (NCD) from 2014 to 2023. We analyzed cases of thyroid surgery, for malignant and benign conditions, recorded in the NCD. A detailed analysis of papillary thyroid carcinoma (PTC) cases was conducted in 2014, 2019, and 2023 to assess TNM classification, surgical procedures, complications, and outcomes. The number of thyroid surgery facilities and the number of thyroid surgeries being performed have both declined since 2020. A trend toward more hemithyroidectomies and fewer total thyroidectomies for PTC is evident. The number of surgeries for cancers < 1cm and lateral node dissection for PTC have also decreased. Endoscopically assisted surgery has increased continuously, accounting for > 4% of thyroid operations in 2020. The incidence of permanent hypoparathyroidism has decreased and perioperative mortality is rare. The changes in surgical trends are aligned with guideline updates and shifts in surgical practice. Future efforts will refine data collection and utilize the NCD to improve thyroid surgical quality and research.

Graph theory provides a fundamental framework for modeling relationships using vertices and edges [1, 2]. Hypergraphs extend this framework by allowing hyperedges that can simultaneously connect multiple vertices [3], while n-Super-HyperGraphs further generalize hypergraphs via iterated power-set constructions to capture hierarchical relationships [4, 5]. In parallel, variousuncertainty modeling paradigms—such as fuzzy sets [6], soft sets [7], intuitionistic fuzzy sets [8–10], neutrosophic sets, and plithogenic sets—have been developed to handle imprecise or indeterminate information. In this paper, we propose a novel framework called the Neutrosophic Soft n-Super-HyperGraph, which integrates neutrosophic logic, soft set theory, and n-Super-HyperGraph structures. This model has the potential to facilitate effective decision-making in complex and uncertain networkedenvironments.

Graph theory is a core branch of mathematics concerned with representing and analyzing relationships among discrete elements. These concepts are widely used in fields such as electrical engineering. For example, graphs play a crucial role in important frameworks including Graph Signal Processing, Electric Circuits, and Bond Graphs. A hypergraph generalizes the concept of a traditional graph by allowing edges—called hyperedges—to connect more than two vertices simultaneously (Berge, 1984). A superhypergraph further extends this idea by incorporating recursively defined powerset layers, enabling hierarchical and self-referential relationships among hyperedges (Smarandache, 2020). In this paper, we extend the frameworks of Graph Signal Processing, Electric Circuits, and Bond Graphs using hypergraphs and superhypergraphs, and investigate their mathematical properties and illustrative examples. These extensions enable the representation of hierarchical structures inherent in Graph Signal Processing, Electric Circuits, and Bond Graphs, providing a more expressive modeling framework. We anticipate that future research will advance computational experiments and practical applications in these domains.

To examine the feasibility of high-frequency sampling of symptoms and gather preliminary data on whether daily exercise behavior is related to daily symptom fluctuations. Seven patients with cancer started a 12-week daily home-based walking and resistance exercise program during chemotherapy. Each day, patients rated pain, numbness/tingling, anxiety, and depression; resistance band exercise duration and perceived exertion; and steps for 12 weeks, as well as their pain at pre-, mid-, and postintervention. Overall, daily symptom ratings showed an expected large variation. Participants took more steps on and after days with less pain; performed more minutes of resistance exercises on days with less pain, numbness/tingling, and anxiety; and reported greater exertion on days with more pain and anxiety. It is feasible to collect daily symptom measures throughout an exercise intervention during chemotherapy. Oncology nurses can help support exercise behavior by offering interventions to reduce interfering symptoms and by promoting helpful beliefs about symptoms.

Rough Sets approximate subsets by defining lower and upper bounds, effectively capturing uncertainty through equivalence classes or indiscernibility relations. Additionally, concepts such as Fuzzy Sets, Neutrosophic Sets, and Soft Sets are well-known for addressing uncertainty, with numerous applications explored in various fields. This paper extends these foundational concepts by introducing six advanced frameworks: the Hyperfuzzy Rough Set, Hyperfuzzy Hyperrough Set, HyperNeutrosophic Rough Set, HyperNeutrosophic Hyperrough Set, Hypersoft Hyperrough Set, and Multigranulation Hyperrough Set. These new models aim to enhance the theoretical understanding and practical handling of uncertainty.

A graph width parameter measures the structural complexity of a graph by assessing how it can be decomposed into simpler components. These parameters are often studied using connectivity systems that satisfy symmetric submodular conditions (Geelen et al., 2006, Oum and Seymour, 2007). Matroids are highly versatile structures with broad applications in optimization theory, combinatorial mathematics, topology, algebra, graph algorithms, game theory, geometry, and network theory, making them a subject of significant interest. Quasi-matroid, as introduced in (Kawahara, 2004) (see also (Kawahara, 2004), extend the concept of matroids by providing a more generalized framework. In this brief paper, we propose the concept of quasi-matroid on a connectivity system and explore their relationship with linear decomposition.

Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective problem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in fields such as social sciences. By incorporating Neutrosophic Sets, we aim to improve their suitability for programming and mathematical analysis, providing advanced methods to tackle complex, multi-dimensional problems. We hope that this research will inspire further studies and foster the development of practical applications across various related disciplines.

Graph theory, a branch of mathematics, examines relationships between entities using vertices and edges. Within this field, Uncertain Graph Theory has emerged to model uncertainties in real world networks. A notable concept in this area is the competition graph, which captures interactions by connecting vertices that ”compete” for the same neighbor, represented by directed edges indicating common neighbors in a digraph. This brief paper introduces the concept of the Generalized Turiyam Neutrosophic Competition Graph and explores its relationships with other graph classes.

In set theory, a filter is a collection of sets that is closed under intersection and includes all supersets of its elements. Within the framework of soft sets mathematical tools developed to handle uncertainty through parameterized subsets-filters and ultrafilters have also been introduced, with further expansions made in fuzzy set theory and Neutrosophic set theory. In this short paper, we introduce the novel concept of a hypersoft filter and provide a brief discussion of its implications.