Towards Optimal Prefix-Free Graph Construction: NP-Hardness and Structural Insights
本文研究了最小化前缀自由图构造问题，证明其为NP难，并通过与de Bruiijn图建立联系揭示结构特性，提出了一种精确的固定参数算法。
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This work proposes a unified framework for efficiently computing matrix elements—also known as group functions—of irreducible representations of the unitary group $U(d)$, accommodating both symbolic and numerical computation requirements. Built upon the Gelfand–Tsetlin basis, the approach integrates group representation theory, algorithms for Schur functions, and parameterizations of unitary matrices commonly used in quantum optics. It enables full representation construction, conversion between Gelfand–Tsetlin patterns and occupation-number states, and evaluation of Schur functions. The study presents the first general-purpose, high-performance library for $U(d)$ group functions implemented in Julia, offering seamless interoperability between quantum information science and representation theory, with export capabilities to Mathematica. Notably, the Wigner D-functions for $SU(2)$ emerge as a special case, significantly enhancing computational efficiency and cross-disciplinary compatibility.
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State Complexity of Multiple Concatenation
This paper investigates the state complexity of concatenating $k$ regular languages. **Problem:** Addressing an open question posed by Caron et al., it examines the optimality and alphabet dependence of concatenation state complexity bounds. **Method:** Leveraging automata-theoretic techniques, the authors construct carefully designed witness languages to systematically characterize the critical behavior of state explosion under varying alphabet sizes. **Contribution/Results:** They establish, for the first time, that the known upper bound for three-language concatenation is tight over a ternary alphabet—and cannot be achieved over a binary alphabet—while simplifying the prior proof and reducing the required alphabet size by one symbol. For general $k$, they derive a tight asymptotic bound $Theta(2^k)$ for concatenation over a $k$-letter alphabet, breaking the previous reliance on $(k+1)$-letter alphabets. They further prove asymptotically tight bounds and exponential lower bounds for binary and ternary cases, and analyze improved upper bounds for special language classes such as unary cyclic languages.
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A global view of diverse construction methods of fuzzy implication functions rooted on F-chains
Despite the diversity of construction methods for fuzzy implication functions, a unified theoretical framework remains lacking. Method: This paper proposes a generalized construction framework based on F-chains, extending the classical F-chain structure by introducing families of fuzzy implications and bimonotonic functions; it systematically unifies classical approaches—including contraposition, aggregation, and thresholding—by revealing their shared structural characteristics. Contribution/Results: Within this new framework, sufficient conditions are established for preserving key logical properties—such as commutativity, continuity, and left/right monotonicity—of the resulting fuzzy implications. To our knowledge, this is the first formal unification of major existing construction methods, offering a theoretically rigorous and broadly applicable paradigm for both the design and analysis of fuzzy implication functions.
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Morphological classification of eclipsing binary stars using computer vision methods
This study addresses the automatic morphological classification of eclipsing binary light curves. We propose an image-based representation method that combines polar-coordinate mapping with hexagonal binning (hexbin) visualization to transform one-dimensional phase-folded light curves into two-dimensional images exhibiting structural robustness and scale invariance. Building upon this representation, we design a two-stage hierarchical classification framework: the first stage distinguishes detached from overcontact systems; the second stage identifies the presence of starspots. We employ transfer learning using pretrained ResNet50 and ViT-Base (patch16_224) models, fine-tuned on synthetic data and applied to multi-band observations. Experiments on real-world datasets—OGLE, DEBCat, and WUMaCat—achieve overall classification accuracies of 94%–100%, substantially outperforming conventional time-series feature-based approaches. Binary configuration identification accuracy exceeds 96%, whereas starspot detection remains challenging.
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Towards Optimal Prefix-Free Graph Construction: NP-Hardness and Structural Insights
本文研究了最小化前缀自由图构造问题，证明其为NP难，并通过与de Bruiijn图建立联系揭示结构特性，提出了一种精确的固定参数算法。
0 citationsRead paper
GroupFunctions.jl: computing individual entries of the irreducible representations of the unitary group U(d)
This work proposes a unified framework for efficiently computing matrix elements—also known as group functions—of irreducible representations of the unitary group $U(d)$, accommodating both symbolic and numerical computation requirements. Built upon the Gelfand–Tsetlin basis, the approach integrates group representation theory, algorithms for Schur functions, and parameterizations of unitary matrices commonly used in quantum optics. It enables full representation construction, conversion between Gelfand–Tsetlin patterns and occupation-number states, and evaluation of Schur functions. The study presents the first general-purpose, high-performance library for $U(d)$ group functions implemented in Julia, offering seamless interoperability between quantum information science and representation theory, with export capabilities to Mathematica. Notably, the Wigner D-functions for $SU(2)$ emerge as a special case, significantly enhancing computational efficiency and cross-disciplinary compatibility.
0 citationsRead paper
State Complexity of Multiple Concatenation
This paper investigates the state complexity of concatenating $k$ regular languages. **Problem:** Addressing an open question posed by Caron et al., it examines the optimality and alphabet dependence of concatenation state complexity bounds. **Method:** Leveraging automata-theoretic techniques, the authors construct carefully designed witness languages to systematically characterize the critical behavior of state explosion under varying alphabet sizes. **Contribution/Results:** They establish, for the first time, that the known upper bound for three-language concatenation is tight over a ternary alphabet—and cannot be achieved over a binary alphabet—while simplifying the prior proof and reducing the required alphabet size by one symbol. For general $k$, they derive a tight asymptotic bound $Theta(2^k)$ for concatenation over a $k$-letter alphabet, breaking the previous reliance on $(k+1)$-letter alphabets. They further prove asymptotically tight bounds and exponential lower bounds for binary and ternary cases, and analyze improved upper bounds for special language classes such as unary cyclic languages.
0 citationsRead paper
A global view of diverse construction methods of fuzzy implication functions rooted on F-chains
Despite the diversity of construction methods for fuzzy implication functions, a unified theoretical framework remains lacking. Method: This paper proposes a generalized construction framework based on F-chains, extending the classical F-chain structure by introducing families of fuzzy implications and bimonotonic functions; it systematically unifies classical approaches—including contraposition, aggregation, and thresholding—by revealing their shared structural characteristics. Contribution/Results: Within this new framework, sufficient conditions are established for preserving key logical properties—such as commutativity, continuity, and left/right monotonicity—of the resulting fuzzy implications. To our knowledge, this is the first formal unification of major existing construction methods, offering a theoretically rigorous and broadly applicable paradigm for both the design and analysis of fuzzy implication functions.
0 citationsRead paper
Morphological classification of eclipsing binary stars using computer vision methods
This study addresses the automatic morphological classification of eclipsing binary light curves. We propose an image-based representation method that combines polar-coordinate mapping with hexagonal binning (hexbin) visualization to transform one-dimensional phase-folded light curves into two-dimensional images exhibiting structural robustness and scale invariance. Building upon this representation, we design a two-stage hierarchical classification framework: the first stage distinguishes detached from overcontact systems; the second stage identifies the presence of starspots. We employ transfer learning using pretrained ResNet50 and ViT-Base (patch16_224) models, fine-tuned on synthetic data and applied to multi-band observations. Experiments on real-world datasets—OGLE, DEBCat, and WUMaCat—achieve overall classification accuracies of 94%–100%, substantially outperforming conventional time-series feature-based approaches. Binary configuration identification accuracy exceeds 96%, whereas starspot detection remains challenging.
0 citationsRead paper