Pingping Shao | Search arXiv

arXiv2026

On the Roots of Connected Domination Polynomials

We determine the distribution of the roots of the connected domination polynomial $D_c(G,x)$. The main tool is a substitution formula for the lexicographic product with a complete graph, $D_c(G[K_n],x)=D_c(G,(x+1)^n-1)$, which we prove here. Combining the formula with two explicit families of seed roots, the real roots of the cycles $C_n$ and the real roots of the joins $C_m\vee C_n$ lying in $(-1,0)$, we prove that the closure of the real connected domination roots is $(-\infty,0]$, and that the closure of all connected domination roots is the whole complex plane. These are the connected domination analogues of the root-density theorems of Brown and Tufts and of Brown and Beaton for the ordinary domination polynomial.

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↗