Small Perturbations Research Articles

Observation of magnetic islands in tokamak plasmas during the suppression of edge-localized modes

AbstractIn tokamaks, a leading platform for fusion energy, periodic filamentary plasma eruptions known as edge-localized modes occur in plasmas with high-energy confinement and steep pressure profiles at the plasma edge. These edge-localized modes could damage the tokamak wall but can be suppressed using small three-dimensional magnetic perturbations. Here we demonstrate that these magnetic perturbations can change the magnetic topology just inside the steep gradient region of the plasma edge. We identify signatures of a magnetic island, and their observation is linked to the suppression of edge-localized modes. We compare high-resolution measurements of perturbed magnetic surfaces with predictions from ideal magnetohydrodynamic theory where the magnetic topology is preserved. Although ideal magnetohydrodynamics adequately describes the measurements in plasmas exhibiting edge-localized modes, it proves insufficient for plasmas where these modes are suppressed. Nonlinear resistive magnetohydrodynamic modelling supports this observation. Our study experimentally confirms the predicted role of magnetic islands in inhibiting the occurrence of edge-localized modes. This will be beneficial for physics-based predictions in future fusion devices to control these modes.

Multiple Solutions for Logarithmic Schrödinger–Poisson Systems with a Small Perturbation

Multiple Solutions for Logarithmic Schrödinger–Poisson Systems with a Small Perturbation

A Topological Investigation of the Cosmic Web Formation

N-body simulations of the evolution of the large-scale structure of the universe (the Cosmic Web) were run while altering attractive gravity laws and initial conditions, in order to infer which properties of the universe are revealed by its current large-scale topology. The Cosmic Web was found to develop regardless of the gravitational alteration made. Significantly altering the initial conditions from Gaussian distribution ones was found to eliminate the Cosmic Web. Thus, we require small random perturbations in otherwise uniform initial conditions in the early universe, under an attractive gravitational force, for the Cosmic Web to develop.

Kink-antikink collisions in hyper-massive models

We study topological kinks and their interactions in a family of scalar field models with a double well potential parametrized by the mass of small perturbations around the vacua, ranging from the mass of the ϕ4 Klein-Gordon model all the way to the limit of infinite mass, which is identified with a non-analytic potential. In particular, we look at the problem of kink-antikink collisions and analyze the windows of capture and escape of the soliton pair as a function of collision velocity and model mass. We observe a disappearance of the capture cases for intermediary masses between the ϕ4 and non-analytic cases. The main features of the kink-antikink scattering are reproduced in a collective coordinates model, including the disappearance of the capture cases.

Modulation instability of whistler wave with electron loss cone distribution in magnetized plasma

Abstract The modulation instability of whistler mode waves caused by thermal electron anisotropy is studied. Based on MHD equations, the nonlinear schrödinger equation (NLSE) that describes the nonlinear modulation of whistler waves is derived by Using the Krylov-Bogoliubov-Mitropolsky (KBM) method. The condition for wave modulation instability is obtained from the loss cone distribution function of thermal electron anisotropy, revealing that the nonlinear growth of the waves tends towards electron perpendicular temperature anisotropy. By setting up continuous background waves and introducing small ion low frequency perturbations, we find that the change in the amplitude of the modulated wave is related with wave number. This finding has been validated through simulations that align with our analytical results. Additionally, we also calculate the maximum amplitude of the wave with loss cone angle and times, which revealed that the electron vertical temperature anisotropy will lead to the modulation instability of the whistler wave. This further confirms the occurrence of the modulation instability of the whistler wave in laboratory plasmas and strengthens their credibility.

Adversarial artifact detection in EEG-based brain-computer interfaces.

Machine learning has achieved significant success in electroencephalogram (EEG) based brain-computer interfaces (BCIs), with most existing research focusing on improving the decoding accuracy. However, recent studies have shown that EEG-based BCIs are vulnerable to adversarial attacks, where small perturbations added to the input can cause misclassification. Detecting adversarial examples is crucial for both understanding this phenomenon and developing effective defense strategies. This paper, for the first time, explores adversarial detection in EEG-based BCIs. We extend several popular adversarial detection approaches from computer vision to BCIs. Two new Mahalanobis distance based adversarial detection approaches, and three cosine distance based adversarial detection approaches, are also proposed, which showed promising performance in detecting three kinds of white-box attacks. We evaluated the performance of eight adversarial detection approaches on three EEG datasets, three neural networks, and four types of adversarial attacks. Our approach achieved an area under the curve (AUC) score of up to 99.99% in detecting white-box attacks. Additionally, we assessed the transferability of different adversarial detectors to unknown attacks. Through extensive experiments, we found that white-box attacks may be easily detected, and differences exist in the distributions of different types of adversarial examples. Our work should facilitate understanding the vulnerability of existing BCI models and developing more secure BCIs in the future.

Mechanistic Studies of Small Molecule Ligands Selective to RNA Single G Bulges.

Small-molecule RNA binders have emerged as an important pharmacological modality. A profound understanding of the ligand selectivity, binding mode, and influential factors governing ligand engagement with RNA targets is the foundation for rational ligand design. Here, we report a novel class of coumarin derivatives exhibiting selective binding affinity towards single G RNA bulges. Harnessing the computational power of all-atom Gaussian accelerated Molecular Dynamics (GaMD) simulations, we unveiled a rare minor groove binding mode of the ligand with a key interaction between the coumarin moiety and the G bulge. This predicted binding mode is consistent with results obtained from structure-activity-relationship (SAR) studies and transverse relaxation measurements by NMR spectroscopy. We further generated 444 molecular descriptors from 69 coumarin derivatives and identified key contributors to the binding events, such as charge state and planarity, by lasso (least absolute shrinkage and selection operator) regression. Strikingly, small structure perturbations on these key contributors, such as the addition of a methyl group that disrupts the planarity of the ligand resulted in > 100-fold reduction in the binding affinity. Our work deepened the understanding of RNA-small molecule interactions and integrated a new generalizable platform for the rational design of selective small-molecule RNA binders.

Nonexistence of the compressible Euler equations with space-dependent damping in high dimensions

Abstract Compressible Euler equations with space-dependent damping in high dimensions R n ( n = 2 , 3 ) {{\bf{R}}}^{n}\hspace{0.33em}\hspace{0.33em}\left(n=2,3) are considered in this article. Assuming that the small initial velocity and small perturbation of the initial density have compact support, we establish finite-time blow-up results for the Euler system, by combining energy estimate and new test functions constructed by the solutions of the following linear elliptic partial differential equations system: − G 1 ( x ) + ∇ ⋅ G 2 → ( x ) = 0 , − G 2 → ( x ) + ∇ G 1 ( x ) = μ G 2 → ( x ) ( 1 + ∣ x ∣ ) λ . \left\{\begin{array}{l}-{G}_{1}\left(x)+\nabla \cdot \overrightarrow{{G}_{2}}\left(x)=0,\\ -\overrightarrow{{G}_{2}}\left(x)+\nabla {G}_{1}\left(x)=\frac{\mu \overrightarrow{{G}_{2}}\left(x)}{{(1+| x| )}^{\lambda }}.\end{array}\right. This result generalizes the one in the literature from 1 − D 1-D to high dimension R n ( n = 2 , 3 ) {{\bf{R}}}^{n}\hspace{0.33em}\hspace{0.33em}\left(n=2,3) .

Simulating adiabatic quantum computing with parameterized quantum circuits

Abstract Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the variational quantum eigensolver on two classical optimization problems, namely MaxCut and number partitioning, and on a quantum-spin configuration problem, the transverse-field ising chain model, and confirm that our approach demonstrates superior performance.

GEOMECHANICAL MODELING OF RESERVOIR DYNAMICS ASSOCIATED WITH SHALLOW INJECTION AND PRODUCTION IN THE DELAWARE BASIN

The Permian Basin is an area of active hydrocarbon production and saltwater disposal, as well as associated induced seismicity and other geomechanical responses that threaten the surface environment. Among the important but not yet fully answered questions are: (i) what are the temporal and spatial changes in stress and pore pressure in response to fluid injection and production, and (ii) how do these changes relate to slip on pre-existing faults and surface deformation? We simulate stress and pore pressure responses to saltwater injection in the Delaware Mountain Group and production from the Wolfcamp and Bone Spring Formations with the aid of 2D geomechanical simulations that capture key mechanical stratigraphic units and representative faults. Primary loading consists of localized pore pressure changes that represent fluid injection into the Delaware Mountain Group and production from the lowermost portion of the Bone Spring Formation, the entire Wolfcamp A Formation, and the uppermost portion of the Wolfcamp B Formation. Injection leads to pore pressure increase, vertical extension, reduction in mean stress, and increase in differential stress in the Delaware Mountain Group. Production leads to decrease in pore pressure, vertical contraction, increase in mean stress, and increase in differential stress in the Bone Spring and Wolfcamp A and B Formations. The net effect of injection and production in our generalized simulations is normal faulting slip on faults that are relatively shallow in the subsurface, similar to faults that are known to have produced seismogenic rupture. The combination of injection and production reproduces a spatially-variant trend in uplift and subsidence, consistent with regional patterns measured in the study area via InSAR analysis. The modeled scenarios with shallow injection and/or production caused only small (lt;0.2 MPa) stress perturbations to propagate downward to basement, which would be unlikely to cause instability of deep-seated seismogenic faults.

Enhancing Adversarial Robustness through Stable Adversarial Training

Deep neural network models are vulnerable to attacks from adversarial methods, such as gradient attacks. Evening small perturbations can cause significant differences in their predictions. Adversarial training (AT) aims to improve the model’s adversarial robustness against gradient attacks by generating adversarial samples and optimizing the adversarial training objective function of the model. Existing methods mainly focus on improving robust accuracy, balancing natural and robust accuracy and suppressing robust overfitting. They rarely consider the AT problem from the characteristics of deep neural networks themselves, such as the stability properties under certain conditions. From a mathematical perspective, deep neural networks with stable training processes may have a better ability to suppress overfitting, as their training process is smoother and avoids sudden drops in performance. We provide a proof of the existence of Ulam stability for deep neural networks. Ulam stability not only determines the existence of the solution for an operator inequality, but it also provides an error bound between the exact and approximate solutions. The feature subspace of a deep neural network with Ulam stability can be accurately characterized and constrained by a function with special properties and a controlled error boundary constant. This restricted feature subspace leads to a more stable training process. Based on these properties, we propose an adversarial training framework called Ulam stability adversarial training (US-AT). This framework can incorporate different Ulam stability conditions and benchmark AT models, optimize the construction of the optimal feature subspace, and consistently improve the model’s robustness and training stability. US-AT is simple and easy to use, and it can be easily integrated with existing multi-class AT models, such as GradAlign and TRADES. Experimental results show that US-AT methods can consistently improve the robust accuracy and training stability of benchmark models.

Asymptotic analysis of sign-changing transmission problems with rapidly oscillating interface

We study the asymptotic behavior of a sign-changing transmission problem, stated in a symmetric oscillating domain obtained by gluing together a positive and a negative material, separated by an imperfect and rapidly oscillating interface. The interface separating the two heterogeneous materials has a periodic microstructure and is a small perturbation of a flat interface. The solution of the transmission problem is continuous and its flux has a jump on the oscillating interface. Under certain conditions on the properties of the two materials, we derive the limit problem and we prove the convergence result. The T-coercivity method is used to handle the lack of coercivity for both the microscopic and the macroscopic limit problems. For more information see https://ejde.math.txstate.edu/Volumes/2024/60/abstr.html

Stochastic optimization of a mass-in-mass cell with piecewise hybrid nonlinear–linear restoring force

This article investigates the optimization under uncertainty of a mass-in-mass meta-cell for its potential use within a metamaterial. The specificity of the proposed mass-in-mass system stems from the hybrid nonlinear–linear stiffness at the inner level. It is well known that these systems are highly sensitivity to small perturbations in loading conditions or design parameters. In fact, the sensitivity is such that the system can exhibit discontinuous behaviors. Therefore the proposed optimization approach not only accounts for sources of uncertainties but also can handle discontinuous responses. The objective of the stochastic optimization is to find the stiffness properties of the mass-in-mass system which minimize the expected value of a specific efficiency metric. In order to better understand the system’s dynamic behavior and the origins of the discontinuities, slow invariant manifolds and frequency response curves are provided. The efficiency of the optimized system with hybrid stiffness is compared with that of a similar optimized system featuring pure cubic nonlinearity.

SMARCD1 is an essential expression-restricted metastasis modifier

Breast cancer is the most frequently diagnosed cancer worldwide, constituting 15% of cases in 2023. The predominant cause of breast cancer-related mortality is metastasis, and a lack of metastasis-targeted therapies perpetuates dismal outcomes for late-stage patients. By using meiotic genetics to study inherited transcriptional network regulation, we have identified, to the best of our knowledge, a new class of “essential expression-restricted” genes as potential candidates for metastasis-targeted therapeutics. Building upon previous work implicating the CCR4-NOT RNA deadenylase complex in metastasis, we demonstrate that RNA-binding proteins NANOS1, PUM2, and CPSF4 also regulate metastatic potential. Using various models and clinical data, we pinpoint Smarcd1 mRNA as a target of all three RNA-BPs. Strikingly, both high and low expression of Smarcd1 correlate with positive clinical outcomes, while intermediate expression significantly reduces the probability of survival. Applying the theory of “essential genes” from evolution, we identify 50 additional genes that require precise expression levels for metastasis to occur. Specifically, small perturbations in Smarcd1 expression significantly reduce metastasis in mouse models and alter splicing programs relevant to the ER+/HER2-enriched breast cancer. Identification subtype-specific essential expression-restricted metastasis modifiers introduces a novel class of genes that, when therapeutically “nudged” in either direction, may significantly improve late-stage breast cancer patients.

Symmetry-breaking bifurcations of pure-quartic solitons in dual-core couplers.

We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (alias phase transitions of the second kind). Direct simulations of the perturbed evolution of PQSs corroborate their stability boundaries predicted by the analysis of small perturbations.

Convergence Rates for Identification of Robin Coefficient from Terminal Observations

This paper deals with the problem of identification of a Robin coefficient (also known as impedance coefficient) in a parabolic PDE from terminal observations of the temperature distributions. The problem is ill-posed in the sense that small perturbation in the observation may lead to a large deviation in the solution. Thus, in order to obtain stable approximations, we employ the Tikhonov-regularization. We propose a weak source condition motivated by the work of Engl and Zou (2000) and obtain a convergence rate of O(δ12)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\delta ^\\frac{1}{2})$$\\end{document}, where δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} is the noise level of the observed data. The obtained rate is better than some of the previous known rates. Moreover, the advantage of the proposed source condition is that the above mentioned convergence rate is obtained without the need for characterizing the range space of modelling operator and its Fréchet derivative, which is in contrast to the general convergence theory of Tikhonov-regularization for non linear operators.

Attention-Enhanced Defensive Distillation Network for Channel Estimation in V2X mm-Wave Secure Communication

Millimeter-wave (mm-wave) technology, crucial for future networks and vehicle-to-everything (V2X) communication in intelligent transportation, offers high data rates and bandwidth but is vulnerable to adversarial attacks, like interference and eavesdropping. It is crucial to protect V2X mm-wave communication from cybersecurity attacks, as traditional security measures often fail to counter sophisticated threats and complex attacks. To tackle these difficulties, the current study introduces an attention-enhanced defensive distillation network (AEDDN) to improve robustness and accuracy in V2X mm-wave communication under adversarial attacks. The AEDDN model combines the transformer algorithm with defensive distillation, leveraging the transformer’s attention mechanism to focus on critical channel features and adapt to complex conditions. This helps mitigate adversarial examples by filtering misleading data. Defensive distillation further strengthens the model by smoothing decision boundaries, making it less sensitive to small perturbations. To evaluate and validate the AEDDN model, this study uses a publicly available dataset called 6g-channel-estimation and a proprietary dataset named MMMC, comparing the simulation results with the convolutional neural network (CNN) model. The findings from the experiments indicate that the AEDDN, especially in the complex V2X mm-wave environment, demonstrates enhanced performance.

Blind image authentication using singular value decomposition with enhanced robustness by augmenting hamming code

Singular value decomposition (SVD) based image authentication has widespread applications for digital media protection including forensic and medical domains due to the high stability and robustness of singular values under small perturbations. However, most of these techniques are non-blind and have high redundancies for the extraction of secret data. The proposed scheme employs a blind extraction strategy by utilizing the intrinsic relationship of coefficient pairs of the U matrix of the host image blocks. This relationship is utilized to hide a secret binary bit after computing a threshold value in constant time. The host image underwent block-wise decomposition and hash-based randomization of blocks, followed by block-wise SVD for embedding secret bits in the U matrix. Hamming coded watermark is embedded for high precision extraction under active attacks. High imperceptibility and strong robustness are observed under attacks when tested across general purpose as well as image datasets and the system outperforms many existing works. Experimental observation shows the average PSNR between the host and marked image and average NCC between embedded and extracted watermark to be 36.98 dB and 0.999 respectively for the SIPI dataset whereas 52.7 dB and 1 respectively for the X-Ray dataset. The system exhibited high robustness under Salt-and-pepper noise (SAPN), Gaussian Noise (GAUN), Cropping (CRP), Median Filtering (MF), Histogram Equalization (HEQ), and Jpeg Compression (JPC) with average NCC values of 0.998, 1, 0.932, 0.999 and 0.967 respectively for X-Ray dataset. The time complexity O (M × N) is observed for both embedding and extraction algorithms for a host image of size M × N.

Efficient random walks for generating random fuzzy measures in Möbius representation in large universe

Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization. Random walks ensure uniform generation and adequate coverage. The Möbius representation of set functions is a valuable tool for establishing the sparse structure of fuzzy measures, with its non-negativity closely linked to monotonicity and convexity/supermodularity checking. We propose three efficient methods for monotonicity verification and convexity/supermodularity verification applicable to random walks in Möbius representations, specifically tailored for universal sets larger than ten inputs and k-order fuzzy measures. We first present the baseline methods by directly inspecting monotonicity and convexity constraints. Building on the observation that the majority of initially generated values exhibit non-negativity, we intentionally track negative Möbius values to enhance the computational performance of these baseline approaches. Further, we introduce the more agile methods that employ insertion and merge sorting techniques for both monotonicity and convexity checks in random walks that involve small perturbations of fuzzy measures. To address sparsity in large-scale scenarios, we focus on two major types of measures: k-additive and k-interactive measures, demonstrating their effectiveness through theoretical analysis and experimental results.

Determination of a small elliptical anomaly in electrical impedance tomography using minimal measurements

Abstract We consider the problem of determining a small elliptical conductivity anomaly in a unit disc from boundary measurements. The conductivity of the anomaly is assumed to be a small perturbation from the constant background. A measurement of voltage across two point-electrodes on the boundary through which a constant current is passed. We further assume the limiting case when the distance between two electrodes go to zero, creating a dipole field. We show that three such measurements suffice to locate the anomaly size and location inside the disc. Two further measurements are needed to obtain the aspect ratio and the orientation of the ellipse. The investigation includes the studies of the stability of the inverse problem and optimal experiment design.