Multimodal cross-city semantic segmentation aims to adapt a network trained on multiple labeled source domains (MSDs) from one city to multiple unlabeled target domains (MTDs) in another city, where the multiple domains refer to different sensor modalities. However, remote sensing data from different sensors increases the extent of domain shift in the fused domain space, making feature alignment more challenging. Meanwhile, traditional fusion methods only consider complementarity within MSDs (or MTDs), which wastes cross-domain relevant information and neglects control over domain shift. To address the above issues, we propose a similarity-inspired fusion and invertible transformation learning network (SFITNet) for multimodal cross-city semantic segmentation. To alleviate the increasing alignment difficulty in multimodal fused domains, an invertible transformation learning strategy (ITLS) is proposed, which adopts a topological perspective on unsupervised domain adaptation. This strategy aims to simulate the potential distribution transformation function between the MSD and the MTD based on invertible neural networks (INNs) after feature fusion, thereby performing distribution alignment independently within the two feature spaces. A cross-domain similarity-inspired information interaction module (CDSiM) is also designed, which considers the correspondence between the MSD and the MTD in the fusion stage, effectively utilizes multimodal complementary information and promotes the subsequent alignment of fused domain shifts. The semantic segmentation tests are completed on the public C2Seg-AB dataset and a new multimodal cross-city Su-Wu dataset. Compared with some state-of-the-art techniques, the experimental results demonstrated the superiority of the proposed SFITNet.

Global Climate Models (GCMs) are essential for climate projections but often exhibit biases, particularly in representing extremes and multivariate dependencies, which limit their utility in impact assessments. Traditional bias correction (BC) methods, such as quantile mapping, address marginal distributions but fail to correct joint extremes and cross-variable relationships. To address these challenges, we propose a Complete Density Correction using Normalizing Flows (CDC-NF), a novel method leveraging invertible transformations to adjust the full joint distribution of GCM outputs. Using observational data from NOAA nClimGrid-daily and CMIP6 GCM projections, The CDC-NF method was applied at a daily temporal resolution to precipitation and maximum temperature outputs from CMIP6 GCM projections. Compared to traditional BC methods, CDC-NF demonstrated substantial improvements in Wasserstein Distance, RMSE, and PBIAS, particularly for the 90th percentile extremes. Additionally, it preserved cross-correlation structure, enhancing reliability in modeling compound extremes. CDC-NF represents a significant advancement in BC, providing a robust framework for addressing GCM biases and improving climate impact studies in a changing climate.

Analyzing and measuring the similarity between two signals is a common task in many vibration-based structural health monitoring applications. Coherence between input and response signals serves as a convenient indicator of damage, based on the premise that nonlinearity due to damage in a linear system manifests as a loss of coherence in specific frequency bands. Because input excitations in civil structures are difficult to measure, damage indicators based on the coherence between two response signals have been developed. These indicators have shown promise in detecting nonlinear behavior in structures that were initially linear. This paper proposes a new damage indicator based on Mutual Information, a nonlinear extension of the squared correlation coefficient, to quantify the similarity between two signals without making assumptions about the nature of their interactions or the underlying dynamics of the system. Mutual Information is distinguished from other nonlinear similarity metrics due to its ability to capture all types of nonlinear dependencies, its high computational efficiency, and its invariance to invertible transformations, such as scaling. The proposed approach is demonstrated using a standard dataset containing experimental data from a three-story aluminum frame structure under 17 different damage states. The results show that the proposed metric can detect deviations from the baseline state due to changes in mass, stiffness, or newly induced nonlinear behavior, suggesting its potential for monitoring changes in the structural system.

SUMMARY Inversion of geophysical data usually exhibits strong non-uniqueness, arising from sparse data coverage, limited number of measurements, inherent nonlinearity of governing physical laws, noise and other factors. Methods based on Monte Carlo sampling are commonly used to explore the posterior model distributions, but these approaches are computationally demanding. Variational inference (VI) provides an alternative by transforming a high-dimensional sampling problem into an optimization problem, thereby significantly reducing the computational time. However, conventional VI methods, which typically use simple distribution families, like Gaussians, to approximate the posterior, may lack flexibility necessary to capture the complexity of the posterior distributions. Normalizing flows (NFs), a type of deep generative models, address this limitation by transforming a simple initial distribution into a highly complex target distribution through a sequence of invertible and differentiable transformations. In this study, we develop an NF-based VI method and apply it to electromagnetic (EM) data. This approach allows for explicit integration of prior knowledge and reference models into the inversion process. Both synthetic tests and field applications on EM data demonstrate that NF-based inversion effectively recovers the posterior model distribution in a more efficient manner, while providing excellent data fitting performance. Unlike many other machine learning algorithms, NFs do not require a training set, making it highly transferable across various inversion problems with minimal adjustments. The proposed NF-based method offers a more robust and computationally efficient solution to uncertainty quantification and shows great potential to be extended to solve 3-D geophysical Bayesian inversions, a major challenge that the geophysical community has faced for decades.

Cross-modal image registration for unmanned aerial vehicle (UAV) platforms presents significant challenges due to large-scale deformations, distinct imaging mechanisms, and pronounced modality discrepancies. This paper proposes a novel multi-scale cascaded registration network based on style transfer that achieves superior performance: up to 67% reduction in mean squared error (from 0.0106 to 0.0068), 9.27% enhancement in normalized cross-correlation, 26% improvement in local normalized cross-correlation, and 8% increase in mutual information compared to state-of-the-art methods. The architecture integrates a cross-modal style transfer network (CSTNet) that transforms visible images into pseudo-infrared representations to unify modality characteristics, and a multi-scale cascaded registration network (MCRNet) that performs progressive spatial alignment across multiple resolution scales using diffeomorphic deformation modeling to ensure smooth and invertible transformations. A self-supervised learning paradigm based on image reconstruction eliminates reliance on manually annotated data while maintaining registration accuracy through synthetic deformation generation. Extensive experiments on the LLVIP dataset demonstrate the method’s robustness under challenging conditions involving large-scale transformations, with ablation studies confirming that style transfer contributes 28% MSE improvement and diffeomorphic registration prevents 10.6% performance degradation. The proposed approach provides a robust solution for cross-modal image registration in dynamic UAV environments, offering significant implications for downstream applications such as target detection, tracking, and surveillance.

Abstract This paper presents a feedback control design for multi‐input linear time‐invariant (LTI) systems with constant commensurate time delay. The key to the design involves a bijective transformation to put the system into a controllable form, aligning all delays in the same channel as the inputs. We establish three conditions for this transformation: a necessary condition, a sufficient condition, which is easily testable and represents the primary contribution of this work, and a necessary and sufficient condition.

Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable transformation between Gaussian and non-Gaussian random distributions. We use normalising flows to compute Bayesian partition functions for non-Gaussian distributions and show how normalising flows can be employed in finding analytical expressions for posterior distributions beyond the Gaussian limit. Flows offer advantages for the numerical evaluation of the partition function itself, as well as for cumulants and for the information entropy. We demonstrate how normalising flows in conjunction with Bayes partitions can be used in inference problems in cosmology and apply them to the posterior distribution for the matter density Ωm and a dark energy equation of state parameter w0 on the basis of supernova data.

In this work, we introduce Modulated Flows (ModFlows), a novel approach for color transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color distribution of a reference image. Our technique is based on optimal transport and executes color transfer as an invertible transformation within the RGB color space. The ModFlows utilizes the bijective property of flows, enabling us to introduce a common intermediate color distribution and build a dataset of rectified flows. We train an encoder on this dataset to predict the weights of a rectified model for new images. After training on a set of optimal transport plans, our approach can generate plans for new pairs of distributions without additional fine-tuning. We additionally show that the trained encoder provides an image embedding, associated only with its color style. The presented method is capable of processing 4K images and achieves the state-of-the-art performance in terms of content and style similarity.

In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of exogenous variables. Our flow-based methods offer flexible model design while maintaining causal consistency regardless of the number of discretization steps. We propose design improvements that enable simultaneous learning of all causal mechanisms and reduce abduction and prediction complexity to linear O(n) relative to the number of layers, independent of the number of causal variables. Empirically, we demonstrate that our method outperforms previous state-of-the-art approaches and delivers consistent performance across a wide range of structural causal models in answering observational, interventional, and counterfactual questions. Additionally, our method achieves a significant reduction in computational time compared to existing diffusion-based techniques, making it practical for large structural causal models.

This study introduces an innovative image encryption algorithm that leverages multiple rounds of matrix scrambling and matrix product transformation. Each round of encryption integrates cross-scrambling operations within the image matrix and invertible matrix product transformations, thereby effectively disrupting pixel positions and values. By iteratively adjusting pixel positions and transforming pixel values, the algorithm significantly enhances the security and robustness of the encryption process. The experimental results demonstrate that the proposed algorithm exhibits excellent resistance to statistical analysis, differential attacks, and other potential threats, thereby ensuring high security and practical applicability.

The standard closed convex hull of a set is defined as the intersection of all images, under the action of a group of rigid motions, of a half-space containing the given set. In this paper we propose a generalisation of this classical notion, that we call a (K, ℍ)-hull, and which is obtained from the above construction by replacing a half-space with some other closed convex subset K of the Euclidean space, and a group of rigid motions by a subset ℍ of the group of invertible affine transformations. The main focus is on the analysis of (K, ℍ)-convex hulls of random samples from K.

Abstract The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While such approximations facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Nonparametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges. Drawing inspiration from recent advances in the fields of measure transport and generative artificial intelligence, this paper develops a new estimation-theoretic framework which can incorporate general invertible transformations in a principled way. Specifically, a conjugate transform filter (CTF) is derived and shown to extend the celebrated Kalman filter to a much broader class of non-Gaussian distributions. The new filter has several desirable properties, such as its ability to preserve statistical relationships in the prior state and converge to highly accurate observations. An ensemble approximation of the new filtering framework is also presented and validated through idealized examples. The numerical demonstrations feature bounded quantities with non-Gaussian distributions, which is a typical challenge in Earth system models. Results suggest that the greatest benefits from the new filtering framework occur when the observation errors are small relative to the forecast uncertainty and when state variables exhibit strong nonlinear dependencies. Significance Statement Data assimilation (DA) is the science of combining numerical models and observations. Common applications include estimating the state of large geophysical systems and inferring unknown model parameters. The Kalman filter and its many variants, which played a crucial role for the success of the Apollo space missions, is still the workhorse of operational DA algorithms. However, Kalman’s theory is based on highly restrictive assumptions which often compromise the DA accuracy. To address this challenge, the present article derives a new filtering theory in which the Kalman filter emerges as a special case. The flexibility of the proposed framework and its ability to integrate powerful mathematical techniques commonly used in artificial intelligence (AI) applications opens promising new avenues for improving conventional DA algorithms.

We show that there are no non-trivial closed subspaces of \(L_2(\mathbb{R}^n)\) that are invariant under invertible affine transformations. We apply this result to neural networks showing that any nonzero \(L_2(\mathbb{R})\) function is an adequate activation function in a one hidden layer neural network in order to approximate every function in \(L_2(\mathbb{R})\) with any desired accuracy. This generalizes the universal approximation properties of neural networks in \(L_2(\mathbb{R})\) related to Wiener's Tauberian Theorems. Our results extend to the spaces \(L_p(\mathbb{R})\) with \(p>1\).

L‐Feistel structure is a new iterative block cipher structure and unifies the Feistel structure and the Lai–Massey structure while maintaining the similarity of encryption and decryption. In this study, we present the first yoyo cryptanalysis against the L‐Feistel structure to evaluate the security under structural attack and give the method to recover the secret round function. We construct the fundamental yoyo distinguisher for the three‐round L‐Feistel structure, which can be used to distinguish the L‐Feistel structure from random permutation and establish the linear equations of the secret round functions. Besides, the fundamental yoyo distinguisher can be extended to more rounds when the invertible linear transformations are given. Then the equivalent structures of the L‐Feistel structure are provided, which helps reduce the guess of the starting point of the secret round functions. Finally, the process of recovering the secret round functions for the three‐round L‐Feistel structure is presented. We believe this study will enrich the application of yoyo cryptanalysis and L‐Feistel structure.

Existing deep learning-based surrogate models facilitate efficient data generation, but fall short in uncertainty quantification, efficient parameter space exploration, and reverse prediction. In our work, we introduce SurroFlow, a novel normalizing flow-based surrogate model, to learn the invertible transformation between simulation parameters and simulation outputs. The model not only allows accurate predictions of simulation outcomes for a given simulation parameter but also supports uncertainty quantification in the data generation process. Additionally, it enables efficient simulation parameter recommendation and exploration. We integrate SurroFlow and a genetic algorithm as the backend of a visual interface to support effective user-guided ensemble simulation exploration and visualization. Our framework significantly reduces the computational costs while enhancing the reliability and exploration capabilities of scientific surrogate models.

Abstract This paper examines the stabilization results for a class of semi‐linear time fractional reaction–diffusion partial differential equations (PDEs) with state delay using the backstepping method. The main goal is to design the boundary control for the system by proving the well‐posedness of the kernel function. The considered reaction–diffusion system is transformed into a stable target system using an invertible Volterra integral transformation. Also, the stability results in the sense of the Lyapunov–Krasovskii theory are proved and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, the results are numerically validated with a fractional‐order Hutchinson's equation.

In this article, we study the output tracking problem for a wave equation with variable coefficients, and subject to boundary control matched disturbances. Both the disturbances and the reference signal are unknown harmonic signal. The performance output is non-collocated with the control input. Initially, we establish an undisturbed auxiliary system and devise an appropriate internal model dynamic to reformulate the tracking error. Subsequently, we introduce an error-based feedback controller, leveraging an invertible transformation to achieve output tracking. The well-posedness and stability of the closed-loop system are established by applying semigroup theory approach. Finally, we illustrate the effectiveness of these theoretical results with numerical simulations. For more information see https://ejde.math.txstate.edu/Volumes/2024/80/abstr.html

Indeed, in signed graphs, the weights on the edges can be both positive and negative; this will provide a solid representation and manipulation framework for complicated relationships among phonetic symbols. Encryption and decryption of phonetic alphabets pose a number of special challenges and opportunities. This paper introduces a novel approach utilizing the eigenvalues and eigenvectors of signed graphs to develop more secure and efficient methods of encoding phonetic alphabets. Presented is a new cryptographic scheme; consider a mapping from phonetic alphabets onto a signed graph. Encryption should be carried out by means of structure-changing transformations of the latter, which leave intact the integrity of the information encoded. This approach allows for secure, invertible transformations to resist typical cryptographic attacks. Here, the decryption algorithm restores the encrypted graph back to the original phonetic symbols by systematically going through steps opposite to that taken during encryption. The proposal of signed graphs in the processes of phonetic alphabet encryption and decryption opens new frontiers of cryptographic practices, which have useful implications for secure communication systems and data protection.

Abstract Aftershocks (ASs) following strong mainshocks (MSs) can exacerbate structural damage or lead to collapse. However, the scarcity of recorded data necessitates reliance on artificial sequences, which have difficulty in characterizing the time‐frequency correlation between MSs and ASs. This study innovatively converts the AS time history prediction into an image translation task, exploiting the invertible transformation between accelerograms and time‐frequency representations. An encoder–decoder neural network is developed to encode the MS information into the latent space of a pre‐trained generative adversarial network, enabling accurate AS predictions through the decoder. The integration of seismic parameters further improves the AS prediction performance. Comparative analyses demonstrate that the proposed method outperforms the traditional ones on accuracy and robustness and reproduces the non‐stationarity of ASs.

Non-collocated control of an anti-stable system of coupled strings under delayed displacements/velocities feedback