SPECTRAL RADIUS,KRONECKER PRODUCTS AND STATIONARITY

Abstract. We provide a stochastic proof of the inequality ρ(A?A+B?B) ≥ρ(A?A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M?N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model will imply stationarity of the linear part, i.e. the linear ARMA model for r= 1 and q= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model with b_ij=0 for i< j, again implies stationarity of its linear part, provided that the stationarity condition given by Bhaskara Rao and his colleagues is met. Interestingly, the conclusion that stationarity of the subdiagonal models, implies that the linear component models cannot be extended to the general non-subdiagonal bilinear models. The last observation is demonstrated via a simple example with p=m= 1, r= 0 and q= 2.     

Super connectivity of Kronecker products of graphs

Let G₁ and G₂ be two connected graphs. The Kronecker product G₁×G₂ has vertex set V(G₁×G₂)=V(G₁)×V(G₂) and the edge set . In this paper, we show that if G is a bipartite graph with κ(G)=δ(G), then G×Kn(n?3) is super-κ.     

Solving the generalized Sylvester matrix equation AV +BW = VF via Kronecker map

This note considers the solution to the generalized Sylvester matrix equation AV ＋ BW = VF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an explicit parametric solution to this matrix equation is established. The proposed solution possesses a very simple and neat form, and allows the matrix F to be undetermined.     

Perfect r-domination in the Kronecker product of two cycles, with an application to diagonal/toroidal mesh

If r?1, and m and n are each a multiple of (r+1)²+r², then each isomorphic component of C_m×C_n admits of a vertex partition into (r+1)²+r² perfect r-dominating sets. The result induces a dense packing of C_m×C_n by means of vertex-disjoint subgraphs, each isomorphic to a diagonal array. Areas of applications include efficient resource placement in a diagonal mesh and error-correcting codes.     

On the electro-osmotic flow in a saturated porous medium

Electro-osmosis in a saturated porous rigid medium is studied by both theoretical and experimental approach. Relationships giving liquid and electrical coupled macroscopic flows are obtained from the homogeneization method. They point out possible non symmetrical cross effects that explain deviations from Onsager reciprocal relations. Experiments on a kaolinite are reported which exhibit an important non symmetrical coupling.     

编码—解码结构的语义分割

目的 语义分割是计算机视觉中一项具有挑战性的任务,其核心是为图像中的每个像素分配相应的语义类别标签。然而,在语义分割任务中,缺乏丰富的多尺度信息和足够的空间信息会严重影响图像分割结果。为进一步提升图像分割效果,从提取丰富的多尺度信息和充分的空间信息出发,本文提出了一种基于编码-解码结构的语义分割模型。方法 运用ResNet-101网络作为模型的骨架提取特征图,在骨架末端附加一个多尺度信息融合模块,用于在网络深层提取区分力强且多尺度信息丰富的特征图。并且,在网络浅层引入空间信息捕获模块来提取丰富的空间信息。由空间信息捕获模块捕获的带有丰富空间信息的特征图和由多尺度信息融合模块提取的区分力强且多尺度信息丰富的特征图将融合为一个新的信息丰富的特征图集合,经过多核卷积块细化之后,最终运用数据依赖的上采样（DUpsampling）操作得到图像分割结果。结果 此模型在2个公开数据集（Cityscapes数据集和PASCAL VOC 2012数据集）上进行了大量实验,验证了所设计的每个模块及整个模型的有效性。新模型与最新的10种方法进行了比较,在Cityscapes数据集中,相比于RefineNet模型、DeepLabv2-CRF模型和LRR（Laplacian reconstruction and refinement）模型,平均交并比（mIoU）值分别提高了0.52%、3.72%和4.42%;在PASCAL VOC 2012数据集中,相比于Piecewise模型、DPN（deep parsing network）模型和GCRF（Gaussion conditional random field network）模型,mIoU值分别提高了6.23%、7.43%和8.33%。结论 本文语义分割模型,提取了更加丰富的多尺度信息和空间信息,使得分割结果更加准确。此模型可应用于医学图像分析、自动驾驶、无人机等领域。     

Stability,performance and sensitivity analysis of I.I.D. jump linear systems

This paper presents a symmetric Kronecker product analysis of independent and identically distributed jump linear systems to develop new, lower dimensional equations for the stability and performance analysis of this type of systems than what is currently available. In addition, new closed form expressions characterising multi-parameter relative sensitivity functions for performance metrics are introduced. The analysis technique is illustrated with a distributed fault-tolerant flight control example where the communication links are allowed to fail randomly.     

一类复矩阵分布的矩的结构

本文就一类复随机矩阵的矩的结构进行了研究，给出了这种结构的矩阵表达式。