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Rare earth dopants are one of the most extensively studied optical emission centers for a broad range of applications such as laser optoelectronics, sensing, lighting, and quantum information technologies due to their narrow optical linewidth and exceptional coherence properties. Epitaxial doped oxide thin films can serve as a promising and controlled host to investigate rare-earth dopants suitable for scalable quantum memories, on-chip lasers and amplifiers. Here, we report high-quality epitaxial thin films of Tm-doped CaZrO$_3$ grown by pulsed laser deposition for infrared optoelectronic and quantum memory applications. We perform extensive structural and chemical characterization to probe the crystallinity of the films and the doping behavior. Low temperature photoluminescence measurements show sharp radiative transitions in the short-wave infrared range of 1.75 - 2 \mu m., Comment: 17 pages, 4 figures

We study rational powers and Rees valuations of invariant ideals, providing explicit descriptions in terms of polyhedra and lattice points. This allows us to show that a version of Musta\c{t}\u{a}-Takagi's summation formula for rational powers holds for these ideals. Moreover, for arbitrary ideals over the complex numbers, we prove a weaker version of this formula that holds for sufficiently large rational numbers.

Auto-regressive models have achieved impressive results in 2D image generation by modeling joint distributions in grid space. In this paper, we extend auto-regressive models to 3D domains, and seek a stronger ability of 3D shape generation by improving auto-regressive models at capacity and scalability simultaneously. Firstly, we leverage an ensemble of publicly available 3D datasets to facilitate the training of large-scale models. It consists of a comprehensive collection of approximately 900,000 objects, with multiple properties of meshes, points, voxels, rendered images, and text captions. This diverse labeled dataset, termed Objaverse-Mix, empowers our model to learn from a wide range of object variations. However, directly applying 3D auto-regression encounters critical challenges of high computational demands on volumetric grids and ambiguous auto-regressive order along grid dimensions, resulting in inferior quality of 3D shapes. To this end, we then present a novel framework Argus3D in terms of capacity. Concretely, our approach introduces discrete representation learning based on a latent vector instead of volumetric grids, which not only reduces computational costs but also preserves essential geometric details by learning the joint distributions in a more tractable order. The capacity of conditional generation can thus be realized by simply concatenating various conditioning inputs to the latent vector, such as point clouds, categories, images, and texts. In addition, thanks to the simplicity of our model architecture, we naturally scale up our approach to a larger model with an impressive 3.6 billion parameters, further enhancing the quality of versatile 3D generation. Extensive experiments on four generation tasks demonstrate that Argus3D can synthesize diverse and faithful shapes across multiple categories, achieving remarkable performance., Comment: Project page: https://argus-3d.github.io/ . Datasets: https://huggingface.co/datasets/BAAI/Objaverse-MIX. arXiv admin note: substantial text overlap with arXiv:2303.14700

Charged lepton flavor violation (CLFV) represents a clear new physics (NP) signal beyond the standard model (SM). In this work, we investigate the CLFV decays of vector mesons $V\rightarrow l_i^{\pm}l_j^{\mp}$ with $V\in\{\phi, J/\Psi, \Upsilon(1S), \Upsilon(2S),\Upsilon(3S)\}$ in the $\mathrm{U}(1)_{X} \mathrm{SSM}$. Considering the SM-like Higgs boson mass within $3\sigma$ region, we discuss the corresponding constraints on the relevant parameter space of the model, which indicate this model can produce significant contributions to such CLFV decays. From the numerical analyses, the main sensitive parameters and CLFV sources originate from the non-diagonal elements correspond to the initial and final generations of the leptons. And the branching ratios to these CLFV processes can easily reach the present experimental upper bounds. Therefore, searching for CLFV processes of vector mesons may be an effective channel to study new physics.

Quantum Anomalous Hall (QAH) state in six quintuple layer Cr$_{0.1}$(Bi$_{0.2}$Sb$_{0.8}$)$_{1.9}$Te$_3$ thin films were studied through scanning tunneling spectroscopy (STS) and electrical transport measurements. While the surface state is gapless above the Curie temperature ($T_\mathrm{C} \approx 30$ K), scanning tunneling spectroscopy (STS) of the sample reveals a topologically non-trivial gap with an average value of $\approx 13.5$ meV at 4.2 K below the ferromagnetic transition. Nonetheless, areal STS scans of the magnetic topological insulator exhibit energy modulations on the order of several meV's in the surface bands which result in the valence band maximum in some regions becoming higher than the energy of the conduction band minimum of some other regions that are spatially separated by no more than 3 nm. First principle calculations demonstrate that the origin of the observed inhomogeneous energy band alignment is an outcome of many-body interactions, namely electron-defect interactions and electron-phonon interactions. Defects play the role of locally modifying the energy landscape of surface bands while electron-phonon interactions renormalize the surface bands such that the surface gap becomes reduced by more than 1 meV as temperature is raised from 0 to 4.2 K. These many-body interactions at a finite temperature result in substantial increase of electron tunneling across the spatially separated conduction band pockets even for finite temperatures well below $T_\mathrm{C}$ , thus driving the magnetic topological insulator out of its QAH insulating phase into a metallic phase at a relatively low temperature., Comment: 15 pages, 15 figures

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first approach is based on the Chow-Liu algorithm, and learns an optimal tree-structured distribution efficiently. The second approach is a modification of the PC algorithm for polytrees that uses partial correlation as a conditional independence tester for constraint-based structure learning. We derive explicit finite-sample guarantees for both approaches, and show that both approaches are optimal by deriving matching lower bounds. Additionally, we conduct numerical experiments to compare the performance of various algorithms, providing further insights and empirical evidence.

The charge density wave (CDW), as a hallmark of vanadium-based kagome superconductor AV3Sb5 (A = K, Rb, Cs), has attracted intensive attention. However, the fundamental controversy regarding the underlying mechanism of CDW therein persists. Recently, the vanadium-based bi-layered kagome metal ScV6Sn6, reported to exhibit a long-range charge order below 94 K, has emerged as a promising candidate to further clarify this core issue. Here, employing micro-focusing angle-resolved photoemission spectroscopy ({\mu}-ARPES) and first-principles calculations, we systematically studied the unique CDW order in vanadium-based bi-layered kagome metals by comparing ScV6Sn6 with its isostructural counterpart YV6Sn6, which lacks a CDW ground state. Combining ARPES data and the corresponding joint density of states (DOS), we suggest that the VHS nesting mechanism might be invalid in these materials. Besides, in ScV6Sn6, we identified multiple hybridization energy gaps resulting from CDW-induced band folding, along with an anomalous band dispersion, implying a potential electron-phonon coupling driven mechanism underlying the formation of the CDW order. Our finding not only comprehensively maps the electronic structure of V-based bi-layer kagome metals but also provide constructive experimental evidence for the unique origin of CDW in this system., Comment: 14 pages, 5 figures

A molecule's 2D representation consists of its atoms, their attributes, and the molecule's covalent bonds. A 3D (geometric) representation of a molecule is called a conformer and consists of its atom types and Cartesian coordinates. Every conformer has a potential energy, and the lower this energy, the more likely it occurs in nature. Most existing machine learning methods for molecular property prediction consider either 2D molecular graphs or 3D conformer structure representations in isolation. Inspired by recent work on using ensembles of conformers in conjunction with 2D graph representations, we propose $\mathrm{E}$(3)-invariant molecular conformer aggregation networks. The method integrates a molecule's 2D representation with that of multiple of its conformers. Contrary to prior work, we propose a novel 2D-3D aggregation mechanism based on a differentiable solver for the Fused Gromov-Wasserstein Barycenter problem and the use of an efficient conformer generation method based on distance geometry. We show that the proposed aggregation mechanism is $\mathrm{E}$(3) invariant and propose an efficient GPU implementation. Moreover, we demonstrate that the aggregation mechanism helps to significantly outperform state-of-the-art molecule property prediction methods on established datasets., Comment: Accepted at ICML 2024 (updated version)

We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivity is not too large. Through the stochastic maximum principle, we adopt the FBSDE approach to investigate the unique existence of the corresponding equilibrium strategies. The corresponding FBSDEs are first solved locally in time, then by controlling the sensitivity of the backward solutions with respect to the initial condition via some suitable apriori estimates for the corresponding Jacobian flows, the global-in-time solution is warranted. Further analysis on these Jacobian flows will be discussed to establish the regularities, such as linear functional differentiability, of the respective value functions that leads to the ultimate classical well-posedness of the master equation on $\mathbb{R}^d$. To the best of our knowledge, it is the first article to deal with the mean field game problem, as well as its associated master equation, with general cost functionals having quadratic growth under the small mean field effect. In this current approach, we directly impose the structural conditions on the cost functionals, rather than conditions on the Hamiltonian. The advantages of this are threefold: (i) compared with imposing conditions on Hamiltonian, the structural conditions imposed in this work are easily verified, and less demanding on the regularity requirements of the cost functionals while solving the master equation; (ii) the displacement monotonicity is basically just a direct consequence of small mean field effect in the structural conditions; and (iii) when the mean field effect is not that small, we can still provide an accurate lifespan for the local existence. The method in this work can be readily extended to the case with nonlinear drift and non-separable cost functionals.

The CMS and ATLAS have recently reported their results searching for light Higgs boson with mass around 95 GeV, based on the full Run 2 data set. In the framework of the CP-violating (CPV) $\mu\nu$SSM, we discuss a $\sim$ 2.9$\sigma$ (local) excess at 95 GeV in the light Higgs boson search in the diphoton decay mode as reported by ATLAS and CMS, together with a $\sim$ 2$\sigma$ excess (local) in the $b\bar{b}$ final state at LEP in the same mass range. By introducing CPV phases as well as by mixing CP-even Higgs and CP-odd Higgs, a lighter Higgs boson in the $\mu\nu$SSM can be produced, which can account for the "di-photon excess"., Comment: 29 pages, 7 figures, accepted for publication in Physical Review D

Bugs exist in hardware, such as CPU. Unlike software bugs, these hardware bugs need to be detected before deployment. Previous fuzzing work in CPU bug detection has several disadvantages, e.g., the length of RTL input instructions keeps growing, and longer inputs are ineffective for fuzzing. In this paper, we propose INSTILLER (Instruction Distiller), an RTL fuzzer based on ant colony optimization (ACO). First, to keep the input instruction length short and efficient in fuzzing, it distills input instructions with a variant of ACO (VACO). Next, related work cannot simulate realistic interruptions well in fuzzing, and INSTILLER solves the problem of inserting interruptions and exceptions in generating the inputs. Third, to further improve the fuzzing performance of INSTILLER, we propose hardware-based seed selection and mutation strategies. We implement a prototype and conduct extensive experiments against state-of-the-art fuzzing work in real-world target CPU cores. In experiments, INSTILLER has 29.4% more coverage than DiFuzzRTL. In addition, 17.0% more mismatches are detected by INSTILLER. With the VACO algorithm, INSTILLER generates 79.3% shorter input instructions than DiFuzzRTL, demonstrating its effectiveness in distilling the input instructions. In addition, the distillation leads to a 6.7% increase in execution speed on average.

Coverage-guided gray-box fuzzing (CGF) is an efficient software testing technique. There are usually multiple objectives to optimize in CGF. However, existing CGF methods cannot successfully find the optimal values for multiple objectives simultaneously. In this paper, we propose a gray-box fuzzer for multi-objective optimization (MOO) called MobFuzz. We model the multi-objective optimization process as a multi-player multi-armed bandit (MPMAB). First, it adaptively selects the objective combination that contains the most appropriate objectives for the current situation. Second, our model deals with the power schedule, which adaptively allocates energy to the seeds under the chosen objective combination. In MobFuzz, we propose an evolutionary algorithm called NIC to optimize our chosen objectives simultaneously without incurring additional performance overhead. To prove the effectiveness of MobFuzz, we conduct experiments on 12 real-world programs and the MAGMA data set. Experiment results show that multi-objective optimization in MobFuzz outperforms single-objective fuzzing in the baseline fuzzers. In contrast to them, MobFuzz can select the optimal objective combination and increase the values of multiple objectives up to 107%, with at most a 55% reduction in the energy consumption. Moreover, MobFuzz has up to 6% more program coverage and finds 3x more unique bugs than the baseline fuzzers. The NIC algorithm has at least a 2x improvement with a performance overhead of approximately 3%.

While vision transformers (ViTs) have shown great potential in computer vision tasks, their intense computation and memory requirements pose challenges for practical applications. Existing post-training quantization methods leverage value redistribution or specialized quantizers to address the non-normal distribution in ViTs. However, without considering the asymmetry in activations and relying on hand-crafted settings, these methods often struggle to maintain performance under low-bit quantization. To overcome these challenges, we introduce SmoothQuant with bias term (SQ-b) to alleviate the asymmetry issue and reduce the clamping loss. We also introduce optimal scaling factor ratio search (OPT-m) to determine quantization parameters by a data-dependent mechanism automatically. To further enhance the compressibility, we incorporate the above-mentioned techniques and propose a mixed-precision post-training quantization framework for vision transformers (MPTQ-ViT). We develop greedy mixed-precision quantization (Greedy MP) to allocate layer-wise bit-width considering both model performance and compressibility. Our experiments on ViT, DeiT, and Swin demonstrate significant accuracy improvements compared with SOTA on the ImageNet dataset. Specifically, our proposed methods achieve accuracy improvements ranging from 0.90% to 23.35% on 4-bit ViTs with single-precision and from 3.82% to 78.14% on 5-bit fully quantized ViTs with mixed-precision.

Roadside perception systems are increasingly crucial in enhancing traffic safety and facilitating cooperative driving for autonomous vehicles. Despite rapid technological advancements, a major challenge persists for this newly arising field: the absence of standardized evaluation methods and benchmarks for these systems. This limitation hampers the ability to effectively assess and compare the performance of different systems, thus constraining progress in this vital field. This paper introduces a comprehensive evaluation methodology specifically designed to assess the performance of roadside perception systems. Our methodology encompasses measurement techniques, metric selection, and experimental trial design, all grounded in real-world field testing to ensure the practical applicability of our approach. We applied our methodology in Mcity\footnote{\url{https://mcity.umich.edu/}}, a controlled testing environment, to evaluate various off-the-shelf perception systems. This approach allowed for an in-depth comparative analysis of their performance in realistic scenarios, offering key insights into their respective strengths and limitations. The findings of this study are poised to inform the development of industry-standard benchmarks and evaluation methods, thereby enhancing the effectiveness of roadside perception system development and deployment for autonomous vehicles. We anticipate that this paper will stimulate essential discourse on standardizing evaluation methods for roadside perception systems, thus pushing the frontiers of this technology. Furthermore, our results offer both academia and industry a comprehensive understanding of the capabilities of contemporary infrastructure-based perception systems., Comment: 6 figures, 8 tables, 14 pages

We report efficient terahertz (THz) generation in epitaxial $\alpha$-W/Co$_{60}$Fe$_{40}$ spintronic emitters. Two types of emitters have been investigated; epitaxial $\alpha$-W$(110)$/Co$_{60}$Fe$_{40}(110)$ and $\alpha$-W$(001)$/Co$_{60}$Fe$_{40}(001)$ deposited on single crystalline Al$_{2}$O$_{3}$($11\bar{2}0$) and MgO($001$) substrates, respectively. First principle calculations of the electronic band structure at the W$(001)$ surface reveal Dirac-type surface states, similar to that reported previously for the W$(110)$ surface. The generated THz radiation is about $10\%$ larger for $\alpha$-W$(110)$/Co$_{60}$Fe$_{40}(110)$ grown on single crystalline Al$_{2}$O$_{3}$($11\bar{2}0$), which is explained by the fact that the $\alpha$-W$(110)$/Co$_{60}$Fe$_{40}(110)$ interface for this emitter is more transparent to the spin current due to the presence of \AA ngstr\" om-scale interface intermixing at the W/CoFe interface. Our results also reveal that the generation of THz radiation is larger when pumping with the laser light from the substrate side, which is explained by a larger part of the laser light due to interference effects in the film stack being absorbed in the ferromagnetic Co$_{60}$Fe$_{40}$ layer in this measurement configuration.

The Schrodinger equation with a Yukawa type of potential is solved analytically. When different boundary conditions are taken into account, a series of solutions are indicated as Bessel function, the first kind of Hankel function and the second kind of Hankel function, respectively. Subsequently, the scattering processes of $K \bar{K}^*$ and $D \bar{ D}^*$ are investigated. In the $K \bar{K}^*$ sector, the $f_1(1285)$ particle is treated as a $K \bar{K}^*$ bound state, therefore, the coupling constant in the $K \bar{K}^*$ Yukawa potential can be fixed according to the binding energy of the $f_1(1285)$ particle. Consequently, a $K \bar{K}^*$ resonance state is generated by solving the Schrodinger equation with the outgoing wave condition, which lie at $1417-i18$MeV on the complex energy plane. It is reasonable to assume that the $K \bar{K}^*$ resonance state at $1417-i18$MeV might correspond to the $f_1(1420)$ particle in the review of Particle Data Group(PDG).In the $D \bar{D}^*$ sector, since the $X(3872)$ particle is almost located at the $D \bar{ D}^*$ threshold, the binding energy of it equals to zero approximately. Therefore, the coupling constant in the $D \bar{ D}^*$ Yukawa potential is determined, which is related to the first zero point of the zero order Bessel function. Similarly to the $K \bar{K}^*$ case, four resonance states are produced as solutions of the Schrodinger equation with the outgoing wave condition. It is assumed that the resonance states at $3885-i1$MeV, $4029-i108$ MeV, $4328-i191$MeV and $4772-i267$MeV might be associated with the $Zc(3900)$, the $X(3940)$, the $\chi_{c1}(4274)$ and $\chi_{c1}(4685)$ particles, respectively. It is noted that all solutions are isospin degenerate., Comment: 9 pages, 2 tables, 4 figures, to be published in Communications in Theoretical Physics

We present emission maps (1.5'$\times$1.5' scale, corresponding to 0.18 pc) of the DCN ($J=2-1$) and DCO$^+$ ($J=2-1$) lines in the 2 mm band toward the Orion KL region obtained with the 2 mm receiver system named B4R installed on the Large Millimeter Telescope (LMT). The DCN emission shows a peak at the Orion KL hot core position, whereas no DCO$^+$ emission has been detected there. The DCO$^+$ emission shows enhancement at the west side of the hot core, which is well shielded from the UV radiation from OB massive stars in the Trapezium cluster. We have derived the abundance ratio of DCN/DCO$^+$ at three representative positions where both species have been detected. The gas components with $V_{\rm {LSR}} \approx 7.5-8.7$ km/s are associated with low abundance ratios of $\sim4-6$, whereas much higher abundance ratios ($\sim22-30$) are derived for the gas components with $V_{\rm {LSR}} \approx 9.2-11.6$ km/s. We have compared the observed abundance ratio to our chemical models and found that the observed differences in the DCN/DCO$^+$ abundance ratios are explained by different densities., Comment: Accepted by The Astrophysical Journal, 13 pages, 5 figures, 5 tables

Meeting-point-based feeder services using EVs have good potential to achieve an efficient and clean on-demand mobility service. However, customer-to-meeting-point, vehicle routing, and charging scheduling need to be jointly optimized to achieve the best system performance. To this aim, we assess the effect of different system parameters and configure them based on our previously developed hybrid metaheuristic algorithm. A set of test instances based on morning peak hour commuting scenarios between the cities of Arlon and Luxembourg are used to evaluate the impact of the set parameters on the optimal solutions. The experimental results suggest that higher meeting point availability can achieve better system performance. By jointly configuring different system parameters, the overall system performance can be significantly improved (-10.8% total kilometers traveled by vehicles compared to the benchmark) to serve all requests. Our experimental results show that the meeting-point-based system can reduce up to 70.2% the fleet size, 6.4% the in-vehicle travel time and 49.4% the kilometers traveled when compared to a traditional door-to-door dial-a-ride system.

This paper addresses the on-demand meeting-point-based feeder electric bus routing and charging scheduling problem under charging synchronization constraints. The problem considered exhibits the structure of the location routing problem, which is more difficult to solve than many electric vehicle routing problems with capacitated charging stations. We propose to model the problem using a mixed-integer linear programming approach based on a layered graph structure. An efficient hybrid metaheuristic solution algorithm is proposed. A mixture of random and greedy partial charging scheduling strategies is used to find feasible charging schedules under the synchronization constraints. The algorithm is tested on instances with up to 100 customers and 49 bus stops/meeting points. The results show that the proposed algorithm provides near-optimal solutions within less one minute on average compared with the best solutions found by a mixed-integer linear programming solver set with a 4-hour computation time limit. A case study on a larger sized case with 1000 customers and 111 meeting points shows the proposed method is applicable to real-world situations.

Recent work showed the possibility of building open-vocabulary large language models (LLMs) that directly operate on pixel representations. These models are implemented as autoencoders that reconstruct masked patches of rendered text. However, these pixel-based LLMs are limited to discriminative tasks (e.g., classification) and, similar to BERT, cannot be used to generate text. Therefore, they cannot be used for generative tasks such as free-form question answering. In this work, we introduce PIXAR, the first pixel-based autoregressive LLM that performs text generation. Consisting of only a decoder, PIXAR can perform free-form generative tasks while keeping the number of parameters on par with previous encoder-decoder models. Furthermore, we highlight the challenges of generating text as non-noisy images and show this is due to using a maximum likelihood objective. To overcome this problem, we propose an adversarial pretraining stage that improves the readability and accuracy of PIXAR by 8.1 on LAMBADA and 8.5 on bAbI -- making it comparable to GPT-2 on text generation tasks. This paves the way to build open-vocabulary LLMs that operate on perceptual input only and calls into question the necessity of the usual symbolic input representation, i.e., text as (sub)tokens.

The paper addresses the problem of meta order execution from a broker-dealer's point of view in Almgren-Chriss model under order fill uncertainty. A broker-dealer agency is authorized to execute an order of trading on client's behalf. The strategies that the agent is allowed to deploy is subject to a benchmark, referred to as the reservation strategy, regulated by the client. We formulate the broker's problem as a utility maximization problem in which the broker seeks to maximize his utility of excess profit-and-loss at the execution horizon. Optimal strategy in feedback form is obtained in closed form. In the absence of execution risk, the optimal strategies subject to reservation strategies are deterministic. We establish an affine structure among the trading trajectories under optimal strategies subject to general reservation strategies using implementation shortfall and target close orders as basis. We conclude the paper with numerical experiments illustrating the trading trajectories as well as histograms of terminal wealth and utility at investment horizon under optimal strategies versus those under TWAP strategies.

The success of the GAN-NeRF structure has enabled face editing on NeRF to maintain 3D view consistency. However, achieving simultaneously multi-view consistency and temporal coherence while editing video sequences remains a formidable challenge. This paper proposes a novel face video editing architecture built upon the dynamic face GAN-NeRF structure, which effectively utilizes video sequences to restore the latent code and 3D face geometry. By editing the latent code, multi-view consistent editing on the face can be ensured, as validated by multiview stereo reconstruction on the resulting edited images in our dynamic NeRF. As the estimation of face geometries occurs on a frame-by-frame basis, this may introduce a jittering issue. We propose a stabilizer that maintains temporal coherence by preserving smooth changes of face expressions in consecutive frames. Quantitative and qualitative analyses reveal that our method, as the pioneering 4D face video editor, achieves state-of-the-art performance in comparison to existing 2D or 3D-based approaches independently addressing identity and motion. Codes will be released., Comment: Our code will be available at: https://github.com/ZHANG1023/FED-NeRF

Serverless computing has emerged as an attractive paradigm due to the efficiency of development and the ease of deployment without managing any underlying infrastructure. Nevertheless, serverless computing approaches face numerous challenges to unlock their full potential in hybrid environments. To gain a deeper understanding and firsthand knowledge of serverless computing in edge-cloud deployments, we review the current state of open-source serverless platforms and compare them based on predefined requirements. We then design and implement a serverless computing platform with a novel edge orchestration technique that seamlessly deploys serverless functions across the edge and cloud environments on top of the Knative serverless platform. Moreover, we propose an offloading strategy for edge environments and four different functions for experimentation and showcase the performance benefits of our solution. Our results demonstrate that such an approach can efficiently utilize both cloud and edge resources by dynamically offloading functions from the edge to the cloud during high activity, while reducing the overall application latency and increasing request throughput compared to an edge-only deployment.

This work presents FaceX framework, a novel facial generalist model capable of handling diverse facial tasks simultaneously. To achieve this goal, we initially formulate a unified facial representation for a broad spectrum of facial editing tasks, which macroscopically decomposes a face into fundamental identity, intra-personal variation, and environmental factors. Based on this, we introduce Facial Omni-Representation Decomposing (FORD) for seamless manipulation of various facial components, microscopically decomposing the core aspects of most facial editing tasks. Furthermore, by leveraging the prior of a pretrained StableDiffusion (SD) to enhance generation quality and accelerate training, we design Facial Omni-Representation Steering (FORS) to first assemble unified facial representations and then effectively steer the SD-aware generation process by the efficient Facial Representation Controller (FRC). %Without any additional features, Our versatile FaceX achieves competitive performance compared to elaborate task-specific models on popular facial editing tasks. Full codes and models will be available at https://github.com/diffusion-facex/FaceX., Comment: Project page: https://diffusion-facex.github.io/

In this study, our goal is to integrate classical mathematical models with deep neural networks by introducing two novel deep neural network models for image segmentation known as Double-well Nets. Drawing inspirations from the Potts model, our models leverage neural networks to represent a region force functional. We extend the well-know MBO (Merriman-Bence-Osher) scheme to solve the Potts model. The widely recognized Potts model is approximated using a double-well potential and then solved by an operator-splitting method, which turns out to be an extension of the well-known MBO scheme. Subsequently, we replace the region force functional in the Potts model with a UNet-type network, which is data-driven and is designed to capture multiscale features of images, and also introduce control variables to enhance effectiveness. The resulting algorithm is a neural network activated by a function that minimizes the double-well potential. What sets our proposed Double-well Nets apart from many existing deep learning methods for image segmentation is their strong mathematical foundation. They are derived from the network approximation theory and employ the MBO scheme to approximately solve the Potts model. By incorporating mathematical principles, Double-well Nets bridge the MBO scheme and neural networks, and offer an alternative perspective for designing networks with mathematical backgrounds. Through comprehensive experiments, we demonstrate the performance of Double-well Nets, showcasing their superior accuracy and robustness compared to state-of-the-art neural networks. Overall, our work represents a valuable contribution to the field of image segmentation by combining the strengths of classical variational models and deep neural networks. The Double-well Nets introduce an innovative approach that leverages mathematical foundations to enhance segmentation performance.

Current Neural Radiance Fields (NeRF) can generate photorealistic novel views. For editing 3D scenes represented by NeRF, with the advent of generative models, this paper proposes Inpaint4DNeRF to capitalize on state-of-the-art stable diffusion models (e.g., ControlNet) for direct generation of the underlying completed background content, regardless of static or dynamic. The key advantages of this generative approach for NeRF inpainting are twofold. First, after rough mask propagation, to complete or fill in previously occluded content, we can individually generate a small subset of completed images with plausible content, called seed images, from which simple 3D geometry proxies can be derived. Second and the remaining problem is thus 3D multiview consistency among all completed images, now guided by the seed images and their 3D proxies. Without other bells and whistles, our generative Inpaint4DNeRF baseline framework is general which can be readily extended to 4D dynamic NeRFs, where temporal consistency can be naturally handled in a similar way as our multiview consistency.

Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the inherent limitations of cross-validation when employed to discern the structure of a Gaussian graphical model. We provide finite-sample bounds on the probability that the Lasso estimator for the neighborhood of a node within a Gaussian graphical model, optimized using a prediction oracle, misidentifies the neighborhood. Our results pertain to both undirected and directed acyclic graphs, encompassing general, sparse covariance structures. To support our theoretical findings, we conduct an empirical investigation of this inconsistency by contrasting our outcomes with other commonly used information criteria through an extensive simulation study. Given that many algorithms designed to learn the structure of graphical models require hyperparameter selection, the precise calibration of this hyperparameter is paramount for accurately estimating the inherent structure. Consequently, our observations shed light on this widely recognized practical challenge., Comment: Preliminary version; 47 pages, 15 figures

We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr\"odinger operator $-\Delta - (d-2)^2/(4|x|^2) -W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted $L^{d/2}-$norm of $W$ which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian., Comment: 15 pages, final version to appear in J. Math. Pures Appl

Let $P_k$ be the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the prime field with two elements, $\mathbb F_2$, with the degree of each $x_i$ being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for $P_k$ as a module over the mod-$2$ Steenrod algebra, $\mathcal{A}.$ It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of $\mathcal{A}$-generators for $P_5$ in the case of the generic degree $m = 2^{d}$ for all $d \geqslant 8$., Comment: 60 pages. arXiv admin note: substantial text overlap with arXiv:2209.12543; text overlap with arXiv:1609.02250 by other authors

In the realm of computer vision and robotics, embodied agents are expected to explore their environment and carry out human instructions. This necessitates the ability to fully understand 3D scenes given their first-person observations and contextualize them into language for interaction. However, traditional research focuses more on scene-level input and output setups from a global view. To address the gap, we introduce EmbodiedScan, a multi-modal, ego-centric 3D perception dataset and benchmark for holistic 3D scene understanding. It encompasses over 5k scans encapsulating 1M ego-centric RGB-D views, 1M language prompts, 160k 3D-oriented boxes spanning over 760 categories, some of which partially align with LVIS, and dense semantic occupancy with 80 common categories. Building upon this database, we introduce a baseline framework named Embodied Perceptron. It is capable of processing an arbitrary number of multi-modal inputs and demonstrates remarkable 3D perception capabilities, both within the two series of benchmarks we set up, i.e., fundamental 3D perception tasks and language-grounded tasks, and in the wild. Codes, datasets, and benchmarks will be available at https://github.com/OpenRobotLab/EmbodiedScan., Comment: A multi-modal, ego-centric 3D perception dataset and benchmark for holistic 3D scene understanding. Project page: http://tai-wang.github.io/embodiedscan

Contrastive representation learning has emerged as an outstanding approach for anomaly detection. In this work, we explore the $\ell_2$-norm of contrastive features and its applications in out-of-distribution detection. We propose a simple method based on contrastive learning, which incorporates out-of-distribution data by discriminating against normal samples in the contrastive layer space. Our approach can be applied flexibly as an outlier exposure (OE) approach, where the out-of-distribution data is a huge collective of random images, or as a fully self-supervised learning approach, where the out-of-distribution data is self-generated by applying distribution-shifting transformations. The ability to incorporate additional out-of-distribution samples enables a feasible solution for datasets where AD methods based on contrastive learning generally underperform, such as aerial images or microscopy images. Furthermore, the high-quality features learned through contrastive learning consistently enhance performance in OE scenarios, even when the available out-of-distribution dataset is not diverse enough. Our extensive experiments demonstrate the superiority of our proposed method under various scenarios, including unimodal and multimodal settings, with various image datasets.

We study the Dirichlet problem for a second order linear elliptic equation in a bounded smooth domain $\Omega$ in $\mathbb{R}^n$, $n \ge 3$, with the drift $\mathbf{b} $ belonging to the critical weak space $L^{n,\infty}(\Omega )$. We decompose the drift $\mathbf{b} = \mathbf{b}_1 + \mathbf{b}_2$ in which $\text{div} \mathbf{b}_1 \geq 0$ and $\mathbf{b}_2$ is small only in a small scale quasi-norm of $L^{n,\infty}(\Omega )$. Under this new smallness condition, we prove existence, uniqueness, and regularity estimates of weak solutions to the problem and its dual. H\"{o}lder regularity and derivative estimates of weak solutions to the dual problem are also established. As a result, we prove uniqueness of very weak solutions slightly below the threshold. When $\mathbf{b}_2 =0$, our results recover those by Kim and Tsai in [SIAM J. Math. Anal. 52 (2020)]. Due to the new small scale quasi-norm, our results are new even when $\mathbf{b}_1=0$., Comment: 47 pages. Questions and comments are welcome

This paper is devoted to solving a class of second order Hamilton-Jacobi-Bellman (HJB) equations in the Wasserstein space, associated with mean field control problems involving common noise. The well-posedness of viscosity solutions to the HJB equation under a new notion is established under general assumptions on the coefficients. Our approach adopts the smooth metric developed by Bayraktar, Ekren, and Zhang [Proc. Amer. Math. Soc. (2023)] as our gauge function for the purpose of smooth variational principle used in the proof of comparison theorem. Further estimates and regularity of the metric, including a novel second order derivative estimate with respect to the measure variable, are derived in order to ensure the uniqueness and existence., Comment: 44 pages

Neural radiance field (NeRF) has achieved great success in novel view synthesis and 3D representation for static scenarios. Existing dynamic NeRFs usually exploit a locally dense grid to fit the deformation field; however, they fail to capture the global dynamics and concomitantly yield models of heavy parameters. We observe that the 4D space is inherently sparse. Firstly, the deformation field is sparse in spatial but dense in temporal due to the continuity of of motion. Secondly, the radiance field is only valid on the surface of the underlying scene, usually occupying a small fraction of the whole space. We thus propose to represent the 4D scene using a learnable sparse latent space, a.k.a. SLS4D. Specifically, SLS4D first uses dense learnable time slot features to depict the temporal space, from which the deformation field is fitted with linear multi-layer perceptions (MLP) to predict the displacement of a 3D position at any time. It then learns the spatial features of a 3D position using another sparse latent space. This is achieved by learning the adaptive weights of each latent code with the attention mechanism. Extensive experiments demonstrate the effectiveness of our SLS4D: it achieves the best 4D novel view synthesis using only about $6\%$ parameters of the most recent work., Comment: 10 pages, 6 figures

We study local holomorphic maps between K\"ahler manifolds preserving $(p,p)$-forms. In this direction, we prove that any such local holomorphic map $F$ is a holomorphic isometry up to a scalar constant provided that $p$ is strictly less than the complex dimension of the domain of $F$. We then study local holomorphic maps between finite dimensional complex space forms preserving invariant $(p,p)$-forms. It was proved by Calabi that there does not exist a local holomorphic isometry between complex space forms $M$ and $N$ provided that $M$ and $N$ are of different types. In this article, we generalize this result to local holomorphic maps between complex space forms $M$ and $N$ preserving invariant $(p,p)$-forms whenever $M$ and $N$ are of different types except for the case where the universal covers of $M, N$ are biholomorphic to $\mathbb{C}^m, \mathbb{P}^n$, respectively and $2\le p=m

Great progress has been made in learning-based object detection methods in the last decade. Two-stage detectors often have higher detection accuracy than one-stage detectors, due to the use of region of interest (RoI) feature extractors which extract transformation-invariant RoI features for different RoI proposals, making refinement of bounding boxes and prediction of object categories more robust and accurate. However, previous RoI feature extractors can only extract invariant features under limited transformations. In this paper, we propose a novel RoI feature extractor, termed Semantic RoI Align (SRA), which is capable of extracting invariant RoI features under a variety of transformations for two-stage detectors. Specifically, we propose a semantic attention module to adaptively determine different sampling areas by leveraging the global and local semantic relationship within the RoI. We also propose a Dynamic Feature Sampler which dynamically samples features based on the RoI aspect ratio to enhance the efficiency of SRA, and a new position embedding, \ie Area Embedding, to provide more accurate position information for SRA through an improved sampling area representation. Experiments show that our model significantly outperforms baseline models with slight computational overhead. In addition, it shows excellent generalization ability and can be used to improve performance with various state-of-the-art backbones and detection methods.

The correlation between net baryon number and electric charge, $\chi_{11}^{\rm BQ}$, can serve as a magnetometer of QCD. This is demonstrated by lattice QCD computations using the highly improved staggered quarks with physical pion mass of $M_\pi=135~$MeV on $N_\tau=8$ and 12 lattices. We find that $\chi_{11}^{\rm BQ}$ along the transition line starts to increase rapidly with magnetic field strength $eB\gtrsim 2M_\pi^2$ and by a factor 2 at $eB\simeq 8M_\pi^2$. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, $\mu_{\rm Q}/\mu_{\rm B}$, shows significant dependence on the magnetic field strength and varies from the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results can provide baselines for effective theory and model studies, and both $\chi_{11}^{\rm BQ}$ and $\mu_{\rm Q}/\mu_{\rm B}$ could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model., Comment: 6 pages main text + 6 pages supplemental material, discussions added on the continuum estimate and extrapolation along with additional lattice QCD simulations on Nt=16 lattices, and the proxy of baryon electric charge correlation as well as the thermal fits to obtain the baryon and electric charge chemical potential

The prevalence of the powerful multilingual models, such as Whisper, has significantly advanced the researches on speech recognition. However, these models often struggle with handling the code-switching setting, which is essential in multilingual speech recognition. Recent studies have attempted to address this setting by separating the modules for different languages to ensure distinct latent representations for languages. Some other methods considered the switching mechanism based on language identification. In this study, a new attention-guided adaptation is proposed to conduct parameter-efficient learning for bilingual ASR. This method selects those attention heads in a model which closely express language identities and then guided those heads to be correctly attended with their corresponding languages. The experiments on the Mandarin-English code-switching speech corpus show that the proposed approach achieves a 14.2% mixed error rate, surpassing state-of-the-art method, where only 5.6% additional parameters over Whisper are trained., Comment: Accepted to ICASSP 2024

Recent advancements in 3D Large Language Models (LLMs) have demonstrated promising capabilities for 3D scene understanding. However, previous methods exhibit deficiencies in general referencing and grounding capabilities for intricate scene comprehension. In this paper, we introduce the use of object identifiers and object-centric representations to interact with scenes at the object level. Specifically, we decompose the input 3D scene into a set of object proposals, each assigned a unique identifier token, which enables efficient object referencing and grounding during user-assistant interactions. Given the scarcity of scene-language data, we model the scene embeddings as a sequence of explicit object-level embeddings, derived from semantic-rich 2D or 3D representations. By employing object identifiers, we transform diverse 3D scene-language tasks into a unified question-answering format, facilitating joint training without the need for additional task-specific heads. With minimal fine-tuning on all downstream tasks, our model significantly outperforms existing methods on benchmarks including ScanRefer, Multi3DRefer, Scan2Cap, ScanQA, and SQA3D.

One-dimensional (1D) van der Waals materials have emerged as an intriguing playground to explore novel electronic and optical effects. We report on inorganic one-dimensional SbPS4 nanotubes bundles obtained via mechanical exfoliation from bulk crystals. The ability to mechanically exfoliate SbPS4 nanobundles offers the possibility of applying modern 2D material fabrication techniques to create mixed-dimensional van der Waals heterostructures. We find that SbPS4 can readily be exfoliated to yield long (> 10 {\mu}m) nanobundles with thicknesses that range from of 1.3 - 200 nm. We investigated the optical response of semiconducting SbPS4 nanobundles and discovered that upon excitation with blue light, they emit bright and ultra-broadband red light with a quantum yield similar to that of hBN-encapsulated MoSe2. We discovered that the ultra-broadband red light emission is a result of a large ~1 eV exciton binding energy and a ~200 meV exciton self-trapping energy, unprecedented in previous material studies. Due to the bright and ultra-broadband light emission, we believe that this class of inorganic 1D van der Waals semiconductors has numerous potential applications including on-chip tunable nanolasers, and applications that require ultra-violet to visible light conversion such as lighting and sensing. Overall, our findings open avenues for harnessing the unique characteristics of these nanomaterials, advancing both fundamental research and practical optoelectronic applications.