Level-One Representations and Vertex Operators of Quantum Affine Superalgebra Uq[gl(N∣N)^]U_q[\hat{gl(N|N)}]

Level-one representations of the quantum affine superalgebra $U_q[\hat{gl(N|N)}]$ associated to the appropriate non-standard system of simple roots and $q$-vertex operators (intertwining operators) associated with the level-one modules are constructed explicitly in terms of free bosonic fields.Comment: Errors in the cocycle factors of the vertex operators and some typos are corrected. LaTex file 17 page

Quantum Affine Lie Algebras, Casimir Invariants and Diagonalization of the Braid Generator

Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation. These eigenvalue formulae are shown to absolutely convergent when the deformation parameter $q$ is such that $|q|>1$. It is proven that the universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight $U_q(\hat{\cal G})$-modules and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin's and Gould's forms to the present affine case. Casimir invariants acting on a specified module are also constructed and their eigenvalues, again absolutely convergent for $|q|>1$, computed by means of the spectral decomposition formula.Comment: 22 pages (many changes are made

Casimir Invariants from Quasi-Hopf (Super)algebras

We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twistings. As a consequence, the elliptic quantum (super)groups, which arise from twisting the normal quantum (super)groups, have the same Casimir invariants as the corresponding quantum (super)groups.Comment: 24 pages, Latex fil

Free field realization of the osp(2n∣2n)osp(2n|2n) current algebra

The $osp(2n|2n)$ current algebra for a {\it generic} positive integer $n$ at general level $k$ is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. The associated screening currents of the first kind are also presented.Comment: Latex file; 21 pages; V2, typos corrected, the new version appears in Phys. Rev.

Graph Few-shot Learning via Knowledge Transfer

Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by aggregating information of its neighbors. However, most GNNs have shallow layers with a limited receptive field and may not achieve satisfactory performance especially when the number of labeled nodes is quite small. To address this challenge, we innovatively propose a graph few-shot learning (GFL) algorithm that incorporates prior knowledge learned from auxiliary graphs to improve classification accuracy on the target graph. Specifically, a transferable metric space characterized by a node embedding and a graph-specific prototype embedding function is shared between auxiliary graphs and the target, facilitating the transfer of structural knowledge. Extensive experiments and ablation studies on four real-world graph datasets demonstrate the effectiveness of our proposed model.Comment: Full paper (with Appendix) of AAAI 202

In vivophotoacoustic microscopy with 7.6-µm axial resolution using a commercial 125-MHz ultrasonic transducer

Photoacoustic microscopy has achieved submicron lateral resolution, but its axial resolution is much lower. Here an axial resolution of 7.6 μm, the highest axial resolution validated by experimental data, has been achieved by using a commercial 125 MHz ultrasonic transducer for signal detection followed by the Wiener deconvolution for signal processing. Limited by the working distance, the high-frequency ultrasonic transducer can penetrate 1.2 mm into biological tissue from the ultrasound detection side. At this depth, the signal-to-noise ratio decreases by 11 dB, and the axial resolution degrades by 36%. The new system was demonstrated in imaging melanoma cells ex vivo and mouse ears in vivo

Comments on Drinfeld Realization of Quantum Affine Superalgebra Uq[gl(m∣n)(1)]U_q[gl(m|n)^{(1)}] and its Hopf Algebra Structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain Drinfeld current realization for quantum affine superalgebra $U_q[gl(m|n)^{(1)}]$. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.Comment: Some errors and misprints corrected and a remark in section 4 removed. 12 pages, Latex fil

Photoacoustic microscopy with 7.6-μm axial resolution

The axial resolution of photoacoustic microscopy (PAM) is much lower than its lateral resolution, which resolves down to the submicron level. Here we achieved so far the highest axial resolution of 7.6 μm by using a commercial 125 MHz ultrasonic transducer for signal detection, followed by the Wiener deconvolution for signal processing. The axial resolution was validated by imaging two layers of red ink in a wedge shape. Melanoma cells were imaged ex vivo with high axial resolution. Compared with a PAM system with a 50 MHz ultrasonic transducer, our high-axial-resolution PAM system resolved the blood vessels in mouse ears in vivo much more clearly in the depth direction

Label-free photoacoustic microscopy of cytochrome c in cells

Cytochrome c is a heme protein normally bound to mitochondria and is important for mitochondrial electron transport and apoptosis initiation. Since cytochrome c is nonfluorescent, it is always labeled with fluorescent molecules for imaging, which, however, may affect normal cellular functions. Here, label-free photoacoustic microscopy (PAM) of mitochondrial cytochrome c was realized for the first time by utilizing the optical absorption around the Soret peak. PAM was demonstrated to be sensitive enough to image mitochondrial cytochrome c at 422 nm wavelength. Mitochondrial cytochrome c in the cytoplasm of fixed fibroblasts was clearly imaged by PAM as confirmed by fluorescent labeling. By showing mitochondrial cytochrome c in various cells, we demonstrated the feasibility of PAM for label-free histology of mouse ear sections. Therefore, PAM can sensitively image cytochrome c in unstained cells at 422 nm wavelength and has great potential for functional imaging of cytochrome c in live cells or in vivo

Quantum Affine Algebras and Universal RR-Matrix with Spectral Parameter

Using the previous obtained universal $R$-matrix for the quantized nontwisted affine Lie algebras $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for the corresponding quantum Lie algebras $U_q(A_1)$ and $U_q(A_2)$. As their applications, we reproduce the well-known results in the fundamental representations and we also derive an extreamly explicit formula of the spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the simplest non-trival case when the tensor product decomposition of the representation with itself has finite multiplicity.Comment: 10 page