Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at arbitrary filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order when the size of the lattice and the number of particles obey some simple arithmetic rules. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Assuming a one-to-one correspondence between the solutions of the Bethe equations and the eigenmodes of the Markov matrix, we derive combinatorial formulae for the orders of degeneracy and the number of multiplets. These results are confirmed by exact diagonalisations of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group.     

New potential symmetries for some evolution equations

In this paper we derive new potential symmetries that seem not to be recorded in the literature. These potential symmetries are determined by considering a generalized potential system, rather than the natural potential system or a general integral variable. An inhomogeneous diffusion equation, a porous medium equation and the Fokker-Planck equation have been considered as application of this procedure.     

On sufficient conditions of locality for hierarchies of symmetries of evolution systems

We present sufficient conditions ensuring the locality of hierarchies of symmetries generated by repeated commutation of master symmetry with a seed symmetry. These conditions are applicable to a large class of (1+1)-dimensional evolution systems. Our results can also be used for proving that the time-independent part of a suitable linear-in-time symmetry is a nontrivial master symmetry and hence the system in question has infinitely many symmetries and is integrable.     

SYMMETRIES OF MECHANICAL SYSTEMS WITH NONLINEAR NONHOLONOMIC CONSTRAINTS

The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic constrained mechanical systems are analysed in two kinds of geometrical frameworks whose evolution equations are Routh's equations and generalized Chaplygin's equations, respectively. The Lagrangian inverse problem and the interrelation between Noether's symmetries and dynamical symmetries are briefly concerned with. Finally an illustrative example is analysed.     

稀疏矩阵向量乘的自动调优

分析稀疏矩阵向量乘(SpMV)程序优化的难点, 介绍两个自动调优的代表性工作: 基于预实现模板的SMAT和从头设计程序的AlphaSparse。详细介绍了它们的设计思路、实现细节、测试结果以及各自的优缺点。最后, 对SpMV自动调优的发展趋势进行了分析和预测。     

A new analytic expression for fast calculation of the transient near and far field of a rectangular baffled piston

Essential to (cardiac) 3D ultrasound are 2D matrix array transducer technology and the associated (two-stage) beam forming. Given the large number of degrees of freedom and the complexity of this problem, simulation tools play an important role. Hereto, the impulse response (IR) method is commonly used. Unfortunately, given the large element count of 2D array transducers, simulation times become significant jeopardizing the efficacy of the design process. The aim of this study was therefore to derive a new analytical expression to more efficiently calculate the IR in order to speed up the calculation process. To compare accuracy and computation time, the reference and the proposed method were implemented in MATLAB and contrasted. For all points of observation tested, the IR with both methods was identical. The mean calculation time however reduced in average by a factor of 3.93 ± 0.03 times. The proposed IR method therefore speeds up the calculation time of the IR of an individual transducer element while remaining perfectly accurate. This new expression will be particularly relevant for 2D matrix transducer design where computation times remain currently a bottle neck in the design process.     

Possible realisation and generalisation of two specific 2×2 forms

For each of a couple of two-dimensional forms for quark mass matrix, it is discussed how that form may be realised in a certain gauge scheme (one of them in the standard model and the other in a scheme based on simple rank two times U(1)) by imposing suitable discrete symmetries and how under a certain small angle approximation that form may be regarded as the simplest member of a family of higher dimensionality forms.     

混响背景下低秩矩阵恢复的目标亮点特征提取

有源声呐探测水下目标时,混响干扰增加了从目标回波信号中提取目标亮点特征的难度.依据目标回波与混响在时频域上能量分布的相关性不同,采用自适应核时频分析方法将目标回波信号变换到时频域上进行分析.通过低秩矩阵恢复方法将目标回波与混响分到稀疏矩阵和低秩矩阵中,从而分离目标回波与混响,降低混响对回波信号的干扰.针对稀疏矩阵采用Hough变换提取回波中的亮点峰,得到目标的亮点特征。通过仿真和实验数据证明在较低信混比情况下通过低秩矩阵恢复方法能够在时频域上进一步区分目标回波与混响,达到抑制混响的目的,便于获取目标亮点特征。     

高维预条件子的填充技术

给出了高维问题差分离散后形成的大型稀疏线性代数方程组预条件子的填充技术,讨论了填充与加速效率、计算量的关系。并把这一技术在实际应用问题中进行检验。     

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization.     

适用于申威众核架构的稀疏矩阵-矩阵乘法

本文提出新一代申威众核架构上稀疏通用矩阵-矩阵乘法(SpGEMM)的并行算法swSpGEMM。设计轻量级并行任务划分有效地应对了矩阵非零元分布引起的负载不均衡问题; 针对累加过程中的不规则访存和指令流水低效问题, 设计了分层稀疏累加器, 在不同输入特征下高效利用申威从核层次化内存, 且减少了整数查找中的指令间依赖, 更有效地发挥硬件的计算能力。SuiteSparse稀疏矩阵测试集中较大规模输入矩阵上, swSpGEMM的性能相比Intel Skylake双CPU上的MKL和NVIDIA A100上的cuSPARSE分别加速了21.1%和95.3%。     

The neutrino mass matrix and (selected) variants of <Emphasis Type="Italic">A</Emphasis><Subscript>4</Subscript>

Recent neutrino oscillation experiments have measured leptonic mixing angles with considerable precision. Many theoretical attempts to understand the peculiar mixing structure, observed in these measurements, are based on non-Abelian flavour symmetries. This talk concentrates exclusively on models based on the non-Abelian symmetry A ₄. A ₄ is particularly well suited to describe three family mixing, and allows to explain the near tri-bimaximal mixing observed. Special emphasis is put here on the discussion of the neutrinoless double beta decay observable 〈:m _ν 〉. Different models based on A ₄ with very similar predictions for neutrino angles can yield vastly different expectations for 〈m _ν 〉. Neutrinoless double beta decay can thus serve, in principle, as a discriminator between different neutrino mass models.      

Symmetries of Energy-Momentum Tensor： Some Basic Facts

It has been pointed out by Hall et al. [Gen. Rel. Gray. 28 （1996） 299.] that matter collineations can be defined by using three different methods. But there arises the question whether one studies matter collineations by using LεTab=0, or LεT^ab = 0 or LεT^b a=0. These alternative conditions are, of. course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.