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We prove that every smooth Fano threefold from the family No 2.8 is K-stable. Such a Fano threefold is a double cover of the blow-up of $\mathbb{P}^3$ at one point branched along an anti-canonical divisor., Comment: 9 pages, comments welcome. v2: to appear in Math. Z

In this paper, we briefly introduce our submission to the Valence-Arousal Estimation Challenge of the 3rd Affective Behavior Analysis in-the-wild (ABAW) competition. Our method utilizes the multi-modal information, i.e., the visual and audio information, and employs a temporal encoder to model the temporal context in the videos. Besides, a smooth processor is applied to get more reasonable predictions, and a model ensemble strategy is used to improve the performance of our proposed method. The experiment results show that our method achieves 65.55% ccc for valence and 70.88% ccc for arousal on the validation set of the Aff-Wild2 dataset, which prove the effectiveness of our proposed method.

We show that there exist infinitely many families of Sasaki-Einstein metrics on every odd-dimensional standard sphere of dimension at least $5$. We also show that the same result is true for all odd-dimensional exotic spheres that bound parallelizable manifolds., Comment: Final version, to appear in Journal of Differential Geometry. 24 pages

Particle robots are novel biologically-inspired robotic systems where locomotion can be achieved collectively and robustly, but not independently. While its control is currently limited to a hand-crafted policy for basic locomotion tasks, such a multi-robot system could be potentially controlled via Deep Reinforcement Learning (DRL) for different tasks more efficiently. However, the particle robot system presents a new set of challenges for DRL differing from existing swarm robotics systems: the low degrees of freedom of each robot and the increased necessity of coordination between robots. We present a 2D particle robot simulator using the OpenAI Gym interface and Pymunk as the physics engine, and introduce new tasks and challenges to research the underexplored applications of DRL in the particle robot system. Moreover, we use Stable-baselines3 to provide a set of benchmarks for the tasks. Current baseline DRL algorithms show signs of achieving the tasks but are yet unable to reach the performance of the hand-crafted policy. Further development of DRL algorithms is necessary in order to accomplish the proposed tasks., Comment: 8 pages, 6 figures; conference paper at ICRA 2022; our code and video is available at https://ai4ce.github.io/DeepParticleRobot/

In this paper, a novel distributed scheduling algorithm is proposed, which aims to efficiently schedule both the uplink and downlink backhaul traffic in the relay-assisted mmWave backhaul network with a tree topology. The handshaking of control messages, calculation of local schedules, and the determination of final valid schedule are all discussed. Simulation results show that the performance of the distributed algorithm can reach very close to the maximum traffic demand of the backhaul network, and it can also adapt to the dynamic traffic with sharp traffic demand change of small-cell BSs quickly and accurately.

This paper investigates the throughput performance issue of the relay-assisted mmWave backhaul network. The maximum traffic demand of small-cell base stations (BSs) and the maximum throughput at the macro-cell BS have been found in a tree-style backhaul network through linear programming under different network settings, which concern both the number of radio chains available on BSs and the interference relationship between logical links in the backhaul network. A novel interference model for the relay-assisted mmWave backhaul network in the dense urban environment is proposed, which demonstrates the limited interference footprint of mmWave directional communications. Moreover, a scheduling algorithm is developed to find the optimal scheduling for tree-style mmWave backhaul networks. Extensive numerical analysis and simulations are conducted to show and validate the network throughput performance and the scheduling algorithm.

Structural design of neural networks is crucial for the success of deep learning. While most prior works in evolutionary learning aim at directly searching the structure of a network, few attempts have been made on another promising track, channel pruning, which recently has made major headway in designing efficient deep learning models. In fact, prior pruning methods adopt human-made pruning functions to score a channel's importance for channel pruning, which requires domain knowledge and could be sub-optimal. To this end, we pioneer the use of genetic programming (GP) to discover strong pruning metrics automatically. Specifically, we craft a novel design space to express high-quality and transferable pruning functions, which ensures an end-to-end evolution process where no manual modification is needed on the evolved functions for their transferability after evolution. Unlike prior methods, our approach can provide both compact pruned networks for efficient inference and novel closed-form pruning metrics which are mathematically explainable and thus generalizable to different pruning tasks. While the evolution is conducted on small datasets, our functions shows promising results when applied to more challenging datasets, different from those used in the evolution process. For example, on ILSVRC-2012, an evolved function achieves state-of-the-art pruning results., Comment: Published at GECCO 2022

Compressing convolutional neural networks (CNNs) by pruning and distillation has received ever-increasing focus in the community. In particular, designing a class-discrimination based approach would be desired as it fits seamlessly with the CNNs training objective. In this paper, we propose class-discriminative compression (CDC), which injects class discrimination in both pruning and distillation to facilitate the CNNs training goal. We first study the effectiveness of a group of discriminant functions for channel pruning, where we include well-known single-variate binary-class statistics like Student's T-Test in our study via an intuitive generalization. We then propose a novel layer-adaptive hierarchical pruning approach, where we use a coarse class discrimination scheme for early layers and a fine one for later layers. This method naturally accords with the fact that CNNs process coarse semantics in the early layers and extract fine concepts at the later. Moreover, we leverage discriminant component analysis (DCA) to distill knowledge of intermediate representations in a subspace with rich discriminative information, which enhances hidden layers' linear separability and classification accuracy of the student. Combining pruning and distillation, CDC is evaluated on CIFAR and ILSVRC 2012, where we consistently outperform the state-of-the-art results.

The system design and algorithm development of mobile 3D printing robots need a realistic simulation. They require a mobile robot simulation platform to interoperate with a physics-based material simulation for handling interactions between the time-variant deformable 3D printing materials and other simulated rigid bodies in the environment, which is not available for roboticists yet. To bridge this gap and enable the real-time simulation of mobile 3D printing processes, we develop a simulation framework that includes particle-based viscoelastic fluid simulation and particle-to-mesh conversion in the widely adopted Gazebo robotics simulator, avoiding the bottlenecks of traditional additive manufacturing simulation approaches. This framework is the first of its kind that enables the simulation of robot arms or mobile manipulators together with viscoelastic fluids. The method is tested using various material properties and multiple collaborating robots to demonstrate its simulation ability for the robots to plan and control the printhead trajectories and to visually sense at the same time the printed fluid materials as a free-form mesh. The scalability as a function of available material particles in the simulation was also studied. A simulation with an average of 5 FPS was achieved on a regular desktop computer., Comment: IROS 2021 Conference in the Simulation Category, 7 pages total, 2 are references

We show that the K-moduli spaces of log Fano pairs $(\mathbb{P}^3, cS)$ where $S$ is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as $c$ varies in the interval $(0,1)$. We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-O'Grady's prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of quartic double solids, and classify all Gorenstein canonical Fano degenerations of $\mathbb{P}^3$., Comment: 56 pages, comments are very welcome. v2: to appear in Invent. Math