Minimality of p-adic rational maps with good reduction

A rational map with good reduction in the field $\mathbb{Q}\_p$ of $p$-adic numbers defines a $1$-Lipschitz dynamical system on the projective line $\mathbb{P}^1(\mathbb{Q}\_p)$ over $\mathbb{Q}\_p$. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, $\mathbb{P}^1(\mathbb{Q}\_p)$ is decomposed into three parts: finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of periodic orbits and minimal subsystems. For any prime $p$, a criterion of minimality for rational maps with good reduction is obtained. When $p=2$, a condition in terms of the coefficients of the rational map is proved to be necessary for the map being minimal and having good reduction, and sufficient for the map being minimal and $1$-Lipschitz. It is also proved that a rational map having good reduction of degree $2$, $3$ and $4$ can never be minimal on the whole space $\mathbb{P}^1(\mathbb{Q}\_2)$.Comment: 21 page

Localizing by Describing: Attribute-Guided Attention Localization for Fine-Grained Recognition

A key challenge in fine-grained recognition is how to find and represent discriminative local regions. Recent attention models are capable of learning discriminative region localizers only from category labels with reinforcement learning. However, not utilizing any explicit part information, they are not able to accurately find multiple distinctive regions. In this work, we introduce an attribute-guided attention localization scheme where the local region localizers are learned under the guidance of part attribute descriptions. By designing a novel reward strategy, we are able to learn to locate regions that are spatially and semantically distinctive with reinforcement learning algorithm. The attribute labeling requirement of the scheme is more amenable than the accurate part location annotation required by traditional part-based fine-grained recognition methods. Experimental results on the CUB-200-2011 dataset demonstrate the superiority of the proposed scheme on both fine-grained recognition and attribute recognition

Study on the Distribution Pattern of PAHs in the Coking Dust from the Coking Environment

AbstractThis paper conducts a study and analyzes five kinds of dust samples of different environment, including an office area,a ground station of the new plant, the first workshop of coking, a top of coke oven and a ground station of the old plant in coking plant and obtaines the distribution pattern of PAHs in the coking dust by the way of ultrasonic extraction and high performance liquid chromatography. The data show that PAHs from the first workshop turns out to be the richest with its content getting up to 12.00μgám-3. By analyzing the single component distribution of PAHs, the results show that there are fourteen kinds of PAHs produced at 5 sites. Through analyzing the particle size of coking dust, its size is mainly below 10μm and its contents exceeds to 75%. The first workshop environment is the highest and reaching 98.39%

MeMaHand: Exploiting Mesh-Mano Interaction for Single Image Two-Hand Reconstruction

Existing methods proposed for hand reconstruction tasks usually parameterize a generic 3D hand model or predict hand mesh positions directly. The parametric representations consisting of hand shapes and rotational poses are more stable, while the non-parametric methods can predict more accurate mesh positions. In this paper, we propose to reconstruct meshes and estimate MANO parameters of two hands from a single RGB image simultaneously to utilize the merits of two kinds of hand representations. To fulfill this target, we propose novel Mesh-Mano interaction blocks (MMIBs), which take mesh vertices positions and MANO parameters as two kinds of query tokens. MMIB consists of one graph residual block to aggregate local information and two transformer encoders to model long-range dependencies. The transformer encoders are equipped with different asymmetric attention masks to model the intra-hand and inter-hand attention, respectively. Moreover, we introduce the mesh alignment refinement module to further enhance the mesh-image alignment. Extensive experiments on the InterHand2.6M benchmark demonstrate promising results over the state-of-the-art hand reconstruction methods