arXiv research

In this paper we study the moduli spaces $Simp^m_n$ of degree $n+1$ morphisms $\mathbb{A}^1_{K} \to \mathbb{A}^1_{K}$ with "ramification length $<m$" over an algebraically closed field $K$. For each $m$, the moduli space $Simp^m_n$ is a Zariski open subset of the space of degree $n+1$ polynomials over $K$ up to $Aut (…

DNNs improve SIMP method but not spatially invariant, study shows.

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and up-sampling operations. In addition, a popular technique, namely U-Net, was adop…

Unbounded primitivity index in free groups linked to Chebyshev function.

Topology design optimization offers tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization approaches. Ideally, with adequate problem statements, to formulate and solve the…

Accurately predicting the possible behaviors of traffic participants is an essential capability for future autonomous vehicles. The majority of current researches fix the number of driving intentions by considering only a specific scenario. However, distinct driving environments usually contain various possible driving…