A Note On K\"ahler-Ricci Flow on Fano Threefolds

In this note, we show that the solution of K\"ahler-Ricci flow on every Fano threefold from the family No.2.23 in the Mori-Mukai's list develops type II singularity. In fact, we show that no Fano threefold from the family No.2.23 admits K\"ahler-Ricci soliton and the Gromov-Hausdorff limit of the K\"ahler-Ricci flow must be a singular $\mathbb{Q}$-Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which K\"ahler-Ricci flow develops type II singularity.Comment: 6 pages, comments are welcome

Local Cliques in ER-Perturbed Random Geometric Graphs

Random graphs are mathematical models that have applications in a wide range of domains. We study the following model where one adds Erd\H{o}s--R\'enyi (ER) type perturbation to a random geometric graph. More precisely, assume $G_\mathcal{X}^{*}$ is a random geometric graph sampled from a nice measure on a metric space $\mathcal{X} = (X,d)$. The input observed graph $\widehat{G}(p,q)$ is generated by removing each existing edge from $G_\mathcal{X}^*$ with probability $p$, while inserting each non-existent edge to $G_\mathcal{X}^{*}$ with probability $q$. We refer to such random $p$-deletion and $q$-insertion as ER-perturbation. Although these graphs are related to the objects in the continuum percolation theory, our understanding of them is still rather limited. In this paper we consider a localized version of the classical notion of clique number for the aforementioned ER-perturbed random geometric graphs: Specifically, we study the edge clique number for each edge in a graph, defined as the size of the largest clique(s) in the graph containing that edge. The clique number of the graph is simply the largest edge clique number. Interestingly, given a ER-perturbed random geometric graph, we show that the edge clique number presents two fundamentally different types of behaviors, depending on which "type" of randomness it is generated from. As an application of the above results, we show that by using a filtering process based on the edge clique number, we can recover the shortest-path metric of the random geometric graph $G_\mathcal{X}^*$ within a multiplicative factor of $3$, from an ER-perturbed observed graph $\widehat{G}(p,q)$, for a significantly wider range of insertion probability $q$ than in previous work

Improving spam filtering in enterprise email systems with blockchain-based token incentive mechanism

Spam has caused serious problems for email systems. To address this issue, numerous spam filter algorithms have been developed, all of which require extensive training on labeled spam datasets to obtain the desired filter performance. However, users\u27 privacy concerns and apathy make it difficult to acquire personalized spam data in real-world applications. When it comes to enterprise email systems, the problem worsens because enterprises are extremely sensitive to the possible disclosure of confidential information during the reporting of spam to the cloud. Targeting these obstacles, this study proposes a blockchain-based token incentive mechanism, with the aim of encouraging users to report spam while protecting business secrets and ensuring the transparency of reward rules. The proposed mechanism also enables a decentralized ecosystem for token circulation, fully utilizing the advantages of blockchain technologies. We developed a prototype of the proposed system, on which we conducted a user experiment to verify our design. Results indicate that the proposed incentive mechanism is effective and can raise the probability of spam reporting by more than 1.4 times

The 2nd Place Solution for 2023 Waymo Open Sim Agents Challenge

In this technical report, we present the 2nd place solution of 2023 Waymo Open Sim Agents Challenge (WOSAC)[4]. We propose a simple yet effective autoregressive method for simulating multi-agent behaviors, which is built upon a well-known multimodal motion forecasting framework called Motion Transformer (MTR)[5] with postprocessing algorithms applied. Our submission named MTR+++ achieves 0.4697 on the Realism Meta metric in 2023 WOSAC. Besides, a modified model based on MTR named MTR_E is proposed after the challenge, which has a better score 0.4911 and is ranked the 3rd on the leaderboard of WOSAC as of June 25, 2023

A Quest to Unravel the Metric Structure Behind Perturbed Networks

Graphs and network data are ubiquitous across a wide spectrum of scientific and application domains. Often in practice, an input graph can be considered as an observed snapshot of a (potentially continuous) hidden domain or process. Subsequent analysis, processing, and inferences are then performed on this observed graph. In this paper we advocate the perspective that an observed graph is often a noisy version of some discretized 1-skeleton of a hidden domain, and specifically we will consider the following natural network model: We assume that there is a true graph G^* which is a certain proximity graph for points sampled from a hidden domain X; while the observed graph G is an Erdos-Renyi type perturbed version of G^*. Our network model is related to, and slightly generalizes, the much-celebrated small-world network model originally proposed by Watts and Strogatz. However, the main question we aim to answer is orthogonal to the usual studies of network models (which often focuses on characterizing / predicting behaviors and properties of real-world networks). Specifically, we aim to recover the metric structure of G^* (which reflects that of the hidden space X as we will show) from the observed graph G. Our main result is that a simple filtering process based on the Jaccard index can recover this metric within a multiplicative factor of 2 under our network model. Our work makes one step towards the general question of inferring structure of a hidden space from its observed noisy graph representation. In addition, our results also provide a theoretical understanding for Jaccard-Index-based denoising approaches

Adversarial Domain Adaptation with Domain Mixup

Recent works on domain adaptation reveal the effectiveness of adversarial learning on filling the discrepancy between source and target domains. However, two common limitations exist in current adversarial-learning-based methods. First, samples from two domains alone are not sufficient to ensure domain-invariance at most part of latent space. Second, the domain discriminator involved in these methods can only judge real or fake with the guidance of hard label, while it is more reasonable to use soft scores to evaluate the generated images or features, i.e., to fully utilize the inter-domain information. In this paper, we present adversarial domain adaptation with domain mixup (DM-ADA), which guarantees domain-invariance in a more continuous latent space and guides the domain discriminator in judging samples' difference relative to source and target domains. Domain mixup is jointly conducted on pixel and feature level to improve the robustness of models. Extensive experiments prove that the proposed approach can achieve superior performance on tasks with various degrees of domain shift and data complexity.Comment: Accepted as oral presentation at 34th AAAI Conference on Artificial Intelligence, 202