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Research Paper#Tropical Geometry, Algebraic Geometry🔬 ResearchAnalyzed: Jan 3, 2026 16:41

Poincaré Duality for Singular Tropical Hypersurfaces

Published:Dec 31, 2025 01:12
1 min read
ArXiv

Analysis

This paper extends Poincaré duality to a specific class of tropical hypersurfaces constructed via combinatorial patchworking. It introduces a new notion of primitivity for triangulations, weaker than the classical definition, and uses it to establish partial and complete Poincaré duality results. The findings have implications for understanding the geometry of tropical hypersurfaces and generalize existing results.
Reference

“The paper finds a partial extension of Poincaré duality theorem to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking.”

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Research Paper#Causal Inference, Machine Learning, Gaussian Processes🔬 ResearchAnalyzed: Jan 3, 2026 18:47

Scalable Heterogeneous Treatment Effect Estimation with Propensity Patchwork Kriging

Published:Dec 29, 2025 13:49
1 min read
ArXiv

Analysis

This paper addresses the computational limitations of Gaussian process-based models for estimating heterogeneous treatment effects (HTE) in causal inference. It proposes a novel method, Propensity Patchwork Kriging, which leverages the propensity score to partition the data and apply Patchwork Kriging. This approach aims to improve scalability while maintaining the accuracy of HTE estimates by enforcing continuity constraints along the propensity score dimension. The method offers a smoothing extension of stratification, making it an efficient approach for HTE estimation.
Reference

“The proposed method partitions the data according to the estimated propensity score and applies Patchwork Kriging to enforce continuity of HTE estimates across adjacent regions.”

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