Inverse Operation Research Articles

Enhanced Compression Medical Image Speed for Computed Radiography

In recent years, there has been a significant surge in the volume of medical imaging data. This surge poses challenges for the functioning of PACS communication systems and image archiving. The most effective solution to address this issue involves compressing images through digital encryption, which optimally utilizes storage space. This process involves reformatting the imaging data by reducing redundancy, leading to image compression. While this reduction in redundancy is readily apparent in individual images, there is a vulnerability in these methods that tends to overlook a source of repetition present in similar stored images. To emphasize this common occurrence, we introduce the term "redundancy group." Similar images are frequently encountered within medical image databases, resulting in a considerable redundancy reduction. In this paper, our focus is on enhancing the control of redundancy extraction in the data used, specifically medical images. To enhance the compression efficiency of standard image compression, we employ improved methods, namely MinMax Predictive (MMP) and Min-Max Differential (MMD). Our experiments demonstrate that these methods lead to a substantial enhancement in brain CT compression, with potential improvements of up to 130% when using Huffman coding. Similar improvements are observed in arithmetic coding, with a 94% improvement compared to the number-arithmetic code and a 37% improvement compared to the Lempel-Ziv compression. These improvements occur when combining the MMP technology with the MMD technology, utilizing inverse operations that result in lossless compression.

Modeling relationships in non-commutative two-operand two-bit cet-operations of a double cycle when permuting the operands

The object of the research is relationships in non-commutative two-operand two-bit CET-operations of a double cycle when operands are permuted. The article is devoted to studying the results of the computational experiment, which is in building a model of relationships in non-commutative two-operand two-bit CET-operations of a double cycle with the operands permutation in order to ensure the possibility of building cryptographic systems with XOR sequence encryption. The theoretical and practical results of the work are obtained on the basis of the computational experiment data. The results of researching the CET-operations data make it possible to build cryptographic systems with XOR sequence ciphering and to improve the quality of low-resource stream encryption systems. The mathematical description of the computational experiment results made it possible to establish relationships between pairs of non-commutative two-operand two-bit CET-operations of a double cycle when operands are permuted. The possibility of constructing a group of commutative two-operand two-bit CET-operations of a double cycle based on the modification of a known two-operand operation by one-operand operations to within the permutation of the crypto-transformation results has been studied. The correctness of constructing a group of CET-operations, both without operand permutation and such that allow operand permutation, has been verified. The model for building a group of asymmetric two-operand two-bit CET-operations of a double cycle, which allow the operands permutation is proposed. Applying the substitution model made it possible to obtain pairs of interrelated operations in this group. The obtained pairs of interconnected operations provide a description of modification for direct and inverse non-commutative CET operations when permuting the operands. The obtained results provide the possibility of building cryptographic systems that encrypt both the input open information under the control of the XOR sequence and the XOR sequence under the control of the input open information. Further research will be aimed at establishing relationships in non-commutative two-operand two-bit CET operations of the triple cycle when operands are permuted.

An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws

High order accuracy fast sweeping methods have been developed in the literature to efficiently solve steady state solutions of hyperbolic partial differential equations (PDEs) on rectangular meshes, while they were not available yet on unstructured meshes. In this paper, we extend high order accuracy fast sweeping methods to unstructured triangular meshes by applying fixed-point iterative sweeping techniques to a fifth-order finite volume unstructured WENO scheme, for solving steady state solutions of hyperbolic conservation laws. Similar as other fast sweeping methods, fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady state solutions. An advantage of fixed-point fast sweeping methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems. This also provides certain convenience in designing high order fast sweeping methods on unstructured meshes. As in the first order fast sweeping methods on triangular meshes, we introduce multiple reference points to determine alternating sweeping directions on unstructured meshes. All the cells on the mesh are ordered according to their centroids' distances to those reference points, and the resulted orderings provide sweeping directions for iterations. To make the residue of the fast sweeping iterations converge to machine zero / round off errors, we follow the approach in our early work of developing the absolutely convergent fixed-point fast sweeping WENO methods on rectangular meshes, and adopt high order WENO scheme with unequal-sized sub-stencils, specifically here a fifth-order finite volume unstructured WENO scheme for spatial discretization. Extensive numerical experiments, including problems with complex domain geometries, are performed to show the accuracy, computational efficiency, and absolute convergence of the presented fifth-order fast sweeping scheme on triangular meshes. Furthermore, the proposed method is compared with the forward Euler time marching method and the popular third order total variation diminishing Rung-Kutta (TVD-RK3) time-marching method for steady state computations. Numerical examples show that the developed fixed-point fast sweeping WENO method is the most efficient scheme among them, and especially it can save up to 70% CPU time costs than TVD-RK3 in order to converge to steady state solutions.

Robust reversible watermarking of JPEG images

Robust reversible watermarking (RRW) is a potential technology for copyright protection and integrity authentication due to its ability in both robustness and reversibility. Currently, there is no detailed report on RRW of JPEG images. In this paper, we propose an RRW algorithm of JPEG images by selecting quantized discrete cosine transform coefficients to construct robust features for watermarking. In the proposed algorithm, a watermark sequence can be embedded into a JPEG image by shifting the histogram of its constructed robust features. For less embedding distortion, smaller file size, and higher structural similarity, an evaluation method has been designed to select those appropriate frequency bands for watermarking. On the receiver side, the watermark can be accurately extracted by reconstructing the robust features, and the original JPEG image can be restored losslessly by performing the inverse operation of the histogram shifting. Experimental results show that the watermark is robust to common image processing operations (e.g., JPEG recompression, JPEG2000 compression, WebP compression, and additive white Gaussian noise), and can effectively resist those attacks from the lossy channels in real life, such as the most popular apps Instagram and WeChat.

Matrix‐based implementation and GPU acceleration of hybrid FEM and peridynamic model for hydro‐mechanical coupled problems

AbstractThe hybrid finite element‐peridynamic (FEM‐PD) models have been evidenced for their exceptional ability to address hydro‐mechanical coupled problems involving cracks. Nevertheless, the non‐local characteristics of the PD equations and the required inversion operations when solving fluid equations result in prohibitively high computational costs. In this paper, a fast explicit solution scheme for FEM‐PD models based on matrix operation is introduced, where the graphics processing units (GPUs) are used to accelerate the computation. An in‐house software is developed in MATLAB in both CPU and GPU versions. We first solve a problem related to pore pressure distribution in a single crack, demonstrating the accuracy of the proposed method by a comparison of FEM‐PD solutions with those of PD‐only models and analytical solutions. Subsequently, several examples are solved, including a one‐dimensional dynamic consolidation problem and the fluid‐driven hydraulic fracture propagation problems in both 2D and 3D cases, to comprehensively validate the effectiveness of the proposed methods in simulating deformation and fracture in saturated porous media under the influence of hydro‐mechanical coupling. In the presented numerical results, some typical strong dynamic phenomena, such as stepwise crack advancement, crack branching, and pressure oscillations, are observed. In addition, we compare the wall times of all the cases executed on both the GPU and CPU, highlighting the substantial acceleration performance of the GPU, particularly when tackling problems with a significant computational workload.

Parallel processing model for low-dose computed tomography image denoising

Low-dose computed tomography (LDCT) has gained increasing attention owing to its crucial role in reducing radiation exposure in patients. However, LDCT-reconstructed images often suffer from significant noise and artifacts, negatively impacting the radiologists’ ability to accurately diagnose. To address this issue, many studies have focused on denoising LDCT images using deep learning (DL) methods. However, these DL-based denoising methods have been hindered by the highly variable feature distribution of LDCT data from different imaging sources, which adversely affects the performance of current denoising models. In this study, we propose a parallel processing model, the multi-encoder deep feature transformation network (MDFTN), which is designed to enhance the performance of LDCT imaging for multisource data. Unlike traditional network structures, which rely on continual learning to process multitask data, the approach can simultaneously handle LDCT images within a unified framework from various imaging sources. The proposed MDFTN consists of multiple encoders and decoders along with a deep feature transformation module (DFTM). During forward propagation in network training, each encoder extracts diverse features from its respective data source in parallel and the DFTM compresses these features into a shared feature space. Subsequently, each decoder performs an inverse operation for multisource loss estimation. Through collaborative training, the proposed MDFTN leverages the complementary advantages of multisource data distribution to enhance its adaptability and generalization. Numerous experiments were conducted on two public datasets and one local dataset, which demonstrated that the proposed network model can simultaneously process multisource data while effectively suppressing noise and preserving fine structures. The source code is available at https://github.com/123456789ey/MDFTN.

A cascaded bit-weighted distribution matching for LDPC-coded PS-64QAM DMT in a high-speed Unamplified IM-DD system

We experimentally demonstrate the generation and transmission of probabilistic shaping (PS) 64-ary quadrature amplitude modulation (64-QAM) discrete multi-tone (DMT) signal with low-density parity-check (LDPC)-coded modulation based on two-stage bit-weighted distribution matching (TS-BWDM) in a high-speed unamplified intensity modulation and direct detection system. The TS-BWDM scheme is based on a two-stage bit-weighted inversion algorithm, which has the advantages of no complex multiplication and division operations and low hardware implementation complexity. As the key content of TS-BWDM, before FEC coding, the bit-weighted intervention operation is used to change the bit probability of a specific sequence in the parallel binary sequence. The two-stage bit-weighted inversion operation and one-stage weight-labeling bit insertion is performed for achieving the target symbol probability distribution. As a result, it does not add a significant amount of extra redundant bits. Additionally, the high-accuracy training symbols-based sampling frequency offset (SFO) estimation method and digital interpolation are used to compensate SFO. In our experiments, the TS-BWDM-based PS-64QAM DMT signals with a net rate of 157.3-Gb/s transmission over 10-km non-zero dispersion- shifted fiber can be achieved. The system performance is investigated under two LDPC code rates (3/4 and 9/10) and three PS parameter values (k = 3, 5 and 9). The experimental results show that the receiver power sensitivity and the system fiber nonlinear effect tolerance can be significantly improved compared with uniformly-distributed signals.

A fast amplitude preserving three-parameter 3D parabolic Radon transform and its application on multiple attenuation

Seismic wavefields propagate through three-dimensional (3D) space, and their precise characterization is crucial for understanding subsurface structures. Traditional 2D algorithms, due to their limitations, are insufficient to fully represent three-dimensional wavefields. The classic 3D Radon transform algorithm assumes that the wavefield's propagation characteristics are consistent in all directions, which often does not hold true in complex underground media. To address this issue, we present an improved 3D three-parameter Radon algorithm that considers the wavefield variation with azimuth and provides a more accurate wavefield description. However, introducing new parameters to describe the azimuthal variation also poses computational challenges. The new Radon transform operator involves five variables and cannot be simply decomposed into small matrices for efficient computation; instead, it requires large matrix multiplication and inversion operations, significantly increasing the computational load. To overcome this challenge, we have integrated the curvature and frequency parameters, simplifying all frequency operators to the same, thereby significantly improving computation efficiency. Furthermore, existing transform algorithms neglect the lateral variation of seismic amplitudes, leading to discrepancies between the estimated multiples and those in the data. To enhance the amplitude preservation of the algorithm, we employ orthogonal polynomial fitting to capture the amplitude spatial variation in 3D seismic data. Combining these improvements, we propose a fast, amplitude-preserving, 3D three-parameter Radon transform algorithm. This algorithm not only enhances computational efficiency while maintaining the original wavefield characteristics, but also improves the representation of seismic data by increasing amplitude fidelity. We validated the algorithm in multiple attenuation using both synthetic and real seismic data. The results demonstrate that the new algorithm significantly improves both accuracy and computational efficiency, providing an effective tool for analyzing seismic wavefields in complex subsurface structures.

Implementing intelligent‐based sparse channel estimation in Multi User‐Multiple Input Multiple Output‐Orthogonal Frequency Division Multiplexing system with hybridized optimization algorithm

SummaryThe channel plays a significant role as the multipath in Multiple Input Multiple Output‐Orthogonal Frequency Division Multiplexing (MIMO‐OFDM) systems. The precoding‐based channel estimation algorithms estimate the channel capacity at the receiver node and they provide efficient channel estimates under worst case channel scenarios. To estimate the channel capacity in the mobile node, semi‐blind scenario is a crucial task in Multi User (MU) MIMO systems. Therefore, a semi blind sparse channel estimation algorithm is demonstrated in the MU‐MIMO system to provide better performance. In the transmitter side, the signal modulation is performed with the help of Quadrature Phase Shift Keying (QPSK), and the modulated signal is given to Pulse Shaping Algorithm (PSA) to reduce the inter‐carrier interference as well as inter symbol interference. At each transmitter, the Inverse Fast Fourier Transforms (IFFT) technique is used for mapping the symbols and then the mapped signal is send to the receiver. In the receiver side, the FFT, pulse reshaping, and QPSK demodulation blocks are serially connected and perform inverse operations of the transmitter in the receiver. Then, the sparse channel is estimated at the receiver by using the semi blind sparse algorithm, where the parameters are optimized by using the Hybridized Drosophila with Virus Colony Search Optimization (HD‐VCSO). The objective function of the developed sparse channel estimation is the reduction of Minimum Mean Square Error (MMSE) in the channel. The performance of the developed sparse channel estimation algorithm is analyzed through different conventional algorithms to validate the effectiveness of the proposed algorithm.

Frequency Offset Estimation for UWB-OFDM System using Weight and Exhaustiveness based Monarch Butterfly Optimization Approach

The performance of an OFDM system has limitation because the carrier frequency offset (CFO) and sampling frequency offset (SFO) is not estimated correctly. Current methods propose the way of obtaining frequency estimation by using the evolutionary algorithm, but the evolution algorithm suffers from the premature convergence problem. In order to provide efficient frequency offset estimation, this paper proposed weight and exhaustiveness based monarch butterfly optimization approach. First, on the transmitter block, for modulating an input symbol, the Hybrid-Quadrature Phase-Shift Keying modulation scheme is used. Brunn’s IFFT is done at each transmitter for symbol mapping and then in each transmitter block cyclic prefix is inserted. After that, WE-MBO algorithm estimates the frequency offset. On receiver side, the inverse operation of the transmitter is performed. After comparison of proposed system with the existing system, the proposed system gave better performance.

Virtual cleaning of sooty murals in ancient temples using twice colour attenuation prior

Murals are artworks painted on walls that represent various cultures, traditions, historical periods, spiritual narratives and civilisations. Unfortunately, before modern preventive measures were implemented, murals suffered considerable degradation from accumulating substances, such as incense oil and carbon, leading to a darkening or blackening phenomenon called soot. The soot severely and extensively damaged the murals’ colour and motifs. However, no highly effective remedy is available to restore them to their original state. A novel approach for virtual cleaning of this degradation uses hyperspectral and image enhancement technologies. Existing techniques for sooty mural image restoration primarily use dark channel prior and Retinex bilateral filtering. During this process, the dark channel prior estimates the concentration of soot and removes it, restoring the mural’s colour with Retinex bilateral filtering. However, this restoration method has issues, such as neglecting the difference between soot and haze, resulting in a generally darker mural image. This result requires brightness adjustment, and the method presents further challenges, such as texture loss, colour distortion in some areas and a reduction in clarity. Therefore, we propose a new technique that integrates an inverse operation and twice colour attenuation prior to cleaning sooty murals. This technique involves normalised cross-correlation to match and stitch images to the different synthesised bands to reconstruct the mural image to be processed, which removes black marks from areas of mural loss. The sooty mural then undergoes an inverse operation, and the colour attenuation prior is used on the inverse image. The processed mural is then inverted again, transforming the colour of soot to white. Finally, the colour attenuation prior is again applied to the colour-changing mural, enabling virtual cleaning of the sooty murals. The results confirm the enhanced adaptability of our novel approach for the virtual cleaning of sooty murals. Moreover, the proposed method exhibits superior performance for various performance parameters.

Hybrid watermarking and encryption techniques for securing three-dimensional information

A hybrid digital watermarking and encryption technique based on the Computer Generated Holography (CGH) and fractional Fourier transform (FRFT) combined with singular value decomposition (SVD) algorithm is proposed for securing three-dimensional (3D) information. Initially, hierarchical 3D information is encrypted using the angular spectrum diffraction method and a random phase key. This process yields a binary real valued CGH, where incorporating a random phase key broadens the key space and adds complexity, effectively scrambling and concealing the 3D information. Subsequently, the encrypted binary real valued CGH is embedded into the host image as a watermark using the FRFT-SVD algorithm. This hybrid approach enhances the security of the watermarking process. In the final step, the CGH watermark is extracted using the inverse operation of the embedding algorithm. Applying the correct optical key and angular spectrum inverse algorithm successfully reconstructs the 3D information. The watermark algorithm’s efficiency significantly improves by leveraging the rapid computational speed and high focusing capabilities of the FRFT. Additionally, integrating SVD enhances the image’s resistance to geometric attacks, thereby improving the algorithm’s invisibility and robustness. The proposed scheme effectively achieves the encryption and digital watermarking of 3D information. Simulation results substantiate the presented watermarking scheme’s efficacy and robustness.

Efficient privacy-preserving Gaussian process via secure multi-party computation

Gaussian processes (GPs), known for their flexibility as non-parametric models, have been widely used in practice involving sensitive data (e.g., healthcare, finance) from multiple sources. With the challenge of data isolation and the need for high-performance models, how to jointly develop privacy-preserving GP for multiple parties has emerged as a crucial topic. In this paper, we propose a new privacy-preserving GP algorithm, namely PP-GP, which employs secret sharing (SS) techniques. Specifically, we introduce a new SS-based exponentiation operation (PP-Exp) through confusion correction and an SS-based matrix inversion operation (PP-MI) based on Cholesky decomposition. However, the advantages of the GP come with a great computational burden and space cost. To further enhance the efficiency, we propose an efficient split learning framework for privacy-preserving GP, named Split-GP, which demonstrably improves performance on large-scale data. We leave the private data-related and SMPC-hostile computations (i.e., random features) on data holders, and delegate the rest of SMPC-friendly computations (i.e., low-rank approximation, model construction, and prediction) to semi-honest servers. The resulting algorithm significantly reduces computational and communication costs compared to PP-GP, making it well-suited for application to large-scale datasets. We provide a theoretical analysis in terms of the correctness and security of the proposed SS-based operations. Extensive experiments show that our methods can achieve competitive performance and efficiency under the premise of preserving privacy.

The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations

Trapezoidal positive/negative fuzzy numbers have no single definition; instead, various authors define them in relation to different concepts. This means that arithmetic operations for trapezoidal fuzzy numbers also differ. For the operations of addition, subtraction, and scalar multiplication, there are not many differences; for multiplication, however, there are many differences. In general, multiplication is divided into various cases. For the inverse operation, there is not much to define; in general, for any trapezoidal fuzzy number u~, u~⊗1u~=i~=(1,1,0,0) does not necessarily apply. As a result of the different arithmetic operations for multiplication and division employed by various authors, several researchers have tackled the same problem and reached different solutions, meaning that the application will also produce different results. To date, many authors have proposed various alternatives for the algebra of the trapezoidal fuzzy number. In this paper, using the parametric form approach to trapezoidal fuzzy numbers, an alternative to multiplication with only one formula is constructed for various cases. Furthermore, based on the definition of multiplication for any trapezoidal fuzzy number, u~ is constructed 1u~ so that u~⊗1u~=i~=(1,1,0,0). Based on these conditions, we show that various properties that apply to real numbers also apply to any trapezoidal fuzzy number. Furthermore, we modify the elementary row operational steps for the trapezoidal fuzzy number matrix, which can be used to determine the inverse of a trapezoidal fuzzy number matrix with the order m×m. We also give the steps and examples necessary to determine the general inverse for a trapezoidal fuzzy number matrix of the order m×n with m ≠n. This ability to easily determine the inverse and general inverse of a trapezoidal fuzzy number matrix has a number of applications, such as solving fully trapezoidal fuzzy number linear systems and fuzzy transportation problems, especially in applications in fields outside of mathematics; for example, the application of triangular fuzzy numbers in medical problems is a topic currently receiving a significant amount of attention.

Inverse Calculation and Regularization Process for the Solar Aspect System (SAS) of HXI Payload on ASO-S Spacecraft

For the ASO-S/HXI payload, the accuracy of the flare reconstruction is reliant on important factors such as the alignment of the dual grating and the precise measurement of observation orientation. To guarantee optimal functionality of the instrument throughout its life cycle, the Solar Aspect System (SAS) is imperative to ensure that measurements are accurate and reliable. This is achieved by capturing the target motion and utilizing a physical model-based inversion algorithm. However, the SAS optical system’s inversion model is a typical ill-posed inverse problem due to its optical parameters, which results in small target sampling errors triggering unacceptable shifts in the solution. To enhance inversion accuracy and make it more robust against observation errors, we suggest dividing the inversion operation into two stages based on the SAS spot motion model. First, the as-rigid-as-possible (ARAP) transformation algorithm calculates the relative rotations and an intermediate variable between the substrates. Second, we solve an inversion linear equation for the relative translation of the substrates, the offset of the optical axes, and the observation orientation. To address the ill-posed challenge, the Tikhonov method grounded on the discrepancy criterion and the maximum a posteriori (MAP) method founded on the Bayesian framework are utilized. The simulation results exhibit that the ARAP method achieves a solution with a rotational error of roughly ±3.″5 (1/2-quantile); both regularization techniques are successful in enhancing the stability of the solution, the variance of error in the MAP method is even smaller—it achieves a translational error of approximately ±18 μm (1/2-quantile) in comparison to the Tikhonov method’s error of around ±24 μm (1/2-quantile). Furthermore, the SAS practical application data indicates the method’s usability in this study. Lastly, this paper discusses the intrinsic interconnections between the regularization methods.

Lookup Table-Based Design of Scalar Multiplication for Elliptic Curve Cryptography

This paper is aimed at using a lookup table method to improve the scalar multiplication performance of elliptic curve cryptography. The lookup table must be divided into two polynomials and requires two iterations of point doubling operation, for which negation operations are needed. It is well known that an inversion operation requires a lot of multiplication time. The advantage of this paper is that we are able to reduce one inverse element calculation for this problem and also improve the basic operations of finite fields through segmentation methods. If the normal basis method is used in the design of the inverse element operation, it must be converted to the normal basis through the standard basis. However, the conversion process requires a lot of matrix operations. Though the anti-element operation has good speed performance, it also increases the computational complexity. Using number theory and grouping methods will greatly improve the performance of inverse element operations. With application of the two-time point doubling operation in the hardware implementation, the developed approach reduces the computing time by 48% as compared with the conventional approach. The computational time of the scalar multiplication using the presented method is further improved by 67% over the traditional algorithm with only an area increase of 12%. Finally, the proposed lookup table-based technique can be utilized for software and hardware implementation, as the developed arithmetic operations are simple and are consistent in their execution.

Fixed-structure parameter-dependent state feedback controller: A scaled autonomous vehicle path-tracking application

This paper introduces theoretical conditions for the computation of a novel type of state-feedback controller that makes use of Linear Parameter Varying approaches for synthesis. The novelty of this new State-Feedback controller lies on the fact that the controller has a fixed structure with constants matrix gains. However, the controller gains are affine on a parameter dependent basis function, which allows the controller to self-schedule according to real-time changes of the varying parameters. This type of controller is conceived with a focus on implementation, as in contrast with most other LPV approaches. The implementation of this Parameter-Dependent State-Feedback controller does not require any online interpolation or matrix inverse operations, independently of the number of varying parameters. The performance of the proposed approach is validated in a Scaled Autonomous Vehicle for steering control in a path tracking application.

Wiener Filter Using the Conjugate Gradient Method and a Third-Order Tensor Decomposition

In linear system identification problems, the Wiener filter represents a popular tool and stands as an important benchmark. Nevertheless, it faces significant challenges when identifying long-length impulse responses. In order to address the related shortcomings, the solution presented in this paper is based on a third-order tensor decomposition technique, while the resulting sets of Wiener–Hopf equations are solved with the conjugate gradient (CG) method. Due to the decomposition-based approach, the number of coefficients (i.e., the parameter space of the filter) is greatly reduced, which results in operating with smaller data structures within the algorithm. As a result, improved robustness and accuracy can be achieved, especially in harsh scenarios (e.g., limited/incomplete sets of data and/or noisy conditions). Besides, the CG-based solution avoids matrix inversion operations, together with the related numerical and complexity issues. The simulation results are obtained in a network echo cancellation scenario and support the performance gain. In this context, the proposed iterative Wiener filter outperforms the conventional benchmark and also some previously developed counterparts that use matrix inversion or second-order tensor decompositions.

Nonintrusive Operator Inference for Chaotic Systems

This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in reduced space without having access to the full order operators appearing in discretized models. Datasets for the physics systems are generated using conventional numerical solvers and then projected to a low-dimensional space via Principal Component Analysis (PCA). In latent space, a least-squares problem is set to fit a quadratic polynomial operator, which is subsequently employed in a time-integration scheme in order to produce extrapolations in the same space. Once solved, the inverse PCA operation is applied to reconstruct the extrapolations in the original space. The quality of the OpInf predictions is assessed via the Normalized Root Mean Squared Error (NRMSE) metric from which the Valid Prediction Time (VPT) is computed. Numerical experiments considering the chaotic systems Lorenz 96 and the Kuramoto-Sivashinsky equation show promising forecasting capabilities of the OpInf reduced order models with VPT ranges that outperform state-of-the-art machine learning (ML) methods such as backpropagation and reservoir computing recurrent neural networks [1], as well as Markov neural operators [2].

A quantum blind signature scheme based on dense coding for non-entangled states

In some schemes, quantum blind signatures require the use of difficult-to-prepare multiparticle entangled states. By considering the communication overhead, quantum operation complexity, verification efficiency and other relevant factors in practical situations, this article proposes a non-entangled quantum blind signature scheme based on dense encoding. The information owner utilizes dense encoding and hash functions to blind the information while reducing the use of quantum resources. After receiving particles, the signer encrypts the message using a one-way function and performs a Hadamard gate operation on the selected single photon to generate the signature. Then the verifier performs a Hadamard gate inverse operation on the signature and combines it with the encoding rules to restore the message and complete the verification. Compared with some typical quantum blind signature protocols, this protocol has strong blindness in privacy protection, and higher flexibility in scalability and application. The signer can adjust the signature operation according to the actual situation, which greatly simplifies the complexity of the signature. By simultaneously utilizing the secondary distribution and rearrangement of non-entangled quantum states, a non-entangled quantum state representation of three bits of classical information is achieved, reducing the use of a large amount of quantum resources and lowering implementation costs. This improves both signature verification efficiency and communication efficiency while, at the same time, this scheme meets the requirements of unforgeability, non-repudiation, and prevention of information leakage.