Dynamic Matrix Research Articles

Dynamic Stiffness for a Levinson Beam Embedded Within a Pasternak Medium Subjected to Axial Load at Both Ends

This work presents accurate values for the dynamic stiffness matrix coefficients of Levinson beams under axial loading embedded in a Winkler–Pasternak elastic foundation. Levinson’s theory accounts for greater shear deformation than the Euler–Bernoulli or Timoshenko theories. Using the dynamic stiffness approach, an explicit algebraic expression is derived from the homogeneous solution of the governing equations. The dynamic stiffness matrix links forces and displacements at the beam’s ends. The Wittrick–Williams algorithm solves the eigenvalue problem for the free vibration and buckling of uniform cross-section parts. Numerical results are validated against published data, and reliability is confirmed through consistency tests. Parametric studies explore the effects of aspect ratio, boundary conditions, elastic medium parameters, and axial force on beam vibration properties. The relative deviation for the fundamental frequency is almost 6.89% for a cantilever beam embedded in the Pasternak foundation, 5.16% for a fully clamped beam, and 4.79% for a clamped–hinged beam. Therefore, Levinson beam theory can be used for calculations relevant to loads with short durations that generate transient responses, such as impulsive loads from high-speed railways, using the mode superposition method.

EIF-SlideWindow: Enhancing Simultaneous Localization and Mapping Efficiency and Accuracy with a Fixed-Size Dynamic Information Matrix

This paper introduces EIF-SlideWindow, a novel enhancement of the Extended Information Filter (EIF) algorithm for Simultaneous Localization and Mapping (SLAM). Traditional EIF-SLAM, while effective in many scenarios, struggles with inaccuracies in highly non-linear systems or environments characterized by significant non-Gaussian noise. Moreover, the computational complexity of EIF/EKF-SLAM scales with the size of the environment, often resulting in performance bottlenecks. Our proposed EIF-SlideWindow approach addresses these limitations by maintaining a fixed-size information matrix and vector, ensuring constant-time processing per robot step, regardless of trajectory length. This is achieved through a sliding window mechanism centered on the robot’s pose, where older landmarks are systematically replaced by newer ones. We assess the effectiveness of EIF-SlideWindow using simulated data and demonstrate that it outperforms standard EIF/EKF-SLAM in both accuracy and efficiency. Additionally, our implementation leverages PyTorch for matrix operations, enabling efficient execution on both CPU and GPU. Additionally, the code for this approach is made available for further exploration and development.

Advanced Control Strategies for Cleaner Energy Conversion in Biomass Gasification

The escalating climate crisis necessitates urgent and decisive action to mitigate greenhouse gas emissions. Gasification stands out as a highly adaptable process for energy conversion, capable of handling a wide range of feedstocks, from coal to biomass. The process plays a significant role in improving sustainability by converting these feedstocks into synthesic gas (syngas), which can be used as a cleaner energy source or as a building block for producing various chemicals. The utilization of syngas obtained through gasification not only reduces the reliance on fossil fuels but also helps in reducing greenhouse gases (GHGs), thereby contributing to a more sustainable energy landscape. To maintain optimal operational conditions and ensure the quality and safety of the product, an effective control system is crucial in the gasification process. This paper presents a comparative analysis of three control strategies applied to a numerical model of rice husk gasification: classical control, fuzzy logic control, and dynamic matrix control. The analysis is based on a comprehensive model that includes the equations necessary to capture the dynamic behavior of the gasification process across its various stages. The goal is to identify the most effective control strategy, and the performance of each control strategy is evaluated based on the integral of the absolute value of the error (IAE). The results indicatethat fuzzy logic control consistently outperforms classical control techniques, demonstrating superior disturbance rejection, enhanced stability, and overall improved control accuracy. These findings highlight the importance of selecting an appropriate advanced control strategy to optimize sustainable gasification processes.

Spatiotemporal Dynamic Graph Convolutional Networks for Air Route Network Congestion Prediction

High-precision air traffic congestion prediction is the basis for implementing refined traffic flow management. However, current prediction approaches are limited to fixed route topologies, neglecting the dynamic spatial dependencies caused by congestion propagation between routes. Additionally, these models do not adequately consider the varying importance of different routes and time points within the time series. This paper proposes a spatiotemporal dynamic graph convolutional network to simultaneously capture the static and dynamic spatial dependencies among air traffic routes. We construct two types of adjacency matrices based on the connections between routes: a static adjacency matrix and a dynamic adjacency matrix. The static adjacency matrix reflects the basic connections between routes, while the dynamic adjacency matrix captures the congestion influence from upstream to downstream routes at each time interval. In the model, these adjacency matrices are first processed through graph convolutional network layers, where a spatial attention mechanism assigns weights to different routes. The processed data are then fed into gated recurrent unit layers, utilizing a temporal attention mechanism to assign varying weights to congestion data at different time. Experiments were conducted on the air route network in Guangdong–Hong Kong–Macao Greater Bay Area of China. The experimental results demonstrate that our proposed method outperforms several existing approaches, particularly those using only static graph convolution methods.

End to end polysemantic cooperative mixed task trainer for UAV target detection

With the rapid advancement and application of Unmanned Aerial Vehicles (UAVs), target detection in urban scenes has made significant progress. Achieving precise 3D reconstruction from oblique imagery is essential for accurate urban object detection in UAV images. However, challenges persist due to low detection accuracy caused by subtle target features, complex backgrounds, and the prevalence of small targets. To address these issues, we introduce the Polysemantic Cooperative Detection Transformer (Pc-DETR), a novel end-to-end UAV image target detection network. Our primary innovation, the Polysemantic Transformer (PoT) Backbone, enhances visual representation by leveraging contextual information to guide a dynamic attention matrix. This matrix, formed through convolutions, captures both static and dynamic features, resulting in superior detection. Additionally, we propose the Polysemantic Cooperative Mixed-Task Training scheme, which employs multiple auxiliary heads for diverse label assignments, boosting the encoder’s learning capacity. This approach customizes queries and optimizes training efficiency without increasing inference costs. Comparative experiments show that Pc-DETR achieves a 3% improvement in detection accuracy over the current state-of-the-art MFEFNet, setting a new benchmark in UAV image detection and advancing methodologies for intelligent UAV surveillance systems.

Generative adversarial network (GAN) model-based design of potent SARS-CoV-2 Mpro inhibitors using the electron density of ligands and 3D binding pockets: insights from molecular docking, dynamics simulation, and MM-GBSA analysis.

Deep learning-based generative adversarial network (GAN) frameworks have recently been developed to expedite the drug discovery process. These models generate novel molecules from scratch and validate them through molecular docking simulation to identify the most promising candidates for a given drug target. In this study, the SARS-CoV-2 main protease (Mpro) was selected as the drug target. Two distinct GAN algorithms were employed to generate novel small molecules. One approach utilized experimental electron density (ED-based) data of ligands for training to generate drug-like molecules, while the second approach leveraged the target binding pocket to capture spatial and bonding relationship between atoms within the binding pockets. The ED-based approach generated approximately 26,000 molecules, whereas the binding pocket-based method produced around 100 molecules. These generated molecules were subsequently ranked based on molecular docking results using the glide XP score (both flexible and rigid docking) and AutoDock Vina. To identify the most potent GAN-derived molecules, molecular docking was also performed on co-crystallized inhibitor molecules of Mpro. The six most promising molecules from these GAN approaches were further evaluated for stability, interactions, and MM-GBSA binding free energy through molecular dynamics simulations. This analysis led to the identification of four potent Mpro inhibitor molecules, all featuring a 2-benzyl-6-bromophenol scaffold. The binding free energies of these compounds were compared with those of other Mpro inhibitors, revealing that our compounds demonstrated better affinity for Mpro than some broad-spectrum protease inhibitors. The dynamic cross-correlation matrix plot indicated strongly correlated and anti-correlated regions, potentially linked to ligand binding.

Near-real-time damage identification under vehicle loads using dynamic graph neural network based on proper orthogonal decomposition

Structural health monitoring (SHM) is essential for managing infrastructure by continuously monitoring performance. To address the complexity of SHM for large systems, this study introduces a dynamic graph neural network (DynGNN) approach for near-real-time damage identification. The approach represents the infrastructure as a graph and uses a dynamic adjacency matrix based on proper orthogonal decomposition (POD) to capture the dynamic characteristics and spatial correlations of responses. The DynGNN model has an autoencoder architecture with one encoder for latent feature extraction and two decoders for capturing spatiotemporal changes and is trained on intact structural responses. The proposed approach employs a damage index based on reconstruction errors for damage identification. In applications to a steel truss bridge under vehicle loads, the proposed approach is tested by real-time simulation using the field test data obtained from the damaged bridge. By incorporating a dynamic adjacency matrix, the results successfully demonstrate that the proposed approach effectively adapts to the time-varying nature of structural responses and can accurately identify damage in near-real time. The novel integration of a dynamic graph structure with POD allows the proposed method to capture both spatial and temporal variations, providing a significant improvement over traditional static methods.

Kernel polynomial method for linear spin wave theory

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

Variation Characteristics of Land Use Change Within the Beijing–Tianjin–Hebei Region During 1985–2022

Land use change generally varies greatly among functional zones in a large area. This study reveals land use change characteristics across seven functional zones in the Beijing–Tianjin–Hebei region during 1985–2022 based on the latest land use planning data, with the land use dynamic degree, transfer matrix, and comprehensive index of land use intensity. Results suggested cropland, forest land, grassland, and built-up land were dominant land use types in most functional zones, generally with significant decreases in cropland and grassland and noticeable increases in built-up land and forest land. Besides, single land use dynamics of built-up land and forest land were generally above 2.00% and 0.40%, while that of grassland and cropland was generally below zero in most functional zones. Comprehensive land use dynamics were very high in the Central Core Functional Zone (Region IV), Bashang Plateau Ecological Protection Zone (Region I), and Eastern Coastal Development Zone (Region III), peaking above 0.70%, and were low in other functional zones. Additionally, the land use degree increased slowly from 267.28 in 1985 to 274.17 in 2022 on average, varying remarkably among various functional zones. These findings provide a firm foundation for formulating more targeted land management policies across various functional zones.

Multi-output discrete grey model tailored for electricity consumption forecast

To address the limitation of many conventional grey forecasting methods that prioritize temporal dynamics analysis while often overlooking the essential spatial characteristics, we developed a multi-output discrete grey model tailored for forecasting electricity consumption in China's Yangtze River Delta, incorporating spatial effects. Specifically, we design a dynamic spatial interaction matrix to precisely capture the spatial correlations among neighboring areas, and integrate multiple sets of fixed-effect parameters to adeptly address spatial heterogeneity. Additionally, we implement regularization technique to prevent overfitting and utilize the Bayesian Optimization algorithm for hyper-parameter adjustment, considerably enhancing the model's stability of parameter estimation and its resilience to noise. Finally, a comprehensive case study, benchmarked against seven other models, highlights our model's outstanding multi-step predictive accuracy and robustness against input data uncertainty, exceeding the performance of existing methods.

Identification and interaction mechanism of novel small molecule antagonists targeting CC chemokine receptor 1/3/5 for treatment of non-small cell lung cancer.

Non-Small Cell Lung Cancer (NSCLC) was one of the most prevalent forms of lung cancer. Due to its ease of invasion and migration, the five-year survival rate was relatively low. Therefore, new strategies for NSCLC treatment were needed. CC chemokine receptor 1/3/5 (CCR1/CCR3/CCR5), a member of the G-protein coupled receptor family, could promote the migration and invasion of NSCLC cells by binding to related chemokines. Consequently, targeting CCR1, CCR3 and CCR5 might prevent the progression of the disease. So far, no compound had been reported as a common antagonist for CCR1, CCR3, and CCR5. In this research, we utilized virtual screening and structural optimization to obtain compound 5, which effectively inhibited the migration and invasion of NSCLC cells. Meanwhile, Western Blot and Enzyme linked immunosorbent assay (ELISA) manifested that compound 5 suppressed migration and invasion of NSCLC cells by suppressing the nuclear factor κB (NF-κB) and the consequently decreased Matrix Metalloproteinase-9(MMP-9) secretion. Moreover, drug affinity responsive target stability (DARTS) experiment and molecular simulations confirmed that compound 5 was capable of binding with CCR1/CCR3/CCR5, and Van der Waals forces were instrumental in the binding process. Ile91, Tyr113, Gln284, and Ser184(CCR1-ligand5), Ile189, Met213, and Leu209(CCR3-ligand5), Phe109, Gln194, and Thr195(CCR5-ligand5) had Van der Waals interactions with ligand 5. Dynamic cross-correlation matrix (DCCM) and free energy landscape (FEL) showed that compound 5 could stably bind to CCR1/CCR3/CCR5 to change conformation of the protein and the tendency of residue movements, leading to a persistent inhibitory effect. This study aimed to provide assistance in the rational design of common antagonists for CCR1, CCR3, and CCR5.

Can storage-discharge characteristics of karst matrix system quantified through recession analysis be reliable?

Storage and subsequent release of water in matrix system is a key function of karst catchments that controlling baseflow variation. Hydrograph recession analysis is currently the economic way to assess storage-discharge characteristics broadly at the catchment scale. However, there is large uncertainty in the related quantification due to recession data extraction. This study, by combining recursive digital filters with different automatic extraction methods, slow flow recession segments were extracted for hydrograph recession analysis and the further dynamic matrix storage (DMS) and related recession time (RT) assessment. The diversity and consistence among DMS and RT derived from different recession extraction methods (REMs) were analyzed, using hydrometric data in 20 catchments in the Wujiang river Basin in southwest China. Results indicate that the estimates of DMS and RT remarkedly varied between different REMs, however the order in which they ranked was mostly consistent. Moreover, the relationships between the derived DMS and RT with catchment physical features that potentially control storage and release processes are mostly consistent. Larger DMS are strongly associated with catchments featured as lower soil saturated hydraulic conductivity and smoother hydrographs. Longer RT are mostly related with drier catchments characterized as less variation of elevation and lower soil saturated hydraulic conductivity. This study highlights not only the uncertainty in quantifying storage and accompanied release characteristics, but also the reliability of storage-discharge characteristics quantified through recession analysis in terms of catchment comparison. Considering the diversity among catchments, ensemble of multi-method estimates of DMS and RT can enhance our understanding of the storage-discharge processes in the karst matrix system.

An accurate and efficient method based on the dynamic stiffness matrix for analyzing wave propagation in defective lattice structures

In this study, we present an efficient and accurate method for analyzing wave propagation in lattice structures with periodic defects, which are composed of three-dimensional (3D) unit cells arranged infinitely in two or three directions, with defects existing periodically along the directions of the arrangement. The unit cell is composed of 3D beams, and the dynamic stiffness formulation of the 3D beam is developed by combining the Timoshenko-Ehrenfest, Rayleigh-Love and torsion theories. Based on the dynamic stiffness matrix, any number or order of natural frequencies of defective lattice structures can be calculated accurately and efficiently using the Wittrick-Williams algorithm. By combining it with the Bloch theorem, the proposed method can be used to calculate the dispersion curves of lattice structures with periodic defects. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. Additionally, the effects of periodic defects in the lattice structures on the bandgap are analyzed.

A Spatial-Temporal Aggregated Graph Neural Network for Docked Bike-sharing Demand Forecasting

Predicting the number of rented and returned bikes at each station is crucial for operators to proactively manage shared bike relocation. Although existing research has proposed spatial-temporal prediction models that significantly advance traffic prediction, these models often neglect the unique characteristics of shared bike systems (BSS). Spatially, the entire bike-sharing system (BSS) experiences peak activity during morning and evening rush hours, whereas, during other periods, activity is localized to local stations, with some recording no rides, highlighting the need to distinguish between global and local spatial information across different times. Temporally, the historical riding records for each station exhibit non-stationary patterns, necessitating the analysis of both global trends and local fluctuations. Existing Graph Neural Network (GNN) approaches to predicting shared bike demand primarily capture static spatial-temporal data and fail to account for the dynamic nature of bike flows. Moreover, these studies focus on global spatial-temporal information without considering local nuances, making it challenging to capture spatiotemporal dynamics in fluctuating BSS. To address these challenges, we introduce the Spatial-Temporal Aggregated Graph Neural Network (STAGNN). Our model first constructs a dynamic adjacent matrix to describe the evolving connections between stations, followed by local and global information layers to capture spatial-temporal information from large-scale shared bike networks accurately. Our methodology has been validated through experiments on four real-world datasets, comparing it against benchmark models to demonstrate superior prediction accuracy. Additionally, we conduct extended experiments on four datasets during the morning and evening rush hours, and the results also affirm the efficacy of the STAGNN in enhancing prediction performance.

A fuzzy activation function based zeroing neural network for dynamic Arnold map image cryptography

As an effective method for time-varying problems solving, zeroing neural network (ZNN) has been frequently applied in science and engineering. In order to improve its performances in practical applications, a fuzzy activation function (FAF) is designed by introducing the fuzzy logic technology, and a fuzzy activation function based zeroing neural network (FAF-ZNN) model for fast solving time-varying matrix inversion (TVMI) is proposed. Rigorous mathematical analysis and comparative simulation experiments with other models guarantee its superior convergence and robustness to noises. In addition, based on the proposed FAF-ZNN model, a new dynamic Arnold map image cryptography algorithm is designed. Specifically, in the new dynamic image encryption, a dynamic key matrix is introduced, and the FAF-ZNN model is applied to fast compute the inversion of the dynamic key matrix for the dynamic Arnold map image cryptography decryption process. The effectiveness of the dynamic image encryption algorithm is verified by experiment results, which enhances the security of existing image encryption algorithms.

Beyond Static Models: Mechanically Dynamic Matrices Reveal New Insights into Cancer and Fibrosis Progression

The dynamic mechanical nature of extracellular matrices (ECMs) is crucial for the mechanosensitive regulation of cell fate. This is evident in pathological conditions such as cancer and fibrosis, which are characterised by highly fibrotic tissue developing over time. This fibrotic progression not only alters tissue mechanics, but also coincides with the reprogramming of resident cells, promoting their differentiation into aberrant phenotypes and increasing drug resistance. Hydrogels, with their tuneable mechanical and biochemical properties, emerge as powerful ECM mimetics to model and study these abnormal, mechanically-driven cell differentiation phenomena. In this review, after establishing how conventional, mechanically static hydrogels contribute to our understanding of the role of altered mechanosensing in cell differentiation during cancer and fibrosis, we explore the research opportunities given by advanced dynamic matrices. Models employing hydrogels that are fast relaxing, plastic or even with temporally switchable mechanics reveal the otherwise hidden role of time-dependent phenomena during disease development.

Dynamic Navigation-Guided Robotic Placement of Zygomatic Implants

Objectives: To assess the feasibility and accuracy of a new prototype robotic implant system for the placement of zygomatic implants in edentulous maxillary models. Methods: The study was carried out on eight plastic models. Cone beam computed tomographs were captured for each model to plan the positions of zygomatic implants. The hand-eye calibration technique was used to register the dynamic navigation system to the robotic spaces. A total of 16 zygomatic implants were placed, equally distributed between the anterior and the posterior parts of the zygoma. The placement of the implants (ZYGAN®, Southern Implants) was carried out using an active six-jointed robotic arm (UR3e, Universal Robots) guided by the dynamic navigation coordinate transformation matrix. The accuracy of the implant placement was assessed using EvaluNav and GeoMagicDesignX® software based on pre- and post-operative CBCT superimposition. Descriptive statistics for the implant deviations and Pearson's correlation analysis of these deviations to force feedback recorded by the robotic arm were conducted. Results: The 3D deviations at the entry and exit points were 1.80 ± 0.96 mm and 2.80 ± 0.95 mm, respectively. The angular deviation was 1.74 ± 0.92°. The overall registration time was 23.8 ± 7.0 minutes for each side of the model. Operative time excluding registration was 66.8 ± 8.8 minutes for each trajectory.The exit point and angular deviations of the implants were positively correlated with the drilling force perpendicular to the long axis of the handpiece and negatively correlated with the drilling force parallel to the long axis of the handpiece. Conclusion: The errors of the dynamic navigation-guided robotic placement of zygomatic implants were within the clinically acceptable limits. Further refinements are required to facilitate the clinical application of the tested integrated robotic-dynamic navigation system. Clinical Significance: Robotic placement of zygomatic implants has the potential to produce a highly predictable outcome irrespective of the operator's surgical experience or fatigue. The presented study paves the way for clinical applications.

GMAEEG: A Self-Supervised Graph Masked Autoencoder for EEG Representation Learning.

Annotated electroencephalogram (EEG) data is the prerequisite for artificial intelligence-driven EEG autoanalysis. However, the scarcity of annotated data due to its high-cost and the resulted insufficient training limits the development of EEG autoanalysis. Generative self-supervised learning, represented by masked autoencoder, offers potential but struggles with non-Euclidean structures. To alleviate these challenges, this work proposes a self-supervised graph masked autoencoder for EEG representation learning, named GMAEEG. Concretely, a pretrained model is enriched with temporal and spatial representations through a masked signal reconstruction pretext task. A learnable dynamic adjacency matrix, initialized with prior knowledge, adapts to brain characteristics. Downstream tasks are achieved by finetuning pretrained parameters, with the adjacency matrix transferred based on task functional similarity. Experimental results demonstrate that with emotion recognition as the pretext task, GMAEEG reaches superior performance on various downstream tasks, including emotion, major depressive disorder, Parkinson's disease, and pain recognition. This study is the first to tailor the masked autoencoder specifically for EEG representation learning considering its non-Euclidean characteristics. Further, graph connection analysis based on GMAEEG may provide insights for future clinical studies.

Identification of novel Influenza virus H3N2 nucleoprotein inhibitors using most promising synthetic Epicatechin derivatives

Influenza A virus is a leading cause of acute respiratory tract infections, posing a significant global health threat and resulting in substantial annual financial losses due to seasonal epidemics. Current treatment options are limited and increasingly ineffective due to viral mutations. This study aimed to identify potential drug candidates targeting the nucleoprotein of the H3N2 subtype of Influenza A virus. We focused on epicatechin derivatives and employed a suite of cheminformatics approaches, including ADMET profiling, drug-likeness evaluation, PASS predictions, molecular docking, molecular dynamics simulations, Principal Component Analysis (PCA), dynamic cross-correlation matrix (DCCM) analyses, and free energy landscape assessments. Molecular docking and dynamics simulations revealed strong and stable binding interactions between the derivatives and the target protein, with complexes 01 and 81 exhibiting the highest binding affinities. Additionally, ADMET profiling indicated favorable pharmacokinetic properties for these compounds, supporting their potential as effective antiviral agents. Compound 81 demonstrated exceptional quantum chemical descriptors, including a small HOMO-LUMO energy gap, high electronegativity, and significant softness, suggesting high chemical reactivity and strong electron-accepting capabilities. These properties enhance Compound 81’s potential to interact effectively with the H3N2 nucleoprotein. Experimental validation is strongly recommended to advance these compounds toward the development of novel antiviral therapies to address the global threat of influenza.

Optimal design of a novel three-stage displacement amplifying mechanism with curved-axis flexure hinges

A novel three-stage displacement amplifying mechanism is proposed by integrating the lever-type, Scott-Russell and double-arm elliptical mechanisms with red blood cell inspired flexure hinges that well balances the displacement amplification ratio and main resonance frequency. Flexure hinges are loaded in tension and bending instead of compression and bending, which can be free from potential buckling problems due to the stress stiffening effects. The combination of the dynamic stiffness matrix method and the discrete-beam transfer matrix method is utilized to rapidly forecast the kinetostatic and dynamic performances of the proposed compliant amplifier, including the curved-axis flexure hinges with complex contour profiles. Then, the Pareto multi-objective optimization strategy, taking those key geometric parameters obtained by the sensitivity analysis into account, is represented based on NSGA-II and a linear frequency solution strategy to accelerate the calculation efficiency and parameter optimization iteration. Based on the application requirement, a point on the Pareto curve is chosen as the optimal configuration for operating conditions. At last, experiments of the piezoelectric compliant amplifier under two types of external mass loads are exhibited. A displacement amplification ratio of 12.2 and main resonance frequency of 1380.5 Hz are achieved for the piezoelectric compliant amplifier under no external mass load.