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Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous time-reversal-symmetry breaking have garnered attention. While the thermodynamics of integer quantum anomalous Hall (IQAH) states have been systematically studied, our theoretical knowledge on thermodynamic properties of FQAH states has been severely limited. Here, we delve into the general thermodynamic response and collective excitations of both IQAH and FQAH states within the paradigmatic flat Chern-band model with remote band considered. Our key findings include: i) In both $\nu$ = 1 IQAH and $\nu$ = 1/3 FQAH states, even without spin fluctuations, the charge-neutral collective excitations would lower the onset temperature of these topological states, to a value significantly smaller than the charge gap, due to band-mixing and multi-particle scattering; ii) By employing large-scale thermodynamic simulations in FQAH states in the presence of strong inter-band mixing between C = $\pm1$ bands, we find that the lowest collective excitations manifest as the zero-momentum excitons in the IQAH state, whereas in the FQAH state, they take the form of magneto-rotons with finite momentum; iii) The unique charge oscillations in FQAH states are exhibited with distinct experimental signatures, which we propose to detect in future experiments.

In his celebrated book "Mathematical Treatise in Nine Sections" of 1247, Qin, Jiushao described the Chinese remainder theorem with great detail and generality. He also gave a method for computing modular inverse under the name of "DaYan deriving one". Historical significance of DaYan deriving one method has been well studied. In this paper, we investigate its modern mathematical nature from the perspectives of number theory and algorithm. One of the remarkable features of Qin's algorithm is that it keeps a state of four variables in a matrix form. Its choice of variables and layout provide natural ways of connecting several important mathematical concepts. An invariant about the state is also observed which provides a convenient yet powerful tool in proving several important mathematical results. The paper first explains Qin's algorithm and proves some of its properties. Then the connection with continued fractions is examined, the results show that the states of Qin's algorithm contain rich information about continued fractions and some classical arguments can be derived easily. The last part of the paper discusses a family of 2-dimensional lattices of number theoretic significance by proving that the shortest vectors of these lattices can be obtained from the states of Qin's algorithm. This result is surprising in that a shortest lattice vector is found in a well-regulated set. A method of computing such shortest vectors is proposed.ed.

We give an adelic version of a spectral reciprocity formula relating $\mathrm{GL}_3 \times \mathrm{GL}_2$ with $\mathrm{GL}_3 \times \mathrm{GL}_1$ and $\mathrm{GL}_1$ moments of $L$-functions discovered by Xiaoqing Li. For many types of the $\mathrm{GL}_3$ representation, we describe the local weight transforms via a decomposition of Voronoi's formula in terms of elementary transforms, which generalizes the one given by Miller--Schmid in a way consistent with the local Langlands correspondence. We obtain some integral representation of the Bessel functions for $\mathrm{GL}_2$ uniformly over all local fields. We announce the dual weight computation in a new case, which identifies the coset problem parallel to that in Petrow--Young's Weyl-type subconvexity for general Dirichlet $L$-functions. The proof and extensive study of other accessible cases will be given in a separate paper., Comment: We add a complete proof of the bound of local kernel function, which we intend to improve on before including it in a submission

General-purpose text decoding approaches are usually adopted for dialogue response generation. Although the quality of the generated responses can be improved with dialogue-specific encoding methods, conversational decoding methods are still under-explored. Inspired by \citet{wu2023learning} that a good dialogue feature space should follow the rules of locality and isotropy, we present a fine-grained conversational decoding method, termed \textit{isotropic and proximal search (IPS)}. Our method is designed to generate the semantic-concentrated response, while still maintaining informativeness and discrimination against the context. Experiments show that our approach outperforms existing decoding strategies in the dialogue field across both automatic and human evaluation metrics. More in-depth analyses further confirm the effectiveness of our approach., Comment: Accepted to EMNLP 2023 Main Conference

Accurately localizing and identifying vertebrae from CT images is crucial for various clinical applications. However, most existing efforts are performed on 3D with cropping patch operation, suffering from the large computation costs and limited global information. In this paper, we propose a multi-view vertebra localization and identification from CT images, converting the 3D problem into a 2D localization and identification task on different views. Without the limitation of the 3D cropped patch, our method can learn the multi-view global information naturally. Moreover, to better capture the anatomical structure information from different view perspectives, a multi-view contrastive learning strategy is developed to pre-train the backbone. Additionally, we further propose a Sequence Loss to maintain the sequential structure embedded along the vertebrae. Evaluation results demonstrate that, with only two 2D networks, our method can localize and identify vertebrae in CT images accurately, and outperforms the state-of-the-art methods consistently. Our code is available at https://github.com/ShanghaiTech-IMPACT/Multi-View-Vertebra-Localization-and-Identification-from-CT-Images., Comment: MICCAI 2023

Ghost imaging in the time domain allows for reconstructing fast temporal objects using a slow photodetector. The technique involves correlating random or pre-programmed probing temporal intensity patterns with the integrated signal measured after modulation by the temporal object. However, the implementation of temporal ghost imaging necessitates ultrafast detectors or modulators for measuring or pre-programming the probing intensity patterns, which is not universally available in all spectral regions especially in the mid-infrared range. Here, we demonstrate a frequency downconversion temporal ghost imaging scheme that enables to extend the operation regime to arbitrary wavelengths regions where fast modulators and detectors are not available. The approach modulates a signal with temporal intensity patterns in the near-infrared and transfers the patterns to an idler via difference-frequency generation at the wavelength of the temporal object to be retrieved. As a proof-of-concept, we demonstrate temporal ghost imaging in the mid-infrared. The scheme is flexible and introduces new possibilities for scan-free pump-probe imaging and the study of ultrafast dynamics in spectral regions where ultrafast modulation or detection is challenging such as the mid-infrared and THz regions.

We systematically study the effects of higher-order interactions on the S = 3/2, 1 orthogonal dimer chains using exact diagonalization and density matrix renormalization group. Due to frustration and higher spin, there are rich quantum phases, including three Haldane phases, two gapless phases and several magnetically ordered phases. To characterize these phases and their phase transitions, we study various physical quantities such as energy gap, energy level crossing, fidelity susceptibility, spin correlation, entanglement spectrum and central charge. According to our calculations, the biquadratic term can enhance the Haldane phase regions. In particular, we numerically identify that a Haldane phase in S = 3/2 case is adiabatically connected to the exact AKLT point when adding bicubic term. Our study on the orthogonal dimer model, which is a 1D version of Shastry-Sutherland model, provides insights into understanding the possible S = 3/2, 1 Haldane phases in quasi-1D and 2D frustrated magnetic materials., Comment: 14 pages, 17 figures

The ability to reversibly toggle between two distinct states in a non-volatile method is important for information storage applications. Such devices have been realized for phase-change materials, which utilizes local heating methods to toggle between a crystalline and an amorphous state with distinct electrical properties. To expand such kind of switching between two topologically distinct phases requires non-volatile switching between two crystalline phases with distinct symmetries. Here we report the observation of reversible and non-volatile switching between two stable and closely-related crystal structures with remarkably distinct electronic structures in the near room temperature van der Waals ferromagnet Fe$_{5-\delta}$GeTe$_2$. From a combination of characterization techniques we show that the switching is enabled by the ordering and disordering of an Fe site vacancy that results in distinct crystalline symmetries of the two phases that can be controlled by a thermal annealing and quenching method. Furthermore, from symmetry analysis as well as first principle calculations, we provide understanding of the key distinction in the observed electronic structures of the two phases: topological nodal lines compatible with the preserved global inversion symmetry in the site-disordered phase, and flat bands resulting from quantum destructive interference on a bipartite crystaline lattice formed by the presence of the site order as well as the lifting of the topological degeneracy due to the broken inversion symmetry in the site-ordered phase. Our work not only reveals a rich variety of quantum phases emergent in the metallic van der Waals ferromagnets due to the presence of site ordering, but also demonstrates the potential of these highly tunable two-dimensional magnets for memory and spintronics applications.

Magnetism in two-dimensional (2D) materials has attracted considerable attention recently for both fundamental understanding of magnetism and their tunability towards device applications. The isostructural Fe$_3$GeTe$_2$ and Fe$_3$GaTe$_2$ are two members of the Fe-based van der Waals (vdW) ferromagnet family, but exhibit very different Curie temperatures (T$_C$) of 210 K and 360 K, respectively. Here, by using angle-resolved photoemission spectroscopy and density functional theory, we systematically compare the electronic structures of the two compounds. Qualitative similarities in the Fermi surface can be found between the two compounds, with expanded hole pockets in Fe$_3$GaTe$_2$ suggesting additional hole carriers compared to Fe$_3$GeTe$_2$. Interestingly, we observe no band shift in Fe$_3$GaTe$_2$ across its T$_C$ of 360 K, compared to a small shift in Fe$_3$GeTe$_2$ across its T$_C$ of 210 K. The weak temperature-dependent evolution strongly deviates from the expectations of an itinerant Stoner mechanism. Our results suggest that itinerant electrons have minimal contributions to the enhancement of T$_C$ in Fe$_3$GaTe$_2$ compared to Fe$_3$GeTe$_2$, and that the nature of ferromagnetism in these Fe-based vdW ferromagnets must be understood with considerations of the electron correlations.

For algebraic stacks over a number field, we define their Brauer-Manin pairings, Brauer-Manin sets, and extend the descent theory of Colliot-Th\'el\`ene and Sansuc. By extending Sansuc's exact sequence, we show the torsionness of Brauer groups of stacks that are locally quotients of varieties by connected groups. With mild assumptions, for stacks that are locally quotients or Deligne-Mumford, we show that the Brauer-Manin obstruction coincides with some other cohomological obstructions such as obstructions given by torsors under connected groups or abelian gerbes, generalizing Harari's original results. For Brauer-Manin sets on these stacks, we show the properties such as descent along a torsor, product preservation are still correct. These results extend classical theories of those on varieties., Comment: 16 pages, revised some proofs (git: 20220302/60acc33)

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms, that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout., Comment: Forthcoming in the Journal of Computational and Graphical Statistics