Hierarchical Matrix Research Articles

Decoration on the inner surface of low-tortuosity microchannels derived from wood plate for highly stable lithium sulfur batteries

The low-tortuosity microchannels of wood-based carbon matrix in free-standing cathodes for lithium sulfur batteries (LSBs) were a double-edged sword, which brought in both a high energy density due to a high sulfur loading and severe shuttle effect for poor cycling stability. Herein, a layer of cellulose aerogel extracted from the wood wall was coated on the inner surface of the low-tortuosity microchannels of the wood plate, which was further transformed into a hierarchical carbon matrix using in free-standing cathode for LSBs. The decorated cathode exhibited a maximal specific capacity of 1377.2 mAh g−1 due to the enhanced utilizing ratio of active materials and exceptional cycling stability even under a high current density (1 C) for more than 500 cycles. Furthermore, the decorated cathode maintained good cycling stability with a higher sulfur areal loading (6.3 mg cm−2). The cellulose-based carbon aerogel coated on the inner surface of low-tortuosity microchannels provided a large specific surface area. This decoration strategy not only provided physical restriction on polysulfides but also increased conversion sites for polysulfides, improving the cycling performance of the wood-based free-standing cathode of LSBs. This work provided a potential structural design strategy for the advanced free-standing cathode of LSBs.

Hierarchical matrix factorization for interpretable collaborative filtering

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user–item interaction matrix into user and item latent matrices. Because the model typically learns each interaction independently, it may overlook the underlying shared dependencies between users and items, resulting in less stable and interpretable recommendations. Based on these insights, we propose “Hierarchical Matrix Factorization” (HMF), which incorporates clustering concepts to capture the hierarchy, where leaf nodes and other nodes correspond to users/items and clusters, respectively. Central to our approach, called hierarchical embeddings, is the additional decomposition of the latent matrices (embeddings) into probabilistic connection matrices, which link the hierarchy, and a root cluster latent matrix. The embeddings are differentiable, allowing simultaneous learning of interactions and clustering using a single gradient descent method. Furthermore, the obtained cluster-specific interactions naturally summarize user–item interactions and provide interpretability. Experimental results on ratings and ranking predictions show that HMF outperforms existing MF methods, in particular achieving a 1.37 point improvement in RMSE for sparse interactions. Additionally, it was confirmed that the clustering integration of HMF has the potential for faster learning convergence and mitigation of overfitting compared to MF, and also provides interpretability through a cluster-centered case study.

HODLR3D: hierarchical matrices for N-body problems in three dimensions

HODLR3D: hierarchical matrices for N-body problems in three dimensions

Adaptive [formula omitted]-matrix computations in linear elasticity

This article deals with the efficient numerical treatment of the Lamé equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM). Using BEM, one is faced with the solution of a system of equations with a fully populated system matrix, which is in general very costly. In order to overcome this difficulty, adaptive and approximate algorithms based on hierarchical matrices and the adaptive cross approximation are proposed. These new methods rely on error estimators and refinement techniques known from adaptivity but are not used here to improve the mesh. We apply these new techniques to both, the efficient solution of Lamé equations and to the multiplication with given data.

Physicochemical synergistic adsorption of CO2 by PEI‐impregnated hierarchical porous polymers

AbstractAmine‐functionalized porous polymers have been considered as a prominent chemical adsorption material for carbon capture and storage (CCS) process, because of their large adsorption capacity and high selectivity. By comparison, the low energy‐consumption for desorption and high recyclability are the advantages of the physical adsorption approach. In this work, an amine‐functionalized hierarchical porous polymer was prepared by HIPE (high internal phase emulsions) template and amine impregnation strategy, and applied as CO2 adsorbent to realize chemical adsorption and physical adsorption simultaneously. First, a hierarchical porous matrix of poly(styrene‐glycidyl methacrylate) was prepared by the HIPE method. The formed meso/micropores in the typical porous polymer matrix could attract CO2 molecules, where the physical adsorption was achieved. Subsequently, PEI (polyethyleneimine) was impregnated into the porous polymer with abundant macropores, and the numerous of amino groups provided the reaction sites, where the chemical adsorption was achieved. As a result, an effective CO2 adsorption material was obtained via controlling the porous structure by changing the volume fraction of dispersive phase, impregnation condition and amine loading. Aided by the chemical adsorption of amino groups, the CO2 adsorption capacity of the obtained adsorbent reached 3.029 mmol/g. Moreover, the CO2 adsorption thermodynamics confirmed the physicochemical synergistic adsorption, and then the Qst reduced to 31–42 kJ/mol and a good cyclic stability was obtained. As conclusion, the porous adsorbent showed a good industrial application prospect. © 2024 Society of Chemical Industry and John Wiley & Sons, Ltd.

Thermally exfoliated graphene oxide doped microporous bio-nanocomposite hydrogel: A promising substrate for biomedical application

Hydrogels have demonstrated significant promise as flexible/wearable sensors for the diagnosis, monitoring, and delivery of personalized medicine for health issues and deficiencies. To this end, a novel approach was employed towards the development of a hybrid hydrogel nanocomposite-based biosensing substrate. The hierarchical hydrogel matrix derived by using polyaniline (PANI)/polyvinyl-alcohol (PVA) biopolymer-matrix, was reinforced with in-house synthesized thermally exfoliated graphene-oxide (TEGO). Fourier transform infrared spectroscopy (FT-IR) confirmed the interfacial-interactions between hydroxyl groups and functional groups of TEGO, a conducive property for immobilization and catalytic activities. X-ray photoelectron spectroscopy (XPS) investigation of the developed nanocomposite hydrogel demonstrated that the addition of nanofiller facilitated the ordered structure of nanocomposite hydrogel. Further, field emission scanning electron microscopy (FE-SEM) investigations revealed interconnected porous microstructure of the nanocomposites, assisted by nucleating effect of TEGO, a supporting micro-environment for the transportation of biomolecules. Impedance analysis and hall effect studies showed that the nanocomposite hydrogel substrate was highly conductive. In vitro cytocompatibility results demonstrated excellent biocompatibility of the bio-nanocomposite hydrogels. Cyclic-voltammetry analysis indicated a reduction in current on the surface due to long-range shattered conjugated network of TEGO and PANI in presence of functional groups. Overall, this study indicates that developed bio-nanocomposite hydrogel substrates are promising candidates for biomedical applications.

Construction and Practical Application of Precision Evaluation System for Labor Education Teaching in Higher Vocational Colleges and Universities

Abstract This paper builds a precise evaluation system for labor education teaching, and uses the Delphi method to test and eliminate the rationality of the indicators of the evaluation system to ensure the rationality of the evaluation system. The hierarchical analysis method is used to establish the hierarchical structure matrix of each index in the evaluation system and to calculate the weight value of each index in the evaluation system. Then, verify the fuzzy comprehensive evaluation set according to the weight value, calculate the value of each index system in the evaluation set, and calculate the comprehensive evaluation results using the weighted average type-bounded operator. The analysis of the precision evaluation of labor education teaching in Higher Vocational College A using this evaluation system reveals that the score of precision evaluation for labor education teaching in this school is low. Teachers lack precise guidance in teaching, and the average evaluation score of the indicator “quality of labor education for A32 students” is only 2.52 points. After implementing this evaluation system in labor education teaching, students’ performance in labor education has significantly changed. The average score of the experimental class is 27.13 points higher than that of the control class, with a significant difference (P=0.003<0.05). The evaluation system in this paper provides a reference for the evaluation of precise teaching of labor education in higher vocational colleges. It lays a foundation for improving the teaching quality of labor education.

Study on Factors Affecting the Progress of Engineering Projects under the EPC Model

This paper studies the factors affecting the progress of engineering projects under the EPC model. By establishing a hierarchical comparison matrix and collecting respondents’ ratings on the importance of these factors through a questionnaire survey, the data was analyzed and summarised using the Analytic Hierarchy Process (AHP). The study identified the key factors influencing progress management by the general contractor in EPC projects. Project participants can focus their efforts and resources on managing these key factors to more effectively manage construction progress, shorten project duration, improve management efficiency, and reduce social burdens and resource waste.

Analysis of English Classroom Teaching Evaluation in Colleges and Universities Based on the Hierarchical Analysis Method

Abstract With the advancement of the new curriculum reform, English teaching in secondary schools has become increasingly important, and it is especially crucial for establishing a scientific evaluation system for English classroom teaching to adapt to the development of social needs and students’ law of language learning. This study aims to construct the evaluation standard of English classroom teaching in colleges and universities and quantitatively analyze English teaching. First, the English classroom teaching evaluation data are preprocessed by text feature analysis and the data feature weights are calculated. Then, the random forest algorithm was applied to categorize the processed data and construct a hierarchical evaluation analysis matrix. The hierarchical evaluation system was then used to English classroom teaching in colleges and universities to investigate its teaching effectiveness. The results of the study show that the difference between teachers’ and students’ evaluations of the evaluation system is tiny, with a difference of only 0.0149, proving the system’s rationality. Three months after the implementation of the English teaching evaluation system, students’ recognition of the system increased in all four classes, with increases of 0.733, 0.5625, 0.5882, and 0.5. This study provides an effective evaluation method for English classroom teaching in colleges and universities, which can help improve teaching quality and effectiveness.

A natural multifunction and multiscale hierarchical matrix as a drug-eluting scaffold for biomedical applications.

Sea urchin spines are biogenic single crystals of magnesium calcite that are stiff, strong, damage tolerant and light and have a bicontinuous porous structure. Here, we showed that the removal of their intraskeletal organic matrix materials did not affect the compressive mechanical properties and generated an open porosity. This matrix was able to adsorb and release oxytetracycline, a broad-spectrum antibiotic. The drug-loaded sea urchin matrix induced bacterial cell death after 4 and 8 hours of incubation of both Gram-negative E. coli and Gram-positive S. aureus strains and this process induces an inhibition of bacterial cell adhesion. In conclusion, this study shows that thermally treated sea urchin spines are a compressive resistant and lightweight matrix able to load drugs and with potential use in spine fusion, a challenging application that requires withstanding high compressive loading.

Hierarchical porous Fe/Ni-based bifunctional oxygen electrocatalysts for rechargeable zinc-air batteries

Developing sustainable and efficient bifunctional catalysts for oxygen reduction (ORR) and evolution (OER) reactions is challenging for energy conversion and storage. This work proposes a hierarchical carbon matrix decorated with nitrogen atoms (NC) as a support for obtaining high-performance electrocatalysts based on iron and nickel (Fe/Ni@N–C). The effect of different Fe:Ni ratios and the pyrolysis conditions on the catalyst performance were investigated by combining electrochemical tests, N2-adsorption-desorption, X-ray diffraction, Transmission Electron Microscopy, and X-ray photoelectron spectroscopy. Once optimized the pyrolysis conditions and the Fe:Ni ratio, the Fe/Ni@N–C catalyst showed high bifunctional OER/ORR activity in a three-electrode cell in an alkaline environment (KOH 1 M), with an overall ΔE for the ORR-OER reaction of 0.75 V. Fe/Ni@N–C was assembled in a rechargeable zinc-air battery, resulting in an excellent electrochemical performance in terms of power density (148.5 mWcm−2) and durability, outperforming the benchmark Pt/C–RuO2.

Hierarchical stability conditions for linear systems with interval time-varying delay

This paper proposes the hierarchical stability conditions for linear systems with an interval time-varying delay. In the matter of the delay, the upper and lower bounds are restricted, but there is no constraint on its derivative. Firstly, based on the state vectors and multiple integral state vectors involved in the delay-related generalized free-matrix-based integral inequalities (GFIIs), the hierarchical Lyapunov-Krasovskii functional (LKF) candidates are constructed. Then, the GFIIs are applied for the approximation of the integral quadratic terms, which will introduce the delay related nonlinear terms in the LKF differential. Next, the novel adjusted matrix-valued high and odd degree polynomial negative definite conditions (NDCs) are provided to acquire the hierarchical linear matrix inequality (LMI) conditions and cope with the nonlinear terms introduced by the GFIIs. Eventually, the advantages of the obtained stability conditions are checked through some numeric examples.

Enzymatic dual-faced Janus structures based on the hierarchical organic-inorganic hybrid matrix for an effective bioremoval and detoxification of reactive blue-19

A novel, dual-faced, and hierarchical type of Janus hybrid structures (JHSs) was assembled through an in situ growing of lipase@cobalt phosphate sheets on the laccase@copper phosphate sponge-like structures. The chemical and structural information of prepared JHSs was investigated by Scanning electron microscopy-energy dispersive X-ray analysis (SEM-EDX), Fourier Transform Infrared Spectroscopy (FTIR), and X-ray diffraction analysis (XRD). The catalytic activity, storage stability, and reusability of JHSs were then investigated. The SEM-EDX analysis clearly confirmed the asymmetric morphology of the fabricated JHSs with two distinct metal distributions. Under optimized synthesis conditions, the prepared JHSs showed 97.8 % and 100 % of laccase and lipase activity, respectively. Compared to the free biocatalysts, the immobilization resulted in ~ a 2-fold increase in laccase and lipase stability at temperatures of >40 °C. The fabricated JHSs maintained 61 % and 90 % of their original laccase and lipase activity upon 12 successive repetition cycles. Up to 80 % of Reactive Blue-19 (RB-19), an anthraquinone-based vinyl sulphone dye, was removed after 5 h treatment with the prepared JHSs (50 % higher than the free forms of laccase and lipase). The dye removal data fitted very well on the pseudo-second-order kinetic model with a rate constant of 0.8 g mg−1 h−1. Following the bioremoval process, bacterial toxicity also decreased by about 70 %. Therefore, the prepared JHSs provide a facile and sustainable approach for the decolorization, biotransformation, and detoxification of RB-19 by integrating enzymatic oxidation and hydrolysis.

Self‐Contained Moisture Management and Evaporative Cooling Through 1D to 3D Hygroscopic All‐Polymer Composites

AbstractSorption‐based moisture management and evaporative cooling represent emerging technologies with substantial potential for energy‐saving personal thermal management (PTM). However, design of high‐performance and durable hygroscopic composites combining efficient heat dissipation with wearing comfort presents significant challenges. Herein, hygroscopic 1D nanofibers and 2D fabrics are developed using two hygroscopic polymers and crosslinking strategies. The design endows the fabrics with self‐contained properties including excellent hygroscopicity, durability, ductility, breathability, washability, and antimicrobial capability. The fabrics exhibit thickness‐independent moisture sorption and equilibrium water uptake of 1.19 g g−1 in 4 h under 90% relative humidity (RH). About 80% of the absorbed water can be rapidly released through mild heating within 10 min. These high moisture sorption/desorption rates outperform the majority of composite desiccants, enabling up to five sorption/desorption cycles per day under a real sky. The hygroscopic fabrics can reduce apparent temperatures and prevent unsightly sweat stains on clothing, improving thermal and clothing comfort. Furthermore, hygroscopic 3D hierarchical matrices are printed, showcasing the potential to use small amounts of hygroscopic materials to boost moisture sorption. This work advances the controlled fabrication of hygroscopic polymer composites, ranging from 1D nanofibers and 2D fabrics to 3D matrices, highlighting their promising prospects for future sorption‐based PTM applications.

Semi-Supervised Classification of Malware Families Under Extreme Class Imbalance via Hierarchical Non-Negative Matrix Factorization with Automatic Model Selection

Identification of the family to which a malware specimen belongs is essential in understanding the behavior of the malware and developing mitigation strategies. Solutions proposed by prior work, however, are often not practicable due to the lack of realistic evaluation factors. These factors include learning under class imbalance, the ability to identify new malware, and the cost of production-quality labeled data. In practice, deployed models face prominent, rare, and new malware families. At the same time, obtaining a large quantity of up-to-date labeled malware for training a model can be expensive. In this article, we address these problems and propose a novel hierarchical semi-supervised algorithm, which we call the HNMFk Classifier , that can be used in the early stages of the malware family labeling process. Our method is based on non-negative matrix factorization with automatic model selection, that is, with an estimation of the number of clusters. With HNMFk Classifier , we exploit the hierarchical structure of the malware data together with a semi-supervised setup, which enables us to classify malware families under conditions of extreme class imbalance. Our solution can perform abstaining predictions, or rejection option, which yields promising results in the identification of novel malware families and helps with maintaining the performance of the model when a low quantity of labeled data is used. We perform bulk classification of nearly 2,900 both rare and prominent malware families, through static analysis, using nearly 388,000 samples from the EMBER-2018 corpus. In our experiments, we surpass both supervised and semi-supervised baseline models with an F1 score of 0.80.

Achieving good ductility in 2.1 GPa grade maraging steel

Maraging steels with ultrahigh strength are important for structural applications, but their low ductility severely limits engineering applications. Here we demonstrate improved ductility can be achieved in 0.18C10Ni8Co3Cr1.6Al1Mo1W maraging steel. This steel exhibits a high yield strength of 1.75 GPa, an ultrahigh tensile strength of 2.09 GPa and a uniform elongation of 5 %. Such good strength-ductility synergy arises from a unique microstructure: a refined hierarchical martensite matrix with dense coherent B2-nanoprecipitates. Strengthening models indicate that the ultrahigh strength can be attributed to block boundary strengthening, dislocation strengthening and precipitation strengthening. Utilizing transmission electron microscope coupled with geometric phase analysis at interrupted deformation stages, we reveal dynamic dislocation-nanoprecipitate and dislocation-dislocation interactions. Notably, mobile dislocations not only cut through nanoprecipitates but also penetrate pre-existing dislocation substructures and lath boundaries. Such deformation behaviors promote dislocation multiplication and accumulation, thereby conferring good strain hardening and ductility.

Organizational and Technological Platform for Monolithic Construction Using Pneumatic Formwork

Introduction: The active implementation of digital technologies in various fields, including in the construction industry, leads to the development of technological platforms to sell multiple products. The study examines the prerequisites for the formation of an organizational and technological platform for monolithic construction using pneumatic formwork, which is a set of material and labor resources and organizational and technological solutions that, through their consolidation with modern digital technologies, allow the implementation of construction projects with specified technical and economic requirements. This study aims to systematize various production and construction solutions, presenting them as a unified organizational and technological system that allows for achieving optimal criteria for construction products. Materials and methods: The factors ensuring its effectiveness were selected and systematized to form an organizational and technological platform. A complex system decomposition is presented at three levels of a hierarchical matrix using the analysis of hierarchies. The level of the stages of the life cycle of buildings and structures is taken as the basis, followed by the level of components of the areas of activity that form the platform's effective formation. At the last, lower level, some factors ensure its effective formation. The analysis of the totality of material and labor resources and organizational and technological solutions that make up the platform for constructing monolithic buildings and structures using pneumatic formwork systems was carried out. Results: For an adequate analytical description, it is proposed to use the a priori ranking method, which makes it possible to decompose the indicated factors influencing the effectiveness of the formation of an organizational and technological platform and to obtain specific criteria and alternatives inherent in the construction of monolithic buildings and structures on pneumatic formwork. The detailed development of an analytical apparatus for obtaining an integral assessment will be the subject of further research. Conclusions: The organizational and technological platform for monolithic construction using pneumatic formwork is an innovative tool for interaction between all participants in implementing such projects, aimed at successfully achieving construction design indicators in terms of time and cost and ensuring the required level of reliability and safety of the constructed facility. The novelty of the proposed approach is determined by the combined consideration of material, technological, organizational, and managerial solutions within a single platform to increase the efficiency of construction product production processes. Doi: 10.28991/CEJ-2023-09-11-010 Full Text: PDF

Highly dispersed conductive and electrocatalytic mediators enabling rapid polysulfides conversion for lithium sulfur batteries

The practical application of Li-S batteries encounters hurdles in maintaining cycling durability and rate capability under realistic conditions. Electrostatic self-assembly stands as a captivating avenue for exploring new frontiers in nanoscale catalysis. Leveraging renewable bio-oil both as a carbon source and self-polymerization precursor, ultrafine Mo2C nanocrystals anchored on bio-oil-derived 3D hierarchical carbon matrix (Mo2C@BOC) are fabricated by a facile NaCl template-assisted electrostatic self-assembly and followed annealing procedure. Densely anchored ultrafine Mo2C nanocrystals, intertwined with highly conductive carbon nanosheets, unveil an enhanced exposure of catalytically active sites for lithium polysulfide immobilization, conversion, and supply amply nucleation sites to mediate the fast precipitation of Li2S2/Li2S. Attributed to these favorable features, Li-S cells based on the as-designed catalytic host attain satisfactory cyclability with a minimum capacity fading rate of 0.0144 % over 1000 cycles and excellent rate capability. Decent performance can be achieved even at a high sulfur loading of 8.0 mg cm−2 and a low electrolyte-to-sulfur ratio of 3.5 µL mg−1. This strategy for solving the shuttle effect under high sulfur loading provides a promising solution for the further development of high-performance Li-S batteries. This work provides a rational strategy for solving the shuttle effect under high sulfur loading and sheds light on the great potential of Mo2C@BOC for developing more practical Li-S batteries.

Heterostructured TiN/TiO2 on the hierarchical N-doped carbon for enhancing the polysulfide immobilization and sulfur reduction in lithium-sulfur battery

The commercialization of lithium-sulfur batteries (LSBs) is impeded by their low sulfur utilization and poor cycling stability. Herein, uniformly distributed TiN/TiO2 heterostructures on the hierarchical nitrogen-doped inter-connected multi-scale porous carbon matrix was developed as an effective polysulfide trapper and catalytic accelerator for sulfur reduction reaction. The performance of synthesized TiN/TiO2 heterostructures in LSBs are compared with those of TiN and TiO2. The synergetic effects of strong polysulfide adsorption of TiO2 and superior catalytical conversion ability of TiN draw rapid trap-diffusion-conversion process and enhance the reaction kinetics. This heterostructure-based LSBs exhibit a high specific capacity of 1458.5 mAhg−1 at 0.1 C and 684.9 mAhg−1 at 5 C. Over 1000 cycles, a high capacity of 576 mA h g−1 is retained with a low-capacity decay of 0.030 % per cycle at 2 C. Moreover, a high area capacity value of 6.65 mAh cm−2 is obtained at 0.5C with a high sulfur loading of 8.2 mg cm−2 and low electrolyte/sulfur ratio (E/S) of 4.7. This study provides a novel strategy to develop the transition metal nitride-oxide heterostructure on a three-dimensional porous carbon framework as efficient electrode materials for LSBs application.

Reflective conditions for radiative transfer in integral form with H-matrices

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective boundary conditions. The fixed point method to solve the system is shown to be monotone. The discretization is done with a P1 Finite Element Method. The convolution integrals are precomputed at every vertex of the mesh and stored in compressed hierarchical matrices, using Partially Pivoted Adaptive Cross-Approximation. Then the fixed point iterations involve only matrix vector products. The method is O(NN3ln⁡N), with respect to the number of vertices, when everything is smooth. A numerical implementation is proposed and tested on two examples. As there are some analogies with ray tracing the programming is complex.