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This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging algorithm. The stability of the imaging scheme is mathematically analyzed. We emphasize that different from the incident plane waves or point sources, the tapered waves with narrow widths bring several benefits in the inverse scattering: 1. local property. A tapered wave can illuminate only on a local part of the boundary of the obstacle, which generates the scattered field; 2. high resolution. We need only reconstruct the boundary near the beam, which improves the quality of some well-known algorithms; 3. fast and easy to implement. Numerical examples are included to demonstrate the effectiveness of the tapered waves., Comment: 16 pages, 11 figures

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.

Large language models (LLMs) have significantly enhanced the performance of numerous applications, from intelligent conversations to text generation. However, their inherent security vulnerabilities have become an increasingly significant challenge, especially with respect to jailbreak attacks. Attackers can circumvent the security mechanisms of these LLMs, breaching security constraints and causing harmful outputs. Focusing on multi-turn semantic jailbreak attacks, we observe that existing methods lack specific considerations for the role of multiturn dialogues in attack strategies, leading to semantic deviations during continuous interactions. Therefore, in this paper, we establish a theoretical foundation for multi-turn attacks by considering their support in jailbreak attacks, and based on this, propose a context-based contextual fusion black-box jailbreak attack method, named Context Fusion Attack (CFA). This method approach involves filtering and extracting key terms from the target, constructing contextual scenarios around these terms, dynamically integrating the target into the scenarios, replacing malicious key terms within the target, and thereby concealing the direct malicious intent. Through comparisons on various mainstream LLMs and red team datasets, we have demonstrated CFA's superior success rate, divergence, and harmfulness compared to other multi-turn attack strategies, particularly showcasing significant advantages on Llama3 and GPT-4.

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

As machine learning gains prominence in various sectors of society for automated decision-making, concerns have risen regarding potential vulnerabilities in machine learning (ML) frameworks. Nevertheless, testing these frameworks is a daunting task due to their intricate implementation. Previous research on fuzzing ML frameworks has struggled to effectively extract input constraints and generate valid inputs, leading to extended fuzzing durations for deep execution or revealing the target crash. In this paper, we propose ConFL, a constraint-guided fuzzer for ML frameworks. ConFL automatically extracting constraints from kernel codes without the need for any prior knowledge. Guided by the constraints, ConFL is able to generate valid inputs that can pass the verification and explore deeper paths of kernel codes. In addition, we design a grouping technique to boost the fuzzing efficiency. To demonstrate the effectiveness of ConFL, we evaluated its performance mainly on Tensorflow. We find that ConFL is able to cover more code lines, and generate more valid inputs than state-of-the-art (SOTA) fuzzers. More importantly, ConFL found 84 previously unknown vulnerabilities in different versions of Tensorflow, all of which were assigned with new CVE ids, of which 3 were critical-severity and 13 were high-severity. We also extended ConFL to test PyTorch and Paddle, 7 vulnerabilities are found to date., Comment: 13 pages, 15 figures

A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the coupled Cauchy data by the representation of the single-layer potentials and the solution to the resulting linear integral system. As a consequence of this decomposition, the original problem of joint inversion is reformulated into two decoupled subproblems: an inverse source problem and an inverse obstacle scattering problem. Then, two sampling-type schemes are proposed to recover the shape of the obstacle and the source locations, respectively. The sampling methods rely on the specific indicator functions defined on target-oriented probing domains of circular shape. The error estimates of the decoupling procedure are established and the asymptotic behaviors of the indicator functions are analyzed. Extensive numerical experiments are also conducted to verify the performance of the sampling schemes., Comment: 24 pages, 10 figures

We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple targets. In the first phase, we develop several indicator functionals to determine the source locations and the polarizations from the total field data, and then we manage to obtain the approximate scattered field. In this phase, only the inner products of the total field with the fundamental solutions are involved in the computation, and thus it is direct and computationally efficient. In the second phase, we propose an iteration method of Newton's type to reconstruct the shape of the obstacle from the approximate scattered field. Using the layer potential representations on an auxiliary curve inside the obstacle, the scattered field together with its derivative on each iteration surface can be easily derived. Theoretically, we establish the uniqueness of the co-inversion problem and analyze the indicating behavior of the sampling-type scheme. An explicit derivative is provided for the Newton-type method. Numerical results are presented to corroborate the effectiveness and efficiency of the proposed method., Comment: 29 pages, 11 figures

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can be decoupled into two inverse problems: an inverse obstacle scattering problem and an inverse source problem, and the corresponding uniqueness can be established. This novel decoupling technique requires some extra data but brings in several salient benefits. First, our method is fast and easy to implement. Second, the boundary condition of the obstacle is not needed. Finally, this approximate decoupling method can be applied to other co-inversion problems, such as determining the medium and its excitation sources. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method., Comment: 18 pages, 5 figures

This paper concerns the simultaneous reconstruction of a sound-soft cavity and its excitation sources from the total-field data. Using the single-layer potential representations on two measurement curves, this co-inversion problem can be decoupled into two inverse problems: an inverse cavity scattering problem and an inverse source problem. This novel decoupling technique is fast and easy to implement since it is based on a linear system of integral equations. Then the uncoupled subproblems are respectively solved by the modified optimization and sampling method. We also establish the uniqueness of this co-inversion problem and analyze the stability of our method. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method., Comment: 21 pages, 7 figures

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape of the obstacle or cavity. First, the scattered fields are approximated by the Fourier-Bessel functions with the measurements on a closed curve. Then, the indicator functions are established by the superpositions of the total fields or their derivatives to the incident point sources. We prove that the indicator functions vanish only on the boundary of the obstacle or cavity. Numerical examples are also included to demonstrate the effectiveness of the method., Comment: 28 pages, 7 figures

We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering the phase information of far-field data. This reference source technique leads to an easy-to-implement phase retrieval formula. Mathematically, the stability of the phase retrieval approach is rigorously justified. Then we employ the Fourier method to deal with the multi-frequency inverse source problem with recovered phase information. Finally, some two and three dimensional numerical results are presented to demonstrate the viability and effectiveness of the proposed method.

This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident waves, we rigorously prove that the location and shape of the cavity as well as its boundary condition can be uniquely determined by the modulus of near-fields at an admissible surface. To our knowledge, this is the first uniqueness result in inverse cavity scattering problems with phaseless near-field data. In this paper, we make use of the phaseless near-field data incurred by the cavity and the point sources, and thus the configuration is more feasible in practice., Comment: 10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1812.03291 and substantial text overlap with arXiv:1905.08242

This paper is devoted to the uniqueness of inverse acoustic scattering problems with the modulus of near-field data. By utilizing the superpositions of point sources as the incident waves, we rigorously prove that the phaseless near-fields collected on an admissible surface can uniquely determine the location and shape of the obstacle as well as its boundary condition and the refractive index of a medium inclusion, respectively. We also establish the uniqueness in determining a locally rough surface from the phaseless near-field data due to superpositions of point sources. These are novel uniqueness results in inverse scattering with phaseless near-field data., Comment: 17 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1812.03291

This paper is concerned with the uniqueness in inverse acoustic scattering problems with the modulus of the far-field patterns co-produced by the obstacle (resp. medium) and the point sources. Based on the superposition of point sources as the incident waves, we overcome the difficulty of translation invariance induced by a single incident plane wave, and rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of far-field patterns. This work is different from our previous work on phaseless inverse scattering problems [2018 Inverse Problems 34, 085002], in which the reference ball technique and the superposition of incident waves were used, and the phaseless far-field data generated only by the the scatterer were considered. In this paper, the phaseless far-field data co-produced by the scatterer and the point sources are used, thus the configuration is practically more feasible. Moreover, since the reference ball is not needed, the justification of uniqueness is much more clear and concise., Comment: 10 pages, 1 figure

This paper is concerned with the Fourier-Bessel method for the boundary value problems of the Helmholtz equation in a smooth simply connected domain. Based on the denseness of Fourier-Bessel functions, the problem can be approximated by determining the unknown coefficients in the linear combination. By the boundary conditions, an operator equation can be obtained. We derive a lower bound for the smallest singular value of the operator, and obtain a stability and convergence result for the regularized solution with a suitable choice of the regularization parameter. Numerical experiments are also presented to show the effectiveness of the proposed method., Comment: 13 pages, 2 figures

In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the inverse scattering system, we propose a system of nonlinear integral equations based iterative scheme to reconstruct both the location and the shape of the obstacle. The reference ball technique causes few extra computational costs, but breaks the translation invariance and brings information about the location of the obstacle. Several validating numerical examples are provided to illustrate the effectiveness and robustness of the proposed inversion algorithm., Comment: 20 pages, 13 figures

This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a major challenge associated with such an inverse problem. We develop a novel strategy to overcome this challenging problem by recovering the radiated fields via adding some reference point sources as extra artificial sources to the inverse source system. This novel reference source technique requires only a few extra data, and brings in a simple phase retrieval formula. The stability of this phase retrieval approach is rigorously analyzed. After the reacquisition of the phase information, the multi-frequency inverse source problem with recovered phase information is solved by the Fourier method, which is non-iterative, fast and easy to implement. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method., Comment: 27 pages, 4 figures

This paper is devoted to the uniqueness in inverse acoustic scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a single incident plane wave. In this paper, based on adding a reference ball as an extra artificial impenetrable obstacle (resp. penetrable homogeneous medium) to the inverse obstacle (resp. medium) scattering system and then using superpositions of a fixed plane wave and some point sources as the incident waves, we rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of far-field patterns. The reference ball technique in conjunction with the superposition of incident waves brings in several salient benefits. First, the framework of our theoretical analysis can be applied to both the inverse obstacle and medium scattering problems. Second, for inverse obstacle scattering, the underlying boundary condition could be of a general type and be uniquely determined. Finally, only a single frequency is needed., Comment: 16 pages, 2 figures

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources with a single wavenumber. Our algorithms are based on some novel indicator functions whose indicating behaviors could be used to locate multiple multipolar sources. The inversion schemes are totally "direct" in the sense that only simple integral calculations are involved in evaluating the indicator functions. Rigorous mathematical justifications are provided and extensive numerical examples are presented to demonstrate the effectiveness, robustness and efficiency of the proposed methods., Comment: 27 pages, 8 figures

This paper considers security risks buried in the data processing pipeline in common deep learning applications. Deep learning models usually assume a fixed scale for their training and input data. To allow deep learning applications to handle a wide range of input data, popular frameworks, such as Caffe, TensorFlow, and Torch, all provide data scaling functions to resize input to the dimensions used by deep learning models. Image scaling algorithms are intended to preserve the visual features of an image after scaling. However, common image scaling algorithms are not designed to handle human crafted images. Attackers can make the scaling outputs look dramatically different from the corresponding input images. This paper presents a downscaling attack that targets the data scaling process in deep learning applications. By carefully crafting input data that mismatches with the dimension used by deep learning models, attackers can create deceiving effects. A deep learning application effectively consumes data that are not the same as those presented to users. The visual inconsistency enables practical evasion and data poisoning attacks to deep learning applications. This paper presents proof-of-concept attack samples to popular deep-learning-based image classification applications. To address the downscaling attacks, the paper also suggests multiple potential mitigation strategies.

Advance in deep learning algorithms overshadows their security risk in software implementations. This paper discloses a set of vulnerabilities in popular deep learning frameworks including Caffe, TensorFlow, and Torch. Contrast to the small code size of deep learning models, these deep learning frameworks are complex and contain heavy dependencies on numerous open source packages. This paper considers the risks caused by these vulnerabilities by studying their impact on common deep learning applications such as voice recognition and image classifications. By exploiting these framework implementations, attackers can launch denial-of-service attacks that crash or hang a deep learning application, or control-flow hijacking attacks that cause either system compromise or recognition evasions. The goal of this paper is to draw attention on the software implementations and call for the community effort to improve the security of deep learning frameworks.