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The existence of edge states is one of the most vital properties of topological insulators. Although tremendous success has been accomplished in describing and explaining edge states associated with PT symmetry breaking, little work has been done on PT symmetry preserving cases. Two-dimensional Schroedinger operators with super honeycomb lattice potentials always have double Dirac cones at the Gamma point - the zero momentum point on their energy bands due to C6 symmetry, PT symmetry, and the "folding" symmetry - caused by an additional translation symmetry. There are two topologically different ways to deform such a system by PT symmetry preserving but folding symmetry breaking perturbations. Interestingly, there exist two gapped edge states on the interface between such two kinds of perturbed materials. In this paper, we illustrate the existence of such PT preserving edge states rigorously for the first time. We use a domain wall modulated Schroedinger operator to model the phenomenon under small perturbations and rigorously prove the existence of two gapped edge states. We also provide a brief interpretation from the point of view of "topology" by the parities of degenerate bulk modes. Our work thoroughly explains the existence of "helical" like edge states in super honeycomb configurations and lays a foundation for the descriptions of topologies of such systems., Comment: 3 Figures

Cross-modal fashion synthesis and editing offer intelligent support to fashion designers by enabling the automatic generation and local modification of design drafts.While current diffusion models demonstrate commendable stability and controllability in image synthesis,they still face significant challenges in generating fashion design from abstract design elements and fine-grained editing.Abstract sensory expressions, \eg office, business, and party, form the high-level design concepts, while measurable aspects like sleeve length, collar type, and pant length are considered the low-level attributes of clothing.Controlling and editing fashion images using lengthy text descriptions poses a difficulty.In this paper, we propose HieraFashDiff,a novel fashion design method using the shared multi-stage diffusion model encompassing high-level design concepts and low-level clothing attributes in a hierarchical structure.Specifically, we categorized the input text into different levels and fed them in different time step to the diffusion model according to the criteria of professional clothing designers.HieraFashDiff allows designers to add low-level attributes after high-level prompts for interactive editing incrementally.In addition, we design a differentiable loss function in the sampling process with a mask to keep non-edit areas.Comprehensive experiments performed on our newly conducted Hierarchical fashion dataset,demonstrate that our proposed method outperforms other state-of-the-art competitors.

We are interested in better understanding ways that students collaborate to solve conceptual physics problems in the context of spherical unit vectors in upper-level E&M, especially problems that have been shown to be difficult for students to solve individually on their own, but which groups of students have been more successful at. Using think-aloud interviews with students in small groups, we ask them to solve together on a large whiteboard conceptual problems from this E&M context. The interviews were video and audio recorded, and qualitatively analyzed using an emergent coding method and the resources framework. Through this analysis, we observed one common mechanism in all three group-interviews whereby students collaborated effectively: first one student activated a conceptual resource and expressed it, then another student took up that idea, and finally the whole group together used that idea to move forward with the problem. This mechanism exemplifies a newer framework: shared resources. We further analyzed students' collaboration through the lens of shared resources and identified multiple instances. We propose that the shared resources construct could be a potential tool to help understand how students collaborate in solving conceptual physics problems. In this paper, we report our methodology and the results from one group interview to illustrate one shared resource we identified and the role it played in helping students collaboratively solve the conceptual problem in this context. Future work and implications for instruction are suggested.

Multi-modal medical image fusion is essential for the precise clinical diagnosis and surgical navigation since it can merge the complementary information in multi-modalities into a single image. The quality of the fused image depends on the extracted single modality features as well as the fusion rules for multi-modal information. Existing deep learning-based fusion methods can fully exploit the semantic features of each modality, they cannot distinguish the effective low and high frequency information of each modality and fuse them adaptively. To address this issue, we propose AdaFuse, in which multimodal image information is fused adaptively through frequency-guided attention mechanism based on Fourier transform. Specifically, we propose the cross-attention fusion (CAF) block, which adaptively fuses features of two modalities in the spatial and frequency domains by exchanging key and query values, and then calculates the cross-attention scores between the spatial and frequency features to further guide the spatial-frequential information fusion. The CAF block enhances the high-frequency features of the different modalities so that the details in the fused images can be retained. Moreover, we design a novel loss function composed of structure loss and content loss to preserve both low and high frequency information. Extensive comparison experiments on several datasets demonstrate that the proposed method outperforms state-of-the-art methods in terms of both visual quality and quantitative metrics. The ablation experiments also validate the effectiveness of the proposed loss and fusion strategy.

The vulnerability of machine learning models to adversarial attacks has been attracting considerable attention in recent years. Most existing studies focus on the behavior of stand-alone single-agent learners. In comparison, this work studies adversarial training over graphs, where individual agents are subjected to perturbations of varied strength levels across space. It is expected that interactions by linked agents, and the heterogeneity of the attack models that are possible over the graph, can help enhance robustness in view of the coordination power of the group. Using a min-max formulation of diffusion learning, we develop a decentralized adversarial training framework for multi-agent systems. We analyze the convergence properties of the proposed scheme for both convex and non-convex environments, and illustrate the enhanced robustness to adversarial attacks., Comment: arXiv admin note: text overlap with arXiv:2303.01936

This work focuses on adversarial learning over graphs. We propose a general adversarial training framework for multi-agent systems using diffusion learning. We analyze the convergence properties of the proposed scheme for convex optimization problems, and illustrate its enhanced robustness to adversarial attacks.

Decompilation aims to transform a low-level program language (LPL) (eg., binary file) into its functionally-equivalent high-level program language (HPL) (e.g., C/C++). It is a core technology in software security, especially in vulnerability discovery and malware analysis. In recent years, with the successful application of neural machine translation (NMT) models in natural language processing (NLP), researchers have tried to build neural decompilers by borrowing the idea of NMT. They formulate the decompilation process as a translation problem between LPL and HPL, aiming to reduce the human cost required to develop decompilation tools and improve their generalizability. However, state-of-the-art learning-based decompilers do not cope well with compiler-optimized binaries. Since real-world binaries are mostly compiler-optimized, decompilers that do not consider optimized binaries have limited practical significance. In this paper, we propose a novel learning-based approach named NeurDP, that targets compiler-optimized binaries. NeurDP uses a graph neural network (GNN) model to convert LPL to an intermediate representation (IR), which bridges the gap between source code and optimized binary. We also design an Optimized Translation Unit (OTU) to split functions into smaller code fragments for better translation performance. Evaluation results on datasets containing various types of statements show that NeurDP can decompile optimized binaries with 45.21% higher accuracy than state-of-the-art neural decompilation frameworks.

Dirac cones are conical singularities that occur near the degenerate points in band structures. Such singularities result in enormous unusual phenomena of the corresponding physical systems. This work investigates double Dirac cones that occur in the vicinity of a fourfold degenerate point in the band structures of certain operators. It is known that such degeneracy originates in the symmetries of the Hamiltonian. We use two dimensional periodic Schr\"odinger operators with novel designed symmetries as our prototype. First, we characterize admissible potentials, termed as super honeycomb lattice potentials. They are honeycomb lattices potentials with a key additional translation symmetry. It is rigorously justified that Schr\"odinger operators with such potentials almost guarantee the existence of double Dirac cones on the bands at the {\Gamma} point, the origin of the Brillouin zone. We further show that the additional translation symmetry is an indispensable ingredient by a perturbation analysis. Indeed, the double cones disappear if the additional translation symmetry is broken. Many numerical simulations are provided, which agree well with our analysis.