Review of the Research on the Identification of Electrical Fire Trace Evidence

AbstractIn this paper, we review the research results about the identification of the electrical fire trace evidence and the fire reason recognition. We point out the existing problems and put forward the corresponding suggestions to promote the development of the cause of the fire investigation and make it better to serve for the work of fire investigation

Energetic Variation with the Anderson Hamiltonian

We study the variation problem associated with the Anderson Hamiltonian in 2-dimensional torus in the paracontrolled distribution framework. We obtain the existence of minimizers by the direct method in the calculus of variations, and show that the Euler-Lagrange equation of the energy functional is an elliptic singular stochastic partial differential equation with the Anderson Hamiltonian. We also establish the L^2 estimates and Schauder estimates for the minimizer as weak solution of the elliptic singular stochastic partial differential equation.Comment: arXiv admin note: text overlap with arXiv:2109.1042

Multiple closed geodesics on Finsler 33-dimensional sphere

In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on $S^3$ with exactly four prime closed geodesics. And then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler $S^3$. In this paper, we proved this conjecture for bumpy Finsler $S^{3}$ if the Morse index of any prime closed geodesic is nonzero.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1504.07007, arXiv:1510.02872, arXiv:1508.0557

Exploring Object Relation in Mean Teacher for Cross-Domain Detection

Rendering synthetic data (e.g., 3D CAD-rendered images) to generate annotations for learning deep models in vision tasks has attracted increasing attention in recent years. However, simply applying the models learnt on synthetic images may lead to high generalization error on real images due to domain shift. To address this issue, recent progress in cross-domain recognition has featured the Mean Teacher, which directly simulates unsupervised domain adaptation as semi-supervised learning. The domain gap is thus naturally bridged with consistency regularization in a teacher-student scheme. In this work, we advance this Mean Teacher paradigm to be applicable for cross-domain detection. Specifically, we present Mean Teacher with Object Relations (MTOR) that novelly remolds Mean Teacher under the backbone of Faster R-CNN by integrating the object relations into the measure of consistency cost between teacher and student modules. Technically, MTOR firstly learns relational graphs that capture similarities between pairs of regions for teacher and student respectively. The whole architecture is then optimized with three consistency regularizations: 1) region-level consistency to align the region-level predictions between teacher and student, 2) inter-graph consistency for matching the graph structures between teacher and student, and 3) intra-graph consistency to enhance the similarity between regions of same class within the graph of student. Extensive experiments are conducted on the transfers across Cityscapes, Foggy Cityscapes, and SIM10k, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, we obtain a new record of single model: 22.8% of mAP on Syn2Real detection dataset.Comment: CVPR 2019; The codes and model of our MTOR are publicly available at: https://github.com/caiqi/mean-teacher-cross-domain-detectio