Rational singularities and qq-birational morphism

In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank $1$ and prove generalizations of standard facts about rational singularities. Moreover, we introduce the notion of $(B_{q+1})$ as a dual notion of well-known Serre's notion of $(S_{q+1})$ and prove a theorem about $q$-birational morphism.Comment: Comments Welcome

Self-Supervised Video Representation Learning with Space-Time Cubic Puzzles

Self-supervised tasks such as colorization, inpainting and zigsaw puzzle have been utilized for visual representation learning for still images, when the number of labeled images is limited or absent at all. Recently, this worthwhile stream of study extends to video domain where the cost of human labeling is even more expensive. However, the most of existing methods are still based on 2D CNN architectures that can not directly capture spatio-temporal information for video applications. In this paper, we introduce a new self-supervised task called as \textit{Space-Time Cubic Puzzles} to train 3D CNNs using large scale video dataset. This task requires a network to arrange permuted 3D spatio-temporal crops. By completing \textit{Space-Time Cubic Puzzles}, the network learns both spatial appearance and temporal relation of video frames, which is our final goal. In experiments, we demonstrate that our learned 3D representation is well transferred to action recognition tasks, and outperforms state-of-the-art 2D CNN-based competitors on UCF101 and HMDB51 datasets.Comment: Accepted to AAAI 201

Modeling the effects of aluminum and ammonium perchlorate addition on the detonation of the high explosives C_4H_8O_8N_8 (HMX) and C_3H_6O_6N_6(RDX)

Metalized high explosives effectively tailor the explosion impulse at lowered detonation pressures of common high performance explosives such as C_3H_6O_6N_6 (RDX) and C_4H_8O_8N_8 (HMX). The presence of aluminum (Al) with and without ammonium perchlorate (AP) allows the subsequent burning for longer and sustained reactions of enhanced blast explosives. The modeling of reaction rate laws for three explosives with varied amounts of Al, AP, RDX, and HMX is reported. The model validation included the rate stick test for understanding the explosive reaction of the three samples and the large-scale gap test for determining their ignition sensitivity. The experimental results confirmed the accuracy of the model in simulating the shock sensitivity and the size effects before detonation failure. The effect of enhanced blast of these explosives in the presence of Al and AP is also reported

Adjoint asymptotic multiplier ideal sheaves

In this paper, we initiate the study of a triple $(X,\Delta,D)$ which consists of a pair $(X,\Delta)$ and a polarizing pseudoeffective divisor $D$. The adjoint asymptotic multiplier ideal sheaf $\mathcal{J}(X,\Delta;\lVert D \rVert)$ associated to the triple gives a simultaneous generalization of the multiplier ideal sheaf $\mathcal{J}(D)$ and asymptotic multiplier ideal sheaf $\mathcal{J}(\lVert D \rVert)$. We describe the closed set defined by the ideal sheaf $\mathcal{J}(X,\Delta;\lVert D \rVert)$ in terms of the minimal model program. We also characterize the case where $\mathcal{J}(X,\Delta;\lVert D \rVert)=\mathcal{O}_X$. Lastly, we also prove a Nadel type vanishing theorem of cohomology using $\mathcal{J}(X,\Delta;\lVert D \rVert)$

Torque-based Deep Reinforcement Learning for Task-and-Robot Agnostic Learning on Bipedal Robots Using Sim-to-Real Transfer

In this paper, we review the question of which action space is best suited for controlling a real biped robot in combination with Sim2Real training. Position control has been popular as it has been shown to be more sample efficient and intuitive to combine with other planning algorithms. However, for position control gain tuning is required to achieve the best possible policy performance. We show that instead, using a torque-based action space enables task-and-robot agnostic learning with less parameter tuning and mitigates the sim-to-reality gap by taking advantage of torque control's inherent compliance. Also, we accelerate the torque-based-policy training process by pre-training the policy to remain upright by compensating for gravity. The paper showcases the first successful sim-to-real transfer of a torque-based deep reinforcement learning policy on a real human-sized biped robot. The video is available at https://youtu.be/CR6pTS39VRE