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We present a gradient-based calibration algorithm to identify the system matrices of a linear port-Hamiltonian system from given input–output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal control with ordinary differential equations and define a constrained optimization problem. The input-to-state stability is discussed which is the key step towards the existence of optimal controls. Further, we derive the first-order optimality system taking into account the port-Hamiltonian structure. Indeed, the proposed method preserves the skew symmetry and positive (semi)-definiteness of the system matrices throughout the optimization iterations. Numerical results with perturbed and unperturbed synthetic data, as well as an example from the PHS benchmark collection [17] demonstrate the feasibility of the approach. [ABSTRACT FROM AUTHOR]

Through analyses of Russian voicing assimilation and German dorsal fricative assimilation, this article argues for a restricted version of structure preservation and a stratal model of Optimality Theory. Structure preservation (Kiparsky 1985) prohibits the creation of allophones early in the phonological computation. The parallel architecture of OT undermines the assumptions of structure preservation, which has been widely rejected within OT. This article demonstrates that processes that are both neutralizing and non-structure-preserving, and which involve overlapping sets of targets and triggers, such as Russian voicing assimilation, result in a ranking paradox in parallel OT. Purely allophonic processes, such as German fricative assimilation, do not pose the same difficulties. Analyses of both processes are proposed within the framework of Stratal OT. The use of multiple strata eliminates the ranking paradox illustrated in Russian voicing assimilation and accounts for the interaction of German fricative assimilation and umlaut. This account predicts that non-structure-preserving neutralization cannot take place at the earliest level of evaluation but must apply after the rich base is filtered to the language-specific inventory and stem-level processes are applied. In the case of Russian, this is substantiated by application of assimilation across clitic boundaries, requiring phrase-level application. [ABSTRACT FROM AUTHOR]

This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear parametrizations such as deep networks. The proposed approach builds on Neural Galerkin schemes that are based on the Dirac--Frenkel variational principle to train nonlinear parametrizations sequentially in time. We first show that only adding constraints that aim to conserve quantities in continuous time can be insufficient because the nonlinear dependence on the parameters implies that even quantities that are linear in the solution fields become nonlinear in the parameters and thus are challenging to discretize in time. Instead, we propose Neural Galerkin schemes that compute at each time step an explicit embedding onto the manifold of nonlinearly parametrized solution fields to guarantee conservation of quantities. The embeddings can be combined with standard explicit and implicit time integration schemes. Numerical experiments demonstrate that the proposed approach conserves quantities up to machine precision. [ABSTRACT FROM AUTHOR]

To address the decline or failure in the autonomous learning capability of traditional transfer learning methods when training and test samples come from different machines, resulting in low cross-machine fault diagnosis rates, we propose a cross-domain manifold structure preservation (CDMSP) method for diagnosing rolling bearing faults across machines. The CDMSP method can induce the manifold space projection matrices of the source and target domains more effectively. This method maps high-dimensional features into a low-dimensional manifold, preserving non-linear relationships and aligning distribution differences while maintaining cross-domain manifold structure consistency. Additionally, highly confidently labeled target domain samples are selected from each mapping result and added to the training dataset to enhance subspace learning in subsequent iterations. The CDMSP method is both simple and effective at capturing the underlying structures and patterns in the data. The CWRU dataset and our self-built test platform dataset were used to validate this method. Experimental results show that CDMSP, as a non-deep domain adaptation method of transfer learning, outperforms similar methods in cross-machine fault identification, achieving a maximum fault identification accuracy of 100 % with excellent convergence performance. Furthermore, simulated diagnostic experiments under noise interference indicate that CDMSP maintains high fault identification accuracy, even in noisy environments. Overall, CDMSP is an efficient and reliable new method for diagnosing cross-machine bearing faults. [ABSTRACT FROM AUTHOR]

Image smoothing is an important processing operation that highlights low-frequency structural parts of an image and suppresses the noise and high-frequency textures. In the paper, we post an intriguing question of how to combine the paired unsmoothed/smoothed images and meaningful edge information to improve the performance of image smoothing. To this end, we propose a structure-preserving image smoothing network, which consists of a main interpreter (MI) and an edge map extractor (EME). The network is trained via contrastive learning on the extended BSD500 dataset. In addition, an edge-aware total variation loss function is utilized to distinguish between non-edge regions and edge maps via a pre-trained EME module, therefore improving the capability of structure preservation. In order to maintain the consistency in structure and background brightness, the outputs from MI are used as anchors for a ternary loss in 1:1 paired positive and negative samples. Experiments on different datasets show that our network outperforms state-of-the-art image smoothing methods in terms of SSIM and PSNR. [ABSTRACT FROM AUTHOR]

Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal interpolation points and the appropriate size of the reduced-order model. An approach that addresses the first problem for linear, unstructured systems is the iterative rational Krylov algorithm (IRKA), which computes optimal interpolation points through iterative updates by solving linear eigenvalue problems. However, in the case of preserving internal system structures, optimal interpolation points are unknown, and heuristics based on nonlinear eigenvalue problems result in numbers of potential interpolation points that typically exceed the reasonable size of reduced-order systems. In our work, we propose a projection-based iterative interpolation method inspired by IRKA for generally structured systems to adaptively compute near-optimal interpolation points as well as an appropriate size for the reduced-order system. Additionally, the iterative updates of the interpolation points can be chosen such that the reduced-order model provides an accurate approximation in specified frequency ranges of interest. For such applications, our new approach outperforms the established methods in terms of accuracy and computational effort. We show this in numerical examples with different structures. [ABSTRACT FROM AUTHOR]

Introduction: Even with recent research advances, effective delivery of a compound to its target cells inside the inner ear remains a challenging endeavor due to anatomical and physiological barriers. Direct intracochlear drug administration with an inner ear catheter (IEC) aims to overcome this obstacle and strives to provide a safe and efficient way for inner ear pharmacotherapy. The goal of this study was to histologically and audiologically evaluate the traumatic properties of a novel IEC for intracochlear drug delivery in a large animal model. Methods: Seven inner ears of piglets that had undergone intracochlear fluorescein isothiocyanate dextran application via an IEC (n = 4) or round window membrane (RWM) puncture with a needle (n = 3) followed by sequential apical perilymph sampling were histologically analyzed. Additionally, obtained objective auditory compound action potential and cochlear microphonic measurements were compared. Cochlear cryosections were stained using hematoxylin and eosin, and preservation of inner ear structures was investigated. Moreover, one cochlea was methylmethacrylate-embedded and analyzed with the IEC in situ. Results: Histological evaluation revealed an atraumatic insertion and subsequent compound application in a majority of IEC-inserted inner ears. Click cochlear compound action potential (CAP) shifts in the IEC groups reached a maximum of 5 dB (1.25 ± 2.5 dB) post administration and prior to perilymph sampling. In comparison, application by RWM puncture generated a maximum click CAP hearing threshold shift of 50 dB (23.3 ± 23.1 dB) coinciding with coagulated blood in the basal cochlear turn in one specimen of the latter group. Furthermore, in situ histology showed an atraumatic insertion of the IEC demonstrating preserved intracochlear structures. Conclusion: The IEC appears to be a promising and efficient way for inner ear drug delivery. The similarities between the porcine and human inner ear enhance the clinical translation of our findings and increase confidence regarding the safe applicability of the IEC in human subjects. [ABSTRACT FROM AUTHOR]

Universal style transfer (UST) infuses styles from arbitrary reference images into content images. Existing methods, while enjoying many practical successes, are unable of explaining experimental observations, including different performances of UST algorithms in preserving the spatial structure of content images. In addition, methods are limited to cumbersome global controls on stylization, so that they require additional spatial masks for desired stylization. In this work, we first provide a systematic Fourier analysis on a general framework for UST. We present an equivalent form of the framework in the frequency domain. The form implies that existing algorithms treat all frequency components and pixels of feature maps equally, except for the zero-frequency component. We connect Fourier amplitude and phase with a widely used style loss and a well-known content reconstruction loss in style transfer, respectively. Based on such equivalence and connections, we can thus interpret different structure preservation behaviors between algorithms with Fourier phase. Given the interpretations, we propose two plug-and-play manipulations upon style transfer methods for better structure preservation and desired stylization. Both qualitative and quantitative experiments demonstrate the improved performance of our manipulations upon mainstreaming methods without any additional training. Specifically, the metrics are improved by 6% in average on the content images from MS-COCO dataset and the style images from WikiArt dataset. We also conduct experiments to demonstrate (1) the abovementioned equivalence, (2) the interpretability based on Fourier amplitude and phase and (3) the controllability associated with frequency components. [ABSTRACT FROM AUTHOR]

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IntroductionEven with recent research advances, effective delivery of a compound to its target cells inside the inner ear remains a challenging endeavor due to anatomical and physiological barriers. Direct intracochlear drug administration with an inner ear catheter (IEC) aims to overcome this obstacle and strives to provide a safe and efficient way for inner ear pharmacotherapy. The goal of this study was to histologically and audiologically evaluate the traumatic properties of a novel IEC for intracochlear drug delivery in a large animal model.MethodsSeven inner ears of piglets that had undergone intracochlear fluorescein isothiocyanate dextran application via an IEC (n = 4) or round window membrane (RWM) puncture with a needle (n = 3) followed by sequential apical perilymph sampling were histologically analyzed. Additionally, obtained objective auditory compound action potential and cochlear microphonic measurements were compared. Cochlear cryosections were stained using hematoxylin and eosin, and preservation of inner ear structures was investigated. Moreover, one cochlea was methylmethacrylate-embedded and analyzed with the IEC in situ.ResultsHistological evaluation revealed an atraumatic insertion and subsequent compound application in a majority of IEC-inserted inner ears. Click cochlear compound action potential (CAP) shifts in the IEC groups reached a maximum of 5 dB (1.25 ± 2.5 dB) post administration and prior to perilymph sampling. In comparison, application by RWM puncture generated a maximum click CAP hearing threshold shift of 50 dB (23.3 ± 23.1 dB) coinciding with coagulated blood in the basal cochlear turn in one specimen of the latter group. Furthermore, in situ histology showed an atraumatic insertion of the IEC demonstrating preserved intracochlear structures.ConclusionThe IEC appears to be a promising and efficient way for inner ear drug delivery. The similarities between the porcine and human inner ear enhance the clinical translation of our findings and increase confidence regarding the safe applicability of the IEC in human subjects.

Microservices have emerged as a prevalent architectural style in modern software development, replacing traditional monolithic architectures. The decomposition of business functionality into distributed microservices offers numerous benefits, but introduces increased complexity to the overall application. Consequently, the complexity of authorization in microservice-based applications necessitates a comprehensive approach that integrates authorization as an inherent component from the beginning. This paper presents a systematic approach for achieving fine-grained user authorization using Attribute-Based Access Control (ABAC). The proposed approach emphasizes structure preservation, facilitating traceability throughout the various phases of application development. As a result, authorization artifacts can be traced seamlessly from the initial analysis phase to the subsequent implementation phase. One significant contribution is the development of a language to formulate natural language authorization requirements and policies. These natural language authorization policies can subsequently be implemented using the policy language Rego. By leveraging the analysis of software artifacts, the proposed approach enables the creation of comprehensive and tailored authorization policies.

A key consideration in the development of numerical schemes for time-dependent partial differential equations (PDEs) is the ability to preserve certain properties of the continuum solution, such as associated conservation laws or other geometric structures of the solution. There is a long history of the development and analysis of such structure-preserving discretization schemes, including both proofs that standard schemes have structure-preserving properties and proposals for novel schemes that achieve both high-order accuracy and exact preservation of certain properties of the continuum differential equation. When coupled with implicit time-stepping methods, a major downside to these schemes is that their structure-preserving properties generally rely on an exact solution of the (possibly nonlinear) systems of equations defining each time step in the discrete scheme. For small systems, this is often possible (up to the accuracy of floating-point arithmetic), but it becomes impractical for the large linear systems that arise when considering typical discretization of space-time PDEs. In this paper, we propose a modification to the standard flexible generalized minimum residual iteration that enforces selected constraints on approximate numerical solutions. We demonstrate its application to both systems of conservation laws and dissipative systems. [ABSTRACT FROM AUTHOR]

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example. [ABSTRACT FROM AUTHOR]

A basic leapfrog integrator and its energy-preserving and variational/symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The methods are based on a four-dimensional formulation of the equations of motion. Structure-preserving properties of the numerical methods are analyzed, in particular conservation and long-time near-conservation of energy and mass shell as well as preservation of volume in phase space. In the non-relativistic limit, the considered methods reduce to the Boris algorithm for non-relativistic charged-particle dynamics and its energy-preserving and variational/symplectic variants. [ABSTRACT FROM AUTHOR]

Microservices have emerged as a prevalent architectural style in modern software development, replacing traditional monolithic architectures. The decomposition of business functionality into distributed microservices offers numerous benefits, but introduces increased complexity to the overall application. Consequently, the complexity of authorization in microservice-based applications necessitates a comprehensive approach that integrates authorization as an inherent component from the beginning. This paper presents a systematic approach for achieving fine-grained user authorization using Attribute-Based Access Control (ABAC). The proposed approach emphasizes structure preservation, facilitating traceability throughout the various phases of application development. As a result, authorization artifacts can be traced seamlessly from the initial analysis phase to the subsequent implementation phase. One significant contribution is the development of a language to formulate natural language authorization requirements and policies. These natural language authorization policies can subsequently be implemented using the policy language Rego. By leveraging the analysis of software artifacts, the proposed approach enables the creation of comprehensive and tailored authorization policies. [ABSTRACT FROM AUTHOR]

A new exponentially fitted version of the discrete variational derivative method for the efficient solution of oscillatory complex Hamiltonian partial differential equations is proposed. When applied to the nonlinear Schrödinger equation, this scheme has discrete conservation laws of charge and energy. The new method is compared with other conservative schemes from the literature on a benchmark problem whose solution is an oscillatory breather wave. [ABSTRACT FROM AUTHOR]

By exploring the localizable representations in deep CNN, weakly supervised object localization (WSOL) methods could determine the position of the object in each image just trained by the classification task. However, the partial activation problem caused by the discriminant function makes the network unable to locate objects accurately. To alleviate this problem, we propose Structure-Preserved Attention Activated Network (SPA2Net), a simple and effective one-stage WSOL framework to explore the ability of structure preservation of deep features. Different from traditional WSOL approaches, we decouple the object localization task from the classification branch to reduce their mutual influence by involving a localization branch which is online refined by a self-supervised structural-preserved localization mask. Specifically, we employ the high-order self-correlation as structural prior to enhance the perception of spatial interaction within convolutional features. By succinctly combining the structural prior with spatial attention, activations by SPA2Net will spread from part to the whole object during training. To avoid the structure-missing issue caused by the classification network, we furthermore utilize the restricted activation loss (RAL) to distinguish the difference between foreground and background in the channel dimension. In conjunction with the self-supervised localization branch, SPA2Net can directly predict the class-irrelevant localization map while prompting the network to pay more attention to the target region for accurate localization. Extensive experiments on two publicly available benchmarks, including CUB-200-2011 and ILSVRC, show that our SPA2Net achieves substantial and consistent performance gains compared with baseline approaches. The code and models are available at https://github.com/MsterDC/SPA2Net. [ABSTRACT FROM AUTHOR]

We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e., pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division such that the method can be applied recursively to achieve full diagonalization. The method is well suited for structured matrices that come up in computational quantum physics and chemistry. In this application context, additional definiteness properties guarantee a convergence of the matrix sign function iteration within two steps when Zolotarev functions are used. The steps are easily parallelizable. Rirthermore, it is shown that the matrix decouples into symmetric definite eigenvalue problems after just one step of spectral division. [ABSTRACT FROM AUTHOR]

Computed Tomography (CT) is a widely use medical image modality in clinical medicine, because it produces excellent visualizations of fine structural details of the human body. In clinical procedures, it is desirable to acquire CT scans by minimizing the X-ray flux to prevent patients from being exposed to high radiation. However, these Low-Dose CT (LDCT) scanning protocols compromise the signal-to-noise ratio of the CT images because of noise and artifacts over the image space. Thus, various restoration methods have been published over the past 3 decades to produce high-quality CT images from these LDCT images. More recently, as opposed to conventional LDCT restoration methods, Deep Learning (DL)-based LDCT restoration approaches have been rather common due to their characteristics of being data-driven, high-performance, and fast execution. Thus, this study aims to elaborate on the role of DL techniques in LDCT restoration and critically review the applications of DL-based approaches for LDCT restoration. To achieve this aim, different aspects of DL-based LDCT restoration applications were analyzed. These include DL architectures, performance gains, functional requirements, and the diversity of objective functions. The outcome of the study highlights the existing limitations and future directions for DL-based LDCT restoration. To the best of our knowledge, there have been no previous reviews, which specifically address this topic. [ABSTRACT FROM AUTHOR]

Abstract Cross-domain classification refers to completing the corresponding classification task in a target domain which lacks label information, by exploring useful knowledge in a related source domain but with different data distribution. Domain adaptation can deal with such cross-domain classification, by reducing divergence of domains and transferring the relevant knowledge from the source to the target. To mine the discriminant information of the source domain samples and the geometric structure information of domains, and thus improve domain adaptation performance, this paper proposes a novel method involving distribution matching and structure preservation for domain adaptation (DMSP). First, it aligns the subspaces of the source domain and target domain on the Grassmann manifold; and learns the non-distorted embedded feature representations of the two domains. Second, in this embedded feature space, the empirical structure risk minimization method with distribution adaptation regularization and intra-domain graph regularization is used to learn an adaptive classifier, further adapting the source and target domains. Finally, we perform extensive experiments on widely used cross-domain classification datasets to validate the superiority of DMSP. The average classification accuracy of DMSP on these datasets is the highest compared with several state-of-the-art domain adaptation methods.

In the modern world, due to the consumers’ pace of life and lifestyle, there is a need for production of frozen food products that are ready-to-eat after defrosting or heating. An important task, therewith, is preservation of the micro- and macrostructure of flour products and aerated desserts. The paper presents an analysis of studies of aspects of production and realization of frozen finished products with the preserved micro- and macrostructure. A possibility of positioning aerated fermented dairy desserts as functional products is substantiated. In investigation of this product category, particular emphasis is placed on the role of the nutrient composition (proteins, fats, stabilizers and emulsifiers) and an importance of technological operations (freezing and fermentation). Attention is given to the state of the structural elements in the frozen and defrosted states. Despite the absence of crystals in defrosted desserts, it is necessary to take into account their influence on dispersity of the air phase in a frozen product. It was found that frozen noodles are a common product type in Asian countries and consumption of this product is growing every year. Other flour products (macaroni, bakery and confectionery products) are in demand as fast-food products. A promising direction in production of finished food products is a search for solutions and components for preservation of the product macrostructure. Among important tasks are maintenance of the marketable appearance of a defrosted product, prevention of the ice crystal growth in the frozen state and preservation of the protein structure. An important place in production of macaroni and bakery products is occupied by selection of cryoprotectants — components having an ability to inhibit the ice crystal growth and facilitating preservation of the product macrostructure. An important aspect of frozen product quality is its safety upon defrostation. In particular, the control of microbiological indicators and the related water activity value is necessary.

Cross-domain classification refers to completing the corresponding classification task in a target domain which lacks label information, by exploring useful knowledge in a related source domain but with different data distribution. Domain adaptation can deal with such cross-domain classification, by reducing divergence of domains and transferring the relevant knowledge from the source to the target. To mine the discriminant information of the source domain samples and the geometric structure information of domains, and thus improve domain adaptation performance, this paper proposes a novel method involving distribution matching and structure preservation for domain adaptation (DMSP). First, it aligns the subspaces of the source domain and target domain on the Grassmann manifold; and learns the non-distorted embedded feature representations of the two domains. Second, in this embedded feature space, the empirical structure risk minimization method with distribution adaptation regularization and intra-domain graph regularization is used to learn an adaptive classifier, further adapting the source and target domains. Finally, we perform extensive experiments on widely used cross-domain classification datasets to validate the superiority of DMSP. The average classification accuracy of DMSP on these datasets is the highest compared with several state-of-the-art domain adaptation methods. [ABSTRACT FROM AUTHOR]

Low-dose computed tomography (LDCT) has been widely used for various clinic applications to reduce the X-ray dose absorbed by patients. However, LDCT is usually degraded by severe noise over the image space. The image quality of LDCT has attracted aroused attentions of scholars. In this study, we propose the bilateral weighted relative total variation (BRTV) used for image restoration to simultaneously maintain edges and further reduce noise, then propose the BRTV-regularized projections onto convex sets (POCS-BRTV) model for LDCT reconstruction. Referring to the spacial closeness and the similarity of gray value between two pixels in a local rectangle, POCS-BRTV can adaptively extract sharp edges and minor details during the iterative reconstruction process. Evaluation indexes and visual effects are used to measure the performances among different algorithms. Experimental results indicate that the proposed POCS-BRTV model can achieve superior image quality than the compared algorithms in terms of the structure and texture preservation. [ABSTRACT FROM AUTHOR]

Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we present a framework for structurepreserving MOR, which allows us to compute structured reduced order models (ROMs) with a much higher accuracy. The framework is based on parameter optimization, i.e., the elements of the system matrices of the ROM are iteratively varied to minimize an objective functional that measures the difference between the FOM and the ROM. The structural constraints can be encoded in the parametrization of the ROM. The method only depends on frequency response data and can thus be applied to a wide range of dynamical systems. We illustrate the effectiveness of our method on a port-Hamiltonian and on a symmetric second-order system in a comparison with other structurepreserving MOR algorithms. [ABSTRACT FROM AUTHOR]

When solving Hamiltonian systems using numerical integrators, preserving the symplectic structure may be crucial for many problems. At the same time, solving chaotic or stiff problems requires integrators to approximate the trajectories with extreme precision. So, integrating Hamilton's equations to a level of scientific reliability such that the answer can be used for scientific interpretation, may be computationally expensive. However, a neural network can be a viable alternative to numerical integrators, offering high-fidelity solutions orders of magnitudes faster. To understand whether it is also important to preserve the symplecticity when neural networks are used, we analyze three well-known neural network architectures that are including the symplectic structure inside the neural network's topology. Between these neural network architectures many similarities can be found. This allows us to formulate a new, generalized framework for these architectures. In the generalized framework Symplectic Recurrent Neural Networks, SympNets and HénonNets are included as special cases. Additionally, this new framework enables us to find novel neural network topologies by transitioning between the established ones. We compare new Generalized Hamiltonian Neural Networks (GHNNs) against the already established SympNets, HénonNets and physics-unaware multilayer perceptrons. This comparison is performed with data for a pendulum, a double pendulum and a gravitational 3-body problem. In order to achieve a fair comparison, the hyperparameters of the different neural networks are chosen such that the prediction speeds of all four architectures are the same during inference. A special focus lies on the capability of the neural networks to generalize outside the training data. The GHNNs outperform all other neural network architectures for the problems considered. • Three different neural network architectures for Hamiltonian systems can be united. • Comparison of neural networks with similar computational costs is important. • A newly introduced neural network architecture can outperform all others. • Not only the number of trainable parameters is important, but also their structure. • Structure-preservation greatly improves the generalization outside of training data. [ABSTRACT FROM AUTHOR]

As an effective strategy for reducing the noisy and redundant information for hyperspectral imagery (HSI), hyperspectral band selection intends to select a subset of original hyperspectral bands, which boosts the subsequent different tasks. In this paper, we introduce a multi-dimensional high-order structure preserved clustering method for hyperspectral band selection, referred to as MHSPC briefly. By regarding original hyperspectral images as a tensor cube, we apply the tensor CP (CANDECOMP/PARAFAC) decomposition on it to exploit the multi-dimensional structural information as well as generate a low-dimensional latent feature representation. In order to capture the local geometrical structure along the spectral dimension, a graph regularizer is imposed on the new feature representation in the lower dimensional space. In addition, since the low rankness of HSIs is an important global property, we utilize a nuclear norm constraint on the latent feature representation matrix to capture the global data structure information. Different to most of previous clustering based hyperspectral band selection methods which vectorize each band as a vector without considering the 2-D spatial information, the proposed MHSPC can effectively capture the spatial structure as well as the spectral correlation of original hyperspectral cube in both local and global perspectives. An efficient alternatively updating algorithm with theoretical convergence guarantee is designed to solve the resultant optimization problem, and extensive experimental results on four benchmark datasets validate the effectiveness of the proposed MHSPC over other state-of-the-arts. [ABSTRACT FROM AUTHOR]

The model reduction problem in the Loewner framework for port-Hamiltonian and network systems on graphs is studied. In particular, given a set of right-tangential interpolation data, the (subset of) left-tangential interpolation data that allow constructing an interpolant possessing a port-Hamiltonian structure is characterized. In addition, conditions under which an interpolant retains the underlying port-Hamiltonian structure of the system generating the data are given by requiring a particular structure of the generalized observability matrix. Ipso facto a characterization of the reduced order model in terms of Dirac structure with the aim of relating the Dirac structure of the underlying port-Hamiltonian system with the Dirac structure of the constructed interpolant is given. This result, in turn, is used to solve the model reduction problem in the Loewner framework for network systems described by a weighted graph. The problem is first solved, for a given clustering, by giving conditions on the right- and left-tangential interpolation data that yield an interpolant possessing a network structure. Thereafter, for given tangential data obtained by sampling an underlying network system, we give conditions under which we can select a clustering and construct a reduced model preserving the network structure. Finally, the results are illustrated by means of a second order diffusively coupled system and a first order network system. [ABSTRACT FROM AUTHOR]

Parallax processing has long been a significant and challenging task in image stitching. In this paper, we study a new hybrid warping model based on multi-homography and structure preservation to achieve accurate alignment of regions at different depths while preserving local and global image structures. The homographies of different depth regions are estimated by dividing matching feature pairs into multiple layers. Then, layered warping is performed by determining the spatial relationships between the image mesh and these multi-homography, and then refining the local and global structural distortions through mesh optimization. Four constraints are considered during the local optimization process, including the local alignment error, global alignment error, and similarity error. In addition, we explore and introduce collinear structures into an objective function as a constraint for mesh optimization warping, which can preserve salient line structures while alleviating distortions in nonoverlapping areas. Furthermore, we develop an optimal seam search method based on seam error evaluation to improve the quality of the seams. Experimental results demonstrate that compared to existing methods, the proposed algorithm presents more accurate stitching results for images with large parallax and preserves salient image structures, and outperforming the existing methods both qualitatively and quantitatively.

Cross-scene knowledge transfer has been proven effective to deal with the small-sample problem in hyperspectral image (HSI) classification. Currently, most of the existing works are based on the homogeneous settings where the source and target HSIs are observed from the same feature space, while the heterogeneous situation, which is more common in real-world applications, is under insufficient exploration. In this article, we propose a novel transfer learning approach for HSI classification, which is capable of transferring discriminative spectral-spatial feature between heterogeneous datasets. Specifically, we first extract spectral-spatial features of source and target scenes by applying the multiscale convolutional sparse decomposition (MCSD) method. By performing MCSD, the spectral information and spatial structure information at different scales can be jointly adapted to learn transferable features for classification. Then, in order to overcome the heterogeneity between the two feature sets, we build a structure preserved distribution alignment (SPDA) model to learn domain-specific projections to map the feature samples into a shared latent subspace where the discriminative knowledge can be effectively transferred. With proper reformulation, we give the analytical solution of the objective function and generate an optimization approach to solve the SPDA model efficiently. Experiments conducted on several real data pairs demonstrate that the proposed approach can explicitly narrow the disparity between heterogeneous HSIs, and yield superior classification results compared with other representative heterogeneous transfer learning methods.

Domain adaptation (DA) aims at facilitating the target model training by leveraging knowledge from related but distribution-inconsistent source domain. Most of the previous DA works concentrate on homogeneous scenarios, where the source and target domains are assumed to share the same feature space. Nevertheless, frequently, in reality, the domains are not consistent in not only data distribution but also the representation space and feature dimensions. That is, these domains are heterogeneous. Although many works have attempted to handle such heterogeneous DA (HDA) by transforming HDA to homogeneous counterparts or performing DA jointly with domain transformation, nearly all of them just concentrate on the feature and distribution alignment across domains, neglecting the structure and classification space preservation for domains themselves. In this work, we propose a novel HDA model, namely, heterogeneous classification space alignment (HCSA), which leverages knowledge from both the source samples and model parameters to the target. In HCSA, structure preservation, distribution, and classification space alignment are implemented, jointly with feature representation by transferring both the source-domain representation and model knowledge. Moreover, we design an alternating algorithm to optimize the HCSA model with guaranteed convergence and complexity analysis. In addition, the HCSA model is further extended with deep network architecture. Finally, we experimentally evaluate the effectiveness of the proposed method by showing its superiority to the compared approaches. [ABSTRACT FROM AUTHOR]

This paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy discrete counterparts of these conditions have conservation laws that approximate the continuous ones. On the basis of this result, we derive conservation laws for a mixed scheme that combines a finite difference method in space with a spectral integrator in time. A range of numerical experiments shows the convergence of the proposed method and its conservation properties. [ABSTRACT FROM AUTHOR]

There are a lot of redundant and irrelevant features in high-dimensional data,which seriously affect the efficiency and quality of data mining and the generalization performance of machine learning.Therefore,feature selection has become an important research direction in the computer field.In this paper,an unsupervised feature selection algorithm is proposed by using the non-linear learning ability of the autoencoder.First,based on the reconstruction error of the autoencoder,a single feature is selec-ted which is important for data reconstruction.Second,the feature weights finally select the feature subsets that contribute greatly to the reconstruction of other features.Manifold learning is introduced to capture the local and non-local structure of the original data space,and L2/1 sparse regularization is added to the feature weights to improve the sparsity of the feature weights so that they can select more distinctive features.Finally,a new objective function is constructed,and a gradient descent algorithm is used to optimize the proposed objective function.Experiments on six different types of typical data sets,and the proposed algorithm is compared with five commonly used unsupervised feature selection algorithms.Experiment results verify that the proposed algorithm can effectively select important features,significantly improve the classification accuracy rate and clustering accuracy rate.

Graph convolutional network has emerged as a focal point in machine learning because of its robust graph processing capability. Most existing graph convolutional network-based approaches are designed for single-view data, yet in many practical scenarios, data is represented through multiple views. Moreover, due to the complexity of multiple views, normal graph generation methods cannot mitigate redundancy to generate a high quality graph. Although the ability of graph convolutional network is undeniable, the quality of graph directly affects its performance. To tackle the aforementioned challenges, this paper proposes a multi-scale graph generation deep learning framework, called multi-scale semi-supervised graph generation based multi-view classification, consisting of two modules: edge sampling and path sampling. The former aims to generate an adjacency graph by selecting edges based on the maximum likelihood among graphs from different views. Meanwhile, the latter seeks to construct an adjacency graph according to the characteristics of paths within the graphs. Finally, the statistical technique is employed to extract commonality and generate a fused graph. Extensive experimental results robustly demonstrate the superior performance of our proposed framework, compared to other state-of-the-art multi-view semi-supervised approaches. • Two alternative sampling methods are provided to collect the structural information, and then a statistical technique is employed to generate a fused graph. • An efficient graph generation framework has been developed to construct graphs in multi-view learning. • Comprehensive evaluations of six real-world datasets show the superiority of the proposed framework. [ABSTRACT FROM AUTHOR]

Low-quality (LQ) images often lead to difficulties in the screening and diagnosis of medical diseases. Unsupervised generative adversarial networks (GAN)-based image enhancement methods offer promising solutions. However, there is a quality-originality trade-off in that they produce visually pleasing results but fail to reserve the originality, especially the structural inputs. Moreover, objectively evaluating structure preservation for unsupervised medical image enhancement tasks (i.e., without reference images) is essential. In this study, we propose (1) Laplacian structural similarity index measure (LaSSIM) - a non-reference objective structure preservation evaluation for unsupervised medical image enhancement methods; and (2) a novel unsupervised GAN-based method called Laplacian medical image enhancement (LaMEGAN) to balance both originality and quality from LQ images. The proposed LaSSIM does not require clean reference images and is superior to SSIM in capturing image structural changes under image degradations, such as strong blurring on various image datasets. Experiments demonstrate that our LaMEGAN effectively balances the quality and originality trade-off. Compared to CycleGAN, which achieves superior quality scores but lacks in structure preservation, LaMEGAN outperforms significantly in structure preservation, scoring 4.05 compared to 3.58 on the mean doctor opinion score (MDOS). Additionally, LaMEGAN produces visually appealing images with quality scores close to CycleGAN in all eight evaluation metrics. The implementation code will be available at https://github.com/AillisInc/USPMIE. • Proposing a non-reference structure preservation evaluation method (LaSSIM), and a novel unsupervised medical image enhancement method (LaMEGAN) to balance the quality-originality trade-off from low-quality images. • LaSSIM outperforms SSIM in capturing image structural changes under degradations across diverse datasets, without the need for clean reference images. • LaMEGAN surpasses CycleGAN in terms of structure preservation while achieving high quality scores under eight evaluation metrics in the throat image enhancement task. [ABSTRACT FROM AUTHOR]

We introduce an efficient structure-preserving model-order reduction technique for the large-scale second-order linear dynamical systems by imposing two-sided projection matrices. The projectors are formed based on the features of the singular value decomposition (SVD) and Krylov-based model-order reduction methods. The left projector is constructed by utilizing the concept of the observability Gramian of the systems and the right one is made by following the notion of the interpolation-based technique iterative rational Krylov algorithm (IRKA). It is well-known that the proficient model-order reduction technique IRKA cannot ensure system stability, and the Gramian based methods are computationally expensive. Another issue is preserving the second-order structure in the reduced-order model. The structure-preserving model-order reduction provides a more exact approximation to the original model with maintaining some significant physical properties. In terms of these perspectives, the proposed method can perform better by preserving the second-order structure and stability of the system with minimized $ \mathcal{H}_2 $-norm. Several model examples are presented that illustrated the capability and accuracy of the introducing technique.

Abstract Computed Tomography (CT) is a widely use medical image modality in clinical medicine, because it produces excellent visualizations of fine structural details of the human body. In clinical procedures, it is desirable to acquire CT scans by minimizing the X-ray flux to prevent patients from being exposed to high radiation. However, these Low-Dose CT (LDCT) scanning protocols compromise the signal-to-noise ratio of the CT images because of noise and artifacts over the image space. Thus, various restoration methods have been published over the past 3 decades to produce high-quality CT images from these LDCT images. More recently, as opposed to conventional LDCT restoration methods, Deep Learning (DL)-based LDCT restoration approaches have been rather common due to their characteristics of being data-driven, high-performance, and fast execution. Thus, this study aims to elaborate on the role of DL techniques in LDCT restoration and critically review the applications of DL-based approaches for LDCT restoration. To achieve this aim, different aspects of DL-based LDCT restoration applications were analyzed. These include DL architectures, performance gains, functional requirements, and the diversity of objective functions. The outcome of the study highlights the existing limitations and future directions for DL-based LDCT restoration. To the best of our knowledge, there have been no previous reviews, which specifically address this topic.

We present a novel numerical method for solving ODEs while preserving polynomial first integrals. The method is based on introducing multiple quadratic auxiliary variables to reformulate the ODE as an equivalent but higher-dimensional ODE with only quadratic integrals to which the midpoint rule is applied. The quadratic auxiliary variables can subsequently be eliminated yielding a midpoint-like method on the original phase space. The resulting method is shown to be a novel discrete gradient method. Furthermore, the averaged vector field method can be obtained as a special case of the proposed method. The method can be extended to higher-order through composition and is illustrated through a number of numerical examples. [ABSTRACT FROM AUTHOR]