Volume 2, Issue 1 (2026)
Table of contents
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Group-Theoretic Symmetry Indices for Modular Building Layouts under Seismic Load Redistribution
Abstract: Symmetry in modular buildings operates simultaneously as an architectural language, a structural regularizer, and a computational design variable. This paper develops a group-theoretic framework for evaluating and optimizing plan symmetry in modular buildings subjected to seismic load redistribution. The building layout is modeled as a finite occupancy–stiffness field defined on a rectangular lattice, where each module encodes both mass and stiffness contributions. Planar reflections and quarter-turn rotations are represented as …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 01–07 Read article
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Quantum-Fuzzy Tensor Operators and Uncertainty-Band Bifurcation for Symmetry-Preserving State Discrimination
Abstract: A tensor-operator framework is developed for fuzzy conjunction, fuzzy disjunction, and symmetry-preserving state discrimination in multi-qubit quantum systems. In this formulation, fuzzy membership and non-membership degrees are represented through expectations of effect operators acting on density matrices, providing a natural bridge between fuzzy logic and quantum measurement theory. Conjunction and disjunction operations are extended to the quantum domain via tensorised channels, constructed using projective measurements and unitary transformations, enabling logical …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 08–15 Read article
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Quantum-Fuzzy Tensor Operators for Multi-Qubit Conjunction, Disjunction, and Symmetry-Preserving State Discrimination
Abstract: The integration of fuzzy logic and quantum information theory raises a fundamental mathematical question: how can degrees of truth be encoded in multi-qubit amplitudes while preserving the unitary dynamics and symmetry structure of quantum state spaces? This paper develops a tensor-operator framework for implementing quantum-fuzzy logical operations on finite qubit registers. Fuzzy truth values are represented by normalized quantum amplitude pairs, enabling logical information to be embedded directly into quantum …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 16–21 Read article
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Representation-Theoretic Symmetry Reduction and Fuzzy-Grey Optimization of Modular Vibration Systems
Abstract: This paper presents a representation-theoretic framework for symmetry-aware vibration control in modular structural systems. Exploiting cyclic symmetry, the mass, damping, and stiffness operators are block-diagonalised into irreducible representations, reducing the full structural dynamics to a collection of lower-dimensional modal subsystems. This decomposition provides both computational efficiency and a rigorous mathematical description of symmetry-preserving dynamic behaviour. To account for imperfections arising in practical implementations, near-symmetry defects in stiffness and damping are …
Published in Emerging Trends in Symmetry · Vol. 2, Issue 1, 2026 · pp. 22–30 Read article