The "Ghost" Symmetry of the BKP hierarchy

In this paper, we systematically develop the "ghost" symmetry of the BKP hierarchy through its actions on the Lax operator $L$, the eigenfunctions and the $\tau$ function. In this process, the spectral representation of the eigenfunctions and a new potential are introduced by using squared eigenfunction potential(SEP) of the BKP hierarchy. Moreover, the bilinear identity of the constrained BKP hierarchy and Adler-Shiota-van-Moerbeke formula of the BKP hierarchy are re-derived compactly by means of the spectral representation and "ghost" symmetry.Comment: 23pages, to appear in Journal of Mathematical Physic

Hybrid CNN and Dictionary-Based Models for Scene Recognition and Domain Adaptation

Convolutional neural network (CNN) has achieved state-of-the-art performance in many different visual tasks. Learned from a large-scale training dataset, CNN features are much more discriminative and accurate than the hand-crafted features. Moreover, CNN features are also transferable among different domains. On the other hand, traditional dictionarybased features (such as BoW and SPM) contain much more local discriminative and structural information, which is implicitly embedded in the images. To further improve the performance, in this paper, we propose to combine CNN with dictionarybased models for scene recognition and visual domain adaptation. Specifically, based on the well-tuned CNN models (e.g., AlexNet and VGG Net), two dictionary-based representations are further constructed, namely mid-level local representation (MLR) and convolutional Fisher vector representation (CFV). In MLR, an efficient two-stage clustering method, i.e., weighted spatial and feature space spectral clustering on the parts of a single image followed by clustering all representative parts of all images, is used to generate a class-mixture or a classspecific part dictionary. After that, the part dictionary is used to operate with the multi-scale image inputs for generating midlevel representation. In CFV, a multi-scale and scale-proportional GMM training strategy is utilized to generate Fisher vectors based on the last convolutional layer of CNN. By integrating the complementary information of MLR, CFV and the CNN features of the fully connected layer, the state-of-the-art performance can be achieved on scene recognition and domain adaptation problems. An interested finding is that our proposed hybrid representation (from VGG net trained on ImageNet) is also complementary with GoogLeNet and/or VGG-11 (trained on Place205) greatly.Comment: Accepted by TCSVT on Sep.201

More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the ket vector and bra vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant

Negative discriminant states in N=4 supersymmetric string theories

Single centered BPS black hole solutions exist only when the charge carried by the black hole has positive discriminant. On the other hand the exact dyon spectrum in heterotic string theory compactified on T^6 is known to contain states with negative discriminant. We show that all of these negative discriminant states can be accounted for as two centered black holes. Thus after the contribution to the index from the two centered black holes is subtracted from the total microscopic index, the index for states with negative discriminant vanishes even for finite values of charges, in agreement with the results from the black hole side. Bound state metamorphosis -- which requires us to identify certain apparently different two centered configurations according to a specific set of rules -- plays a crucial role in this analysis. We also generalize these results to a class of CHL string theories.Comment: LaTeX file, 32 pages; v2: reference added; v3: added new section 3.