Columns Of Matrix Research Articles

Exploring a novel tubular-type modular reactor for solar-driven thermochemical energy storage

Thermochemical energy storage (TCES) has gained extensive attention as a potential solution to address the mismatch between solar thermal energy production and demand. In this study, a novel tubular-type modular TCES reactor is introduced. COMSOL modelling of the system is developed and experimentally validated using a laboratory-scale TCES system. Both types of reactors show similar temperature increases, intensifying with higher inlet relative humidity. Their maximum temperature lifts exceeding 26 °C at 90 % RH. Tubular designs offer better axial flexural strength and dispersion of TCES composite materials compared to plate structures. This property of tubular structures beneficial reducing bed thickness and pressure drop and enhancing equivalent thermal efficiency. Simulations show tubular-type modular reactors reduce pressure drop by 4–5 times compared to plate-type modular reactors, increasing equivalent thermal efficiency by nearly 7% points. Increasing the number of reactor beds and inner tube radius improves equivalent thermal efficiency due to reduced bed thickness and pressure drop. As the number of matrix rows and columns in the reactor bed increases from 2 to 10, bed thickness decreases from 0.058 m to 0.012 m, reducing pressure drop from 845.53 Pa to 38 Pa and increasing equivalent thermal efficiency from 78.82 % to 96.61 %.

Convex Subspace Clustering by Adaptive Block Diagonal Representation.

Subspace clustering is a class of extensively studied clustering methods where the spectral-type approaches are its important subclass. Its key first step is to desire learning a representation coefficient matrix with block diagonal structure. To realize this step, many methods were successively proposed by imposing different structure priors on the coefficient matrix. These impositions can be roughly divided into two categories, i.e., indirect and direct. The former introduces the priors such as sparsity and low rankness to indirectly or implicitly learn the block diagonal structure. However, the desired block diagonalty cannot necessarily be guaranteed for noisy data. While the latter directly or explicitly imposes the block diagonal structure prior such as block diagonal representation (BDR) to ensure so-desired block diagonalty even if the data is noisy but at the expense of losing the convexity that the former's objective possesses. For compensating their respective shortcomings, in this article, we follow the direct line to propose adaptive BDR (ABDR) which explicitly pursues block diagonalty without sacrificing the convexity of the indirect one. Specifically, inspired by Convex BiClustering, ABDR coercively fuses both columns and rows of the coefficient matrix via a specially designed convex regularizer, thus naturally enjoying their merits and adaptively obtaining the number of blocks. Finally, experimental results on synthetic and real benchmarks demonstrate the superiority of ABDR to the state-of-the-arts (SOTAs).

Selected Columns of the Density Matrix in an Atomic Orbital Basis I: An Intrinsic and Non-iterative Orbital Localization Scheme for the Occupied Space.

In this work, we extend the selected columns of the density matrix (SCDM) methodology [J. Chem. Theory Comput. 2015, 11, 1463-1469]─a non-iterative and real-space procedure for generating localized occupied orbitals for condensed-phase systems─to the construction of local molecular orbitals (LMOs) in systems described using non-orthogonal atomic orbital (AO) basis sets. In particular, we introduce three different theoretical and algorithmic variants of SCDM (referred to as SCDM-M, SCDM-L, and SCDM-G) that can be used in conjunction with the AO basis sets used in standard quantum chemistry codebases. The SCDM-M and SCDM-L variants are based on a pivoted QR factorization of the Mulliken and Löwdin representations of the density matrix and are tantamount to selecting a well-conditioned set of projected atomic orbitals (PAOs) and projected (symmetrically-) orthogonalized atomic orbitals, respectively, as proto-LMOs that can be orthogonalized to exactly span the occupied space. The SCDM-G variant is based on a real-space (grid) representation of the wavefunction, and therefore has the added flexibility of considering a large number of grid points (or δ functions) when selecting a set of well-conditioned proto-LMOs. A detailed comparative analysis across molecular systems of varying size, dimensionality, and saturation level reveals that the LMOs generated by these three non-iterative/direct SCDM variants are robust, comparable in orbital locality to those produced with the iterative Boys or Pipek-Mezey (PM) localization schemes, and completely agnostic toward any single orbital locality metric. Although all three SCDM variants are based on the density matrix, we find that the character of the generated LMOs can differ significantly between SCDM-M, SCDM-L, and SCDM-G. In this regard, only the grid-based SCDM-G procedure (like PM) generates LMOs that qualitatively preserve σ-π symmetry (in systems such as s-trans alkenes), and are well-aligned with chemical (i.e., Lewis structure) intuition. While the direct and standalone use of SCDM-generated LMOs should suffice for most chemical applications, our findings also suggest that the use of these orbitals as an unbiased and cost-effective (initial) guess also has the potential to improve the convergence of iterative orbital localization schemes, in particular for large-scale and/or pathological molecular systems.

Red cell antibodies or noise? A case series on reactivity against the ingredients in column matrix

Abstract Noise in the immunohematological investigations can be described as a false reactivity of red blood cells (RBCs) in serologic testing that is not related to the interaction of RBC antigens and antibodies that the test system is intended to detect. These false-positive reactions can cause confusion during the cross-matching and RBC antibody screening and may result in delays in patient transfusion. Although these antibodies are predominantly clinically insignificant, proper laboratory work-up is indicated to avoid misidentification of a clinically significant antibody as a noise. In this report, we describe the three rare cases where the reactivity was found against the ingredients of the column matrix (glass beads). It is imperative that such reactivity is recognized and resolved during the investigation of blood group discrepancies, positive RBC antibody screens and in cases of positive cross-matches.

Observability Analysis and Restoration for Distribution Grids: A Robust Greedy Numerical Algorithm

This paper presents a robust and efficient algorithm for analyzing and restoring the observability of distribution grids. A linearized load flow model is used to characterize three-and multi-phase distribution grids under balanced and unbalanced conditions. Assuming that metering devices are installed to measure nodal magnitudes at some buses, the rank of the matrix associated with the non-metered magnitudes is determined by using a greedy strategy combined with a Gram-Schmidt orthonormalization procedure. Unlike other numerical-based techniques, the proposed algorithm avoids common errors caused by denominators close to zero. As an additional salient feature, a mathematically sound stopping criterion is provided to guarantee the robustness of the proposed algorithm. Furthermore, for unobservable grids, the algorithm identifies the linearly dependent rows in the aforementioned matrix, which correspond to the buses that should be metered to restore grid observability. The effective performance of the proposed algorithm is illustrated using several medium-and low-voltage benchmarks with up to 906 buses.

Lower Bounds for Column Matrix Approximations

Lower Bounds for Column Matrix Approximations

LOWER BOUNDS FOR COLUMN MATRIX APPROXIMATIONS

We show a connection between lower and upper bounds on the column matrix approximation accuracy and the bounds on the norms of the pseudoinverses of the submatrices of orthogonal matrices. This connection is exploited to derive lower bounds for column approximations accuracy in spectral and Frobenius norms.

Reversibly selective encryption for medical images based on coupled chaotic maps and steganography

The security and confidentiality of medical images are of utmost importance due to frequent issues such as leakage, theft, and tampering during transmission and storage, which seriously impact patient privacy. Traditional encryption techniques applied to entire images have proven to be ineffective in guaranteeing timely encryption and preserving the privacy of organ regions separated from the background. In response, this study proposes a specialized and efficient local image encryption algorithm for the medical field. The proposed encryption algorithm focuses on the regions of interest (ROI) within massive medical images. Initially, the Laplacian of Gaussian operator and the outer boundary tracking algorithm are employed to extract the binary image and achieve ROI edge extraction. Subsequently, the image is divided into ROI and ROB (regions outside ROI). The ROI is transformed into a row vector and rearranged using the Lorenz hyperchaotic system. The rearranged sequence is XOR with the random sequence generated by the Henon chaotic map. Next, the encrypted sequence is arranged according to the location of the ROI region and recombined with the unencrypted ROB to obtain the complete encrypted image. Finally, the least significant bit algorithm controlled by the key is used to embed binary image into the encrypted image to ensure lossless decryption of the medical images. Experimental verification demonstrates that the proposed selective encryption algorithm for massive medical images offers relatively ideal security and higher encryption efficiency. This algorithm addresses the privacy concerns and challenges faced in the medical field and contributes to the secure transmission and storage of massive medical images.

Neutrino Mixing Sum Rules and the Littlest Seesaw

In this work, we study the neutrino mixing sum rules arising from discrete symmetries and the class of Littlest Seesaw (LS) neutrino models. These symmetry-based approaches all offer predictions for the cosine of the leptonic CP phase cosδ in terms of the mixing angles, θ13, θ12, θ23, while the LS models also predict the sine of the leptonic CP phase sinδ, as well as making other predictions. In particular, we study the solar neutrino mixing sum rules, arising from charged lepton corrections to tri-bimaximal (TB), bimaximal (BM), golden ratio (GR) and hexagonal (HEX) neutrino mixing, and the atmospheric neutrino mixing sum rules, arising from preserving one of the columns of these types of mixing—for example, the first or second column of the TB mixing matrix (TM1 or TM2)—and we confront them with an up-to-date global fit of the neutrino oscillation data. We show that some mixing sum rules, such as an atmospheric neutrino mixing sum rule arising from a version of neutrino golden ratio mixing (GRa1), are already excluded at 3σ, and we determine the remaining models allowed by the data. We also consider the more predictive LS models (which obey the TM1 sum rules and offer further predictions) based on constrained sequential dominance CSD(n) with n≈3. We compare for the first time the three cases n=2.5, n=3 and n=1+6≈3.45, which are favored by theoretical models, using a new type of analysis to accurately predict the observables θ12, θ23 and δ. We study all the above approaches, solar and atmospheric mixing sum rules and LS models, together so that they may be compared and to give an up-to-date analysis of the predictions of all of these possibilities, when confronted with the most recent global fits.

A local POE-based self-calibration method using position and distance constraints for collaborative robots

Collaborative robots are designed to not only work alongside humans but also adapt to new tasks quickly. To improve their absolute accuracy, self-calibration methods utilizing portable measurement devices are cost-effective solutions. Based on the local frame representation of the Product-of-Exponential (POE) formula, a new modular kinematic error model is derived for collaborative robots, in which all geometric errors in a joint-link assembly, i.e., a dyad, are lumped into a local rigid body motion applied to its nominal joint axis. Its major advantage over the conventional local POE-based kinematic error model is that all columns in the error transformation Jacobian matrix are functions of joint displacements, which is critical to formulate singularity-free self-calibration models based on geometric constraints. A portable and cost-effective self-calibration device with both position and distance constraints is proposed for collaborative robots, which can readily collect a wide range of constraint errors by drag teaching within a collaborative robot’s workspace. Additionally, a two-step self-calibration method is established for both the robot arm and its base calibration. Its effectiveness and robustness are validated through simulations and experiments. The experimental results on Aubo i5 show that its average position error is significantly reduced from 4.11mm to 0.36mm after calibration.

Dynamic mode decomposition of deformation fields in elastic and elastic–plastic solids

Without recourse to constitutive assumptions, without knowledge of material properties, and without solving any of the conservation equations, we construct deformation fields for linear solids using Dynamic Mode Decomposition (DMD). Originally developed for analyzing experimental or computational field variables in fluid mechanics, it takes as input vectors of flow variables assembled as columns of a data matrix, and requires a remarkably few lines of code. It is a natural fit for solid mechanics wherein surface displacements can be used for the analysis. Vectors of surface displacements are arrayed in columns to created a data matrix. Singular Value Decomposition of the time-shifted data matrix affords selection of dominant modes (rank) in the deformation field. The DMD algorithm operates on time-shifted data matrices, obtains a reduced-order model that can reconstruct the deformation field, and also provides the dominant temporal and spatial modes of the deformation. In the case of linear elastic solids, DMD can be used to: reconstruct or predict the displacement states. In elastic–plastic solids, the transition from elastic to plastic results in the eigenvalues of the low-rank data matrix going out of the unit circle (implying an unstable growth mode). Using a combination of finite element analyses and displacement measurements obtained using Digital Image Correlation (DIC), we make the case for using DMD for state-estimation and state prediction in elastic solids and identifying onset of plasticity in elastic–plastic solids.

State of charge estimation for lithium-ion battery based on adaptive extended Kalman filter with improved residual covariance matrix estimator

The accurate estimation of the state of charge (SOC) in lithium-ion batteries plays a pivotal role in battery management systems. This paper proposes an improved adaptive extended Kalman filter (IAEKF) algorithm for more precise SOC estimation. Initially, a novel characteristic parameter is introduced to assess the suitability of the forgetting factor in the adaptive forgetting factor recursive least squares (AFFRLS) algorithm. This evaluation aims to improve the accuracy of recognizing the parameters of the battery model. Additionally, an even function with adjustable parameters is constructed to solve the appropriate value for the forgetting factor. Subsequently, the correlation coefficients of the residual series at different moments are approximated by mathematical transformations that link the inner products of the column vectors in the constructed residual matrix to the calculation of the correlation coefficients. By comparing it with optimized thresholds using particle swarm optimization, one can adjust the sliding window length to enhance the estimation accuracy of IAEKF. The experimental results confirm that IAEKF achieves superior estimation accuracy and robustness compared to other AEKF algorithms, and the accuracy of AFFRLS parameter identification is higher than that of recursive least squares, thereby substantiating the effectiveness of the proposed algorithms.

The Schur decomposition of discrete Sine and Cosine transformations of type IV

Eigendecomposition of discrete sine and cosine transformations of type IV is the main objective of this study. A closed form formula for eigenvectors is derived using the property that a square of the transform matrix is proportional to the identity matrix. Odd and even transform sizes are considered separately. In both cases, it has been demonstrated that the eigenvectors can be obtained by a straightforward modification of the columns of the transformation matrix. Comparing this approach with the related works, it provides a simple explanation of the eigendecomposition with a reliable numerical stability. Additionally, these eigenvectors can be used to obtain the eigendecomposition of the counterpart offset discrete Fourier transform.

Study on the aesthetic evaluation method of applying symmetry analysis in industrial product styling design

Abstract The evaluation of product styling design is transformed into a complex nonlinear solution problem by symmetry analysis in this paper. The equilibrium matrix decomposition evaluation system calculates the stored matrix singular values in product styling design and proves that symmetry can be obtained from the stress matrix row vector. The regression algorithm is used to process multiple industrial product design objectives, and each design element in product styling is coded to obtain the fitness evaluation of individual industrial products. It is found that the satisfaction score in product styling design is 97.4, the weight index of logo novelty element is up to 7, and the regression coefficient of plane shape is 0.269, to improve the scientific and feasibility of aesthetic evaluation of industrial product styling design.

A model-free-based control chart for batch process using U-statistics

Batch processes are known to generate time series of successive measurements of many process variables in each run and the main challenge is to capture and accommodate the variability in the batch domain (batch-to-batch variability) and in the time domain (data with serial correlation). Classical approaches are focused on the first goal by applying multivariate techniques in the columns of a data matrix, in which each row has the data for the entire batch run. Those approaches are grounded in the traditional Multiway Principal Component Analysis (MPCA). Recent approaches are focused on the balance between the two sources, taking into account the time series nature of the data mainly by using time series models and neural network methods to directly accommodate the variability in the time domain. This paper proposes a model-free approach based on U-statistics theory. Through this theory, we can build a group of control charts (named V charts) capable of monitoring batch processes considering both sources of variability. In general, the new batch under monitoring is evaluated according to a group of reference in-control samples, based on the distance measures from those batches. The proposed approach is really flexible since we avoid model identification, parameter estimates issues and it is able to accommodate the within and between batch variability. Additionally, our method is suitable to deal with a wide range of batch data features, since under weak conditions, the distribution of the V statistics remains well known. It makes the V-based charts able to be used in different kinds of processes. We are focused here on controlling changes caused by data drifts (including trends) and by data serial correlation (data dynamics). Through the simulated and real batch process, we show that the V charts work well, including a scenario with very few reference batches available.

Assessment of Essential Information in the Fourier Domain to Accelerate Raman Hyperspectral Microimaging.

In the context of multivariate curve resolution (MCR) and spectral unmixing, essential information (EI) corresponds to the most linearly dissimilar rows and/or columns of a two-way data matrix. In recent works, the assessment of EI has been revealed to be a very useful practical tool to select the most relevant spectral information before MCR analysis, key features being speed and compression ability. However, the canonical approach relies on the principal component analysis to evaluate the convex hull that encapsulates the data structure in the normalized score space. This implies that the evaluation of the essentiality of each spectrum can only be achieved after all the spectra have been acquired by the instrument. This paper proposes a new approach to extract EI in the Fourier domain (EIFD). Spectral information is transformed into Fourier coefficients, and EI is assessed from a convex hull analysis of the data point cloud in the 2D phasor plots of a few selected harmonics. Because the coordinate system of a phasor plot does not depend on the data themselves, the evaluation of the essentiality of the information carried by each spectrum can be achieved individually and independently from the others. As a result, time-consuming operations like Raman spectral imaging can be significantly accelerated exploiting a chemometric-driven (i.e., based on the EI content of a spectral pixel) procedure for data acquisition and targeted sampling. The usefulness of EIFD is shown by analyzing Raman hyperspectral microimaging data, demonstrating a potential 50-fold acceleration of Raman acquisition.

Model resolution-based deconvolution for improved quantitative susceptibility mapping.

Quantitative susceptibility mapping (QSM) utilizes the relationship between the measured local field and the unknown susceptibility map to perform dipole deconvolution. The aim of this work is to introduce and systematically evaluate the model resolution-based deconvolution for improved estimation of the susceptibility map obtained using the thresholded k-space division (TKD). A two-step approach has been proposed, wherein the first step involves the TKD susceptibility map computation and the second step involves the correction of this susceptibility map using the model-resolution matrix. The TKD-estimated susceptibility map can be expressed as the weighted average of the true susceptibility map, where the weights are determined by the rows of the model-resolution matrix, and hence a deconvolution of the TKD susceptibility map using the model-resolution matrix yields a better approximation to the true susceptibility map. The model resolution-based deconvolution is realized using closed-form, iterative, and sparsity-regularized implementations. The proposed approach was compared with L2 regularization, TKD, rescaled TKD in superfast dipole inversion, the modulated closed-form method, and iterative dipole inversion, as well as sparsity-regularized dipole inversion. It was observed that the proposed approach showed a substantial reduction in the streaking artifacts across 94 test volumes considered in this study. The proposed approach also showed better error reduction and edge preservation compared with other approaches. The proposed model resolution-based deconvolution compensates for the truncation of zero coefficients in the dipole kernel at the magic angle and hence provides a closer approximation to the true susceptibility map compared with other direct methods.

Metaheuristic Biclustering Algorithms: From State-of-the-art to Future Opportunities

Biclustering is an unsupervised machine-learning technique that simultaneously clusters rows and columns in a data matrix. Over the past two decades, the field of biclustering has emerged and grown significantly, and currently plays an essential role in various applications such as bioinformatics, text mining, and pattern recognition. However, finding significant biclusters in large-scale datasets is an NP-hard problem that can be formulated as an optimization problem. Therefore, metaheuristics have been applied to address biclustering problems due to their (i) ability to efficiently explore search spaces of complex optimization problems, (ii) capability to find solutions in reasonable computation time, and (iii) facility to adapt to different problem formulations, as they are considered general-purpose heuristic algorithms. Although several studies on biclustering approaches have been proposed, a comprehensive study using metaheuristics for bicluster analysis is missing. This work presents a survey of metaheuristic approaches to address the biclustering problem in various scientific applications. The review focuses on the underlying optimization methods and their main search components: representation, objective function, and variation operators. A specific discussion on single versus multi-objective approaches is presented. Finally, some emerging research directions are presented.

Targeting performance and user-friendliness: GPU-accelerated finite element computation with automated code generation in FEniCS

This paper studies the use of automated code generation to provide user-friendly GPU acceleration for solving partial differential equations (PDEs) with finite element methods. By extending the FEniCS framework and its automated compiler, we have achieved that a high-level description of finite element computations written in the Unified Form Language is auto-translated to parallelised CUDA C++ code. The auto-generated code provides GPU offloading for the finite element assembly of linear equation systems which are then solved by a GPU-supported linear algebra backend.Specifically, we explore several auto-generated optimisations of the resulting CUDA C++ code. Numerical experiments show that GPU-based linear system assembly for a typical PDE with first-order elements can benefit from using a lookup table to avoid repeatedly carrying out numerous binary searches, and that further performance gains can be obtained by assembling a sparse matrix row by row. More importantly, the extended FEniCS compiler is able to seamlessly couple the assembly and solution phases for GPU acceleration, so that all unnecessary CPU–GPU data transfers are eliminated. Detailed experiments are used to quantify the negative impact of these data transfers, which can entirely destroy the potential of GPU acceleration if the assembly and solution phases are offloaded to GPU separately. Finally, a complete, auto-generated GPU-based PDE solver for a nonlinear solid mechanics application is used to demonstrate a substantial speedup over running on dual-socket multi-core CPUs, including GPU acceleration of algebraic multigrid as the preconditioner.

Efficiency of any weighted geometric mean of the columns of a reciprocal matrix

We focus upon the reciprocal matrix component of the often discussed Analytic Hierarchy Process and its approximation by a consistent matrix formed from an efficient vector. It is known that a vector is efficient for a reciprocal matrix A if and only if a certain digraph is strongly connected. Here, we give a transparent and relatively simple matricial proof of this important result. Then we show that any Hadamard weighted geometric mean of the columns of a reciprocal matrix is efficient. This is a major generalization of the known result that the Hadamard geometric mean of all columns is efficient, and of the recent result that the geometric mean of any subset of the columns is efficient.