Pingping Shao | Searcharxiv

arXiv2026

Generalizations and Applications of the Brown--Tufts Lemma

Brown and Tufts proved in 2014 the substitution formula for the domination polynomial under graph substitution (the lexicographic product), and used it to show that the closure of the domination roots is the whole complex plane. In this paper we undertake a systematic study of the extent to which this lemma extends to the most common domination variants. We first prove that the connected domination polynomial satisfies exactly the same substitution formula. We then show that the formula fails for both independent domination and total domination: for independent domination we give a counterexample and establish a corrected formula, and for total domination we exhibit a concrete counterexample. Finally, applying the substitution formula for the connected domination polynomial, we prove that the closure of the real connected domination roots is $(-\infty,0]$, and that the closure of the connected domination roots is the whole complex plane.

math.CO↗

arXiv2024

APS-LSTM: Exploiting Multi-Periodicity and Diverse Spatial Dependencies for Flood Forecasting

Accurate flood prediction is crucial for disaster prevention and mitigation. Hydrological data exhibit highly nonlinear temporal patterns and encompass complex spatial relationships between rainfall and flow. Existing flood prediction models struggle to capture these intricate temporal features and spatial dependencies. This paper presents an adaptive periodic and spatial self-attention method based on LSTM (APS-LSTM) to address these challenges. The APS-LSTM learns temporal features from a multi-periodicity perspective and captures diverse spatial dependencies from different period divisions. The APS-LSTM consists of three main stages, (i) Multi-Period Division, that utilizes Fast Fourier Transform (FFT) to divide various periodic patterns; (ii) Spatio-Temporal Information Extraction, that performs periodic and spatial self-attention focusing on intra- and inter-periodic temporal patterns and spatial dependencies; (iii) Adaptive Aggregation, that relies on amplitude strength to aggregate the computational results from each periodic division. The abundant experiments on two real-world datasets demonstrate the superiority of APS-LSTM. The code is available: https://github.com/oopcmd/APS-LSTM.

cs.LG↗