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In this paper, we derive a novel Unique Continuation Principle (UCP) for a system of second-order elliptic PDEs system and apply it to investigate inverse problems in conductive scattering. The UCP relaxes the typical assumptions imposed on the domain or boundary with certain interior transmission conditions. This is motivated by the study of the associated inverse scattering problem and enables us to establish several novel unique identifiability results for the determination of generalized conductive scatterers using a single far-field pattern, significantly extending the results in [12,18]. A key technical advancement in our work is the combination of Complex Geometric Optics (CGO) techniques from [12,18] with the Fourier expansion method to microlocally analyze corner singularities and their implications for inverse problems. We believe that the methods developed can have broader applications in other contexts.

The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. The photo-thermal effect actually involves two physical processes: electromagnetic scattering and heat transfer, described by a nonlinear coupled system of Maxwell's equation and the heat transfer equation. The nonlinear coupling term in the system is represented by the square of the modulus of the electromagnetic (missing the phase information of the electromagnetic field), and the absence of this phase information poses a significant challenge to the reconstruction of the internal source. In addition, the interaction and mutual influence of multiple physical fields, including electric field, magnetic field and temperature field, add to the complexity involved in the inversion of the internal source. Based on the potential theory and asymptotic analysis, we prove that the internal source can be uniquely determined up to sign by the external temperature field. This provides a solid theoretical basis for designing the internal source inversion algorithm and further exploring the theoretical aspects of photo-thermal effect.

In this paper, we develop a mathematical framework for generating strong customized field concentration locally around the inhomogeneous medium inclusion via surface transmission resonance. The purpose of this paper is twofold. Firstly, we show that for a given inclusion embedded in an otherwise uniformly homogeneous background space, we can design an incident field to generate strong localized field concentration at any specified places around the inclusion. The aforementioned customized field concentration is crucially reliant on the peculiar spectral and geometric patterns of certain transmission eigenfunctions. Secondly, we prove the existence of a sequence of transmission eigenfunctions for a specific wavenumber and they exhibit distinct surface resonant behaviors, accompanying strong surface-localization and surface-oscillation properties. These eigenfunctions as the surface transmission resonant modes fulfill the requirement for generating the field concentration.

In this short note, we present a probabilistic perspective on the Schiffer's problem in the inverse scattering theory, which asks whether one can uniquely determine the shape of an unknown obstacle by a single far-field measurement. It is a longstanding problem and has received considerable studies in the literature. We show that this conjecture holds true in more general settings in the probability sense. Our new perspective has important implications from the practical viewpoint and also points an interesting direction of research for broader inverse problems.

This paper investigates the simultaneous reconstruction of the running cost function and the internal topological structure within the mean-field games (MFG) system utilizing partial boundary data. The inverse problem is notably challenging due to factors such as nonlinear coupling, the necessity for multi-parameter reconstruction, constraints on probability measures, and the limited availability of measurement information. To address these challenges, we propose an innovative approach grounded in a higher-order linearization method. This method is tailored for inverse problems in MFG systems that involve Dirichlet and Neumann boundary conditions. Initially, we present unique reconstruction results for the cost function and internal topological structure of the MFG system under various homogeneous boundary conditions. Subsequently, we extend these results to accommodate inhomogeneous boundary conditions. These findings greatly enhance our understanding of simultaneous reconstruction in complex MFG systems.

This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded obstacles and the EM waves cannot penetrate inside the obstacles. Such a situation naturally arises in studying inverse EM scattering problems from complex mediums with partial boundary measurements, or inverse problems from EM mediums with metal inclusions. We develop a novel theoretical framework by showing that the embedded obstacles can be effectively approximated by a certain isotropic medium with a specific choice of material parameters. We derive sharp estimates to verify this effective approximation and also discuss the practical implications of our results to the inverse problems mentioned above, which are longstanding topics in inverse scattering theory.

This paper introduces a memory-reduction third-order compact gas-kinetic scheme (CGKS) for solving compressible Euler and Navier-Stokes equations on 3D unstructured meshes. The scheme utilizes a time-evolution gas distribution function to provide a time-evolution solution at cell interfaces, enabling the implementation of Hermite WENO techniques for high-order reconstruction. However, the HWENO method needs to store a coefficients matrix for the quadratic polynomial to achieve third-order accuracy, resulting in high memory usage. A novel reconstruction method, built upon HWENO reconstruction, has been designed to enhance computational efficiency and reduce memory usage compared to the original CGKS. The simple idea is that the first-order and second-order terms of the quadratic polynomials are determined in a two-step way. In the first step, the second-order terms are obtained from the reconstruction of a linear polynomial of the first-order derivatives by only using the cell-averaged slopes, since the second-order derivatives are nothing but the "derivatives of derivatives". Subsequently, the first-order terms left can be determined by the linear reconstruction only using cell-averaged values. Thus, we successfully split one quadratic least-square regression into several linear least-square regressions, which are commonly used in a second-order finite volume code. Since only a small matrix inversion is needed in a 3-D linear least-square regression, the computational cost for the new reconstruction is dramatically reduced and the storage of the reconstruction-coefficient matrix is no longer necessary. The proposed new reconstruction technique can reduce the overall computational cost by about 20 to 30 percent. The challenging large-scale unsteady numerical simulation is performed, which demonstrates that the current improvement brings the CGKS to a new level for industrial applications., Comment: arXiv admin note: substantial text overlap with arXiv:2402.02075

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled systems, we enforce non-negativity of the solutions, aligning with realistic scenarios in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction in measurement/observation data due to averaging effects, the nonlinear coupling between multiple equations, and the nonlocality arising from fractional-type derivatives. These factors present significant challenges to our inverse problem, and such inverse problems have never been explored in previous literature. To address these challenges, we develop new and effective schemes. Our approach involves properly controlling the injection of different source terms to obtain multiple sets of mean flux data. This allows us to achieve unique identifiability results and accurately determine the unknown parameters. Finally, we establish a connection between our study and practical applications in biology, further highlighting the relevance of our work in real-world contexts., Comment: Keywords: inverse problems, partial data measurements, nonlocal coupled parabolic systems, fractional coupled diffusion systems, mathematical biology

Combinatorial optimization (CO) is one of the most fundamental mathematical models in real-world applications. Traditional CO solvers, such as Branch-and-Bound (B&B) solvers, heavily rely on expert-designed heuristics, which are reliable but require substantial manual tuning. Recent studies have leveraged deep learning (DL) models as an alternative to capture rich feature patterns for improved performance on GPU machines. Nonetheless, the drawbacks of high training and inference costs, as well as limited interpretability, severely hinder the adoption of DL methods in real-world applications. To address these challenges, we propose a novel deep symbolic optimization learning framework that combines their advantages. Specifically, we focus on the node selection module within B&B solvers -- namely, deep symbolic optimization for node selection (Dso4NS). With data-driven approaches, Dso4NS guides the search for mathematical expressions within the high-dimensional discrete symbolic space and then incorporates the highest-performing mathematical expressions into a solver. The data-driven model captures the rich feature information in the input data and generates symbolic expressions, while the expressions deployed in solvers enable fast inference with high interpretability. Experiments demonstrate the effectiveness of Dso4NS in learning high-quality expressions, outperforming existing approaches on a CPU machine. Encouragingly, the learned CPU-based policies consistently achieve performance comparable to state-of-the-art GPU-based approaches.

We present Follow-Your-Emoji, a diffusion-based framework for portrait animation, which animates a reference portrait with target landmark sequences. The main challenge of portrait animation is to preserve the identity of the reference portrait and transfer the target expression to this portrait while maintaining temporal consistency and fidelity. To address these challenges, Follow-Your-Emoji equipped the powerful Stable Diffusion model with two well-designed technologies. Specifically, we first adopt a new explicit motion signal, namely expression-aware landmark, to guide the animation process. We discover this landmark can not only ensure the accurate motion alignment between the reference portrait and target motion during inference but also increase the ability to portray exaggerated expressions (i.e., large pupil movements) and avoid identity leakage. Then, we propose a facial fine-grained loss to improve the model's ability of subtle expression perception and reference portrait appearance reconstruction by using both expression and facial masks. Accordingly, our method demonstrates significant performance in controlling the expression of freestyle portraits, including real humans, cartoons, sculptures, and even animals. By leveraging a simple and effective progressive generation strategy, we extend our model to stable long-term animation, thus increasing its potential application value. To address the lack of a benchmark for this field, we introduce EmojiBench, a comprehensive benchmark comprising diverse portrait images, driving videos, and landmarks. We show extensive evaluations on EmojiBench to verify the superiority of Follow-Your-Emoji., Comment: Project Page: https://follow-your-emoji.github.io/

With the recent advancement in large language models (LLMs), there is a growing interest in combining LLMs with multimodal learning. Previous surveys of multimodal large language models (MLLMs) mainly focus on multimodal understanding. This survey elaborates on multimodal generation and editing across various domains, comprising image, video, 3D, and audio. Specifically, we summarize the notable advancements with milestone works in these fields and categorize these studies into LLM-based and CLIP/T5-based methods. Then, we summarize the various roles of LLMs in multimodal generation and exhaustively investigate the critical technical components behind these methods and the multimodal datasets utilized in these studies. Additionally, we dig into tool-augmented multimodal agents that can leverage existing generative models for human-computer interaction. Lastly, we discuss the advancements in the generative AI safety field, investigate emerging applications, and discuss future prospects. Our work provides a systematic and insightful overview of multimodal generation and processing, which is expected to advance the development of Artificial Intelligence for Generative Content (AIGC) and world models. A curated list of all related papers can be found at https://github.com/YingqingHe/Awesome-LLMs-meet-Multimodal-Generation, Comment: 52 Pages with 16 Figures, 12 Tables, and 545 References. GitHub Repository at: https://github.com/YingqingHe/Awesome-LLMs-meet-Multimodal-Generation

In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel unique identifiability results for the intrinsic structure of these anomalies in mean field games systems, including their topological structure and parameter configurations, in several general scenarios of practical interest, including traffic flow, market economics and epidemics. To the best of our knowledge, this is the first work that considers anomalies in the state space for the nonlinear coupled MFG system., Comment: Keywords: Stationary mean field games, inverse boundary problems, anomalies in state space, singularities, uniqueness

In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, social sciences, finance, and transportation. The inverse design and decoding of MFGs offer valuable means to extract information from observed data and gain insights into the intricate underlying dynamics and strategies of these complex physical systems. This paper presents a novel approach to the study of inverse problems in MFGs by analyzing the Cauchy data around their unknown stationary states. This study distinguishes itself from existing inverse problem investigations in three key significant aspects: Firstly, we consider MFG problems in a highly general form. Secondly, we address the technical challenge of the probability measure constraint by utilizing Cauchy data in our inverse problem study. Thirdly, we enhance existing high order linearization methods by introducing a novel approach that involves conducting linearization around non-trivial stationary states of the MFG system, which are not a-priori known. These contributions provide new insights and offer promising avenues for studying inverse problems for MFGs. By unraveling the hidden structure of MFGs, researchers and practitioners can make informed decisions, optimize system performance, and address real-world challenges more effectively., Comment: Keywords: Mean field games, inverse problems, Cauchy data, unique continuation principle, unique identifiability

This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the dynamics of different populations. In the theoretical analysis of the physical setup, it is crucial to ensure non-negativity of solutions. To address this, we employ the high-order variation method and introduce modifications to the systems. Additionally, we propose a novel approach called transformative asymptotic technique that enables the recovery of the diffusion coefficient preceding the Laplace operator, presenting a pioneering method for this type of problems. Through these techniques, we offer comprehensive insights into the unique identifiability aspect of inverse problems associated with multi-population aggregation models., Comment: 29 pages, Keywords: inverse multi-population aggregation model, positive solutions, unique identifiability, transformative asymptotic technique, high-order variation method

In this paper, we develop a general mathematical framework for the electro-osmosis problem to design simultaneous microscale electric and hydrodynamic cloaking in a Hele-Shaw configuration. A novel approach to achieving simultaneously cloaking both the electric and flow fields through a combination of scattering-cancellation technology and an electro-osmosis effect is proposed. In the design, the electric field is manipulated with scattering-cancellation technology while the pressure with electro-osmosis effect. As proof of this concept, the perfect electric and hydrodynamic cloaking conditions are derived for the cloaks with the cross-sectional shape being annulus or confocal ellipses using the layer potential techniques. Furthermore, we also propose an optimization scheme for the design of approximate cloaks within general geometries and prove the well-posedness of the optimization problem. In particular, the conditions that can ensure the simultaneous occurrence of approximate cloaks for general geometries are also established. Our theoretical findings are validated by a variety of numerical results and guide efficiently designing electric-related multiphysics cloaking., Comment: arXiv admin note: substantial text overlap with arXiv:2302.07495

We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the low-frequency regime, we derive low-frequency expansions that provide integral representations for the solutions of the Maxwell equations. For the leading-order term $\bE_0$ of the asymptotic expansion of the electric field, we prove that it has the blow up order of $\epsilon^{-1} |\ln \epsilon|^{-1}$ within the radial geometry, where $\epsilon$ signifies the asymptotic distance between the inclusions. By delicate analysis of the integral operators involved, we further prove the boundedness of the first-order term $\bE_1$. We also conduct extensive numerical experiments which not only corroborate the theoretical findings but also provide more discoveries on the field concentration in the general geometric setup. Our study provides the first treatment in the literature on field concentration between nearly-touching material inclusions for the full Maxwell system.

By following the study in [24], we consider an inverse boundary problem for the mean field game system where a probability density constraint is enforced on the game agents. That is, we consider the case that reflective boundary conditions are enforced and hence the population distribution of the game agents should be treated as a probability measure which preserves both positivity and the total population. This poses significant challenges for the corresponding inverse problems in constructing suitable ``probing modes" which should fulfill such a probability density constraint. We develop an effective scheme in tackling such a case which is new to the literature., Comment: arXiv admin note: substantial text overlap with arXiv:2212.09110

This study is based on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and aims to explore early detection and disease progression in Alzheimer's disease (AD). We employ innovative data preprocessing strategies, including the use of the random forest algorithm to fill missing data and the handling of outliers and invalid data, thereby fully mining and utilizing these limited data resources. Through Spearman correlation coefficient analysis, we identify some features strongly correlated with AD diagnosis. We build and test three machine learning models using these features: random forest, XGBoost, and support vector machine (SVM). Among them, the XGBoost model performs the best in terms of diagnostic performance, achieving an accuracy of 91%. Overall, this study successfully overcomes the challenge of missing data and provides valuable insights into early detection of Alzheimer's disease, demonstrating its unique research value and practical significance.

Planning module is an essential component of intelligent vehicle study. In this paper, we address the risk-aware planning problem of UGVs through a global-local planning framework which seamlessly integrates risk assessment methods. In particular, a global planning algorithm named Coarse2fine A* is proposed, which incorporates a potential field approach to enhance the safety of the planning results while ensuring the efficiency of the algorithm. A deterministic sampling method for local planning is leveraged and modified to suit off-road environment. It also integrates a risk assessment model to emphasize the avoidance of local risks. The performance of the algorithm is demonstrated through simulation experiments by comparing it with baseline algorithms, where the results of Coarse2fine A* are shown to be approximately 30% safer than those of the baseline algorithms. The practicality and effectiveness of the proposed planning framework are validated by deploying it on a real-world system consisting of a control center and a practical UGV platform., Comment: 15 pages, 18 figures, submit to T-IV

In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves cell-averaged flow variables and their gradients on the original mesh. Mesh coarsening employs a two-step parallel agglomeration algorithm using a random hash for cell interface selection and a geometric skewness metric for deletion confirmation, ensuring both efficiency and robustness. For the coarser meshes, first-order kinetic flux vector splitting (KFVS) schemes with explicit or implicit time-stepping are used. The proposed multigrid CGKS is tested across various flow regimes on hybrid unstructured meshes, demonstrating significant improvements. A three-layer V-cycle multigrid strategy, coupled with an explicit forward Euler method on coarser levels, results in a convergence rate up to ten times faster than standard CGKS. In contrast, the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method offers limited convergence acceleration. Our findings indicate that the explicit multigrid CGKS is highly scalable and effective for large-scale computations, marking a substantial step forward in computational fluid dynamics.

As the latest advancements in natural language processing, large language models (LLMs) have achieved human-level language understanding and generation abilities in many real-world tasks, and even have been regarded as a potential path to the artificial general intelligence. To better facilitate research on LLMs, many open-source LLMs, such as Llama 2 and Falcon, have recently been proposed and gained comparable performances to proprietary models. However, these models are primarily designed for English scenarios and exhibit poor performances in Chinese contexts. In this technical report, we propose YAYI 2, including both base and chat models, with 30 billion parameters. YAYI 2 is pre-trained from scratch on a multilingual corpus which contains 2.65 trillion tokens filtered by our pre-training data processing pipeline. The base model is aligned with human values through supervised fine-tuning with millions of instructions and reinforcement learning from human feedback. Extensive experiments on multiple benchmarks, such as MMLU and CMMLU, consistently demonstrate that the proposed YAYI 2 outperforms other similar sized open-source models.

In this paper, we consider the inverse problem of determining the coefficients of interaction terms within some Lotka-Volterra models, with support from boundary observation of its non-negative solutions. In the physical background, the solutions to the predator-prey model stand for the population densities for predator and prey and are non-negative, which is a critical challenge in our inverse problem study. We mainly focus on the unique identifiability issue and tackle it with the high-order variation method, a relatively new technique introduced by the second author and his collaborators. This method can ensure the positivity of solutions and has broader applicability in other physical models with non-negativity requirements. Our study improves this method by choosing a more general solution $(u_0,v_0)$ to expand around, achieving recovery for all interaction terms. By this means, we improve on the previous results and apply this to physical models to recover coefficients concerning compression, prey attack, crowding, carrying capacity, and many other interaction factors in the system. Finally, we apply our results to study three specific cases: the hydra-effects model, the Holling-Tanner model and the classic Lotka-Volterra model.

This work presents HeadArtist for 3D head generation from text descriptions. With a landmark-guided ControlNet serving as the generative prior, we come up with an efficient pipeline that optimizes a parameterized 3D head model under the supervision of the prior distillation itself. We call such a process self score distillation (SSD). In detail, given a sampled camera pose, we first render an image and its corresponding landmarks from the head model, and add some particular level of noise onto the image. The noisy image, landmarks, and text condition are then fed into the frozen ControlNet twice for noise prediction. Two different classifier-free guidance (CFG) weights are applied during these two predictions, and the prediction difference offers a direction on how the rendered image can better match the text of interest. Experimental results suggest that our approach delivers high-quality 3D head sculptures with adequate geometry and photorealistic appearance, significantly outperforming state-ofthe-art methods. We also show that the same pipeline well supports editing the generated heads, including both geometry deformation and appearance change., Comment: Amazing results are shown in https://kumapowerliu.github.io/HeadArtist. Accepted by SIGGRAPH 2024

The increased demand for 3D data in AR/VR, robotics and gaming applications, gave rise to powerful generative pipelines capable of synthesizing high-quality 3D objects. Most of these models rely on the Score Distillation Sampling (SDS) algorithm to optimize a 3D representation such that the rendered image maintains a high likelihood as evaluated by a pre-trained diffusion model. However, finding a correct mode in the high-dimensional distribution produced by the diffusion model is challenging and often leads to issues such as over-saturation, over-smoothing, and Janus-like artifacts. In this paper, we propose a novel learning paradigm for 3D synthesis that utilizes pre-trained diffusion models. Instead of focusing on mode-seeking, our method directly models the distribution discrepancy between multi-view renderings and diffusion priors in an adversarial manner, which unlocks the generation of high-fidelity and photorealistic 3D content, conditioned on a single image and prompt. Moreover, by harnessing the latent space of GANs and expressive diffusion model priors, our method facilitates a wide variety of 3D applications including single-view reconstruction, high diversity generation and continuous 3D interpolation in the open domain. The experiments demonstrate the superiority of our pipeline compared to previous works in terms of generation quality and diversity., Comment: Project page: http://raywzy.com/CAD/

This paper is concerned with the unique identification of the shape of a scatterer through a single far-field pattern in an inverse elastic medium scattering problem with a generalized transmission boundary condition. The uniqueness issue by a single far-field measurement is a challenging problem in inverse scattering theory, which has a long and colorful history. In this paper, we demonstrate the well-posedness of the direct problem by the variational approach. We establish the uniqueness results by a single far-field measurement under a generic scenario when dealing with underlying elastic scatterers exhibiting polygonal-nest or polygonal-cell structures. Furthermore, for a polygonal-nest or polygonal-cell structure scatterer associated with density and boundary impedance parameters as piecewise constants, we show that these physical quantities can be uniquely determined simultaneously by a single far-field measurement. The corresponding proof relies heavily on examining the singular behaviour of a coupled PDE system near a corner in a microlocal manner.

In this paper, we revisit the bioluminescence tomography (BLT) problem, where one seeks to reconstruct bioluminescence signals (an internal light source) from external measurements of the Cauchy data. As one kind of optical imaging, the BLT has many merits such as high signal-to-noise ratio, non-destructivity and cost-effectiveness etc., and has potential applications such as cancer diagnosis, drug discovery and development as well as gene therapies and so on. In the literature, BLT is extensively studied based on diffusion approximation (DA) equation, where the distribution of peak sources is to be reconstructed and no solution uniqueness is guaranteed without adequate a priori information. Motivated by the solution uniqueness issue, several theoretical results are explored. The major contributions in this work that are new to the literature are two-fold: first, we show the theoretical uniqueness of the BLT problem where the light sources are in the shape of $C^2$ domains or polyhedral- or corona-shaped; second, we support our results with plenty of problem-orientated numerical experiments.

In this paper, we develop a theoretical framework for time-harmonic wave scattering on hyperbolic spaces. Using the limiting absorption principle (LAP), we derive the explicit forms of the ingoing and outgoing Green functions of the Helmholtz operator of hyperbolic spaces, and verify that they are the fundamental solutions. Then we establish accurate characterisations of the asymptotic behaviours of the Green functions and use them to establish the ingoing and outgoing radiation conditions, which are analogues to the Sommerfeld radiation conditions in the Euclidean setting. Moreover, we prove a Rellich's type theorem which guarantees that the scattered field as well as its far-field pattern are uniquely defined. Within the framework, we consider the scattering from a source and a potential respectively. To our best knowledge, the theoretical framework is new to the literature and it paves the way for many subsequent developments for wave scattering on hyperbolic spaces.

In this paper, we develop a general mathematical framework for enhanced hydrodynamic near-cloaking of electro-osmotic flow for more complex shapes, which is obtained by simultaneously perturbing the inner and outer boundaries of the perfect cloaking structure. We first derive the asymptotic expansions of perturbed fields and obtain a first-order coupled system. We then establish the representation formula of the solution to the first-order coupled system using the layer potential techniques. Based on the asymptotic analysis, the enhanced hydrodynamic near-cloaking conditions are derived for the control region with general cross-sectional shape. The conditions reveal the inner relationship between the shapes of the object and the control region. Especially, for the shape of a deformed annulus or confocal ellipses cylinder, the cloaking conditions and relationship of shapes are quantified more accurately. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking.

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method., Comment: 28 pages, 3 figures

This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lam\'e system in a bounded domain with a mixed homogeneous boundary condition. We also allow the occurrence of discontinuities in both the displacement and traction fields on the fault curve/surface. By the variational approach, we first prove the well-posedness of the direct dislocation problem in a rather general setting with the Lam\'e parameters being real-valued $L^\infty$ functions and satisfy the strong convexity condition. Next, by considering the scenario that the Lam\'e parameters are constant and the fault curve/surface possesses certain corner singularities, we establish a local characterisation of the slip vectors at the corner points over the dislocation curve/surface. In our study the dislocation is geometrically rather general and may be open or closed. For both cases, we establish the uniqueness results for the inverse problem of determining the dislocation curve/surface and the slips.

By integrating complementary information from RGB image and depth map, the ability of salient object detection (SOD) for complex and challenging scenes can be improved. In recent years, the important role of Convolutional Neural Networks (CNNs) in feature extraction and cross-modality interaction has been fully explored, but it is still insufficient in modeling global long-range dependencies of self-modality and cross-modality. To this end, we introduce CNNs-assisted Transformer architecture and propose a novel RGB-D SOD network with Point-aware Interaction and CNN-induced Refinement (PICR-Net). On the one hand, considering the prior correlation between RGB modality and depth modality, an attention-triggered cross-modality point-aware interaction (CmPI) module is designed to explore the feature interaction of different modalities with positional constraints. On the other hand, in order to alleviate the block effect and detail destruction problems brought by the Transformer naturally, we design a CNN-induced refinement (CNNR) unit for content refinement and supplementation. Extensive experiments on five RGB-D SOD datasets show that the proposed network achieves competitive results in both quantitative and qualitative comparisons., Comment: Accepted by ACM MM 2023

We propose and study several inverse problems associated with the nonlinear progressive waves that arise in infrasonic inversions. The nonlinear progressive equation (NPE) is of a quasilinear form $\partial_t^2 u=\Delta f(x, u)$ with $f(x, u)=c_1(x) u+c_2(x) u^n$, $n\geq 2$, and can be derived from the hyperbolic system of conservation laws associated with the Euler equations. We establish unique identifiability results in determining $f(x, u)$ as well as the associated initial data by the boundary measurement. Our analysis relies on high-order linearisation and construction of proper Gaussian beam solutions for the underlying wave equations. In addition to its theoretical interest, we connect our study to applications of practical importance in infrasound waveform inversion.

In this paper, we propose and study the utilization of the Dirichlet-to-Neumann (DN) map to uniquely identify the discount functions $r, k$ and cost function $F$ in a stationary mean field game (MFG) system. This study features several technical novelties that make it highly intriguing and challenging. Firstly, it involves a coupling of two nonlinear elliptic partial differential equations. Secondly, the simultaneous recovery of multiple parameters poses a significant implementation challenge. Thirdly, there is the probability measure constraint of the coupled equations to consider. Finally, the limited information available from partial boundary measurements adds another layer of complexity to the problem. Considering these challenges and problems, we present an enhanced higher-order linearization method to tackle the inverse problem related to the MFG system. Our proposed approach involves linearizing around a pair of zero solutions and fulfilling the probability measurement constraint by adjusting the positive input at the boundary. It is worth emphasizing that this technique is not only applicable for uniquely identifying multiple parameters using full-boundary measurements but also highly effective for utilizing partial-boundary measurements.

In a bounded domain $\Omega \subset \mathbb{R}^d$ over time interval $(0,T)$, we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian. We attach the non-zero Robin boundary condition. We first prove the Lipschitz stability in $\Omega \times (\varepsilon, T-\varepsilon)$ with given $\varepsilon>0$ for the determination of the solutions by Dirichlet data on arbitrarily chosen subboundary of $\partial\Omega$. Next we prove the Lipschitz stability for an inverse problem of determining spatially varying factors of source terms and a coefficient by extra boundary data and spatial data at an intermediate time., Comment: arXiv admin note: substantial text overlap with arXiv:2304.06673

In this work, we are concerned with inverse problems involving poly-fractional operators, where the poly-fractional operator is of the form \[P( (-\Delta_g)^s)u := \sum_{i=1}^M \alpha_i(-\Delta_{g_i})^{s_i}u\] for $s=(s_1,\dots,s_M)$, $0

We study the general physical properties of Fermi blazars using the Fermi fourth source catalog data (4FGL-DR2). The quasi-simultaneous multiwavelength data of Fermi blazar are fitted by using the one-zone leptonic model to obtain some physical parameters, such as jet power, magnetic field and Doppler factor. We study the distributions of the derived physical parameter as a function of black hole mass and accretion disk luminosity. The main results are as follows. (1) For a standard thin accretion disk, the jet kinetic power of most FSRQs can be explained by the BP mechanism. However, the jet kinetic power of most BL Lacs can not be explained by both the BZ mechanism or the BP mechanism. The BL Lacs may have ADAFs surrounding their massive black holes. (2) After excluding the redshift, there is a moderately strong correlation between the jet kinetic power and jet radiation power and the accretion disk luminosity for Fermi blazars. These results confirm a close connection between jet and accretion. The jet kinetic power is slightly larger than the accretion disk luminosity for Fermi blazars. (3) There is a significant correlation between jet kinetic power and gamma-ray luminosity and radio luminosity for Fermi blazars, which suggests that gamma-ray luminosity and radio luminosity can be used to indicate the jet kinetic power., Comment: 13pages,8 figures, accept for publication in ApJS

We present XFormer, a novel human mesh and motion capture method that achieves real-time performance on consumer CPUs given only monocular images as input. The proposed network architecture contains two branches: a keypoint branch that estimates 3D human mesh vertices given 2D keypoints, and an image branch that makes predictions directly from the RGB image features. At the core of our method is a cross-modal transformer block that allows information to flow across these two branches by modeling the attention between 2D keypoint coordinates and image spatial features. Our architecture is smartly designed, which enables us to train on various types of datasets including images with 2D/3D annotations, images with 3D pseudo labels, and motion capture datasets that do not have associated images. This effectively improves the accuracy and generalization ability of our system. Built on a lightweight backbone (MobileNetV3), our method runs blazing fast (over 30fps on a single CPU core) and still yields competitive accuracy. Furthermore, with an HRNet backbone, XFormer delivers state-of-the-art performance on Huamn3.6 and 3DPW datasets.

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems, we mainly consider the non-negative solutions of the coupled equations, which are consistent with realistic settings in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction of the measurement/observation data due to averaging effects, the nonlinear coupling of multiple equations, and the non-negative constraints on the solutions, which pose significant challenges to the inverse problems. We develop a new and effective scheme to tackle the inverse problems and achieve unique identifiability results by properly controlling the injection of different source terms to obtain multiple sets of mean flux data. The approach relies on certain monotonicity properties which are related to the intrinsic structures of the coupled PDE system. We also connect our study to biological applications of practical interest.

The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a system of two nonlinear parabolic partial differential equations with two opposite directions of time 0