arXiv subjects
Publications and source records attributed to Yiping Chen.
Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-projective generator with vanishing self-extensions in all positive degrees, is shown to be invariant under certain singular equivalences induced by adjoint pairs, which occur often in matrix algebras, recollements and change of rings. Accordingly, several reduction methods are established to study this conjecture.
In December 2019, COVID-19 were detected in Wuhan City, Hubei Province of China. SARS-CoV-2 rapidly spread to the whole Chinese mainland with the people during the Chinese Spring Festival Travel Rush. As of 19 February 2020, 74576 confirmed cases of COVID-19 had been reported in Chinese Mainland. What kind of cities have more confirmed cases, and is there any relationship between GDP and confirmed cases? In this study, we explored the relationship between the confirmed cases of COVID-19 and GDP at the prefectural-level, found a positive correlation between them. This finding warns high GDP areas should pay more prevention and control efforts when an epidemic outbreak, as they have greater risks than other areas nearby.
Middle-echo, which covers one or a few corresponding points, is a specific type of 3D point cloud acquired by a multi-echo laser scanner. In this paper, we propose a novel approach for automatic segmentation of trees that leverages middle-echo information from LiDAR point clouds. First, using a convolution classification method, the proposed type of point clouds reflected by the middle echoes are identified from all point clouds. The middle-echo point clouds are distinguished from the first and last echoes. Hence, the crown positions of the trees are quickly detected from the huge number of point clouds. Second, to accurately extract trees from all point clouds, we propose a 3D deep learning network, PointNLM, to semantically segment tree crowns. PointNLM captures the long-range relationship between the point clouds via a non-local branch and extracts high-level features via max-pooling applied to unordered points. The whole framework is evaluated using the Semantic 3D reduced-test set. The IoU of tree point cloud segmentation reached 0.864. In addition, the semantic segmentation network was tested using the Paris-Lille-3D dataset. The average IoU outperformed several other popular methods. The experimental results indicate that the proposed algorithm provides an excellent solution for vegetation segmentation from LiDAR point clouds.
When matter undergoes a continuous phase transition on a finite timescale, the Kibble-Zurek mechanism predicts universal scaling behavior with respect to structure formation. The scaling is dependent on the universality class and is irrelevant to the details of the system. Here, we examine this phenomenon by controlling the timescale of the phase transition to a Bose-Einstein condensate using sympathetic cooling of a ultracold Bose thermal could with tunable interactions in an elongated trap. The phase transition results in a diverse number of bright solitons and grey solitons in the condensate that undergo attractive and repulsive interactions, respectively. The power law dependence of the average soliton number on the timescale of the phase transition is measured for each interaction and compared. The results support the Kibble-Zurek mechanism, in that the scaling behavior is determined by universality and does not rely on the interaction properties.
This paper deals with the geometric multi-model fitting from noisy, unstructured point set data (e.g., laser scanned point clouds). We formulate multi-model fitting problem as a sequential decision making process. We then use a deep reinforcement learning algorithm to learn the optimal decisions towards the best fitting result. In this paper, we have compared our method against the state-of-the-art on simulated data. The results demonstrated that our approach significantly reduced the number of fitting iterations.
It is widely recognized that the deeper networks or networks with more feature maps have better performance. Existing studies mainly focus on extending the network depth and increasing the feature maps of networks. At the same time, horizontal expansion network (e.g. Inception Model) as an alternative way to improve network performance has not been fully investigated. Accordingly, we proposed NeuroTreeNet (NTN), as a new horizontal extension network through the combination of random forest and Inception Model. Based on the tree structure, in which each branch represents a network and the root node features are shared to child nodes, network parameters are effectively reduced. By combining all features of leaf nodes, even less feature maps achieved better performance. In addition, the relationship between tree structure and the performance of NTN was investigated in depth. Comparing to other networks (e.g. VDSR\_5) with equal magnitude parameters, our model showed preferable performance in super resolution reconstruction task.
Approximation sequences and derived equivalences occur frequently in the research of mutation of tilting objects in representation theory, algebraic geometry and noncommutative geometry. In this paper, we introduce symmetric approximation sequences in additive categories and weakly $n$-angulated categories which include (higher) Auslander-Reiten sequences (triangles) and mutation sequences in algebra and geometry,and show that such sequences always give rise to derived equivalences between the quotient rings of endomorphism rings of objects in the sequences modulo some ghost and coghost ideals.
We report the first all-optical production of a superfluid Bose-Fermi mixture with two spin states of $^6$Li (fermion) and one spin state of $^7$Li (boson) under the resonant magnetic field of the s-wave Feshbach resonance of the fermions. Fermions are cooled efficiently by evaporative cooling and they serve as coolant for bosons. As a result, a superfluid mixture can be achieved by using a simple experimental apparatus and procedures, as in the case of the all-optical production of a single Bose-Einstein condensate (BEC). We show that the all-optical method enables us to realize variety of ultracold Bose-Fermi mixtures.
In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient algebras of $n$-perforated Yoneda algebras. This result generalizes some results of Hu, König and Xi. And it also establishes a connection between higher cluster theory and derived equivalences. Namely, in a cluster tilting subcategory of a triangulated category, an Auslander-Reiten $n$-angle implies a derived equivalence between two quotient algebras. This result can be compared with the fact that an Auslander-Reiten sequence suggests a derived equivalence between two algebras which was proved by Hu and Xi.
In this paper, we construct derived equivalences between two subrings of relevant $Φ$-Auslander-Yoneda rings from an arbitrary short exact sequence in an abelian category. As a consequence, any short exact sequence in an abelian category gives rise to a derived equivalence between two subrings of endomorphism rings. These results generalize some methods on constructing derived equivalences.
In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds for a class of Harada algebras and a class of tiled triangular algebras.
We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erdős-Rényi (ER) and scale-free (SF) networks under various types of node removal strategies. The removal strategies are: random removal, high degree removal and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results.
We study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter ($S \equiv AL^{-1/ν}$ for $d$-dimensional lattices, and $S\equiv AN^{-1/3}$ for random networks) determines the distributions of the optimal path length, including both strong and weak disorder regimes. Here $ν$ is the percolation connectivity exponent, and $A$ depends on the percolation threshold and $P(w)$. For $P(w)$ uniform, Poisson or Gaussian the crossover from weak to strong does not occur, and only weak disorder exists.