Rational cubic fourfolds in Hassett divisors

We prove that every Hassett's Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two subvarieties, parametrizing rational cubic fourfolds, in the moduli space of smooth cubic fourfolds.Comment: 10 page

Classification of full exceptional collections of line bundles on three blow-ups of P3\mathbb{P}^{3}

A fullness conjecture of Kuznetsov says that if a smooth projective variety $X$ admits a full exceptional collection of line bundles of length $l$, then any exceptional collection of line bundles of length $l$ is full. In this paper, we show that this conjecture holds for $X$ as the blow-up of $\mathbb{P}^{3}$ at a point, a line, or a twisted cubic curve, i.e. any exceptional collection of line bundles of length 6 on $X$ is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such $X$.Comment: 28 pages. To appear in Journal of the Korean Mathematical Society, A previous version with a different title appeared as [CGP17025] at https://cgp.ibs.re.kr/archive/preprints/201

Pop-up SLAM: Semantic Monocular Plane SLAM for Low-texture Environments

Existing simultaneous localization and mapping (SLAM) algorithms are not robust in challenging low-texture environments because there are only few salient features. The resulting sparse or semi-dense map also conveys little information for motion planning. Though some work utilize plane or scene layout for dense map regularization, they require decent state estimation from other sources. In this paper, we propose real-time monocular plane SLAM to demonstrate that scene understanding could improve both state estimation and dense mapping especially in low-texture environments. The plane measurements come from a pop-up 3D plane model applied to each single image. We also combine planes with point based SLAM to improve robustness. On a public TUM dataset, our algorithm generates a dense semantic 3D model with pixel depth error of 6.2 cm while existing SLAM algorithms fail. On a 60 m long dataset with loops, our method creates a much better 3D model with state estimation error of 0.67%.Comment: International Conference on Intelligent Robots and Systems (IROS) 201

From Micro to Macro: Uncovering and Predicting Information Cascading Process with Behavioral Dynamics

Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus on predicting the final cascade sizes. As cascades are typical dynamic processes, it is always interesting and important to predict the cascade size at any time, or predict the time when a cascade will reach a certain size (e.g. an threshold for outbreak). In this paper, we unify all these tasks into a fundamental problem: cascading process prediction. That is, given the early stage of a cascade, how to predict its cumulative cascade size of any later time? For such a challenging problem, how to understand the micro mechanism that drives and generates the macro phenomenons (i.e. cascading proceese) is essential. Here we introduce behavioral dynamics as the micro mechanism to describe the dynamic process of a node's neighbors get infected by a cascade after this node get infected (i.e. one-hop subcascades). Through data-driven analysis, we find out the common principles and patterns lying in behavioral dynamics and propose a novel Networked Weibull Regression model for behavioral dynamics modeling. After that we propose a novel method for predicting cascading processes by effectively aggregating behavioral dynamics, and propose a scalable solution to approximate the cascading process with a theoretical guarantee. We extensively evaluate the proposed method on a large scale social network dataset. The results demonstrate that the proposed method can significantly outperform other state-of-the-art baselines in multiple tasks including cascade size prediction, outbreak time prediction and cascading process prediction.Comment: 10 pages, 11 figure