Combinatorial insight of Riemann Boundary value problem in lattice walk problems

Enumeration of quarter-plane lattice walks with small steps is a classical problem in combinatorics. An effective approach is the kernel method and the solution is derived by positive term extraction. Another approach is to reduce the lattice walk problem to a Carleman type Riemann boundary value problem (RBVP) and solve it by complex analysis. There are two parameter characterizing the solutions of a Carleman type Riemann Boundary value problem, the index $\chi$ and the conformal gluing function $w(x)$. In this paper, we propose a combinatorial insight to the RBVP approach. We show that the index can be treated as the canonical factorization in the kernel method and the conformal gluing function can be turned into a conformal mapping such that after this mapping, the positive degree terms and the negative degree terms can be naturally separated. The combinatorial insight of RBVP provide a connection between the kernel method, the RBVP approach and the Tutte's invariant method

Mathematical Model of Dynamic Games of Imperfect Agency--Based on Conspiracy of SMEs and Bank Managers

Abstract: In China, state-owned commercial banks have monopoly position on the banking loan market. This paper constructs a two-stage dynamic game model to analyze the conspiracy in decision-making of bank loans, based on the establishment of relationship lend between SMEs and managers in large banks. Results indicate the existence of an optimal equilibrium as the solution of conspiracy. A revised mathematical model analysis with relaxed assumption shows that: if the state-owned banks have the mastery of large amounts of capital, supervision of SMEs lending are weak, and bank manager has the control of complete information of enterprises, the conspiracy tendencies for both parties will be more obvious. The conspiracy based on relationship lends between banks and enterprises will greatly damage the interests of banks and extrude high-quality SMEs.Key words: Mathematical Model; Dynamic Game; Conspiracy;Relationship Len

Novel Class Discovery for Long-tailed Recognition

While the novel class discovery has recently made great progress, existing methods typically focus on improving algorithms on class-balanced benchmarks. However, in real-world recognition tasks, the class distributions of their corresponding datasets are often imbalanced, which leads to serious performance degeneration of those methods. In this paper, we consider a more realistic setting for novel class discovery where the distributions of novel and known classes are long-tailed. One main challenge of this new problem is to discover imbalanced novel classes with the help of long-tailed known classes. To tackle this problem, we propose an adaptive self-labeling strategy based on an equiangular prototype representation of classes. Our method infers high-quality pseudo-labels for the novel classes by solving a relaxed optimal transport problem and effectively mitigates the class biases in learning the known and novel classes. We perform extensive experiments on CIFAR100, ImageNet100, Herbarium19 and large-scale iNaturalist18 datasets, and the results demonstrate the superiority of our method. Our code is available at https://github.com/kleinzcy/NCDLR.Comment: TMLR2023, Final versio

Magnetic island formation and rotation braking induced by low-Z impurity penetration in an EAST plasma

Recent observations of the successive formations of the 4=1; 3=1, and 2=1 magnetic islands as well as the subsequent braking of the 2=1 mode during a low-Z impurity penetration process in EAST experiments are well reproduced in our 3D resistive MHD simulations. The enhanced parallel current perturbation induced by impurity radiation predominately contributes to the tearing mode growth, and the 2=1 island rotation is mainly damped by the impurity accumulation as results of the influence from high n modes.Comment: 21 pages, 9 figure

Hybrid phase-change Lattice Boltzmann simulation of vapor condensation on vertical subcooled walls

Saturated vapor condensation on homogenous and heterogeneous subcooled walls is presented in this study by adopting a hybrid phase-change multiple-relaxation-time Lattice Boltzmann model. The effects of wall wettability on the condensation process, including droplets’ growth, coalescence and falling, and the influence of vapor flow to condensation are investigated. The results demonstrate that the heat fluxes around the triple-phase contact lines are higher than that in other cold areas in homogeneous subcooled walls, which actually indicates the fact that filmwise condensation is preventing the continuous condensation process. Furthermore, the dropwise condensation can be formed more easily on the heterogeneous surface with a mixed surface wettability. At last, the dynamic process of condensation of continuous vapor flow is also investigated by considering the homogenous and heterogeneous subcooled surfaces. The results show that the heterogeneous surface with mixed wettability doesn’t contribute to the formation, growth of droplets, when compared to the homogeneous surface. It is expected that this study can bring more attentions to simulate condensation using multiphase LBM for complex geometries in heat transfer community