Entanglement Entropy for Descendent Local Operators in 2D CFTs

We mainly study the R\'enyi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and R\'enyi entropy for a class of descendent operators, which are generated by $\cal{L}^{(-)}\bar{\cal{L}}^{(-)}$ onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the R\'enyi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the R\'enyi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by $\sum_{} d_{\{n_i\}\{n_j\}}(\prod_{i} L_{-n_i}\prod_{j}{\bar L}_{-n_j})$ on the primary operator. For these operators, the entanglement entropy and R\'enyi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the R\'enyi entropy of the excited operators in deformed CFT. The R\'enyi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.Comment: 30 pages, 2 figures; minor revion, references adde

T-UNet: Triplet UNet for Change Detection in High-Resolution Remote Sensing Images

Remote sensing image change detection aims to identify the differences between images acquired at different times in the same area. It is widely used in land management, environmental monitoring, disaster assessment and other fields. Currently, most change detection methods are based on Siamese network structure or early fusion structure. Siamese structure focuses on extracting object features at different times but lacks attention to change information, which leads to false alarms and missed detections. Early fusion (EF) structure focuses on extracting features after the fusion of images of different phases but ignores the significance of object features at different times for detecting change details, making it difficult to accurately discern the edges of changed objects. To address these issues and obtain more accurate results, we propose a novel network, Triplet UNet(T-UNet), based on a three-branch encoder, which is capable to simultaneously extract the object features and the change features between the pre- and post-time-phase images through triplet encoder. To effectively interact and fuse the features extracted from the three branches of triplet encoder, we propose a multi-branch spatial-spectral cross-attention module (MBSSCA). In the decoder stage, we introduce the channel attention mechanism (CAM) and spatial attention mechanism (SAM) to fully mine and integrate detailed textures information at the shallow layer and semantic localization information at the deep layer.Comment: 21 pages, 11 figures, 6 table

Large Misalignment between Stellar Bar and Dust Pattern in NGC 3488 Revealed by Spitzer and SDSS

A large position angle misalignment between the stellar bar and the distribution of dust in the late-type barred spiral NGC 3488 was discovered, using mid-infrared images from the Spitzer Space Telescope and optical images from the Sloan Digital Sky Survey (SDSS). The angle between the bar and dust patterns was measured to be 25+-2deg, larger than most of the misalignments found previously in barred systems based on Ha or HI/CO observations. The stellar bar is bright at optical and 3.6um, while the dust pattern is more prominent in the 8um band but also shows up in the SDSS u and g-band images, suggesting a rich interstellar medium environment harboring ongoing star formation. This angular misalignment is unlikely to have been caused by spontaneous bar formation. We suggest that the stellar bar and the dust pattern may have different formation histories, and that the large misalignment was triggered by a tidal interaction with a small companion. A statistical analysis of a large sample of nearby galaxies with archival Spitzer data indicates that bar structure such as that seen in NGC 3488 is quite rare in the local Universe.Comment: 18 pages, 4 figures, 1 table, accepted for publication in New Astronom

A Generalization of Bell Polynomials and Multinomial Expansions via Permutations on Partitions, by Perturbation expansions of Functional Determinants

We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type theorems in many sense. In particular, we give the new formulas as the double counting of Bell polynomial, Binomial Theorem and Multinomial Theorem.Comment: 17 page