Binary Matrix Research Articles

Laser speckle interferometry approach for measuring the first wall surface micro-morphology in fusion devices with only single interferogram based on Hilbert transform

During the operation of the EAST device, the surface morphology of the first wall in will change due to the erosion and redeposition from plasma-wall interaction (PWI). In this paper, a novel phase extraction approach using only single interferogram based on twice Hilbert transform (THT) has been proposed and implemented. The current approach has a significant advance for eliminating the phase-shifting errors in principle, but the problems of phase flipping and loss due to ignoring non-physical negative frequency spectrum must to be overcome. To address these problems a judgement method is proposed in current investigation to distinguish the regions of the negative spatial frequency. Then a binary matrix was developed to modify the wrapped phase of the measured interferogram. The validation of the proposed THT approach has been demonstrated by the micro-morphology reconstruction of laser ablation craters on molybdenum (Mo) and tungsten (W) tiles, which are commonly used as the first wall in EAST device. Results indicate that the THT approach has a reasonable measurement accuracy with relative errors around 10%. Also, the current THT approach presents an enhanced robust under the EAST-like vibrational environments.

Implementation of a non-standard system for simplifying Peirce-Webb functions

The object of research are models of optimal logic circuits based on universal Peirce-Webb functions. The problem solved is the efficiency of the technique for simplifying the Peirce-Webb functions. The extension of the non-standard system to the simplification of Peirce-Webb functions makes it possible to discover new rules of equivalent transformations of Boolean functions, and to complete the simplification procedure in one step. A feature of the simplification of functions in the Peirce-Webb basis by a non-standard system is fixing the digital project at the level of abstraction, followed by the application of the mechanism of logical synthesis to generate the corresponding equivalent at the level of gates of the logic circuit. The result of the transformation of the terms of the binary matrix in the end is some combinatorial system, metadata that can explain other data, for example, determine the minimum function for another logical basis. The interpretation of the result consists in the use of combinatorial properties of binary structures of functions in the Peirce-Webb basis and binary structures of functions in the basic basis. These properties do not depend on the selected logical basis, which makes it possible to carry out equivalent transformations on binary matrices of Peirce-Webb functions according to the rules of the algebra of the main basis. It has been experimentally confirmed that a non-standard system enables: – to reduce the algorithmic complexity of simplifying the Peirce-Webb functions; – to increase the performance of the simplification of Peirce-Webb functions by 200–300 %; – to demonstrate the visibility of the process of simplifying functions. In terms of application, the non-standard system of simplifying the Peirce-Webb functions could ensure the transfer of innovations to material production: from conducting fundamental research, expanding the capabilities of digital component design technology to organizing serial or mass production of novelties.

Machine learning-driven discovery of high-performance MEMS disk resonator gyroscope structural topologies

The design of the microelectromechanical system (MEMS) disc resonator gyroscope (DRG) structural topology is crucial for its physical properties and performance. However, creating novel high-performance MEMS DRGs has long been viewed as a formidable challenge owing to their enormous design space, the complexity of microscale physical effects, and time-consuming finite element analysis (FEA). Here, we introduce a new machine learning-driven approach to discover high-performance DRG topologies. We represent the DRG topology as pixelated binary matrices and formulate the design task as a path-planning problem. This path-planning problem is solved via deep reinforcement learning (DRL). In addition, we develop a convolutional neural network-based surrogate model to replace the expensive FEA to provide reward signals for DRL training. Benefiting from the computational efficiency of neural networks, our approach achieves a significant acceleration ratio of 4.03 × 105 compared with FEA, reducing each DRL training run to only 426.5 s. Through 8000 training runs, we discovered 7120 novel structural topologies that achieve navigation-grade precision. Many of these surpass traditional designs in performance by several orders of magnitude, revealing innovative solutions previously unconceived by humans.

Secure authentication and encryption via diffraction imaging-based encoding and vector decomposition

Abstract Traditional optical encryption systems have security risks due to their linearity and usually encounter problems such as the heavy burden of key transmission and storage. This paper proposes a novel security-enhanced optical image authentication and encryption framework that combines diffractive imaging-based encryption with the vector decomposition algorithm (VDA). Chaotic random phase masks (CRPMs) are used to encrypt data for authentication via VDA, and a pair of complementary binary matrix keys are utilized to extract information from the encrypted data to generate ciphertext. During the authentication and decryption processes, a sparse reference image is reconstructed from the ciphertext for verification. If the authentication is successful, image decryption can be executed using a key-assisted phase retrieval algorithm. The employment of nonlinear VDA, an additional layer of authentication, and the use of CRPMs and binary matrix keys enhance security and address key burden concerns. Simulation results demonstrate the feasibility, effectiveness, and security of the scheme.

Noise-robust and data-efficient compressed ghost imaging via the preconditioned S-matrix method

The design of the illumination pattern is crucial for improving imaging quality of ghost imaging (GI). The S-matrix is an ideal binary matrix for use in GI with non-visible light and other particles since there are no uniformly configurable beam-shaping modulators in these GI regimes. However, unlike widely researched GI with visible light, there is relatively little research on the sampling rate and noise resistance of compressed GI based on the S-matrix. In this paper, we investigate the performance of compressed GI using the S-matrix as the illumination pattern (SCSGI) and propose a post-processing method called preconditioned S-matrix compressed GI (PSCSGI) to improve the imaging quality and data efficiency of SCSGI. Simulation and experimental results demonstrate that compared with SCSGI, PSCSGI can improve imaging quality in noisy conditions while utilizing only half the amount of data used in SCSGI. Furthermore, better reconstructed results can be obtained even when the sampling rate is as low as 5%. The proposed PSCSGI method is expected to advance the application of binary masks based on the S-matrix in GI.

NAS FD Lung: A novel lung assist diagnostic system based on neural architecture search

In the detection and recognition of lung nodules, pulmonary nodules vary in size and shape and contain many similar tissues and organs around them, leading to the problems of both missed detection and false detection in existing detection algorithms. Designing proprietary detection and recognition networks manually requires substantial professional expertise. This process is time-consuming and labour-intensive and leads to issues like parameter redundancy and improper feature selection. Therefore, this paper proposes a new pulmonary CAD (computer-aided diagnosis) system for pulmonary nodules, NAS FD Lung (Using the NAS approach to search deep FPN and DPN networks), that can automatically learn and generate a deep learning network tailored to pulmonary nodule detection and recognition task requirements. NAS FD Lung aims to use automatic search to generate deep learning networks in the auxiliary diagnosis of pulmonary nodules to replace the manual design of deep learning networks. NAS FD Lung comprises two automatic search networks: BM NAS-FPN (Using NAS methods to search for deep FPN structures with Binary operation and Matrix multiplication fusion methods) network for nodule detection and NAS-A-DPN (Using the NAS approach to search deep DPN networks with attention mechanism) for nodule identification. The proposed technique is tested on the LUNA16 dataset, and the experimental results show that the model is superior to many existing state-of-the-art approaches. The detection accuracy of lung nodules is 98.23%. Regarding the lung nodules classification, the accuracy, specificity, sensitivity, and AUC values achieved 96.32%,97.14%,95.82%, and 98.33%, respectively.

Quasi-static/dynamic energy absorption characteristics and micromechanical behavior of Al/Ep cast metal braided tubular structures

As a low-density, high-strength material with high energy release potential, Al/Ep cast metal braided tubes have a wide range of application prospects in the combatant shell, which is one of the most important means to realize the integrated destructive effect of kill and blast. In this paper, Al/Ep composites with mass ratios of 3:7, 4:6 and 5:5 were prepared, and the intrinsic model of Al/Ep was established by studying its quasi-static and dynamic mechanical properties. The Al/Ep cast three-dimensional braided metal skeletons were used to obtain the required cast braided tubes with different mass ratios, and the destruction behaviors of the tubes under axial and radial compressive loads were analyzed by a combination of experimental and numerical simulations. The results show that the addition of Al particles can significantly improve the elastic-plastic properties of Al/Ep composites, and the energy storage and absorption capacities are positively correlated with the ratio of the relative contents of Al powder. When the mass ratio of Al powder to epoxy resin is 5:5, the energy absorption of Al/Ep composites is 23.16 MJ/m3, which is optimal among similar specimens and much higher than that of pure epoxy resin materials (the energy absorption of epoxy resin is 9.63 MJ/m3). The strength of binary resin matrix composites is improved, and the intrinsic models of three kinds of different mass ratios of Al/Ep composites are obtained. The intrinsic models of various Al/Ep cast braided tubes with crushing force efficiency CFE, energy absorption capacity, and specific energy absorption SEA decreased with the ratio of mass occupied by the braided filaments.

Neutrosophic Binary Relation Matrices for Enhanced Medical Diagnosis

Medical diagnosis often relies on intricate relationships between symptoms, diseases, and patient data. Traditional methods struggle to account for the inherent uncertainties and indeterminacies within this process. This paper proposes the application of Neutrosophic Binary Relation Matrices (NBRMs) for enhanced uncertainty management in medical diagnosis. NBRMs offer a novel framework by incorporating truth (T), indeterminacy (I), and falsity (F) degrees to represent these relationships. We explore the mathematical structure of NBRMs and discuss their potential in modeling complex symptom-disease associations, incorporating individual patient factors, and developing more nuanced decision support systems. By leveraging NBRMs, we can potentially improve diagnostic accuracy and navigate the complexities of medical data. This paper paves the way for further research on utilizing neutrosophic logic to enhance medical diagnosis and contribute to more informed healthcare decisions.

Acetated starch inclusion to tailor the hierarchical structure and sol-gel features of middle gluten wheat starch-based binary matrices

Acetated starch inclusion to tailor the hierarchical structure and sol-gel features of middle gluten wheat starch-based binary matrices

On Matrix Representations of Homeomorphism Classes

In this study, we investigate the matrix representations of homeomorphism classes. Considering well-known concepts such as the matrix of ones, column-sum, row-sum, one's complement, Hadamard product, and regular addition for matrices, we explore binary matrices' relationships with subsets of a finite set. The main results establish connections between matrix operations and set operations, providing insights into the structure of homeomorphism classes. The paper concludes with the formulation of a topology on a set based on specific matrix conditions.

NIR-I Activated Orthogonal NIR-IIb/c Emissions in a Lanthanide-Doped Nanoparticle for Fluorescence Imaging and Information Encryption.

Applying the orthogonal principle for distinguishable second near-infrared (NIR-II) emissions has brought new dimensions for ratio fluorescence imaging (RFI) detection and information encryption, deepening the tissue detection depth and improving signal-to-noise ratio and information security. However, the orthogonal NIR-II emissions underlying these advanced optical applications have been reported only in heterogeneous structures and mixtures, limiting their practicality and potential impact. Herein, NIR-I-activated orthogonal NIR-IIb/c (1530/1825nm) emissions nanoparticles (ONNPs) are developed by spatially separated doping of Tm3+ and Er3+ emitter upon switching 808 and 980nm excitations. RFI techniques and orthogonal NIR-II emission ONNPs are used to demonstrate vessel depth detection based on wavelength-dependent optical attenuation properties in tissue. The superiority of the optical coding and encoding process in a 4×1 binary matrix is demonstrated for anticounterfeiting and decryption imaging of quick-response (QR) code for information storage. The research progress of this NIR-II orthogonal emissions probe will drive the development of biomedical sensing, imaging safety, and future biophotonics technologies.

Knowledge-map and research trends of circulating tumor cells in breast cancer: a scientometric analysis

Assessing circulating tumor cells (CTCs) in early-stage breast cancer patients can help identify relapse risk for timely interventions. Molecular analysis of CTCs can reveal vulnerabilities for personalized treatment options in metastatic breast cancer. This study aims to summarize CTCs in breast cancer research understanding and evaluate research trends. Extracted from the Web of Science Core Collection, publications on CTCs in breast cancer studies spanning from January 1, 2008, to December 21, 2023, were included. Co-authorships, references, and keywords were analyzed using Bibliometrix R packages and VOSviewer software. References and keywords burst detection were conducted with CiteSpace, and BICOMB was utilized to generate high-frequency keyword layouts. Biclustering analysis of the binary co-keyword matrix was performed using gCLUTO. 1747 articles focusing on CTCs in breast cancer were identified. The USA and the University of Texas MD Anderson Cancer Center demonstrated the highest productivity at the national and institutional levels, respectively. The journal “CANCERS” had the highest publication outputs on this subject. Pantel K emerged as the foremost author with the highest publication and co-citation counts. Analysis of co-keywords unveiled five prominent research areas concerning CTCs in breast cancer. The prognostic and predictive roles of CTCs in breast cancer have substantial implications for clinical practice. Nevertheless, precise assessment of CTCs, encompassing its quantities and attributes through advanced technologies, and its role in detecting minimal residual disease in breast cancer, continue to pose notable challenges. In conclusion, recent advancements and trends in CTCs research in breast cancer are examined through scientometric analysis in this study. The results provide valuable insights for the formulation of novel approaches in CTCs research, emphasizing the current research frontiers.

On Matrix Representation of Extension Field GF(pL) and Its Application in Vector Linear Network Coding.

For a finite field GF(pL) with prime p and L>1, one of the standard representations is L×L matrices over GF(p) so that the arithmetic of GF(pL) can be realized by the arithmetic among these matrices over GF(p). Based on the matrix representation of GF(pL), a conventional linear network coding scheme over GF(pL) can be transformed to an L-dimensional vector LNC scheme over GF(p). Recently, a few real implementations of coding schemes over GF(2L), such as the Reed-Solomon (RS) codes in the ISA-L library and the Cauchy-RS codes in the Longhair library, are built upon the classical result to achieve matrix representation, which focuses more on the structure of every individual matrix but does not shed light on the inherent correlation among matrices which corresponds to different elements. In this paper, we first generalize this classical result from over GF(2L) to over GF(pL) and paraphrase it from the perspective of matrices with different powers to make the inherent correlation among these matrices more transparent. Moreover, motivated by this correlation, we can devise a lookup table to pre-store the matrix representation with a smaller size than the one utilized in current implementations. In addition, this correlation also implies useful theoretical results which can be adopted to further demonstrate the advantages of binary matrix representation in vector LNC. In the following part of this paper, we focus on the study of vector LNC and investigate the applications of matrix representation related to the aspects of random and deterministic vector LNC.

Efficient and Effective One-Step Multiview Clustering.

Multiview clustering algorithms have attracted intensive attention and achieved superior performance in various fields recently. Despite the great success of multiview clustering methods in realistic applications, we observe that most of them are difficult to apply to large-scale datasets due to their cubic complexity. Moreover, they usually use a two-stage scheme to obtain the discrete clustering labels, which inevitably causes a suboptimal solution. In light of this, an efficient and effective one-step multiview clustering (E2OMVC) method is proposed to directly obtain clustering indicators with a small-time burden. Specifically, according to the anchor graphs, the smaller similarity graph of each view is constructed, from which the low-dimensional latent features are generated to form the latent partition representation. By introducing a label discretization mechanism, the binary indicator matrix can be directly obtained from the unified partition representation which is formed by fusing all latent partition representations from different views. In addition, by coupling the fusion of all latent information and the clustering task into a joint framework, the two processes can help each other and obtain a better clustering result. Extensive experimental results demonstrate that the proposed method can achieve comparable or better performance than the state-of-the-art methods. The demo code of this work is publicly available at https://github.com/WangJun2023/EEOMVC.

Evaluation of Genetic Diversity in Sorghum Genotypes via Simple Sequence Repeat (SSR) Markers

This study aimed to evaluate the genetic diversity of 20 sorghum [Sorghum bicolor (L.) Moench] genotypes via simple sequence repeat (SSR) markers, with a focus on identifying drought-tolerant varieties. Leaf samples were collected from three-week-old seedlings, and genomic DNA was extracted via the CTAB method, a widely recognized protocol for obtaining high-quality DNA. The DNA samples were quantified to ensure consistent template concentrations for amplification via 25 SSR primers. PCR amplification was performed, followed by agarose gel electrophoresis to separate and visualize the SSR band patterns, which were then recorded in a binary matrix format on the basis of the presence or absence of bands. Among the SSR primers used, nine were polymorphic, generating 13 scorable markers, highlighting the genetic variability among the genotypes. The polymorphic information content (PIC) values ranged across the SSR loci, with the Xtxp145 locus exhibiting the highest PIC value of 0.998, indicating its high discriminatory power and informativeness in differentiating between genotypes. Genetic similarity indices were calculated via Jaccard's similarity coefficient [1], and the data were subjected to cluster analysis via the unweighted pair group method with arithmetic mean (UPGMA) method. The resulting dendrogram grouped the genotypes into seven main clusters at a 50% similarity threshold, underscoring the genetic diversity present within the sorghum genotypes studied. Cluster I contained a single genotype, SVD-1272R, whereas, Cluster II included seven genotypes with subcluster formation. Cluster III comprised one ungrouped genotype, SPV-486. Cluster IV included eight genotypes, whereas Clusters V, VI, and VII each contained a single ungrouped genotype. This dendrogram illustrates the genetic diversity and relationships among the sorghum genotypes on the basis of similarity indices. The findings of this study confirmed the efficacy of SSR markers in assessing genetic diversity and emphasized their potential utility in breeding programs aimed at improving drought tolerance.

Image encryption algorithm based on a novel 2D logistic‐sine‐coupling chaos map and bit‐level dynamic scrambling

SummaryThis paper develops a new image encryption algorithm based on a novel two‐dimensional chaotic map and bit‐level dynamic scrambling. First, multiple one‐dimensional chaotic maps are coupled to construct a novel two dimensions Logistic‐Sine‐coupling chaos map (2D‐LSCCM). The performance analysis shows that the 2D‐LSCCM has more complex chaotic characteristics and wider chaotic range than many extant 2D chaos maps. Second, original image matrix combines with hash algorithm SHA‐256 to generate a hash value. The initial values of 2D‐LSCCM are generated based on the hash value. Third, the original image matrix is divided into multiple sub‐matrices by wavelet transform, followed by scrambling by an improved Knuth shuffle algorithm. Fourth, the scrambled multiple sub‐matrices are stitched into an image matrix of and converted into a binary matrix. The chaotic sequence generated by 2D‐LSCCM is introduced as a control sequence to control the bit‐level scrambling of pixel points, which realizes the bit‐level dynamic scrambling. Finally, the diffusion operation is performed by parameter par and chaotic sequence to obtain the final encrypted image. The algorithm security analysis and simulation examples demonstrate the effectiveness of the proposed encryption scheme.

Robust sparse recovery with sparse Bernoulli matrices via expanders

Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with lower storage costs and faster decoding algorithms. In particular, Bernoulli (p) matrices formed by independent identically distributed (i.i.d.) Bernoulli (p) random variables are of practical relevance in the context of noise-blind recovery in nonnegative compressed sensing.In this work, we investigate the robust nullspace property of Bernoulli (p) matrices. Previous results in the literature establish that such matrices can accurately recover n-dimensional s-sparse vectors with m=O(sc(p)log⁡ens) measurements, where c(p)≤p is a constant dependent only on the parameter p. These results suggest that in the sparse regime, as p approaches zero, the (sparse) Bernoulli (p) matrix requires significantly more measurements than the minimal necessary, as achieved by standard isotropic subgaussian designs. However, we show that this is not the case.Our main result characterizes, for a wide range of sparsity levels s, the smallest p for which sparse recovery can be achieved with the minimal number of measurements. We also provide matching lower bounds to establish the optimality of our results and explore connections with the theory of invertibility of discrete random matrices and integer compressed sensing.

Multimodal anti-counterfeiting and optical storage application based on luminescence reversible modification and color change of photochromic phosphor

Reversible upconversion luminescence (RUCL) modification based on photochromism has received considerable interest due to its potential applications in optical storage and invisible optical anti-counterfeiting. Herein, white β-Ba2ScAlO5: Yb3+, Er3+ (β-BSAO-YE) phosphor was irradiated with 254 nm light, which caused the phosphor to turn blue due to the increase of oxygen vacancy. The blue β-BSAO-YE phosphor returns to its original color upon stimulation with 808 nm laser light or 125 °C, exhibiting a double photo-induced reversible photochromic change. The green and red upconversion luminescence (UCL) of the β-BSAO-YE were reversibly modified according to their photochromic properties. The UCL modification changes the luminescence color of the pattern, indicating that β-BSAO-YE phosphor is an ideal compound anti-counterfeit agent. The light information recorded on the β-BSAO-YE binary photochromic dot matrix can be read under ultraviolet (UV) and near-infrared (NIR) excitation, demonstrating the potential application of β-BSAO-YE phosphors as optical data storage media. In addition, the cyclic experiment showed good photochromic and UCL modulation repeatability. The new luminescent β-BSAO-YE not only proposes a new way to exploring upconversion red light materials, but also provides new materials for optical storage, optical information and optical anti-counterfeiting.

Music Similarity Ranking: Case Study Fairphonic

Fairphonic Pte Ltd is a technology company operating in the music sector. Fairphonic provides services to detect content on social media that is suspected of copyright infringement. Fairphonic utilizes audio features for the detection process. The current algorithm used by Fairphonic requires pairwise comparison, and the content to be compared is collected through a scraping process immediately after the process is run. Fairphonic has hundreds of thousands of music data in their database. Fairphonic desires a more scalable algorithm to compare an input music piece with the entire Fairphonic music catalog. This research uses features such as Harmonic Pitch Class Profile (HPCP), Chroma, and Rhythm Pattern. The study compares previously researched algorithms, namely binary similarity matrix, Euclidean distance, and similarity matrix profile. The results show that the combination of HPCP with the binary similarity matrix yields the highest Mean Average Precision of 0.989. Speed testing by performing comparisons 10 times shows that the combination of Chroma and the similarity matrix profile is 72% faster compared to the combination of HPCP with the binary similarity matrix. The author recommends the Chroma and similarity matrix profile algorithm for music similarity ranking due to its faster process.

A Bayesian flexible model for testing Granger causality

A new Bayesian hypothesis testing procedure for evaluating the Granger causality between two or more time series is proposed. The test is based on a flexible model for the joint evolution of multiple series, where a latent binary matrix indicates whether there is a Granger-causal relationship between such time series. The model is specified through a dependent Geometric stick-breaking process that generalizes the standard parametric Gaussian vector autoregression model, whereas the prior distribution of the latent matrix ensures a multiple testing correction. A Monte Carlo simulation study is provided for comparing the robustness of the proposed hypothesis test with state-of-the-art alternatives. The results show that this proposal performs better than competing approaches. Finally, the new test is applied to real economic data.