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In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based formulation where the neural network is defined on a spatiotemporal domain, our methodology utilizes finite element basis functions in the time direction where the space-dependent coefficients are defined as the output of a neural network. We then apply the Galerkin or collocation projection in the time direction to obtain a system of PDEs for the space-dependent coefficients which is approximated in the framework of PINN. The advantages of such a hybrid formulation are twofold: statistical errors are avoided for the integral in the time direction, and the neural network's output can be regarded as a set of reduced spatial basis functions. To further alleviate the difficulties from high dimensionality and low regularity, we have developed an adaptive sampling strategy that refines the training set. More specifically, we use an explicit density model to approximate the distribution induced by the PDE residual and then augment the training set with new time-dependent random samples given by the learned density model. The effectiveness and efficiency of our proposed method have been demonstrated through a series of numerical experiments., Comment: 25pages

Sequential propagation of chaos (SPoC) is a recently developed tool to solve mean-field stochastic differential equations and their related nonlinear Fokker-Planck equations. Based on the theory of SPoC, we present a new method (deepSPoC) that combines the interacting particle system of SPoC and deep learning. Under the framework of deepSPoC, two classes of frequently used deep models include fully connected neural networks and normalizing flows are considered. For high-dimensional problems, spatial adaptive method are designed to further improve the accuracy and efficiency of deepSPoC. We analysis the convergence of the framework of deepSPoC under some simplified conditions and also provide a posterior error estimation for the algorithm. Finally, we test our methods on a wide range of different types of mean-field equations.

In this paper, we propose an efficient derivative-free version of a martingale neural network SOC-MartNet proposed in Cai et al. [2] for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations and stochastic optimal control problems (SOCPs) with controls on both drift and volatility. The solution of the HJB equation consists of two steps: (1) finding the optimal control from the value function, and (2) deriving the value function from a linear PDE characterized by the optimal control. The linear PDE is reformulated into a weak form of a new martingale formulation from the original SOC-MartNet where all temporal and spatial derivatives are replaced by an univariate, first-order random finite difference operator approximation, giving the derivative free version of the SOC-MartNet. Then, the optimal feedback control is identified by minimizing the mean of the value function, thereby avoiding the need for pointwise minimization on the Hamiltonian. Finally, the optimal control and value function are approximated by neural networks trained via adversarial learning using the derivative-free formulation. This method eliminates the reliance on automatic differentiation for computing temporal and spatial derivatives, offering significant efficiency in solving high-dimensional HJB equations and SOCPs.

Prompted by the recent discovery of high-temperature superconductivity in La$_3$Ni$_2$O$_7$ under pressure, this study delves into a theoretical investigation of spin excitations within this intriguing material. Employing self-consistent mean-field calculations, we find that superconductivity in this compound is predominantly governed by interlayer pairing mechanisms. In the superconducting state, our analysis uncovers a notable absence of a spin resonance mode, a finding that deviates from conventional expectations. Furthermore, we reveal a spectrum of energy-dependent incommensurate spin excitations. The observed incommensurate structures are elegantly explained by the nesting effect of energy contours, providing a coherent and comprehensive account of experimental observations. The implications of these spin excitations in La$_3$Ni$_2$O$_7$ are profound, offering critical insights into the superconducting mechanism at play. Our results not only contribute to the understanding of this novel superconductor but also pave the way for further research into the interplay between spin dynamics and unconventional superconductivity in layered materials., Comment: 7 pages, 6 figures

Link prediction has become a critical problem in network science and has thus attracted increasing research interest. Popularity and similarity are two primary mechanisms in the formation of real networks. However, the roles of popularity and similarity mechanisms in link prediction across various domain networks remain poorly understood. Accordingly, this study used orbit degrees of graphlets to construct multi-order popularity- and similarity-based network link predictors, demonstrating that traditional popularity- and similarity-based indices can be efficiently represented in terms of orbit degrees. Moreover, we designed a supervised learning model that fuses multiple orbit-degree-based features and validated its link prediction performance. We also evaluated the mean absolute Shapley additive explanations of each feature within this model across 550 real-world networks from six domains. We observed that the homophily mechanism, which is a similarity-based feature, dominated social networks, with its win rate being 91\%. Moreover, a different similarity-based feature was prominent in economic, technological, and information networks. Finally, no single feature dominated the biological and transportation networks. The proposed approach improves the accuracy and interpretability of link prediction, thus facilitating the analysis of complex networks., Comment: 40 pages, 9 figures

We calculate the exact values of the quasinormal frequencies for massless perturbations with spin $s\leq2$ moving in pure accelerating spacetime. We use two different methods to transfer the perturbation equations into the form of hypergeometric differential equations and obtain the same quasinormal frequencies. These purely imaginary spectra are shown to be independent of the spin of the perturbation and match those of the so-called acceleration modes of accelerating black holes after taking the Minkowski limit. This implies that the acceleration modes actually originate from the pure accelerating spacetime and the appearance of black holes would deform the spectra. In addition, we calculate the quasinormal frequencies of scalar, electromagnetic and gravitational perturbations of $D$-dimensional de Sitter spacetime and compare them with previous results to verify the validity of our method., Comment: 12 pages. arXiv admin note: text overlap with arXiv:gr-qc/0605027 by other authors

The construction of highly coherent x-ray sources has enabled new research opportunities across the scientific landscape. The maximum raw data rate per beamline now exceeds 40 GB/s, posing unprecedented challenges for the online processing and offline storage of the big data. Such challenge is particularly prominent for x-ray photon correlation spectroscopy (XPCS), where real time analyses require simultaneous calculation on all the previously acquired data in the time series. We present a homomorphic compression scheme to effectively reduce the computational time and memory space required for XPCS analysis. Leveraging similarities in the mathematical expression between a matrix-based compression algorithm and the correlation calculation, our approach allows direct operation on the compressed data without their decompression. The lossy compression reduces the computational time by a factor of 10,000, enabling real time calculation of the correlation functions at kHz framerate. Our demonstration of a homomorphic compression of scientific data provides an effective solution to the big data challenge at coherent light sources. Beyond the example shown in this work, the framework can be extended to facilitate real-time operations directly on a compressed data stream for other techniques.

Weakly-supervised medical image segmentation is a challenging task that aims to reduce the annotation cost while keep the segmentation performance. In this paper, we present a novel framework, SimTxtSeg, that leverages simple text cues to generate high-quality pseudo-labels and study the cross-modal fusion in training segmentation models, simultaneously. Our contribution consists of two key components: an effective Textual-to-Visual Cue Converter that produces visual prompts from text prompts on medical images, and a text-guided segmentation model with Text-Vision Hybrid Attention that fuses text and image features. We evaluate our framework on two medical image segmentation tasks: colonic polyp segmentation and MRI brain tumor segmentation, and achieve consistent state-of-the-art performance., Comment: accepted by MICCAI 2024

The $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) family of Kagome metals hosts unconventional charge density wave order whose nature is still an open puzzle. Accumulated evidences point to a time-reversal symmetry breaking orbital flux phase that carries loop currents. Such an order may support anomalous Hall effect. However, the polar Kerr effect measurements that probe the a.c. anomalous Hall conductivity seems to have yielded contradictory results. We first argue on symmetry grounds that some previously proposed orbital flux order, most notably the one with Star-of-David distortion, shall not give rise to anomalous Hall or polar Kerr effects. We further take the tri-hexagonal orbital flux phase as an exemplary Kagome flux order that does exhibit anomalous Hall response, and show that the Kerr rotation angle at two relevant experimental optical frequencies generally reaches microradians to sub-milliradians levels. A particularly sharp resonance enhancement is observed at around $\hbar \omega =1$ eV, suggesting exceedingly large Kerr rotation at the corresponding probing frequencies not yet accessed by previous experiments. Our study can help to interpret the Kerr measurements on $A$V$_3$Sb$_5$ and to eventually resolve the nature of their CDW order., Comment: 7+1 pages

Adaptive networks can sense and adjust to dynamic environments to optimize their performance. Understanding their nanoscale responses to external stimuli is essential for applications in nanodevices and neuromorphic computing. However, it is challenging to image such responses on the nanoscale with crystallographic sensitivity. Here, the evolution of nanodomain networks in (PbTiO3)n/(SrTiO3)n superlattices was directly visualized in real space as the system adapts to ultrafast repetitive optical excitations that emulate controlled neural inputs. The adaptive response allows the system to explore a wealth of metastable states that were previously inaccessible. Their reconfiguration and competition were quantitatively measured by scanning x-ray nanodiffraction as a function of the number of applied pulses, in which crystallographic characteristics were quantitatively assessed by assorted diffraction patterns using unsupervised machine-learning methods. The corresponding domain boundaries and their connectivity were drastically altered by light, holding promise for light-programmable nanocircuits in analogy to neuroplasticity. Phase-field simulations elucidate that the reconfiguration of the domain networks is a result of the interplay between photocarriers and transient lattice temperature. The demonstrated optical control scheme and the uncovered nanoscopic insights open opportunities for remote control of adaptive nanoscale domain networks.

We investigates the electronic structure and superconducting gaps in the charge density wave (CDW) states of vanadium-based Kagome superconductors AV$_3$Sb$_5$, focusing on the concurrent presence of CDW and superconducting orders. Two predominant CDW configurations are explored: the trihexagonal (TrH) and star-of-David (SoD) patterns, involving charge bond order (CBO) and chiral flux phase (CFP), corresponding to real and imaginary bond orders. In the isotropic $s$-wave superconducting state, the presence of CBO alone maintains an isotropic superconducting gap, whereas the introduction of CFP induces anisotropy in the gap, manifesting time-reversal symmetry breaking due to the CFP. Our analysis extends to the topological properties of these states, revealing a marked topological phase transition in the TrH configuration from a trivial to a non-trivial state with increasing CFP intensity. This transition suggests that the introduction of CFP could catalyze the emergence of topological superconductivity, potentially leading to the presence of Majorana excitations. The results contribute significantly to understanding the complex interplay between various CDW patterns and superconductivity in Kagome superconductors. They provide a theoretical framework for the diverse experimental observations of energy gaps and open new avenues for research into topological superconductivity and its potential applications. This study underscores the necessity for further experimental and theoretical exploration to unveil novel interwinded quantum states and functionalities in these intriguing materials., Comment: 8 pages, 6 figures

Scanning X-ray nanodiffraction microscopy is a powerful technique for spatially resolving nanoscale structural morphologies by diffraction contrast. One of the critical challenges in experimental nanodiffraction data analysis is posed by the convergence angle of nanoscale focusing optics which creates simultaneous dependency of the far-field scattering data on three independent components of the local strain tensor - corresponding to dilation and two potential rigid body rotations of the unit cell. All three components are in principle resolvable through a spatially mapped sample tilt series however traditional data analysis is computationally expensive and prone to artifacts. In this study, we implement NanobeamNN, a convolutional neural network specifically tailored to the analysis of scanning probe X-ray microscopy data. NanobeamNN learns lattice strain and rotation angles from simulated diffraction of a focused X-ray nanobeam by an epitaxial thin film and can directly make reasonable predictions on experimental data without the need for additional fine-tuning. We demonstrate that this approach represents a significant advancement in computational speed over conventional methods, as well as a potential improvement in accuracy over the current standard.

Long-standing anomalous experimental results from short-baseline neutrino experiments have persisted for decades. These results, when interpreted with one or more light sterile neutrinos, are inconsistent with numerous null results experimentally. However, if the sterile neutrino decays en route to the detector, this can mimic $\nu_\mu \to \nu_e$ oscillation signals while avoiding many of these external constraints. We revisit this solution to the MiniBooNE and LSND puzzles in view of new data from the MicroBooNE experiment at Fermilab. Using MicroBooNE's liquid-argon time-projection chamber search for an excess of $\nu_e$ in the Booster beam, we derive new limits in two models' parameter spaces of interest: where the sterile neutrino decays (I) via mixing with the active neutrinos, or (II) via higher-dimensional operators. We also provide an updated, comprehensive fit to the MiniBooNE neutrino- and antineutrino-beam data, including appearance ($\nu_e$) and disappearance ($\nu_\mu$) channels. Despite alleviating the tension with muon neutrino disappearance experiments, we find that the latest MicroBooNE analysis rules out the decaying sterile neutrino solution in a large portion of the parameter space at more than $99\%$ CL., Comment: 16 pages, 12 figures, 1 table

The current variants of the Segment Anything Model (SAM), which include the original SAM and Medical SAM, still lack the capability to produce sufficiently accurate segmentation for medical images. In medical imaging contexts, it is not uncommon for human experts to rectify segmentations of specific test samples after SAM generates its segmentation predictions. These rectifications typically entail manual or semi-manual corrections employing state-of-the-art annotation tools. Motivated by this process, we introduce a novel approach that leverages the advantages of online machine learning to enhance Segment Anything (SA) during test time. We employ rectified annotations to perform online learning, with the aim of improving the segmentation quality of SA on medical images. To improve the effectiveness and efficiency of online learning when integrated with large-scale vision models like SAM, we propose a new method called Auxiliary Online Learning (AuxOL). AuxOL creates and applies a small auxiliary model (specialist) in conjunction with SAM (generalist), entails adaptive online-batch and adaptive segmentation fusion. Experiments conducted on eight datasets covering four medical imaging modalities validate the effectiveness of the proposed method. Our work proposes and validates a new, practical, and effective approach for enhancing SA on downstream segmentation tasks (e.g., medical image segmentation)., Comment: Project Link: https://sam-auxol.github.io/AuxOL/

Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of $10^2$ pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.

Understanding how student peers influence learning outcomes is crucial for effective education management in complex social systems. The complexities of peer selection and evolving peer relationships, however, pose challenges for identifying peer effects using static observational data. Here we use both null-model and regression approaches to examine peer effects using longitudinal data from 5,272 undergraduates, where roommate assignments are plausibly random upon enrollment and roommate relationships persist until graduation. Specifically, we construct a roommate null model by randomly shuffling students among dorm rooms and introduce an assimilation metric to quantify similarities in roommate academic performance. We find significantly larger assimilation in actual data than in the roommate null model, suggesting roommate peer effects, whereby roommates have more similar performance than expected by chance alone. Moreover, assimilation exhibits an overall increasing trend over time, suggesting that peer effects become stronger the longer roommates live together. Our regression analysis further reveals the moderating role of peer heterogeneity. In particular, when roommates perform similarly, the positive relationship between a student's future performance and their roommates' average prior performance is more pronounced, and their ordinal rank in the dorm room has an independent effect. Our findings contribute to understanding the role of college roommates in influencing student academic performance., Comment: 56 pages, 4 figures, 2 tables, with Supplementary Information

Current fundus image analysis models are predominantly built for specific tasks relying on individual datasets. The learning process is usually based on data-driven paradigm without prior knowledge, resulting in poor transferability and generalizability. To address this issue, we propose MM-Retinal, a multi-modal dataset that encompasses high-quality image-text pairs collected from professional fundus diagram books. Moreover, enabled by MM-Retinal, we present a novel Knowledge-enhanced foundational pretraining model which incorporates Fundus Image-Text expertise, called KeepFIT. It is designed with image similarity-guided text revision and mixed training strategy to infuse expert knowledge. Our proposed fundus foundation model achieves state-of-the-art performance across six unseen downstream tasks and holds excellent generalization ability in zero-shot and few-shot scenarios. MM-Retinal and KeepFIT are available at https://github.com/lxirich/MM-Retinal., Comment: Early Accepted by The International Conference on Medical Image Computing and Computer Assisted Intervention(MICCAI)2024

Fluxonium qubits are recognized for their high coherence times and high operation fidelities, attributed to their unique design incorporating over 100 Josephson junctions per superconducting loop. However, this complexity poses significant fabrication challenges, particularly in achieving high yield and junction uniformity with traditional methods. Here, we introduce an overlap process for Josephson junction fabrication that achieves nearly 100% yield and maintains uniformity across a 2-inch wafer with less than 5% variation for the phase slip junction and less than 2% for the junction array. Our compact junction array design facilitates fluxonium qubits with energy relaxation times exceeding 1 millisecond at the flux frustration point, demonstrating consistency with state-of-the-art dielectric loss tangents and flux noise across multiple devices. This work suggests the scalability of high coherence fluxonium processors using CMOS-compatible processes, marking a significant step towards practical quantum computing.

The community plays a crucial role in understanding user behavior and network characteristics in social networks. Some users can use multiple social networks at once for a variety of objectives. These users are called overlapping users who bridge different social networks. Detecting communities across multiple social networks is vital for interaction mining, information diffusion, and behavior migration analysis among networks. This paper presents a community detection method based on nonnegative matrix tri-factorization for multiple heterogeneous social networks, which formulates a common consensus matrix to represent the global fused community. Specifically, the proposed method involves creating adjacency matrices based on network structure and content similarity, followed by alignment matrices which distinguish overlapping users in different social networks. With the generated alignment matrices, the method could enhance the fusion degree of the global community by detecting overlapping user communities across networks. The effectiveness of the proposed method is evaluated with new metrics on Twitter, Instagram, and Tumblr datasets. The results of the experiments demonstrate its superior performance in terms of community quality and community fusion., Comment: This paper was accepted by IEEE Transactions on Computational Social Systems(TCSS)

In this paper, we propose a martingale-based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is needed for the infimum of the Hamiltonian, \inf_{u \in U} H(t,x,u, z,p), and stochastic optimal control problems (SOCPs) with controls on both drift and volatility. We reformulate the HJB equations for the value function by training two neural networks, one for the value function and one for the optimal control with the help of two stochastic processes - a Hamiltonian process and a cost process. The control and value networks are trained such that the associated Hamiltonian process is minimized to satisfy the minimum principle of a feedback SOCP, and the cost process becomes a martingale, thus, ensuring the value function network as the solution to the corresponding HJB equation. Moreover, to enforce the martingale property for the cost process, we employ an adversarial network and construct a loss function characterizing the projection property of the conditional expectation condition of the martingale. Numerical results show that the proposed SOC-MartNet is effective and efficient for solving HJB-type equations and SOCPs with a dimension up to 2000 in a small number of epochs (less than 20) or stochastic gradient method iterations (less than 2000) for the training.

Comprehending the association between social capabilities and individual psychological traits is paramount for educational administrators. Presently, many studies heavily depend on online questionnaires and self-reported data, while analysis of the connection between offline social networks and mental health status remains scarce. By leveraging a public dataset encompassing on-campus dining activities over 21 weeks, we establish student co-occurrence networks and closely observe the changes in network topology over time. Empirical analysis shows that the node centralities of the student co-occurrence networks exhibit significantly positive correlation with the enhancement of the flourishing trait within the field of mental well-being. Our findings offer potential guidance for assisting students in maintaining a positive mental health status., Comment: 14 pages, 2 figures, 1 Table

While finite-time blowup solutions have been studied in depth for the Keller-Segel equation, a fundamental model describing chemotaxis, the existence of finite-time blowup solutions to chemotaxis-fluid models remains largely unexplored. To fill this gap in the literature, we use a quantitative method to directly construct a smooth finite-time blowup solution for the Keller-Segel-Navier-Stokes system with buoyancy in 3D. The heart of the proof is to establish the non-radial finite-codimensional stability of an explicit self-similar blowup solution to 3D Keller-Segel equation with the abstract semigroup tool from [Merle-Rapha\"el-Rodnianski-Szeftel, 2022], which partially generalizes the radial stability result [Glogi\'c-Sch\"orkhuber, 2024] to the non-radial setting. Additionally, we introduce a robust localization argument to find blowup solutions with non-negative density and finite mass., Comment: 32 pages

Surface acoustic wave devices are key components for processing radio frequency signals in wireless communication because these devices offer simultaneously high performance, compact size and low cost. The optimization of the device structure requires a quantitative understanding of energy conversion and loss mechanisms. Stroboscopic full-field diffraction x-ray microscopy studies of a prototypical one-port resonator device revealed the existence of unanticipated acoustic loss. A non-uniform acoustic excitation in the active area was responsible for the substantial end and side leakages observed at the design frequency. Quantitative analysis of the strain amplitude using a wave decomposition method allowed the determination of several key device parameters. This high-resolution spatiotemporal strain imaging technique is, more generally, suited for studying nanophononics, specifically when the feature size is smaller than optical wavelengths. The strain sensitivity allows precise measurement of acoustic waves with picometer-scale amplitude.

We explore the superconducting pairing mechanisms in the trilayer $\mathrm{La}_4\mathrm{Ni}_3\mathrm{O}_{10}$ material through self-consistent mean-field calculations. Our findings demonstrate that intralayer pairings are substantially weaker compared to interlayer ones. Remarkably, in the state characterized by interlayer pairing, we detect the presence of partially gapped Fermi surfaces, a fascinating occurrence attributable to the disparity between the inner and outer conducting layers of $\mathrm{La}_4\mathrm{Ni}_3\mathrm{O}_{10}$. Moreover, this study provides valuable insights into the lower superconducting transition temperatures observed in $\mathrm{La}_4\mathrm{Ni}_3\mathrm{O}_{10}$ compounds. This contributes to a deeper understanding of its distinct superconducting attributes., Comment: 6 pages, 5 figures

Controlling the Mott transition through strain engineering is crucial for advancing the development and application of memristive and neuromorphic computing devices. Yet, Mott insulators are heterogeneous due to intrinsic phase boundaries and extrinsic defects, posing significant challenges to fully understanding the impact of local microscopic distortions on the local Mott transition. Addressing these challenges demands structural characterizations at the relevant length scale. Here, using a synchrotron-based scanning X-ray nanoprobe, we studied the real-space structural heterogeneity during the structural phase transition in a V2O3 thin film. Through temperature-dependent metal-insulator phase coexistence mapping, we report a variation in the local transition temperature of up to 7 K across the film and the presence of the transition hysteresis at the nanoscale. Furthermore, a detailed quantitative analysis demonstrates that the spatial heterogeneity of the transition is closely tied to the tilting of crystallographic planes in the pure insulating phase. Our work highlights the impact of local heterogeneity on the Mott transition and lays the groundwork for future innovations in harnessing strain heterogeneity within Mott systems for the next-generation computational technologies.

Recently, promptable segmentation models, such as the Segment Anything Model (SAM), have demonstrated robust zero-shot generalization capabilities on static images. These promptable models exhibit denoising abilities for imprecise prompt inputs, such as imprecise bounding boxes. In this paper, we explore the potential of applying SAM to track and segment objects in videos where we recognize the tracking task as a prompt denoising task. Specifically, we iteratively propagate the bounding box of each object's mask in the preceding frame as the prompt for the next frame. Furthermore, to enhance SAM's denoising capability against position and size variations, we propose a multi-prompt strategy where we provide multiple jittered and scaled box prompts for each object and preserve the mask prediction with the highest semantic similarity to the template mask. We also introduce a point-based refinement stage to handle occlusions and reduce cumulative errors. Without involving tracking modules, our approach demonstrates comparable performance in video object/instance segmentation tasks on three datasets: DAVIS2017, YouTubeVOS2018, and UVO, serving as a concise baseline and endowing SAM-based downstream applications with tracking capabilities.

Link prediction is a paradigmatic and challenging problem in network science, which aims to predict missing links, future links and temporal links based on known topology. Along with the increasing number of link prediction algorithms, a critical yet previously ignored risk is that the evaluation metrics for algorithm performance are usually chosen at will. This paper implements extensive experiments on hundreds of real networks and 25 well-known algorithms, revealing significant inconsistency among evaluation metrics, namely different metrics probably produce remarkably different rankings of algorithms. Therefore, we conclude that any single metric cannot comprehensively or credibly evaluate algorithm performance. Further analysis suggests the usage of at least two metrics: one is the area under the receiver operating characteristic curve (AUC), and the other is one of the following three candidates, say the area under the precision-recall curve (AUPR), the area under the precision curve (AUC-Precision), and the normalized discounted cumulative gain (NDCG). In addition, as we have proved the essential equivalence of threshold-dependent metrics, if in a link prediction task, some specific thresholds are meaningful, we can consider any one threshold-dependent metric with those thresholds. This work completes a missing part in the landscape of link prediction, and provides a starting point toward a well-accepted criterion or standard to select proper evaluation metrics for link prediction., Comment: 20 pages, 9 figures

We investigate the single-particle spectra of recently discovered kagome superconductors. We examine nine distinct superconducting pairing symmetries, including the uniform $s$-wave pairing function, nearest-neighbor and next-nearest-neighbor $s$-wave pairing, $p+ip$ pairing, $d+id$ pairing, and $f$-wave pairing states. These pairing states can be classified into irreducible representations of the $C_{6v}$ point group. Our findings suggest that these pairing states can be differentiated by analyzing the energy bands, spectral function, and local density of states. Additionally, we explore the single impurity effect, which could potentially assist in further distinguishing these pairing symmetries., Comment: 11 pages, 9 figures, To appear in Phys. Rev. B

Link prediction aims to predict the potential existence of links between two unconnected nodes within a network based on the known topological characteristics. Evaluation metrics are used to assess the effectiveness of algorithms in link prediction. The discriminating ability of these evaluation metrics is vitally important for accurately evaluating link prediction algorithms. In this study, we propose an artificial network model, based on which one can adjust a single parameter to monotonically and continuously turn the prediction accuracy of the specifically designed link prediction algorithm. Building upon this foundation, we show a framework to depict the effectiveness of evaluating metrics by focusing on their discriminating ability. Specifically, a quantitative comparison in the abilities of correctly discerning varying prediction accuracies was conducted encompassing nine evaluation metrics: Precision, Recall, F1-Measure, Matthews Correlation Coefficient (MCC), Balanced Precision (BP), the Area Under the receiver operating characteristic Curve (AUC), the Area Under the Precision-Recall curve (AUPR), Normalized Discounted Cumulative Gain (NDCG), and the Area Under the magnified ROC (AUC-mROC). The results indicate that the discriminating abilities of the three metrics, AUC, AUPR, and NDCG, are significantly higher than those of other metrics.

Sampling from Boltzmann distributions, particularly those tied to high-dimensional and complex energy functions, poses a significant challenge in many fields. In this work, we present the Energy-Based Diffusion Generator (EDG), a novel approach that integrates ideas from variational autoencoders and diffusion models. EDG leverages a decoder to transform latent variables from a simple distribution into samples approximating the target Boltzmann distribution, while the diffusion-based encoder provides an accurate estimate of the Kullback-Leibler divergence during training. Notably, EDG is simulation-free, eliminating the need to solve ordinary or stochastic differential equations during training. Furthermore, by removing constraints such as bijectivity in the decoder, EDG allows for flexible network design. Through empirical evaluation, we demonstrate the superior performance of EDG across a variety of complex distribution tasks, outperforming existing methods.

We have conducted a theoretical investigation of the topological phenomena associated with chiral superconducting pairing states induced in a doped Kane-Mele model on a honeycomb lattice. Through numerical analysis, we have obtained exotic phase diagrams for both the $d+id$ and $p+ip$ superconducting states. In the case of the $d+id$ pairing state, higher Chern number states with $\left| C \right| = \pm 4$ emerge. The Chern number decreases as the spin-orbit coupling is introduced. For the $p+ip$ pairing state, additional phase transition lines are present in the overdoped region near the Van Hove singularity point, leading to the emergence of higher Chern number phases with $\left| C \right| = \pm 6$. These higher Chern number phases are further verified through the bulk-edge correspondence. To understand the origin of the exotic topological phase diagrams in the chiral superconducting state, we have examined the electronic structure at the phase transition lines. This investigation provides insight into the complex interplay between chiral superconductivity and topological properties, potentially paving the way for the discovery of new materials with unique topological properties., Comment: 9 pages, 6 figures