The Geometric Construction of WZW Effective Action in Non-commutative Manifold

By constructing close one cochain density ${\Omega^1}_{2n}$ in the gauge group space we get WZW effective Lagrangian on high dimensional non-commutative space.Especially consistent anomalies derived from this WZW effective action in non-commutative four-dimensional space coincides with those by L.Bonora etc.Comment: 9 pages, latex, no figure

Bethe Ansatz for the Spin-1 XXX Chain with Two Impurities

By using algebraic Bethe ansatz method, we give the Hamitonian of the spin-1 XXX chain associated with $sl_2$ with two boundary impurities.Comment: 8 pages, latex, no figures, to be appeared in Commun. Theor. Phy

Vortex Dynamics in Amorphous MoSi Superconducting Thin Films

Vortex dynamics in superconductors have received a great deal of attention from both fundamental and applied researchers over the past few decades. Because of its critical role in the energy relaxation process of type II superconductors, vortex dynamics have been deemed a key factor for the emerging superconducting devices, but the effect of irradiation on vortex dynamics remains unclear. With the support of electrical transport measurements under external magnetic fields and irradiation, photon effect on vortex dynamics in amorphous MoSi (a MoSi) superconducting thin films are investigated in this work. The magnetic field dependent critical vortex velocity v* derived from the Larkin Ovchinnikov model is not significantly affected by irradiation. However, vortex depinning is found to be enhanced by photon-induced reduction in potential barrier, which mitigates the adverse effect of film inhomogeneity on superconductivity in the a MoSi thin films. The thorough understanding of the vortex dynamics in a MoSi thin films under the effect of external stimuli is of paramount importance for both further fundamental research in this area and optimization of future superconducting devices

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.Comment: 23 page

Incremental Task Learning with Incremental Rank Updates

Incremental Task learning (ITL) is a category of continual learning that seeks to train a single network for multiple tasks (one after another), where training data for each task is only available during the training of that task. Neural networks tend to forget older tasks when they are trained for the newer tasks; this property is often known as catastrophic forgetting. To address this issue, ITL methods use episodic memory, parameter regularization, masking and pruning, or extensible network structures. In this paper, we propose a new incremental task learning framework based on low-rank factorization. In particular, we represent the network weights for each layer as a linear combination of several rank-1 matrices. To update the network for a new task, we learn a rank-1 (or low-rank) matrix and add that to the weights of every layer. We also introduce an additional selector vector that assigns different weights to the low-rank matrices learned for the previous tasks. We show that our approach performs better than the current state-of-the-art methods in terms of accuracy and forgetting. Our method also offers better memory efficiency compared to episodic memory- and mask-based approaches. Our code will be available at https://github.com/CSIPlab/task-increment-rank-update.gitComment: Code will be available at https://github.com/CSIPlab/task-increment-rank-update.gi

The Exact Solution of the SU(3) Hubbard Model

The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the coordinate Bethe ansatz method. Then, with the help quantum inverse scattering method we solve the nested transfer matrix and give the eigenvalues, the eigenvectors and the Bethe ansatz equations. Finally, we obtain the exactly analytic solution for the ground state.Comment: 19 pages, latex, no figure

Integrability of the Heisenberg Chains with Boundary Impurities and Their Bethe Ansatz

In this paper, we show the integrability of spin-1/2 XXZ Heisenberg chain with two arbitrary spin boundary Impurities. By using the fusion method, we generalize it to the spin-1 XXZ chain. Then the eigenvalues of Hamiltonians of these models are obtained by the means of Bethe ansatz method.Comment: 13 pages, latex, no figures, to be appeared in J.Phys.