Shipping Containers for Sustainable Housing Development

Engineering and ArchitectureDue to global warming and rapid growth of population, there is a high demand for buildings and houses that have reliable quality and sustainable features, such as waste material reuse and low emissions.Intermodal Freight Shipping Container (ISO container) is one of the ideal green construction materials having many advantages and applications. Recyclability, ease of manufacture and assembling, and various constructional forms allow ISO containers possibly the next house-building trend and revolution in civil engineering structure and construction. However, unfortunately, there is few studies and application on shipping containers cooperating with permanent structures as building components. In this study, the objectives were to model and conduct the theoretical analysis and the finite element simulation to show stress and deflection distribution on ISO containers under different loading scenarios, in order to carry out a participatory construction guide for shipping container building components. To better understand load distributions, yielding components and strength contribution and non-contribution areas on shipping container structures with artificial cutting doors and windows, I used both real-life examples and finite element simulation models to proceed loading case analysis. Through the process of analysis, ABAQUS was mainly used to conduct linear and nonlinear finite element analysis using small mesh units to show differences and results of the molded and unmolded shipping container structures. The study is still in progress. After the first stage---loading analysis, the Mises Stress Contours were generated to show stress distribution and simulated the deflecting shape of the shipping containers under different loading cases. Next, I will focus on the analysis of energy performance. The study analyzing different loading scenarios is to stimulate real situation structural loading scenarios from the building components that may apply on some parts of the shipping containers. The study will also help understand most of the structural features and some noticeably reinforced areas of the shipping containers if applied to building construction.Undergraduate Engineering Office - Honors Research Distinction ProgramAcademic Major: Civil Engineerin

Optimal diameter estimates of three-dimensional Ricci limit spaces

In this note, we prove that positive scalar curvature can pass to three dimensional Ricci limit spaces of non-negative Ricci curvature when it splits off a line. As a corollary, we obtain an optimal Bonnet-Myers type upper bound. Moreover, we obtain a similar statement in all dimensions for Alexandrov spaces of non-negative curvature.Comment: 6 pages, a similar result for non-negative sectional curvature is adde

Positive Scalar Curvature Meets Ricci Limit Spaces

We investigate how the positive scalar curvature controls the size of a Ricci limit space when it comes from a sequence of $n$-manifolds with non-negative Ricci curvature and strictly positive scalar curvature lower bound. We prove such a limit space can split off $\mathbb{R}^{n-2}$ at most, and when the maximal splitting happens, the other non-splitting factor has an explicit uniform diameter upper bound. Besides, we study some other consequences of having positive scalar curvature for manifolds using Ricci limit spaces techniques, for instance volume gap estimates and volume growth order estimates.Comment: 22 pages. Some conditions added to the theorem 1.1 due to a gap in the original proof, and the proof is slightly changed accordingly. A corollary about the first Betti number is adde

A direct approach to sharp Li-Yau Estimates on closed manifolds with negative Ricci lower bound

Recently, Qi S.Zhang [26] has derived a sharp Li-Yau estimate for positive solutions of the heat equation on closed Riemannian manifolds with the Ricci curvature bounded below by a negative constant. The proof is based on an integral iteration argument which utilizes Hamilton's gradient estimate, heat kernel Gaussian bounds and parabolic Harnack inequality. In this paper, we show that the sharp Li-Yau estimate can actually be obtained directly following the classical maximum principle argument, which simplifies the proof in [26]. In addition, we apply the same idea to the heat and conjugate heat equations under the Ricci flow and prove some Li-Yau type estimates with optimal coefficients.Comment: 14 page

Advancing Adversarial Robustness Through Adversarial Logit Update

Deep Neural Networks are susceptible to adversarial perturbations. Adversarial training and adversarial purification are among the most widely recognized defense strategies. Although these methods have different underlying logic, both rely on absolute logit values to generate label predictions. In this study, we theoretically analyze the logit difference around successful adversarial attacks from a theoretical point of view and propose a new principle, namely Adversarial Logit Update (ALU), to infer adversarial sample's labels. Based on ALU, we introduce a new classification paradigm that utilizes pre- and post-purification logit differences for model's adversarial robustness boost. Without requiring adversarial or additional data for model training, our clean data synthesis model can be easily applied to various pre-trained models for both adversarial sample detection and ALU-based data classification. Extensive experiments on both CIFAR-10, CIFAR-100, and tiny-ImageNet datasets show that even with simple components, the proposed solution achieves superior robustness performance compared to state-of-the-art methods against a wide range of adversarial attacks. Our python implementation is submitted in our Supplementary document and will be published upon the paper's acceptance

WM-NET: Robust Deep 3D Watermarking with Limited Data

The goal of 3D mesh watermarking is to embed the message in 3D meshes that can withstand various attacks imperceptibly and reconstruct the message accurately from watermarked meshes. Traditional methods are less robust against attacks. Recent DNN-based methods either introduce excessive distortions or fail to embed the watermark without the help of texture information. However, embedding the watermark in textures is insecure because replacing the texture image can completely remove the watermark. In this paper, we propose a robust deep 3D mesh watermarking WM-NET, which leverages attention-based convolutions in watermarking tasks to embed binary messages in vertex distributions without texture assistance. Furthermore, our WM-NET exploits the property that simplified meshes inherit similar relations from the original ones, where the relation is the offset vector directed from one vertex to its neighbor. By doing so, our method can be trained on simplified meshes(limited data) but remains effective on large-sized meshes (size adaptable) and unseen categories of meshes (geometry adaptable). Extensive experiments demonstrate our method brings 50% fewer distortions and 10% higher bit accuracy compared to previous work. Our watermark WM-NET is robust against various mesh attacks, e.g. Gauss, rotation, translation, scaling, and cropping

Weakly non-collapsed RCD spaces are strongly non-collapsed

We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second named author in full generality. One of the auxiliary results of independent interest that we obtain is about the link between the properties $\quad$- $\mathrm{tr}(\mathrm{Hess}f)=\Delta f$ on $U\subset\mathsf{X}$ for every $f$ sufficiently regular, $\quad$- $\mathfrak{m}=c\mathscr{H}^n$ on $U\subset\mathsf{X}$ for some $c>0$, where $U\subset \mathsf{X}$ is open and $\mathsf{X}$ is a - possibly collapsed - RCD space of essential dimension $n$.Comment: 31 page