Residual Matrix Research Articles

An alternating projection algorithm for the “approximate” GCD calculation

In the paper an approach is proposed for calculating the “best” approximate GCD of a set of coprime polynomials. The algorithm is motivated by the factorisation of the Sylvester resultant matrix of polynomial sets with nontrivial GCD. In the (generic) case of coprime polynomial sets considered here the aim is to minimise the norm of the residual error matrix of the inexact factorisation in order to compute the “optimal” approximate GCD. A least-squares alternating projection algorithm is proposed as an alternative to the solution of the corresponding optimisation problem via nonlinear programming techniques. The special structure of the problem in this case, however, means that the algorithm can be reduced to a sequence of standard subspace projections and hence no need arises to compute gradient vectors, Hessian matrices or optimal step-lengths. An estimate of the asymptotic convergence rate of the algorithm is finally established via the inclination of two subspaces.

Unsupervised Feature Selection Based on Low-Rank Regularized Self-Representation

Feature selection aims to find a set of features that are concise and have good generalization capabilities by removing redundant, uncorrelated, and noisy features. Recently, the regularized self-representation (RSR) method was proposed for unsupervised feature selection by minimizing the L2,1 norm of residual matrix and self-representation coefficient matrix. In this paper, we find that minimizing the L2,1 norm of the self-representation coefficient matrix cannot effectively extract the features with strong correlation. Therefore, by adding the minimum constraint on the kernel norm of the self-representation coefficient matrix, a new unsupervised feature selection method named low-rank regularized self-representation (LRRSR) is proposed, which can effectively discover the overall structure of the data. Experiments show that the proposed algorithm has better performance on clustering tasks than RSR and other related algorithms.

Neoliberalismo e proteção social no capitalismo: as “redes de proteção” ao adolescente em conflito com a lei no Brasil

This article aims to make explicit the relationships between the advancement of neoliberalism and the institutionalization of the so called safety nets for the adolescents submitted to the instances of administration and control of juvenile crime in Brazil. It is a bibliographical and documentary research of exploratory-descriptive character, whose collection, systematization and data analysis followed the hermeneutic-dialectic method. The research results show that the currently accepted network social protection model for the administration of juvenile crime in Brazil has incorporated the specific type of state attention that is included in the Residual Matrix of Social Protection. The social results of the capitalist mode of production, the adherence of the Brazilian State to the principles of neoliberalism and neoconservatism, the juridical-administrative and social production of the infractional act as well as the differential classification of juvenile crime explain the economic character and the class nature present in the opposition between the private property and the unequal distribution of the socially produced material wealth.

Mechanism of powellite crystallite expansion within nano-phase separated amorphous matrices under Au-irradiation.

A fundamental approach was taken to understand the implications of increased nuclear waste loading in the search for new materials for long-term radioisotope encapsulation. This study focused on the formation and radiation tolerance of glass ceramics with selectively induced CaMoO4 as a form to trap the problematic fission product molybdenum. Several samples were synthesised with up to 10 mol% MoO3 within a soda lime borosilicate matrix, exhibiting phase separation on the nano scale according to thermal analysis, which detected two glass transition temperatures. It is predicted that these two phases are a result of spinodal decomposition with Si-O-Ca-O-Si and Si-O-Ca-O-B units, with the latter phase acting as a carrier for MoO3. The solubility limit of molybdenum within this matrix was 1 mol%, after which crystallisation of CaMoO4 occurred, with crystallite size (CS) increasing and cell parameters decreasing as a function of [MoO3]. These materials were then subjected to irradiation with 7 MeV Au3+ ions to replicate the nuclear interactions resulting from α-decay. A dose of 3 × 1014 ions per cm2 was achieved, resulting in 1 dpa of damage within a depth of ∼1.5 μm, according to TRIM calculations. Glasses and glass ceramics were then analysed using BSE imaging, XRD refinement, and Raman spectroscopy to monitor changes induced by accumulated damage. Irradiation was not observed to cause any significant changes to the residual amorphous network, nor did it cause amorphisation of CaMoO4 based on the relative changes to particle size and density. Furthermore, the substitution of Ca2+ to form water-soluble Na2/NaGd-MoO4 assemblages did not occur, indicating that CaMoO4 is resilient to chemical modification following ion interactions. Au-irradiation did however cause CaMoO4 lattice parameter expansion, concurrent to growth in CS. This is predicted to be a dual parameter mechanism of alteration based on thermal expansion from electronic coupling, and the accumulation of defects arising from atomic displacements.

Correlation between structure and magnetic properties of “finemet” type microwires

Effect of geometrical parameters (metallic core diameter, glass cover thickness) on the structure and magnetic properties of glass-coated Fe-Si-B-Nb-Cu microwires is investigated. The structure of as-prepared Fe73.8Cu1Nb3.1Si13B9.1 microwire is nanocrystalline, consisting of α-Fe(Si) crystallites in a residual amorphous matrix. It is shown that great residual stresses arising at the manufacturing processes greatly influence the microstresses and crystallite sizes of α-Fe(Si) crystals. An increasing of stress magnitude results to structure refinement. The size of α-Fe(Si) crystals and crystallized volume fraction decrease from approximately 105 nm and 71 % to 9 nm and 34 %, respectively, with glass cover thickness increasing. Grain size refinement of α-Fe(Si) leads to the considerable decrease of coercivity of microwires from 1800 A/m to 160 A/m.

Robust mixed source localization in WSN using swarm intelligence algorithms

Passive localization and classification algorithms for mixed near-field and far-field sources have mainly been investigated for antenna arrays with regular or symmetrical geometry. However, these algorithms may not be applicable to wireless sensor networks, where spatially distributed sensor nodes form an array of random geometry. This paper proposes squared error norm of residual fitting error matrix (SRFEM) cost function for mixed source localization, which does not place any constraint on the geometry of antenna array. The proposed cost function is optimized using computationally simple swarm intelligence (SI) algorithms. Convergence performance of three SI algorithms, i.e., particle swarm optimization, Whale optimization, and Grey Wolf optimization is investigated to obtain estimates of the source location parameters with a minimal number of iterations or computational complexity. In order to provide robustness for the SRFEM cost function, this paper proposes an impulse denoising technique based on the long-short term memory recurrent neural network (LSTM-RNN). Simulation results confirm that, in the presence of AWGN, the proposed SRFEM cost function outperforms existing techniques based on the uniform linear array and approaches the theoretical Cramer-Rao lower bound even for a fewer number of snapshots. Further, simulation analysis also reveals that LSTM-RNN provides better mixed localization performance under impulse noise as compared to the bounded noise covariance approach at high signal-to-noise values.

In Vitro Digestion of Apple Tissue Using a Dynamic Stomach Model: Grinding and Crushing Effects on Polyphenol Bioaccessibility.

Food structure is a key determinant for the release of phenolic compounds during gastric and intestinal digestion. We evaluated the bioaccessibility of polyphenols from apple tissue during gastric digestion in vitro from bio-mechanical perspectives including the effects of gastric juice and mucin on the apple tissue matrix under simulated stomach peristalsis. The gastric model system was effective in releasing polyphenols because of simultaneous compression and extrusion, with 3 times higher release from coarse than from fine particles. However, bioaccessibility of polyphenols was reduced up to 44% in the presence of both cell walls and gastric mucin. Most individual phenolic molecules were gradually released and were stable in the gastric environment, except for procyanidin B2. The study suggests that the bioaccessibility of polyphenols from apples in the upper digestive tract is dependent on mechanical disintegration and the residual matrix present in the swallowed bolus.

Hyperspectral Anomaly Detection via Tensor- Based Endmember Extraction and Low-Rank Decomposition

Due to the limited resolution of hyperspectral sensors, anomalous targets expressed with subpixels are often mixed with nonhomogeneous backgrounds. This fact makes anomalies difficult to distinguish from the surrounding background. From this perspective, a novel hyperspectral anomaly detection (AD) algorithm based on endmember extraction and low-rank representation (LRR) is proposed. For the characteristics of pixels in hyperspectral images (HSIs), the proposed algorithm employs an endmember extraction technology to yield an abundance matrix for AD, thereby gathering more feature information compared with the direct use of a raw image. In addition, a dictionary construction strategy based on Tucker decomposition, and the ${k}$ -means++ clustering method is proposed to make the dictionary more stable and discriminative. An LRR method based on the dictionary is applied to obtain a sparse residual matrix. Finally, anomalies can be determined by the response of the residual matrix. Experiments on three hyperspectral data sets validate the performance of the proposed algorithm.

Low-rank nonnegative matrix factorization on Stiefel manifold

Low rank is an important but ill-posed problem in the development of nonnegative matrix factorization (NMF) algorithms because the essential information is often encoded in a low-rank intrinsic data matrix, whereas noise and outliers are contained in a residue matrix. Most existing NMF approaches achieve low rank by directly specifying the dimensions of the factor matrices. A few others impose the low rank constraint on the factor matrix and use the alternating direction method of multipliers to solve the optimization problem. In contrast to previous approaches, this paper proposes a novel method for low-rank nonnegative matrix factorization on a Stiefel manifold (LNMFS), which utilizes the low rank structure of intrinsic data and transforms it into a Frobenius norm of the latent factors. To obtain orthogonal factors as distinct patterns, we further impose orthogonality constraints by assuming that the basis matrix lies on a Stiefel manifold. In addition, to improve the robustness of the data in a manifold structure, we incorporate the graph smoothness of the coefficient matrix. Finally, we develop an efficient alternative iterative algorithm to solve the optimization problem and provide proof of its convergence. Extensive experiments on real-world datasets demonstrate the superiority of the proposed method compared with other representative NMF-based algorithms.

Synthesis and characterization of urchin-like CuO nanorod/TiCu-based metallic glass core-shell powders with surface photovoltage performance

The core-shell urchin-like powders (i.e. the microsized core composed of the residual metallic glass matrix powders and short CuO nanorod as the shell) were obtained through selective hydrothermal dealloying and annealed oxidation methods. TiCu-based metallic glass powders were used as precursors. Furthermore, the morphology and photoelectric conversion property of urchin-like CuO nanorod/metallic matrix powders were comprehensively investigated. These core-shell powders possess considerable surface photovoltage properties, and the sample annealed at 500 °C in air exhibits optimal surface photoelectric responses in visible light range (~600 nm). The surface photovoltage property was determined by the synergistic effect of crystallinity and surface morphology for the CuO phase. This study provides a strategy for in-situ synthesis of novel micro-nano-sized core-shell functional materials using facile dealloying and annealing of multiple-component alloys. The advantage of obtained products will further accelerate their applications in the green industry since this kind of micro-nano-sized powder material is easy to separate and recycle.

Retrieving a contingency table from a correspondence analysis solution

Correspondence analysis (CA) is a dimension reduction technique for categorical data. In particular, CA is typically applied to a contingency matrix in order to visualize the relationships within and between the categories of the two variables as represented by its rows and columns. The CA solution can be obtained by considering a singular value decomposition of the so-called matrix of standardized residuals. Inverse correspondence analysis considers the problem of retrieving the data underlying a given low-dimensional CA solution. Using the specific structure of the CA solutions as well as the characteristics of the original data we formulate the inverse CA problem in an integer linear programming context. Considering various conditions involving the dimensions of the original data matrix, the number of observations, the precision and dimensionality of the CA solution, we show that by solving the integer linear programs, the original data can be retrieved.

Weighted sparse principal component analysis

Sparse principal component analysis (SPCA) has been shown to be a fruitful method for the analysis of high-dimensional data. So far, however, no method has been proposed that allows to assign elementwise weights to the matrix of residuals, although this may have several useful applications. We propose a novel SPCA method that includes the flexibility to weight at the level of the elements of the data matrix. The superior performance of the weighted SPCA approach compared to unweighted SPCA is shown for data simulated according to the prevailing multiplicative-additive error model. In addition, applying weighted SPCA to genomewide transcription rates obtained soon after vaccination, resulted in a biologically meaningful selection of variables with components that are associated to the measured vaccine efficacy. The MATLAB implementation of the weighted sparse PCA method is freely available from https://github.com/katrijnvandeun/WSPCA.

A nonlocal operator method for solving partial differential equations

A nonlocal operator method is proposed which is generally applicable for solving partial differential equations (PDEs) of mechanical problems. The nonlocal operator can be regarded as the integral form “equivalent” to the differential form in the sense of a nonlocal interaction model for solving the unknown field. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method, thus it circumvents many difficulties in the calculation of shape functions and their derivatives. The nonlocal operator method can consistently applied with common procedure leading to the weak forms, i.e. the variational principle and the weighted residual method. Based on these, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. Higher order nonlocal operators and higher order operator energy functional are hereby generalized. A highlighted of the present method is the functional derived based on the nonlocal operator can convert the construction of residual and stiffness matrix into a series of matrix multiplications using the predefined nonlocal operators. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support, the two basic elements introduced in the paper. Several numerical examples of different types of PDEs are presented in the end to show the effectiveness of the present method and also serve for validation.

Psychometric validation of PROMIS® Anxiety and Depression Item Banks for the Brazilian population

Scientific evidence indicates that depression and anxiety symptoms may be understood as risk factors associated with the incidence and progression of chronic diseases. Considering the lack of mental health assessment tools that meet strict methodological standards, the authors have chosen to validate the psychometric properties of Anxiety and Depression Item Banks - Emotional Distress domain of the Patient-Reported Outcomes Measurement Information System (PROMIS®) for the Brazilian population. In this study, 606 adults responded to the self-administered Anxiety and Depression Item Banks, which were calibrated using Factor Analyses (Exploratory and Confirmatory analysis) and adjustment of the Graded Response Model. Transcultural validity was assessed by Differential Item Functioning (DIF). The two-factor analysis confirmed the unidimensionality of Emotional Distress Items (CFI = 0.96, TLI = 0.96, RMSEA = 0.05). The residual correlation matrix did not identify item pairs with local dependence. Indicators marked with DIF presented a low impact for gender, age, and language variables. The instrument demonstrated greater reliability in the moderate-severe range, indicating that the error reduction is reflected in the - 1.0 to + 3.0 amplitude. The psychometric measurements of Anxiety and Depression Item Banks in the Brazilian version were equivalent to those in the original version. Additional research contemplating patients with different levels of emotional distress are necessary to better comprehend the results obtained in this study.

Revealing favorable and unfavorable residues in cooperative positions in protease cleavage sites

Proteases play critical roles in a wide variety of fundamental biological functions, and numerous protease inhibitors have been developed to treat various diseases including cancer. A wide range of experimental and computational methods have been developed to investigate the specificity and catalytic mechanisms of proteases. However, these methods only focused on the preferences of a single position around a cleavage site in a substrate, rarely on the compositionality of the subsites. We present new methods to quantify the specificity of proteases by considering the combinatorial patterns of amino acid residuals of cleavage sites in substrates. By incorporating the preference at positions, we modeled three types of favorable combinations of residues in cleavage sites. Moreover, by constructing a relationship weight matrix of residues between two positions, we can easily identify unfavorable combinations of residues at the positions. Applying these methods to a set of known cleavage sites of proteases, we revealed numerous favorable and unfavorable residues in cooperative positions in the protease cleavage sites. The results can help understand the specificity and catalytic mechanisms of proteases. To our knowledge, this is the first study that quantifies unfavorable combinations of amino acids between two sites. Furthermore, this method is not limited to the study of proteases and cleavage sites, and can be generalized to uncover the relationships of residues at meaningful sites in other proteins.

Hyperspectral Anomaly Detection via Convolutional Neural Network and Low Rank With Density-Based Clustering

Over the last two decades, anomaly detection (AD) has been known to play a critical role in hyperspectral image analysis, which provides a new way to distinguish the targets from the background without prior knowledge. Recently, the representation-based methods were proposed and soon became a significant type of methods on hyperspectral AD. In this paper, a novel AD algorithm based on convolutional neural network (CNN) and low-rank representation (LRR) is proposed. First, a CNN model is built and trained on hyperspectral image (HSI) datasets to accurately obtain the resulting abundance maps. Compared with the raw dataset, abundance maps contain more distinctive features to identify anomalies from the background. Second, a dictionary is constructed by the density-based spatial clustering of applications with noise (DBSCAN) algorithm to stably represent the background component. Third, a matrix decomposition method based on LRR is adopted. In this way, a coefficient matrix corresponding to the constructed dictionary is obtained, which is low rank. At the same time, a residual matrix can be obtained as well, which is sparse. Finally, anomalies can be extracted from the residual matrix. The experimental results show that the proposed method achieves a superior performance compared to some of the state-of-the-art methods in the field of hyperspectral AD.

English

English

Properly handling negative values in the calculation of binding constants by physicochemical modeling of spectroscopic titration data

AbstractTo implement equilibrium hard‐modeling of spectroscopic titration data, the analyst must make a variety of crucial data processing choices that address negative absorbance and molar absorptivity values. The efficacy of three such methodological options is evaluated via high‐throughput Monte Carlo simulations, root‐mean‐square error surface mapping, and two mathematical theorems. Accuracy of the calculated binding constant values constitutes the key figure of merit used to compare different data analysis approaches. First, using singular value decomposition to filter the raw absorbance data prior to modeling often reduces the number of negative values involved but has little effect on the calculated binding constant despite its ability to address spectrometer noise. Second, both truncation of negative molar absorptivity values and the fast nonnegative least squares algorithms are superior to unconstrained regression because they avoid local minima; however, they introduce bias into the calculated binding constants in the presence of negative baseline offsets. Finally, we establish two theorems showing that negative values are best addressed when all the chemical solutions leading to the raw absorbance data are the result of mixing exactly two distinct stock solutions. This allows the raw absorbance data to be shifted up, eliminating negative baseline offsets, without affecting the concentration matrix, residual matrix, or calculated binding constants. Otherwise, the data cannot be safely upshifted. A comprehensive protocol for analyzing experimental absorbance datasets with is included.

Surface and structural characterization of amorphous Fe,Co-based melt-spun ribbons subjected to heat treatment processes

In this paper, the effect of the heat treatment process on the surface morphology, crystallization process and magnetic properties of Fe38Co38Mo8B15Cu ribbons produced by melt spinning was investigated. Number of protrusions uniformly distributed on surfaces of as-quenched ribbons were identified by atomic force microscopy (AFM). AFM results also indicated that variation of surface morphology of density, size, and shape of protrusions along the ribbon surface. According to magnetic force microscopy (MFM) analysis, the magnetic domain walls were not observed for annealing temperatures of 300 °C–360 °C. After annealing at 420 °C, the domains grow wider and align parallel to each other. Minor amounts of bcc-FeCo nano-sized crystalline grains which homogeneously and randomly distributed to the residual amorphous matrix were observed by the transmission electron microscopy (TEM). The crystalline grains are enlarged and became more visible. The best coercivity and saturation magnetization values were obtained at 360–420 °C.

Reconstruction of compressively sampled MR images based on a local shrinkage thresholding algorithm with curvelet transform.

To reduce the magnetic resonance imaging (MRI) data acquisition time and improve the MR image reconstruction performance, reconstruction algorithms based on the iterative shrinkage thresholding algorithm (ISTA) are widely used. However, these traditional algorithms use global threshold shrinkage, which is not efficient. In this paper, a novel algorithm based on local threshold shrinkage, which is called the local shrinkage thresholding algorithm (LSTA), was proposed. The LSTA can shrink differently for different elements from the residual matrix to adjust the shrinkage speed for each element of the image during the iterative process. Then, by taking advantage of the sparser characteristics of the curvelet transform, the LSTA combined with the curvelet transform (CLSTA) can make the construction process more efficient. Finally, compared with ISTA, the generalized thresholding iterative algorithm (GTIA) and the fast iterative shrinkage threshold algorithm (FISTA), when analysing human (brain and cervical) MR images, a conclusion can be drawn that the proposed method has better reconstruction performance in terms of the mean square error (MSE), the peak signal to noise ratio (PNSR), the structural similarity index measure (SSIM), the normalized mutual information (NMI), the transferred edge information (TEI) and the number of iterations. The proposed method can better maintain the detailed information of the reconstructed images and effectively decrease the blurring of the images edges. Graphical abstract.