Gradient Flow Research Articles

TeaViTNet: Tea Disease and Pest Detection Model Based on Fused Multiscale Attention

The tea industry, as one of the most globally important agricultural products, is characterized by pests and diseases that pose a serious threat to yield and quality. These diseases and pests often present different scales and morphologies, and some pest and disease target sizes can be tiny and difficult to detect. To solve these problems, we propose TeaViTNet, a multi-scale attention-based tea pest and disease detection model that combines CNNs and Transformers. First, MobileViT is used as the feature extraction backbone network. MobileViT captures and analyzes the tiny pest and disease features in the image via a self-attention mechanism and global feature extraction. Second, the EMA-PANet network is introduced to optimize the model’s learning and attention to the Apolygus lucorum and leaf blight regions via an efficient multi-scale attention module with cross-space learning, which improves the model’s ability to understand multi-scale information. In addition, RFBNet is embedded in the module to further expand the perceptual range and effectively capture the information of tiny features in tea leaf images. Finally, the ODCSPLayer convolutional block is introduced, aiming to focus on acquiring richer gradient flow information. The experimental results show that the TeaViTNet model proposed in this paper has an average accuracy of 89.1%, which is a significant improvement over the baseline network MobileViT and is capable of accurately detecting Apolygus lucorum and leaf blight of different scales and complexities.

Mathematical Modeling and Statistical Exploration of Residual Computing Based Convolutional Neural Network Based Classifier for Complex Image Demarcation

The advent of deep learning has revolutionized the field of medical image analysis, particularly in complex tasks like brain image segmentation and classification. Among the various deep learning architectures, Convolutional Neural Networks (CNNs) have shown remarkable ability in extracting hierarchical features from medical images. The mathematical framework of our proposed Res-CNN is grounded in the principles of functional analysis and optimization theory. We employ the calculus of variations to model the propagation of activations within the network, optimizing a cost function tailored for the segmentation and classification of brain images. The structural integrity of the network is encoded through well-defined mathematical formulations, capturing the essence of residual blocks that allow the seamless flow of gradients during back propagation.from a statistical perspective, the robustness of the ResNet model is validated through rigorous exploratory data analysis. We systematically dissect the statistical properties of the network's predictions, employing methods such as hypothesis testing to ascertain the significance of the improvements offered by residual computing. Furthermore, Bayesian inference is utilized to gauge the uncertainty in the network's parameters, providing a probabilistic interpretation of the segmentation results. The efficacy of our model is further quantified through comprehensive experiments on diverse datasets of brain images. Statistical metrics such as accuracy, sensitivity, specificity, and area under the ROC curve (AUC) serve as the benchmarks for performance evaluation, solidifying the merit of our mathematical and statistical approach in the domain of medical image analysis. The ResNet50 demonstrates superior performance in segmenting and classifying interact patterns within brain images, paving the way for significant advancements in diagnostic methodologies.

Reduced membrane model for liquid crystal polymer networks: Asymptotics and computation

We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex stretching energy. We show a formal asymptotic derivation of the 2D membrane model from 3D rubber elasticity. We construct approximate solutions with point defects. We design a finite element method with regularization, and propose a nonlinear gradient flow with Newton inner iteration to solve the non-convex discrete minimization problem. We present numerical simulations of practical interests to illustrate the ability of the model and our method to capture rich physical phenomena.

Liquid chromatography–tandem mass spectrometry method for mycophenolic acid and its glucuronide determination in saliva samples from children with nephrotic syndrome

BackgroundSaliva sampling is one of the methods of therapeutic drug monitoring for mycophenolic acid (MPA) and its metabolite, mycophenolic acid glucuronide (MPAG). The study describes the liquid chromatography tandem mass spectrometry (LC–MS/MS) method developed for saliva MPA and MPAG determination in children with nephrotic syndrome.MethodsThe mobile phase consisted of methanol and water at gradient flow, both with 0.1% formic acid. Firstly, 100 µL of saliva was evaporated at 45 °C for 2 h to dryness, secondly, it was reconstituted in the mobile phase, and finally 10 µL was injected into the LC–MS/MS system. Saliva from ten children with nephrotic syndrome treated with mycophenolate mofetil was collected with Salivette®.ResultsFor MPA and MPAG, within the 2–500 ng/mL range, the method was selective, specific, accurate and precise within-run and between-run. No carry-over and matrix effects were observed. Stability tests showed that MPA and MPAG were stable in saliva samples if stored for 2 h at room temperature, 18 h at 4 °C, and at least 5 months at − 80 °C as well as after three freeze–thaw cycles, in a dry extract for 16 h at 4 °C, and for 8 h at 15 °C in the autosampler. The analytes were not adsorbed onto Salivette® cotton swabs. For concentrations above 500 ng/mL, the samples may be diluted twofold. In children, saliva MPA and MPAG were within the ranges of 4.6–531.8 ng/mL and 10.7–183.7 ng/mL, respectively.ConclusionsThe evaluated LC–MS/MS method has met the validation requirements for saliva MPA and MPAG determination in children with nephrotic syndrome. Further studies are needed to explore plasma–saliva correlations and assess their potential contribution to MPA monitoring.Graphical abstract

Stochastic homogenization of nonlocal reaction–diffusion problems of gradient flow type

Stochastic homogenization of nonlocal reaction–diffusion problems of gradient flow type

Efficient and stable SAV-based methods for gradient flows arising from deep learning

The optimization algorithm plays an important role in deep learning and significantly affects the stability and efficiency of the training process, and consequently the accuracy of the neural network approximation. A suitable (initial) learning rate is crucial for the optimization algorithm in deep learning. However, a small learning rate is usually needed to guarantee the convergence of the optimization algorithm, resulting in a slow training process. We develop in this work efficient and energy stable optimization methods for function approximation problems as well as solving partial differential equations using deep learning. In particular, we consider the gradient flows arising from deep learning from the continuous point of view, and employ the particle method (PM) and the smoothed particle method (SPM) for the space discretization while we adopt SAV-based schemes, combined with the adaptive strategy used in Adam algorithm, for the time discretization. To illustrate the effectiveness of the proposed methods, we present a number of numerical tests to demonstrate that the SAV-based schemes significantly improve the efficiency and stability of the training as well as the accuracy of the neural network approximation. We also show that the SPM approach gives a slightly better accuracy than the PM approach. We further demonstrate the advantage of using adaptive learning rate in dealing with more complex problems.

Correction to: Universal formula for the flavor non-singlet axial-vector current from the gradient flow

Correction to: Universal formula for the flavor non-singlet axial-vector current from the gradient flow

Normalized penalty gradient flow: A continuous-time approach for solving constrained nonconvex nonsmooth optimization problems

To avoid calculating penalty parameters, this paper introduces a continuous-time approach that combines the normalized gradient flow with the penalty method to solve the nonconvex nonsmooth optimization problem with a convex constraint set. Subsequently, this approach is extended to solve nonconvex nonsmooth optimization with a box constraint set and affine equality constraints. Compared with the current methods, the proposed approach does not require calculating the penalty parameters, allows the objective function to be nonconvex or nonsmooth, and allows the initial point to be arbitrarily selected. It is proved that the solution trajectory with any initial point converges to the critical point set of the optimization problem. Finally, the effectiveness of the proposed approach is authenticated through several numerical experiments.

Correction to: Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism

Correction to: Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism

Experimental and Numerical Simulation of Catalyst Deactivation Caused by Transient Turbulence in Gradient Flow Field

Experimental and Numerical Simulation of Catalyst Deactivation Caused by Transient Turbulence in Gradient Flow Field

Experimental investigation of flow patterns and rheological characteristics of compressed air foam in horizontal tube

The use of compressed air foam (CAF) for fire suppression has undergone rapid development in recent years. It has been successfully applied in fire incidents in the petroleum and chemical industries. The increasing need to fighting fires at high elevations necessitates an understanding of the rheological characteristics, pressure gradient changes, flow characteristics, and regularities of CAF within long firehoses. Therefore, this paper focuses on an investigation of the flow characteristics of CAF at foaming agent concentrations ranging from 0.1% to 1.2% and gas–liquid ratios ranging from 5 to 25. Specifically, it explores foam characteristics, pressure loss, and the relationship between flow rate and foaming agent concentration. The findings reveal that CAF exhibits four flow patterns: wave flow, elastic flow, ring flow, and dispersion flow. For most CAF firefighting applications, a foaming agent concentration of 0.3%–0.5% and a gas–liquid ratio of approximately 10 are suitable. However, for fire isolation purposes, a foaming agent concentration of 0.7%–1.0% and a gas–liquid ratio of over 15 should be employed. By utilizing a power-law rheological model and an experimental regression method, a prediction model is obtained for the flow characteristics and pressure loss of CAF in pipelines. The predictions of the model exhibit an error of less than 10% when compared with experimental results, validating the model. The results of this study provide a theoretical basis and technical support for understanding liquid supply resistance loss, which is crucial for maximizing firefighting effectiveness.

Accelerated Gradient Flow for Directed Graphs With Event-Based Broadcasting

Accelerated Gradient Flow for Directed Graphs With Event-Based Broadcasting

Prediction-correction pedestrian flow by means of minimum flow problem

We study a new variant of mathematical prediction-correction model for crowd motion. The prediction phase is handled by a transport equation where the vector field is computed via an eikonal equation [Formula: see text], with a positive continuous function [Formula: see text] connected to the speed of the spontaneous travel. The correction phase is handled by a new version of the minimum flow problem. This model is flexible and can take into account different types of interactions between the agents, from gradient flow in Wassersetin space to granular type dynamics like in sandpile. Furthermore, different boundary conditions can be used, such as non-homogeneous Dirichlet (e.g. outings with different exit-cost penalty) and Neumann boundary conditions (e.g. entrances with different rates). Combining finite volume method for the transport equation and Chambolle–Pock’s primal dual algorithm for the eikonal equation and minimum flow problem, we present numerical simulations to demonstrate the behavior in different scenarios.

Long-term bio-functional performance of a novel, self-positioning balloon expandable transcatheter biological aortic valve system in the ovine aortic banding model.

The aim of the study was to evaluate bio-functionality of a novel, proprietary balloon-expandable biological transcatheter aortic valve implantation (TAVI) system (InFlow, CardValve Consortium, Poland) in an ovine model of aortic banding. Surgical ascending aorta banding was created in 21 sheep. Two weeks later, 18 biological valves were implanted within the model using 15-16 F InFlow TAVI systems and carotid cut-down approach. Follow-up transthoracic echocardiography was performed at 30, 90, and 180-day. At designated time, animals were euthanized and valves harvested for analysis. All sheep survived the banding procedure. There were 4 (22%) procedure related deaths within a 7-day period. During the observation an additional 2 sheep died. In one, the valve dislocated after the procedure - the animal was excluded. Two animals completed 30-day follow up, five 90-day follow-up and four terminal follow-up of 180 days. Valves examined via transesophageal echocardiography showed proper hemodynamic parameters without evidence of structural valve deterioration. The maximum and average flow gradients at 180 days were 31.4 (23.3-37.7) and 17.5 (13.1-20.2) mmHg, respectively. There was one case of moderate insufficiency and no case of perivalvular leaks. By histopathology, there were no inflammation, thrombosis, nor calcifications in any tested valves at long-term follow-up. Neointimal coverage of stent struts increased with time from basal part in "early" groups to nearly 3/4 of stent length in the 180-day group. The pannus tissue showed maturation that increased with time with no stenotic "collar" visible in orthotopically implanted valves. The study showed good hemodynamic performance, durability and biocompatibility of the novel biological THV.

Energy diminishing implicit-explicit Runge–Kutta methods for gradient flows

This study focuses on the development and analysis of a group of high-order implicit-explicit (IMEX) Runge–Kutta (RK) methods that are suitable for discretizing gradient flows with nonlinearity that is Lipschitz continuous. We demonstrate that these IMEX-RK methods can preserve the original energy dissipation property without any restrictions on the time-step size, thanks to a stabilization technique. The stabilization constants are solely dependent on the minimal eigenvalues that result from the Butcher tables of the IMEX-RKs. Furthermore, we establish a simple framework that can determine whether an IMEX-RK scheme is capable of preserving the original energy dissipation property or not. We also present a heuristic convergence analysis based on the truncation errors. This is the first research to prove that a linear high-order single-step scheme can ensure the original energy stability unconditionally for general gradient flows. Additionally, we provide several high-order IMEX-RK schemes that satisfy the established framework. Notably, we discovered a new four-stage third-order IMEX-RK scheme that reduces energy. Finally, we provide numerical examples to demonstrate the stability and accuracy properties of the proposed methods.

Design and investigation of novel gradient flow fields for proton exchange membrane fuel cell

Ensuring sufficient gas supply and high distribution uniformity are crucial issues in the flow field design to improve the performance and durability of proton exchange membrane fuel cell (PEMFC). However, previous studies often ignore the gas-water distribution variations along the flow direction and adopt identical design for the entire flow field, resulting in unsatisfactory performance. To fill in this gap, this paper innovatively proposes two types of gradient flow field (gradient narrowing and gradient droplet) considering the gas-water distribution characteristics. The channel of the gradient narrowing flow field gradually decreases in all directions along the flow direction, and the gradient droplet flow field is composed of staggered droplet blocks, and the distribution density gradually decreases along the flow direction. The Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is used for the comprehensive evaluation of flow fields. The results demonstrate that the gradient flow field can significantly improve the performance and physical field distribution. The gradient narrowing flow field has the best performance, with 11.39 % improvement in peak power density, 77.96 % increment in average oxygen mass fraction, and 43.11 % improvement in oxygen uniformity compared to parallel flow field. Further, the key geometric parameters sensitivity analysis of gradient narrowing flow field is carried out. This study contributes to understanding the underlying mechanism of mass transfer properties in the novel gradient flow field, and exploring its potential for high-performance flow fields design.

Neural network models for the quaternion singular value decompositions

We develop two neural network models for computing the quaternion singular value decomposition (QSVD), which can be shown to arise as gradient flows or Riemannian-gradient flows on the product of Stiefel manifold over the quaternion skew-field and their geometric and dynamical properties are investigated. Numerical experiments including color image compression indicate the feasibility and effectiveness of the proposed neural network models.

The seepage driving mechanism and effect of CO2 displacing CH4 in coal seam under different pressures

The technology of CO2-ECBM holds the potential to enhance the efficiency of coalbed CH4 extraction by boosting the driving force of CH4 seepage and the desorption of adsorbed CH4 in coal. To investigate the seepage characteristics and displacement effects of gas during CO2-ECBM, the experiment of CO2 displacing CH4 in coal was conducted using a triaxial experimental system within a displacement pressure range of 1.5–4.0 MPa. The results showed that increased displacement pressure led to large coal swelling. This swelling caused a reduction in permeability, leading to high resistance to gas flow and the generation of elevated pore pressure. The distribution of the pore pressure in coal displayed a nonlinear feature, predominantly influenced by coal swelling during CO2 adsorption process. With the injection of CO2, the pressure field in the coal transitioned from an unstable to a stable state. The coal strain induced by CO2/CH4 adsorption-desorption varied, leading to the variation in pore pressure gradient and seepage flow rate, which ultimately impacted the displacement efficiency. The evolution of pressure field during CO2-ECBM provides valuable guidance for displacement effects. It contributes to a parametric optimization for CO2-ECBM application in CH4 extraction.

Aerodynamic and Aeroacoustic Effects of Different Transition Mechanisms on an Airfoil

The paper delves into the detailed sound generation and propagation mechanisms associated with tripping-induced flow perturbations and trailing-edge scattering using wall-resolved large-eddy simulations. Two distinct boundary-layer tripping techniques, namely a geometrically resolved stair strip and an artificially modeled trip using suction and blowing, are investigated. To facilitate comparison, the natural boundary-layer transition is also simulated as a baseline scenario. The analysis takes into account a Reynolds number of 4×105, a Mach number of 0.058, and a nonzero angle of attack of 6.25° over a NACA 0012 airfoil configuration. The mechanisms for sound generation and propagation related to trailing-edge noise remain consistent across the three transition scenarios. However, boundary-layer tripping notably leads to intricate, scenario-specific noise generation: there is an interaction between the laminar separation bubble and tripping for the stair strip case, whereas laminar boundary-layer instability is evident for the suction and blowing scenario. Aerodynamic flowfields involving acoustic noise sources, their propagating natures near the wall, and far-field acoustics are cross-examined in detail. The comprehensive analysis of observed phenomena provides valuable insights for understanding nonlinear flow and acoustic interactions relevant to airfoil noise and designing new types of trips under adverse pressure gradient flows.

Utility and optimal dose of nicorandil for physiological assessment of the femoropopliteal artery.

Nicorandil is widely used as a vasodilator for the physiological assessment of coronary arteries because of its usefulness and safety; however, there are no data on its use in peripheral arteries. To identify the utility of nicorandil and its appropriate dose for the physiological assessment on the femoropopliteal artery. We retrospectively enrolled patients from three institutes in which physiological assessment was carried out with various doses of nicorandil before treatment. Twenty-four femoropopliteal artery stenotic lesions from 22 patients were included. The nicorandil doses used were 2, 4, and 6 mg. Twenty-two lesions were also assessed using 30 mg of papaverine. The pressure gradient (PG) and peripheral fractional flow reserve (pFFR) were calculated based on the mean and systolic pressure levels. We examined the correlation of each parameter with the peak systolic velocity ratio (PSVR) based on the duplex ultrasound images using Spearman's rank correlation coefficient. Systemic blood pressure was assessed for safety. The correlations were higher for mean pressure-based parameters than for systolic pressure-based parameters. As the nicorandil dose increased, the correlations among PG, pFFR, and PSVR also increased (mean pressure-based PG: 2 mg, r = 0.360; 4 mg, r = 0.498; 6 mg, r = 0.694, mean pressure-based pFFR: 2 mg, r = -0.479; 4 mg, r = -0.469; 6 mg, r = -0.641). The blood pressure after the administration of 6 mg of nicorandil was low, and the median systemic mean pressure was 65 mmHg. A 4 mg dose of nicorandil is effective and safe for the mean pressure-based physiological assessment of lesions in the femoropopliteal artery.