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When scanning a document printed on both sides by using an electronic scanner, the printed material on the back (front) side may be transmitted to the front (back) side. This phenomenon is called show-through. The problem to remove the show-through from scanned images is called the show-through removal in the literature. In this paper, we propose a new method of show-through removal based on the following principle. The proposed method uses two scanned images with the front side and with the back side as input images. The proposed method is based on Ahmed's Blind Image Deconvolution method discovered in 2013, which succeeded in formulating Blind Image Deconvolution as a nuclear norm minimization. Since the structure of show-through removal resembles that of Blind Image Deconvolution, we discovered that the show-through removal can be reformulated into a nuclear norm minimization in the space of outer product matrix constructed from an image vector and a point spread function vector of blurring. Using this key idea, we constructed the proposed method as follows. First, our cost function consists of the following three terms. The first term is the data term and the second term is the nuclear norm derived from the above reformulation. The third term is a regularization term to overcome the underdetermined nature of show-through removal problem and the existence of noise in the measured images. The regularization term consists of Total Variation imposed on the images. The resulting nuclear norm minimization problem is solved by using Accelerated Proximal Gradient method and Singular Value Projection with some problem-specific modifications, which converges fast and requires a simple implementation. We show results of simulation studies as well as results of real image experiments to demonstrate the performances of the proposed method. [ABSTRACT FROM AUTHOR]

Detecting small targets and handling target occlusion and overlap are critical challenges in weld defect detection. In this paper, we propose the S-YOLO model, a novel weld defect detection method based on the YOLOv8-nano model and several mathematical techniques, specifically tailored to address these issues. Our approach includes several key contributions. Firstly, we introduce omni-dimensional dynamic convolution, which is sensitive to small targets, for improved feature extraction. Secondly, the NAM attention mechanism enhances feature representation in the region of interest. NAM computes the channel-wise and spatial-wise attention weights by matrix multiplications and element-wise operations, and then applies them to the feature maps. Additionally, we replace the SPPF module with a context augmentation module to improve feature map resolution and quality. To minimize information loss, we utilize Carafe upsampling instead of the conventional upsampling operations. Furthermore, we use a loss function that combines IoU, binary cross-entropy, and focal loss to improve bounding box regression and object classification. We use stochastic gradient descent (SGD) with momentum and weight decay to update the parameters of our model. Through rigorous experimental validation, our S-YOLO model demonstrates outstanding accuracy and efficiency in weld defect detection. It effectively tackles the challenges of small target detection, target occlusion, and target overlap. Notably, the proposed model achieves an impressive 8.9% improvement in mean Average Precision (mAP) compared to the native model. [ABSTRACT FROM AUTHOR]

As sensors operating at the edge continue to evolve, the amount of data that edge devices need to process is increasing. Cloud computing methods have been proposed to process complex data on edge devices that are powered by limited resources. However, the existing cloud computing approach, which provides services from servers determined at the compile stage on the edge, is not suitable for the metamorphic edge device proposed in this paper. Therefore, we have realized the operation of metamorphic edge devices by changing the service that accelerates the application in real time according to the surrounding environmental conditions on the edge device. The on-cloud linking approach separates the code for communication from the edge and server into a linkable glue layer. The separated communication code in the linkable glue layer is reconfigured in real time according to the environment of the edge device. To verify the computational acceleration of cloud computing and the real-time service change of the metamorphic edge device, we operated services that perform matrix multiplication operations with one process, two processes, and four processes in parallel on the edge–cloud system based on the on-cloud linking approach. Through the experiments, it was confirmed that the on-cloud linking approach changes the service provided in real time according to changes in external environmental data without changing the code built into the edge. When a square matrix operation with 1000 rows was loaded onto the proposed platform, the size of the code embedded into the edge device decreased by 8.88% and the operation time decreased by 96.7%. [ABSTRACT FROM AUTHOR]

Object detection plays a vital role in remote sensing applications. Although object detection has achieved proud results in natural images, these methods are difficult to be directly applied to remote sensing images. Remote sensing images often have complex backgrounds and small objects, which results in a highly unbalanced distribution of foreground and complex background information. In order to solve the above problems, this paper proposes a multi-head channel and spatial trans-attention (MCSTA) module, which performs remote pixel interaction from the channel and spatial dimensions respectively to complete the attention feature capture function. It is a plug-and-play module that can be easily embedded in any other natural image object detection convolutional neural network, making it quickly applicable to remote sensing images. First, in order to reduce computational complexity and improve feature richness, we use a special linear convolution to obtain three projection features instead of the simple matrix multiplication transformation in Transformer. Second, we obtain trans-attention maps in different dimensions in a manner similar to the self-attention mechanism to capture the interrelationships of features in channels and spaces. In this process, we use a multi-head mechanism to perform parallel operations to improve speed. Furthermore, in order to avoid large-scale matrix operations, we specially designed an attention blocking mode to reduce computer memory usage and increase operation speed. Finally, we embedded the trans-attention module into YOLOv8, added a new detection head and optimized the feature fusion method, thus designing a lightweight small object detection model named TA-YOLO for remote sensing images. It has fewer parameters than the benchmark model YOLOv8, and its mAP on the PASCAL VOC and VisDrone data sets increased by 1.3% and 6.2% respectively. The experimental results prove the powerful function of the trans-attention module and the excellent performance of TA-YOLO. [ABSTRACT FROM AUTHOR]

This paper investigates the one-bit function perturbation (OBFP) impact on the robust set stability of Boolean networks with disturbances (DBNs). Firstly, the dynamics of these networks are converted into the algebraic forms utilizing the semi-tensor product (STP) method. Secondly, OBFP's impact on the robust set stability of DBNs is divided into two situations. Then, by constructing a state set and defining an index vector, several necessary and sufficient conditions to guarantee that a DBN under OBFP can stay robust set stable unchanged are provided. Finally, a biological example is proposed to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Let D be a division ring such that either char(D) ≠ 2, 3 or D is not a field and char(D) ≠ 2. Let R = Mn(D) be the matrix ring over D, where n > 1. Let m, k be fixed invertible elements in R. The main purpose of the paper is to give a description of a bijective additive map f : R → R, satisfying the identity f(x)f(y) = m for every x, y ∈ R with xy = k, which gives a correct version of a result due to Catalano et al. in 2019. [ABSTRACT FROM AUTHOR]

Binary neural networks (BNNs) are variations of artificial/deep neural network (ANN/DNN) architectures that constrain the real values of weights to the binary set of numbers {−1,1}. By using binary values, BNNs can convert matrix multiplications into bitwise operations, which accelerates both training and inference and reduces hardware complexity and model sizes for implementation. Compared to traditional deep learning architectures, BNNs are a good choice for implementation in resource-constrained devices like FPGAs and ASICs. However, BNNs have the disadvantage of reduced performance and accuracy because of the tradeoff due to binarization. Over the years, this has attracted the attention of the research community to overcome the performance gap of BNNs, and several architectures have been proposed. In this paper, we provide a comprehensive review of BNNs for implementation in FPGA hardware. The survey covers different aspects, such as BNN architectures and variants, design and tool flows for FPGAs, and various applications for BNNs. The final part of the paper gives some benchmark works and design tools for implementing BNNs in FPGAs based on established datasets used by the research community. [ABSTRACT FROM AUTHOR]

Kinematic modeling is essential for planning and controlling continuum robot motion. The traditional Denavit Hartenberg (DH) model involves complex matrix multiplication operations, resulting in computationally intensive inverse solutions and trajectory planning. Solving position and orientation changes in continuum robots using the double quaternion rule can reduce computational complexity. However, existing dual quaternion methods are direct equational transformations of DH rules and do not give a complete modeling process. They usually require more interpretability when applying continuum robot kinematic modeling. This paper uses the dual quaternion method to establish a kinematic model of a continuum robot. It uses a two-section continuum robot model to compare the advantages of dual quaternion and traditional modeling methods. In addition, this paper proposes a five-polynomial interpolation algorithm based on the dual quaternion method for trajectory planning of continuum robots. This method accurately models spatial bending and torsional motions of singularity-free continuum robots. [ABSTRACT FROM AUTHOR]

With the development of computer science technology, theory and method of image segmentation are widely used in fish discrimination, which plays an important role in improving the efficiency of fisheries sorting and biodiversity studying. However, the existing methods of fish images segmentation are less accurate and inefficient, which is worthy of in-depth exploration. Therefore, this paper proposes an atrous pyramid GAN segmentation network aimed at increasing accuracy and efficiency. This paper introduces an atrous pyramid structure, and the GAN module is added before the CNN backbone in order to augment the dataset. The Atrous pyramid structure first fuses the input and output of the dilated convolutional layer with a small sampling rate and then feeds the fused features into the subsequent dilated convolutional layer with a large sampling rate to obtain dense multiscale contextual information. Thus, by capturing richer contextual information, this structure improves the accuracy of segmentation results. In addition to the aforementioned innovation, various data enhancement methods, such as MixUp, Mosaic, CutMix, and CutOut, are used in this paper to enhance the model's robustness. This paper also improves the loss function and uses the label smoothing method to prevent model overfitting. The improvement is also tested by extensive ablation experiments. As a result, our model's F1-score, GA, and MIoU were tested on the validation dataset, reaching 0.961, 0.981, and 0.973, respectively. This experimental result demonstrates that the proposed model outperforms all the other contrast models. Moreover, in order to accelerate the deployment of the encapsulated model on hardware, this paper optimizes the execution time of the matrix multiplication method on Hbird E203 based on Strassen's algorithm to ensure the efficient operation of the model on this hardware platform. [ABSTRACT FROM AUTHOR]

Matrix multiplication plays a crucial role in various engineering and scientific applications. Cannon's algorithm, executed within two-dimensional systolic arrays, significantly enhances computational efficiency through parallel processing. However, as the matrix size increases, reliability issues become more prominent. Although the previous work has proposed a fault-tolerant mechanism, it is only suitable for scenarios with a limited number of faulty processing elements (PEs). This paper introduces a pair-matching mechanism, assigning a fault-free PE as a proxy for each faulty PE to execute its tasks. Our fault-tolerant mechanism comprises two stages: in the first stage, each fault-free PE completes its designated computations; in the second stage, computations intended for each faulty PE are executed by its assigned fault-free PE proxy. The experimental results demonstrate that compared to the previous work, our approach not only significantly improves the fault tolerance of systolic arrays (applicable to scenarios with a higher number of faulty PEs) but also reduces circuit areas. Therefore, the proposed approach proves effective in practical applications. [ABSTRACT FROM AUTHOR]

This paper studies the problem of minimizing the total cost, including computation cost and communication cost, in the system of two-sided secure distributed matrix multiplication (SDMM) under an arbitrary collusion pattern. In order to perform SDMM, the two input matrices are split into some blocks, blocks of random matrices are appended to protect the security of the two input matrices, and encoded copies of the blocks are distributed to all computing nodes for matrix multiplication calculation. Our aim is to minimize the total cost, overall matrix splitting factors, number of appended random matrices, and distribution vector, while satisfying the security constraint of the two input matrices, the decodability constraint of the desired result of the multiplication, the storage capacity of the computing nodes, and the delay constraint. First, a strategy of appending zeros to the input matrices is proposed to overcome the divisibility problem of matrix splitting. Next, the optimization problem is divided into two subproblems with the aid of alternating optimization (AO), where a feasible solution can be obtained. In addition, some necessary conditions for the problem to be feasible are provided. Simulation results demonstrate the superiority of our proposed scheme compared to the scheme without appending zeros and the scheme with no alternating optimization. [ABSTRACT FROM AUTHOR]

A locally repairable code (LRC) is a code that can recover any symbol of a codeword by reading at most r other symbols, denoted by r -LRC. In this paper, we study binary and ternary linear LRCs with disjoint repair groups and minimum distance d = 6. Using the intersection subspaces technique, we explicitly construct dimensional optimal LRCs. First, based on the intersection subspaces constructed by t -spread, a construction of binary LRCs is designed. Particularly, a class of binary linear LRCs with r = 11 is optimal in terms of achieving a sphere-packing type upper bound. Next, by using the Kronecker product of two matrices, two classes of dimensional optimal ternary LRCs with small locality (r = 3, 5) are presented. Compared to previous results, our construction is more flexible regarding code parameters. Finally, we also discuss the parameters of a code obtained by applying a shortening operation to our LRCs. We show that these shortened LRCs are also k -optimal. [ABSTRACT FROM AUTHOR]

Large-scale symmetric and asymmetric matrices have emerged in predicting the relationship between genes and diseases. The emergence of large-scale matrices increases the computational complexity of the problem. Therefore, using low-rank matrices instead of original symmetric and asymmetric matrices can greatly reduce computational complexity. In this paper, we propose an approximation conjugate gradient method for solving the low-rank matrix recovery problem, i.e., the low-rank matrix is obtained to replace the original symmetric and asymmetric matrices such that the approximation error is the smallest. The conjugate gradient search direction is given through matrix addition and matrix multiplication. The new conjugate gradient update parameter is given by the F-norm of matrix and the trace inner product of matrices. The conjugate gradient generated by the algorithm avoids SVD decomposition. The backtracking linear search is used so that the approximation conjugate gradient direction is computed only once, which ensures that the objective function decreases monotonically. The global convergence and local superlinear convergence of the algorithm are given. The numerical results are reported and show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

A key part of modern deep neural network (DNN) applications is matrix multiplication. As DNN applications are becoming more diverse, there is a need for both dense and sparse matrix multiplications to be accelerated by hardware. However, most hardware accelerators are designed to accelerate either dense or sparse matrix multiplication. In this paper, we propose VerSA, a versatile systolic array architecture for both dense and sparse matrix multiplications. VerSA employs intermediate paths and SRAM buffers between the rows of the systolic array (SA), thereby enabling an early termination in sparse matrix multiplication with a negligible performance overhead when running dense matrix multiplication. When running sparse matrix multiplication, 256 × 256 VerSA brings performance (i.e., an inverse of execution time) improvement and energy saving by 1.21×–1.60× and 7.5–30.2%, respectively, when compared to the conventional SA. When running dense matrix multiplication, VerSA results in only a 0.52% performance overhead compared to the conventional SA. [ABSTRACT FROM AUTHOR]

In the context of rapid product iteration, design conflicts arise from discrepancies in designers' understanding of user needs, influenced by subjective preferences, behavioural stances, and other factors. This paper proposes a product conceptual design approach based on the design conflict perspective. First, user comments and design documents are collected. Natural language processing (NLP) methods, including cleaning, filtering, lexical segmentation, feature clustering, and sentiment analysis, are employed to identify design themes. The intuitionistic fuzzy sets (IFSs) and term frequency–inverse document frequency (TF-IDF) algorithms are then utilized to obtain evaluation matrices for the products from both users and designers. Subsequently, design conflicts between users and designers are calculated, and an optimal configuration for product conceptual design is determined through regression analysis and planning methods. Finally, the proposed method is validated using a mobile phone as a product example, and suggestions for product improvement are presented. The results indicate that considering design conflicts as a factor in product design and synthesizing designer and user product concepts enhance the accuracy and reliability of product conceptual design generation. The findings of this study offer new insights into the conceptual design configuration for product iteration. [ABSTRACT FROM AUTHOR]

PURPOSE: Start-ups are widely acknowledged as crucial catalysts for innovation and drivers of economic progress. However, their vulnerability to failure continues to pose a persistent and significant obstacle. In light of this, the study intends to ascertain the various elements responsible for the elevated incidence of start-up failures and examine their contextual associations. It further aims to establish the hierarchical structure and identify the crucial factors of start-up failure. METHODOLOGY: The paper uses the Interpretive Structural Modeling (ISM) approach to determine the structural hierarchy and interconnections among the causes of start-up failures identified through the comprehensive analysis of existing literature and experts' opinions. MICMAC (Cross-Impact Matrix Multiplication Applied to Classification) analysis is also being utilized to categorize these identified failure causes into autonomous, independent, dependent, and linking factors by their driving and dependency powers. FINDINGS: A structural framework depicting the interrelationships among the factors has been derived, showing the failure factor, 'poor market positioning' factor at the highest level, and the 'lack of entrepreneurial efficiency' at the lowest level of the model. The results also revealed that lack of entrepreneurial efficiency, poor management, and external environmental issues are the most significant independent factors upon which all other failure factors rely. It also categorizes 'poor market positioning' as the dependent factor, signifying its passive role in the failure of start-ups. IMPLICATIONS: As previous literature has discussed the various factors responsible for the failure of start-ups in isolation, the current study fills out the gap in the literature by establishing linkages among those factors. The study's insights emphasize the value of effective management teams and entrepreneurial skills in averting start-up failures. It highlights the importance of skill development and mentorship to enhance the capabilities of entrepreneurs and their teams. Furthermore, the research indicates that policymakers and support groups can create focus initiatives addressing issues like market validation, team dynamics, and financial management to enhance the start-up environment. These initiatives may encompass entrepreneurship training, financial assistance, and mentorship through the 'Start-up India' Program, Bharat Fund platform, etc. ORIGINALITY AND VALUE: Previous studies on entrepreneurial failure are based on AHP (Analytical Hierarchical Process), content analysis, and quality management methodologies. This is potentially the first study using the ISM-MICMAC approach that explores the complex world of start-up failures in India and illustrates the relative influence and interdependence of various failure factors of start-ups through a hierarchical model. [ABSTRACT FROM AUTHOR]

To adequately facilitate project digital responsibility implementation (PDRI), a solid comprehension of the influencing factors and effective strategies that influence project digital responsibility implementation are necessary. Surprisingly, despite the increased interest in digital responsibility over the last few years, there still is a significant dearth of digital responsibility implementation. In practice, the factors that influence project digital responsibility implementation are complex and interconnected, not simple and isolated. Due to the omission of the causal relationship between these influencing factors, the project digital responsibility is not implemented effectively. This paper describes the process of identifying and classifying the factors influencing the project digital responsibility implementation, taking into account the network of interconnected factors. Four primary data sources and methodologies yielded new insights into the nature of these influential factors: a systematic literature review, semistructured interviews, fuzzy interpretative structural modeling, and cross-impact matrix multiplication applied to classification. Our analysis demonstrates that the 26 factors influencing project digital responsibility implementation interact and form a 9-level hierarchy. The 26 factors can be subdivided further into four dimensions: project dimension, stakeholder dimension, market environment dimension, and government dimension. Notably, the influencing factors in the government dimension have the most driving force, and adjusting the influencing factor in this dimension can enhance the influencing factors in the other dimensions. Finally, 11 policy proposals are proposed along 4 dimensions. This study bridges the knowledge gap of PDRI by providing new insights targeting the factors influencing PDRI. The findings provide valuable information for policy makers and practitioners to adopt effective measures to promote the implementation of PDRI. [ABSTRACT FROM AUTHOR]

The paper deals with the factorization of the matrices of discrete wavelet transform based on the Galois functions of different orders. It is used the known method of factorization of the matrices of the discrete Haar transform. Factorized matrices of transforms are presented in the form of a product of sparse matrices. This representation is the basis for building fast transforms algorithms. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks (CNNs) have been incredibly effective for object detection tasks. YOLOv4 is a state-of-the-art object detection algorithm designed for embedded systems. It is based on YOLOv3 and has improved accuracy, speed, and robustness. However, deploying CNNs on embedded systems such as Field Programmable Gate Arrays (FPGAs) is difficult due to their limited resources. To address this issue, FPGA-based CNN architectures have been developed to improve the resource utilization of CNNs, resulting in improved accuracy and speed. This paper examines the use of General Matrix Multiplication Operations (GEMM) to accelerate the execution of YOLOv4 on embedded systems. It reviews the most recent GEMM implementations and evaluates their accuracy and robustness. It also discusses the challenges of deploying YOLOv4 on autonomous vehicle datasets. Finally, the paper presents a case study demonstrating the successful implementation of YOLOv4 on an Intel Arria 10 embedded system using GEMM. [ABSTRACT FROM AUTHOR]

In this paper, two new estimators E 2 k - 1 , 0 (1) (f) and E 2 k - 1 , M (1) (f) of characteristic function and an estimator E 2 k - 1 , M (2) (f) of function of H o ¨ lder's class H α [ 0 , 1) of order 0 < α ⩽ 1 have been established using Bernoulli wavelets. A new technique has been applied for solving Volterra integral equation of second kind using Bernoulli wavelet operational matrix of integration as well as product operational matrix. These matrices have been utilized to reduce the Volterra integral equation into a system of algebraic equations, which are easily solvable. Some examples are illustrated to show the validity and efficiency of proposed technique of this research paper. [ABSTRACT FROM AUTHOR]

Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users’ local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the existence of a global caching gain that scales with the total memory in the system, in addition to the known local caching gain in uncoded systems. This paper formulates a novel cache-aided matrix multiplication retrieval problem, relevant for data analytics and machine learning applications. In the considered problem, each cache-aided user requests the product of two matrices from the library. A structure-agnostic solution is to treat each possible matrix product as an independent file and use the MAN coded caching scheme for single file retrieval. This paper proposes two structure-aware schemes, which partition each matrix in the library by either rows or columns and let a subset of users cache some sub-matrices, that improve on the structure-agnostic scheme. For the case where the library matrices are “fat” matrices, the structure-aware row-partition scheme is shown to be order optimal under some constraint. [ABSTRACT FROM AUTHOR]

In this paper, two randomized block Kaczmarz methods to compute inner inverses of any rectangular matrix A are presented. These are iterative methods without matrix multiplications and their convergence is proved. The numerical results show that the proposed methods are more efficient than iterative methods involving matrix multiplications for the high-dimensional matrix. [ABSTRACT FROM AUTHOR]

This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo 2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal. The design is a classical–quantum hybrid. The quantum components are a new circuit design for implementing matrix multiplication modulo 2, and a variational circuit to be optimized. The classical components are the optimizer, which measures the cost function and updates the quantum parameters for each iteration, and the controller that runs the quantum job and classical optimizer iterations. We propose two alternative ansatze or templates for the variational circuit and present results showing that the rotation ansatz designed specifically for this problem provides the most direct path to a valid solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using the custom rotations ansatz, is on par with the block Wiedemann algorithm, which is the best-known to date solution for this problem. [ABSTRACT FROM AUTHOR]

Backpack computers require powerful, intelligent computing capabilities for field wearables while taking energy consumption into careful consideration. A recommended solution for this demand is the CPU + NPU-based SoC. In many wearable intelligence applications, the Fourier Transform is an essential, computationally intensive preprocessing task. However, due to the unique structure of the NPU, the conventional Fourier Transform algorithms cannot be applied directly to it. This paper proposes two NPU-accelerated Fourier Transform algorithms that leverage the unique hardware structure of the NPU and provides three implementations of those algorithms, namely MM-2DFT, MV-2FFTm, and MV-2FFTv. Then, we benchmarked the speed and energy efficiency of our algorithms for the gray image edge filtering task on the Huawei Atlas200I-DK-A2 development kits against the Cooley-Tukey algorithm running on CPU and GPU platforms. The experiment results reveal MM-2DFT outperforms OpenCL-based FFT on NVIDIA Tegra X2 GPU for small input sizes, with a 4- to 8-time speedup. As the input image resolution exceeds 2048, MV-2FFTv approaches GPU computation speed. Additionally, two scenarios were tested and analyzed for energy efficiency, revealing that cube units of the NPU are more energy efficient. The vector and CPU units are better suited for sparse matrix multiplication and small-scale inputs, respectively. [ABSTRACT FROM AUTHOR]

Mixed-integer linear programming (MILP) techniques are widely used in cryptanalysis, aiding in the discovery of optimal linear and differential characteristics. This paper delves into the analysis of block ciphers KLEIN and PRINCE using MILP, specifically calculating the best linear and differential characteristics for reduced-round versions. Both ciphers employ matrix multiplication in their diffusion layers, which we model using multiple XOR operations. To this end, we propose two novel MILP models for multiple XOR operations, which use fewer variables and constraints, proving to be more efficient than standard methods for XOR modeling. For differential cryptanalysis, we identify characteristics with a probability of 2-59 for 7 rounds of KLEIN and a probability of 2-56 for 7 rounds of PRINCE. In linear cryptanalysis, we identify characteristics with a bias of 2-27 for 6 rounds of KLEIN and a bias of 2-29 for 7 rounds of PRINCE. These results establish the best single-key differential and linear distinguishers for these ciphers in the literature. [ABSTRACT FROM AUTHOR]

This work employs the carbon emission factor method to offer real-world instances for carbon footprint accounting, allowing for a thorough analysis of the carbon footprint and important influencing elements throughout the materialization stage of prefabricated housing. To identify the 18 important influencing factors that need to be examined from the five stages of building material production, conveyance of building materials, component manufacturing, component transportation, and building, this paper applies the DEMATEL-ISM-MICMAC (Decision-Making Trial and Evaluation Laboratory–Interpretive Structure Modeling–Cross-Influence Matrix Multiplication) model based on data quantification. Following the findings, the case project's physical phase generated a carbon footprint of approximately 4.68 × 106 kg CO2. The building materials' production and processing phase contributed the highest carbon footprint of the entire physical phase, totaling 4,005,935.99 kg CO2, or 88.24% of the total carbon footprint. To determine the centrality and causality of the influencing factors, four major influencing factors—energy consumption of raw materials (S4), construction planning and organization (S15), transportation energy type (S6), and waste disposal (S2)—were identified using the DEMATEL approach. The influencing factor system hierarchy was divided into six levels using the ISM technique. Level L6, which comprises one influencing factor for organizing and planning, is construction planning and organization (S15). Utilizing the MICMAC technique, it was possible to identify the energy consumption of raw materials (S4) as the primary cause of the materialization phase of built dwellings' carbon footprint. The building material production phases have the largest influence on carbon footprints, according to both case accounting and modeling research. The study's findings can offer some conceptual guidance for the creation of low-carbon emission reduction schemes. [ABSTRACT FROM AUTHOR]

With the proliferation of data and machine learning techniques, there is a growing need to develop methods that enable collaborative training and prediction of sensitive data while preserving privacy. This paper proposes a new protocol for privacy-preserving Naive Bayes classification using secure two-party computation (STPC). The key idea is to split the training data between two noncolluding servers using STPC to train the model without leaking information. The servers secretly share their data and the intermediate computations using cryptographic techniques like Beaver's multiplication triples and Yao's garbled circuits. We implement and evaluate our protocols on the MNIST dataset, demonstrating that they achieve the same accuracy as plaintext computation with reasonable overhead. A formal security analysis in the semi-honest model shows that the scheme protects the privacy of the training data. Our work advances privacy-preserving machine learning by enabling secure outsourced Naive Bayes classification with applications such as fraud detection, medical diagnosis, and predictive analytics on confidential data from multiple entities. The modular design allows embedding different secure matrix multiplication techniques, making the framework adaptable. This line of research paves the way for practical and secure data mining in a distributed manner, upholding stringent privacy regulations. [ABSTRACT FROM AUTHOR]

Multidimensional hierarchical sum aggregations can be formulated as matrix multiplications involving dummy matrices which can be referred to as model matrices. In contrast to standard model matrices, all categories of all variables must be included. For this purpose, the R package SSBtools includes functionality to create model matrices in two alternative ways, by model formulas or by so-called hierarchies. The latter means a coding of hierarchical relationships, and this can be done in several ways. Tree-shaped hierarchies are not required. The internal standard in the package is a parent-child coding. Functionality to find hierarchies automatically from the data is also included. The model matrix functionality is applied in several R packages for statistical disclosure control. This enables general implementation of methods and a flexible user interface. This paper describes the model matrix and hierarchy functions in SSBtools, as well as the methods and functions behind it. [ABSTRACT FROM AUTHOR]

The Number Theoretic Transform (NTT) has been widely used to speed up polynomial multiplication in lattice-based post-quantum algorithms. All NTT operands use modular arithmetic, especially modular multiplication, which significantly influences NTT hardware implementation efficiency. Until now, most hardware implementations used Digital Signal Processing (DSP) to multiply two integers and optimally perform modulo computations from the multiplication product. This paper presents a customized Lattice-DSP (L-DSP) for modular multiplication based on the Karatsuba algorithm, Vedic multiplier, and modular reduction methods. The proposed L-DSP performs both integer multiplication and modular reduction simultaneously for lattice-based cryptography. As a result, the speed and area efficiency of the L-DSPs are 283 MHz for 77 SLICEs, 272 MHz for 87 SLICEs, and 256 MHz for 101 SLICEs with the parameters q of 3329, 7681, and 12,289, respectively. In addition, the N − 1 multiplier in the Inverse-NTT (INTT) calculation is also eliminated, reducing the size of the Butterfly Unit (BU) in CRYSTAL-Kyber to about 104 SLICEs, equivalent to a conventional multiplication in the other studies. Based on the proposed DSP, a Point-Wise Matrix Multiplication (PWMM) architecture for CRYSTAL-Kyber is designed on a hardware footprint equivalent to 386 SLICEs. Furthermore, this research is the first DSP designed for lattice-based Post-quantum Cryptography (PQC) modular multiplication. [ABSTRACT FROM AUTHOR]

With the rapid development of Internet technology and the arrival of the era of big data, the rapid expansion of network information resources has formed massive information. Massive information resources have brought great convenience to people's lives. However, it becomes more and more difficult to find the content that interests you, which is the phenomenon of "information overload." In order to solve this problem, a solution based on personalized recommendation technology is proposed. In personalized recommendation technology, collaborative filtering algorithm is the most widely used technology. Clustering technology can effectively divide objects into groups, so that the similarity of attributes between objects in the same group is high, and the similarity of objects in different groups is low. The core step of the filtering recommendation algorithm is to find the similar neighbors of the target user by calculating the similarity. Applying the clustering technology to the recommendation can effectively improve the performance of the recommendation system. Aiming at the real-time problem of collaborative filtering recommendation, this paper introduces a method of firstly clustering users on the user item rating matrix, and finding the nearest neighbors in the clusters with high similarity with the target user, which effectively reduces the query space and improves the recommendation. This paper proposes a method to measure the user's preference for item attributes, which is used in the above clustering process to improve the recommendation accuracy while retaining the advantage of reducing the query space. Aiming at the problem of poor recommendation accuracy, this paper proposes a fuzzy-improved K-means algorithm to cluster items in the product attribute matrix, and then fuses the similarity of the belongingness of items to clusters in the fuzzy clustering. The similarity calculated on the score matrix shows that this method is better than the traditional hybrid recommendation in accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative image compression scheme by utilizing the Adaptive Discrete Wavelet Transform-based Lifting Scheme (ADWT-LS). The most important feature of the proposed DWT lifting method is splitting the low-pass and high-pass filters into upper and lower triangular matrices. It also converts the filter execution into banded matrix multiplications with an innovative lifting factorization presented with fine-tuned parameters. Further, optimal tuning is the most important contribution that is achieved via a new hybrid algorithm known as Lioness-Integrated Whale Optimization Algorithm (LI-WOA). The proposed algorithm hybridizes the concepts of both the Lion Algorithm (LA) and Whale Optimization Algorithm (WOA). In addition, innovative cosine evaluation is initiated in this work under the CORDIC algorithm. Also, this paper defines a single objective function that relates multi-constraints like the Peak Signal-to-Noise Ratio (PSNR) as well as Compression Ratio (CR). Finally, the performance of the proposed work is compared over other conventional models regarding certain performance measures. [ABSTRACT FROM AUTHOR]

The image secret sharing scheme shares a secret image as multiple shadows. The secret image can be recovered from shadow images that meet a threshold number. However, traditional image secret sharing schemes generally reuse the Lagrange's interpolation in the recovery stage to obtain the polynomial in the sharing stage. Since the coefficients of the polynomial are the pixel values of the secret image, it is able to recover the secret image. This paper presents an implementation of the image secret sharing scheme based on matrix operations. Different from the traditional image secret sharing scheme, this paper does not use the method of Lagrange's interpolation in the recovery stage, but first identifies the participants as elements to generate a matrix and calculates its inverse matrix. By repeating the matrix multiplication, the polynomial coefficients of the sharing stage are quickly derived, and then the secret image is recovered. By theoretical analysis and the experimental results, the implementation of secret image sharing based on matrix operation is higher than Lagrange's interpolation in terms of efficiency. [ABSTRACT FROM AUTHOR]

Algorithms for noise removal are either complex or ineffective, and the optimal control with inequality constrains makes the algorithm even more complex. Now the condition is changed completely, and the tropical algebra is an extremely simple tool for this purpose. The tropical algebra-based filter has obvious advantages over traditional ones, and an inequality constrain can be converted to a tropical polynomial, making the tropical algebra much attractive in engineering applications. In this paper, idempotents on multiplicative semigroups of tropical matrices are studied. First, the concepts of tropical algebra and the semigroup of tropical matrices under multiplication are introduced. Second, the structure of idempotents on the semigroup of 3 × 3 tropical matrices under multiplication is given. Finally, as examples, the tropical addition is used as a filter for noise removal, and a simple optimization is given where the constraint is given by the tropical algebra. The paper has opened the path for a new way to noise removal and optimization. [ABSTRACT FROM AUTHOR]

Establishment of a performance evaluation model is a hotspot of current research. In this paper, the performance bottleneck is analyzed quantitatively, which provided programmers with a guidance to optimize the performance bottleneck. This paper takes a matrix as an example; the matrix is divided into a dense matrix or a sparse matrix. For dense matrix, the performance is first analyzed in a quantitative way, and an evaluation model is developed, which includes the instruction pipeline, shared memory, and global memory. For sparse matrix, this paper aims at the four formats of CSR, ELL, COO, and HYB, through the observation data obtained from the actual operation of large datasets, finds the relationship between the running time, dataset form, and storage model, and establishes their relational model functions. Through practical test and comparison, the error between the execution time of the test dataset that is predicted by the model function and the actual running time is found to be within a stable finite deviation threshold, proving that the model has certain practicability. [ABSTRACT FROM AUTHOR]

Featured Application: The method studied in this paper is applied to the control calculation of manipulator, especially the matrix chain multiplication in the calculation of forward and inverse kinematics solutions of manipulator. Intelligence development has put forward increasing requirements of real-time planning and dynamic feedback in controlling robotic arms. It has become essential in engineering applications to complete the kinematics calculation of complex manipulators in real time. This paper proposes a matrix cascading multiplication equivalent reduced-order parallel computing method for the multiplication of homogeneous matrices in the process of forward and inverse kinematics solutions, which reduces the order of the matrix according to the distribution of zero vectors in the homogeneous matrix calculations. The method removes the unnecessary multiplication in joint homogeneous matrixes containing zero vectors. It obtains the optimal calculation order of the cascade matrix multiplication through dynamic planning searches, improving the efficiency of effective dot product calculation by parallel computation. Calculation processes and specific examples are presented in this paper. Compared with the previous algorithms, the proposed algorithm reduces the calculation cycle by 90%, effectively improving the real-time calculation efficiency in the complex control process. [ABSTRACT FROM AUTHOR]

Multiple-input multiple-output (MIMO) technology is one of the key technical approaches to improve the spectrum efficiency of wireless communication. Modern communication systems employ MIMO and high-order quadrature amplitude modulation (QAM) to maximize spectral efficiency. However, with the increase in the number of antennas and modulation orders, it is very challenging to design a low-complexity and high-efficiency MIMO receiver. In recent years, with the rapid development of new technologies such as artificial intelligence, more and more researchers have tried to apply machine learning techniques in the field of communication to break through the performance of traditional communication algorithms. In this paper, we propose a new low-complexity MIMO detection algorithm: an artificial intelligence-assisted expectation propagation (EP) detection algorithm. Neural network models are used to learn and map some of the time-consuming steps in the EP detection algorithm, converting the complex operation process into a few matrix multiplication operations in order to reduce the complexity of the detection algorithm. It is verified that the method proposed in this paper can approximate the performance of the original EP detection algorithm with reduced complexity and is applicable in different scenarios. [ABSTRACT FROM AUTHOR]

Geometric errors are important factors that affect the accuracy of multi-axis CNC machine tools. In this paper, three aspects of research work are carried out. First, two kinds of error modeling methods are proposed, i.e., tool tip coordinates error modeling (TTC) and kinematic chain transmission error modeling (KCT). This work resolves the theoretical confusion existing in the error modeling process in the past. Second, left matrix multiplication and right matrix multiplication have different meanings for geometric error modeling; this paper makes a detailed analysis and summarizes four identification algorithms for geometric errors based on the above theory. Third, a new R-test device is developed. For the traditional commercial R-test, it is usually difficult to adjust the position and orientation, so it is hard to directly obtain the vectors of the sensor axes and to ensure that the intersection of the sensor axes and the center of precision ball coincide accurately. However, this new R-test with the addition of positioning datums and a sliding table overcomes these problems. The calibration of the R-test is described in detail. Finally, a four-point measurement experiment for identifying the geometric errors of a rotary axis has been conducted, and the effectiveness of the measurement method is verified by a prediction experiment and a comparative experiment of double ball bar (DBB). [ABSTRACT FROM AUTHOR]

The new-generation Sunway supercomputer has ultra-high computing capacity. But due to the unique heterogeneous architecture of the supercomputer, the open-source versions of basic linear algebra subprograms (BLAS) are insufficient for performance or compatibility. In addition, due to the update of the architecture, BLAS based on the previous Sunway could not fully exploit the performance of the successor. To address the challenges, we propose an optimized BLAS on the new-generation Sunway supercomputer in this paper. Specially, for achieving efficient computation, a parallel optimization method based on the new-generation Sunway for the Level-1 BLAS computing between vectors and the Level-2 BLAS computing between vectors and matrices is first proposed. Then, an adaptive scheduling algorithm for various data sizes is proposed, which is used to balance the tasks of core groups. Finally, to achieve highly efficient general matrix multiplication (GEMM) kernels, a parallel optimization method based on the new-generation Sunway for the Level-3 BLAS computing between matrices is proposed, which includes source-level optimization as well as assembly-level optimization. Experimental results show that the memory bandwidth utilization of the optimized Level-1/2 BLAS exceeds 95%, and the computational efficiency of the optimized GEMM kernel exceeds 94%. [ABSTRACT FROM AUTHOR]

This paper proposes a new hardware approach for accelerating matrix vector multiplication (MVM) employing systolic array architecture and parallel data processing units, which is particularly useful in multiplication intensive applications such as neural networks. The hardware complexity of the parallel computations is reduced by a technique named as split-matrix approach, in which the larger matrices are split into smaller matrices. In the proposed architecture, 8-bit fixed-point representation is considered and matrices are treated to be circulant in nature. The resulting MVM architecture benefits with reduced implementation complexity in terms of cell area, reduced delay, and power consumption. It is found to result in a 13.9% reduction in logic cell area and a 38.15% reduction in total power consumption when compared to those of the latest baseline design. Also, the proposed architecture is able to achieve a considerably improved minimum permissible clock period of 0.410ns. The development of a long short-term memory (LSTM) architecture using the proposed design also serves to prove the effectiveness of the proposed MVM architecture. The LSTM developed using the proposed MVM provides a 37.57% reduction in the cell area and a 22.86% reduction in the total power in comparison with the latest baseline design and is able to achieve a minimum clock period of 0.42 ns. [ABSTRACT FROM AUTHOR]

Solutions of a group of conjugate time-varying matrix equations are discussed in this paper. Through mathematical derivation, the solutions to this group of equations are equivalent to the solutions to a class of conjugate time-invariant matrix equations. Further, the related conditions of solvability are obtained and the general explicit solutions are represented by using quasicontrollability and quasiobservability matrices. A detailed algorithm is presented to make the calculation process clear, and the effectiveness of the algorithm is verified by a concrete example. The proposed algorithm can provide complete solutions to the considered equation in explicit parametric form and its main computation includes solving an ordinary linear algebraic equation and some matrix multiplication operations. [ABSTRACT FROM AUTHOR]

Discriminative dictionary learning has been extensively used for pattern classification tasks. By incorporating different kinds of label information into the dictionary learning framework, a dictionary can be attained that represents the original signal with discriminative reconstruction. The previous works learn the dictionary in the original space which limits the dictionary learning performance. In this paper, we propose an approach, namely Deep Discriminative Dictionary Pair Learning (D 3 PL) for image classification. The input of D 3 PL is not the matrix collected by original gray images or hand-crafted features but the relatively deeper features derived from autoencoders. Then, a structured dictionary is designed based on the discriminative contributions across different classes to reconstruct the deep feature. In addition, the associated structured projective dictionary is learned as well to guarantee the decoders updating towards the minimal error of deconvolution operator. By leveraging the discriminative-dictionary-learning-based loss function and the autoencoder loss function, D 3 PL can simultaneously learn the deep potential feature and the corresponding dictionary pair. In the testing phase of D 3 PL, the minimum error between the deep feature and the structured projective component with regard to different classes can directly indicate the label by a basic matrix multiplication operation. Experimental results on challenging Extended Yale B, AR, UMIST, COIL20, Scene 15, and Caltech101 datasets demonstrate that the proposed D 3 PL outperforms the prominent dictionary learning methods. [ABSTRACT FROM AUTHOR]

With the development of engineering technology, engineering has higher requirements for the accuracy and the scale of simulation calculation. The computational efficiency of traditional serial programs cannot meet the requirements of engineering. Therefore, reducing the calculation time of the temperature control simulation program has important engineering significance for real-time simulation of temperature field and stress field, and then adopting more reasonable temperature control and crack prevention measures. GPU parallel computing is introduced into the temperature control simulation program of massive concrete to solve this problem and the optimization is carried out. Considering factors such as GPU clock rate, number of cores, parallel overhead and Parallel Region, the improved GPU parallel algorithm analysis indicator formula is proposed. It makes up for the shortcomings of traditional formulas that focus only on time. According to this formula, when there are enough threads, the parallel effect is limited by the size of the parallel domain, and when the parallel domain is large enough, the efficiency is limited by the parallel overhead and the clock rate. This paper studies the optimal Kernel execution configuration. Shared memory is utilized to improve memory access efficiency by 155%. After solving the problem of bank conflicts, an accelerate rate of 437.5× was realized in the subroutine of the matrix transpose of the solver. The asynchronous parallel of data access and logical operation is realized on GPU by using CUDA Stream, which can overlap part of the data access time. On the basis of GPU parallelism, asynchronous parallelism can double the computing efficiency. Compared with the serial program, the accelerate rate of inner product matrix multiplication of the GPU asynchronous parallel program is 61.42×. This study further proposed a theoretical formula of data access overlap rate to guide the selection of the number of CUDA streams to achieve the optimal computing conditions. The GPU parallel program compiled and optimized by the CUDA Fortran platform can effectively improve the computational efficiency of the simulation program for concrete temperature control, and better serve engineering computing. [ABSTRACT FROM AUTHOR]

Dynamic Mode Decomposition with Control is a powerful technique for analyzing and modeling complex dynamical systems under the influence of external control inputs. In this paper, we propose a novel approach to implement this technique that offers computational advantages over the existing method. The proposed scheme uses singular value decomposition of a lower order matrix and requires fewer matrix multiplications when determining corresponding approximation matrices. Moreover, the matrix of dynamic modes also has a simpler structure than the corresponding matrix in the standard approach. To demonstrate the efficacy of the proposed implementation, we applied it to a diverse set of numerical examples. The algorithm's flexibility is demonstrated in tests: accurate modeling of ecological systems like Lotka-Volterra, successful control of chaotic behavior in the Lorenz system and efficient handling of large-scale stable linear systems. This showcased its versatility and efficacy across different dynamical systems. [ABSTRACT FROM AUTHOR]

Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general n × n block matrices. In the first part, the inverses of 2 × 2 block matrices are given, where one of the blocks is a non-singular matrix, a result which can be generalised to a block matrix of any size, by splitting it into four blocks. The second part focuses on the determinants, which is covered in two different methods. In the first approach, we revise a formula for the determinant of a block matrix A, with blocks elements of R; a commutative subring of M n × n (F) . The determinants of tensor products of two matrices are also given in this part. In the second method for computing the determinant, we give the general formula, which would work for any block matrix, regardless of the ring or the field under consideration. The individual formulas for determinants of 2 × 2 and 3 × 3 block matrices are also produced here. [ABSTRACT FROM AUTHOR]

Aiming at the stability of a medium-voltage DC network based on a modular multilevel converter (MMC), this paper proposes an admittance stability criterion considering the influence of current-limiting inductors at the medium voltage side, which prevents the complex products and matrix calculations of traditional criteria. The DC admittance model DC transformers (DCTs) under different working modes are then established based on Thevenin/Norton equivalent circuit methods to analyze the stability of the DC system based on the proposed admittance stability criterion, which proves that the voltage resonance problem at the medium voltage side can be improved by adding active damping control strategies on DCTs also proves the effectiveness of the proposed stability criterion. The time-domain simulation and the hardware-in-loop simulation are then built in PLECS and RT Box to further verify the correctness of the system stability analysis and the effectiveness of the proposed admittance criterion, which provides a theoretical basis and technical reserve for the stable operation of the DC distribution power system. [ABSTRACT FROM AUTHOR]

A random matrix needs large storage space and is difficult to be implemented in hardware, and a deterministic matrix has large reconstruction error. Aiming at these shortcomings, the objective of this paper is to find an effective method to balance these performances. Combining the advantages of the incidence matrix of combinatorial designs and a random matrix, this paper constructs a structured random matrix by the embedding operation of two seed matrices in which one is the incidence matrix of combinatorial designs, and the other is obtained by Gram–Schmidt orthonormalization of the random matrix. Meanwhile, we provide a new model that applies the structured random matrices to semi-tensor product compressed sensing. Finally, compared with the reconstruction effect of several famous matrices, our matrices are more suitable for the reconstruction of one-dimensional signals and two-dimensional images by experimental methods. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to derive the Jacobian matrix of a hybrid mechanism by applying a velocity operator to the transformation matrix. This Jacobian matrix is capable of deducing hybrid singularities, which cannot be identified by using the screw-based Jacobian or velocity-based Jacobian. The transformation matrix was obtained based on the algebraic geometry approach, and it becomes the key point since it was used to not only formulate the Jacobian matrix, but also to define the motion type of hybrid mechanisms. In this paper, two hybrid mechanisms were investigated, which were composed of two distinct parallel mechanisms mounted in series. Hybrid Mechanisms 1 and 2 were composed of 3-PRP-3-RPS and 3-RPS-3-PRP (the underlined P is an actuated joint), respectively. The motion types of Hybrid Mechanisms 1 and 2 were determined from the product of the transformation matrices of the 3-PRP and 3-RPS parallel mechanisms, and vice versa. The developed method was employed to establish the Jacobian matrix to which the conditioning index was applied. Therefore, the kinematic performances of the two hybrid mechanisms can be compared for a given bone surgery trajectory within the workspace. It turns out that Hybrid Mechanism 1 has superior performance than that of Mechanism 2, which indicates that Mechanism 1 is better at transmitting power to the moving platform. [ABSTRACT FROM AUTHOR]

A 2D metric space has a limited number of properties through which it can be described. This metric space may comprise objects such as a scalar, a vector, and a rank-2 tensor. The paper provides a comprehensive description of relations between objects in 2D space using the matrix product of vectors, geometric product, and dot product of complex numbers. These relations are also an integral part of the Lagrange's identity. The entire structure of derived theoretical relationships describing properties of 2D space draws on the Lagrange's identity. The description of how geometric algebra and tensor calculus are interconnected is given here in a comprehensive and essentially clear manner, which is the main contribution of this paper. A new term in this regard is the total geometric and matrix product, which—in a simple manner—predetermines and defines the existence of differential relations such as the gradient, the divergence, and the curl of a vector field. In addition, geometric interpretation of tensors is pointed out, expressed through angular parameters known from the literature as a tensor glyph. This angular interpretation of the tensor has an unequivocal analytical form, and the paper shows how it is linked to the classical tensor denoted by indices. [ABSTRACT FROM AUTHOR]