The weak Lefschetz property of artinian algebras associated to paths and cycles

Given a base field $\Bbbk$ of characteristic zero, for each graph $G$, we associate the artinian algebra $A(G)$ defined by the edge ideal of $G$ and the squares of the variables. We study the weak Lefschetz property of $A(G)$. We classify some classes of graphs with relatively few edges, including paths and cycles, such that its associated artinian ring has the weak Lefschetz property.Comment: 21 pages. Comments are welcome

selective dissolution of woody biomass under hydrothermal conditions

Abstract This study analyzes semi-continuous hydrothermal hydrolysis of lignocellulosic biomass operating between 200°C and 300°C with constant inlet water flow rate. Experiments were executed in a novel reactor system that offered a nearly linear temperature behavior during the heating period with heating rates between 40°C/min and 60 °C/min and a nearly flat temperature profile during retention. Experimental results suggest that conversion efficiency improved at higher temperatures. After completion of the batch, solid and liquid products were collected and mass balance closures reached an average of 89%. It was discovered that, regardless of the temperature, a minimum of 90% of the total dissolution occurs within the first 15 minutes of the reaction. This work identifies various stages and conditions that favor the dissolution of certain components (hemicellulose, cellulose or lignin)

sFuzz: An efficient adaptive fuzzer for solidity smart contracts

Ministry of Education, Singapore under its Academic Research Funding Tier

Music-Driven Group Choreography

Music-driven choreography is a challenging problem with a wide variety of industrial applications. Recently, many methods have been proposed to synthesize dance motions from music for a single dancer. However, generating dance motion for a group remains an open problem. In this paper, we present $\rm AIOZ-GDANCE$, a new large-scale dataset for music-driven group dance generation. Unlike existing datasets that only support single dance, our new dataset contains group dance videos, hence supporting the study of group choreography. We propose a semi-autonomous labeling method with humans in the loop to obtain the 3D ground truth for our dataset. The proposed dataset consists of 16.7 hours of paired music and 3D motion from in-the-wild videos, covering 7 dance styles and 16 music genres. We show that naively applying single dance generation technique to creating group dance motion may lead to unsatisfactory results, such as inconsistent movements and collisions between dancers. Based on our new dataset, we propose a new method that takes an input music sequence and a set of 3D positions of dancers to efficiently produce multiple group-coherent choreographies. We propose new evaluation metrics for measuring group dance quality and perform intensive experiments to demonstrate the effectiveness of our method. Our project facilitates future research on group dance generation and is available at: https://aioz-ai.github.io/AIOZ-GDANCE/Comment: accepted in CVPR 202