Selected work

Representative Papers

Topological Data Analysis and Graph-Theoretic Approaches for Tennis Match Prediction

Jul 26, 2026

This study addresses the challenge of accurately predicting professional tennis match outcomes in the absence of conventional player rankings. Leveraging ATP singles match data from 2000 to 2025, the authors construct a competitive network among players and introduce the down-star filtration—a novel application in tennis prediction—while systematically evaluating four topological summary methods (VAB, HNAV, HWNAV, and OW-HNPV). By integrating persistent homology, refined band-depth analysis, centrality measures, an enhanced Katz similarity index, and time-weighted edges, their purely topological model achieves a prediction accuracy of 63.56% without any ranking information. A hybrid model incorporating additional features further improves performance to 66.2% accuracy (AUC = 0.719), demonstrating that network topological features provide significant complementary value for match outcome prediction.

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Machine Learning-Guided Quota Optimization for Multi-Round Two-Sided Matching

Jun 11, 2026

This study addresses the challenge of quota optimization in small-scale two-sided matching markets—such as sorority recruitment—characterized by scarce data and multi-round interaction constraints. The authors propose a dynamic quota allocation framework that integrates machine learning with operations research: compatibility scores are predicted using random forests, and integer linear programming dynamically optimizes invitation quotas across rounds, followed by final matching via the deferred acceptance algorithm. A novel robust fallback mechanism is introduced to handle scenarios with weak predictive signals, alongside an interactive tool designed for coordinators. Evaluated on a dataset of only 282 samples, the method achieves a ROC-AUC of 0.5822, yields quota allocations highly consistent with human decisions, and produces final matches aligning with the actual 2025 recruitment outcomes at 96.4% individual-level consistency and 100% match feasibility.

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On the History of the Square and Multiply Algorithm

May 30, 2026

This study investigates the historical origins and formalization of the square-and-multiply algorithm, clarifying its cross-cultural evolution spanning over two millennia. Through rigorous historical documentation, textual analysis, and comparative historiography of mathematics, the paper systematically traces the algorithm’s development from its embryonic binary notions in Pingala’s Sanskrit prosody in ancient India, through refinements by Arabic scholars al-Uqlidisi and al-Biruni, to its first explicit articulation as a general-purpose algorithm by al-Kashi. The research affirms al-Kashi’s originality in formulating the algorithm in its universal form, elucidates the profound mathematical significance underlying Pingala’s early work, and fills a critical gap in scholarly understanding of the origins of this foundational computational method.

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From Historical Puzzles to Grammatical Constraints: Circular Partitions, Generalized Run-Length Encodings, and Polynomial-Time Decidability

Jan 04, 2026arXiv.org

This work investigates a circular partitioning problem inspired by the Josephus problem, incorporating block-pattern constraints from context-free grammars to determine the existence of valid sentences. By reducing the sentence existence problem under grammatical constraints to a regular language membership problem, the authors propose a novel modeling approach based on generalized run-length encoding and Stirling numbers, establishing—for the first time—a formal connection between circular partitioning and grammaticality under block-pattern constraints. The proposed algorithm leverages deterministic finite automata and standard parsing techniques to achieve polynomial-time decidability. Both theoretical analysis and empirical evaluation, including experiments on historical and synthetic datasets, demonstrate the method’s correctness and computational efficiency.

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Hierarchical Persistence Velocity for Network Anomaly Detection: Theory and Applications to Cryptocurrency Markets

Dec 16, 2025

Existing anomaly detection methods for time-varying networks—particularly in cryptocurrency markets—overlook the dynamic evolution speed of topological structures. Method: We propose Overlaid Weighted Hierarchical Normalized Persistence Velocity (OW-HNPV), the first approach to use “topological velocity”—i.e., the birth-and-death rate of features in persistence diagrams—as the core metric, replacing conventional cumulative existence measures. OW-HNPV incorporates an overlaid weighting scheme to enhance robustness and provides a rigorous proof of Lipschitz stability to ensure mathematical reliability. Contribution/Results: Evaluated on topological data analysis (TDA)-driven dynamic network modeling and Ethereum transaction graphs, OW-HNPV achieves a 10.4% AUC improvement in 7-day price anomaly prediction and significantly outperforms baselines—including VAB, persistence landscapes, and persistence images—in medium-term (4–7 day) forecasting.

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Recent publications

Latest Papers

Topological Data Analysis and Graph-Theoretic Approaches for Tennis Match Prediction

Jul 26, 2026

This study addresses the challenge of accurately predicting professional tennis match outcomes in the absence of conventional player rankings. Leveraging ATP singles match data from 2000 to 2025, the authors construct a competitive network among players and introduce the down-star filtration—a novel application in tennis prediction—while systematically evaluating four topological summary methods (VAB, HNAV, HWNAV, and OW-HNPV). By integrating persistent homology, refined band-depth analysis, centrality measures, an enhanced Katz similarity index, and time-weighted edges, their purely topological model achieves a prediction accuracy of 63.56% without any ranking information. A hybrid model incorporating additional features further improves performance to 66.2% accuracy (AUC = 0.719), demonstrating that network topological features provide significant complementary value for match outcome prediction.

0 citationsRead paper

Machine Learning-Guided Quota Optimization for Multi-Round Two-Sided Matching

Jun 11, 2026

This study addresses the challenge of quota optimization in small-scale two-sided matching markets—such as sorority recruitment—characterized by scarce data and multi-round interaction constraints. The authors propose a dynamic quota allocation framework that integrates machine learning with operations research: compatibility scores are predicted using random forests, and integer linear programming dynamically optimizes invitation quotas across rounds, followed by final matching via the deferred acceptance algorithm. A novel robust fallback mechanism is introduced to handle scenarios with weak predictive signals, alongside an interactive tool designed for coordinators. Evaluated on a dataset of only 282 samples, the method achieves a ROC-AUC of 0.5822, yields quota allocations highly consistent with human decisions, and produces final matches aligning with the actual 2025 recruitment outcomes at 96.4% individual-level consistency and 100% match feasibility.

0 citationsRead paper

On the History of the Square and Multiply Algorithm

May 30, 2026

This study investigates the historical origins and formalization of the square-and-multiply algorithm, clarifying its cross-cultural evolution spanning over two millennia. Through rigorous historical documentation, textual analysis, and comparative historiography of mathematics, the paper systematically traces the algorithm’s development from its embryonic binary notions in Pingala’s Sanskrit prosody in ancient India, through refinements by Arabic scholars al-Uqlidisi and al-Biruni, to its first explicit articulation as a general-purpose algorithm by al-Kashi. The research affirms al-Kashi’s originality in formulating the algorithm in its universal form, elucidates the profound mathematical significance underlying Pingala’s early work, and fills a critical gap in scholarly understanding of the origins of this foundational computational method.

0 citationsRead paper

From Historical Puzzles to Grammatical Constraints: Circular Partitions, Generalized Run-Length Encodings, and Polynomial-Time Decidability

Jan 04, 2026arXiv.org

This work investigates a circular partitioning problem inspired by the Josephus problem, incorporating block-pattern constraints from context-free grammars to determine the existence of valid sentences. By reducing the sentence existence problem under grammatical constraints to a regular language membership problem, the authors propose a novel modeling approach based on generalized run-length encoding and Stirling numbers, establishing—for the first time—a formal connection between circular partitioning and grammaticality under block-pattern constraints. The proposed algorithm leverages deterministic finite automata and standard parsing techniques to achieve polynomial-time decidability. Both theoretical analysis and empirical evaluation, including experiments on historical and synthetic datasets, demonstrate the method’s correctness and computational efficiency.

0 citationsRead paper

Hierarchical Persistence Velocity for Network Anomaly Detection: Theory and Applications to Cryptocurrency Markets

Dec 16, 2025

Existing anomaly detection methods for time-varying networks—particularly in cryptocurrency markets—overlook the dynamic evolution speed of topological structures. Method: We propose Overlaid Weighted Hierarchical Normalized Persistence Velocity (OW-HNPV), the first approach to use “topological velocity”—i.e., the birth-and-death rate of features in persistence diagrams—as the core metric, replacing conventional cumulative existence measures. OW-HNPV incorporates an overlaid weighting scheme to enhance robustness and provides a rigorous proof of Lipschitz stability to ensure mathematical reliability. Contribution/Results: Evaluated on topological data analysis (TDA)-driven dynamic network modeling and Ethereum transaction graphs, OW-HNPV achieves a 10.4% AUC improvement in 7-day price anomaly prediction and significantly outperforms baselines—including VAB, persistence landscapes, and persistence images—in medium-term (4–7 day) forecasting.

0 citationsRead paper