Gradient Fractionation Research Articles

Deep ocular tumor classification model using cuckoo search algorithm and Caputo fractional gradient descent

While digital ocular fundus images are commonly used for diagnosing ocular tumors, interpreting these images poses challenges due to their complexity and the subtle features specific to tumors. Automated detection of ocular tumors is crucial for timely diagnosis and effective treatment. This study investigates a robust deep learning system designed for classifying ocular tumors. The article introduces a novel optimizer that integrates the Caputo fractional gradient descent (CFGD) method with the cuckoo search algorithm (CSA) to enhance accuracy and convergence speed, seeking optimal solutions. The proposed optimizer’s performance is assessed by training well-known Vgg16, AlexNet, and GoogLeNet models on 400 fundus images, equally divided between benign and malignant classes. Results demonstrate the significant potential of the proposed optimizer in improving classification accuracy and convergence speed. In particular, the mean accuracy attained by the proposed optimizer is 86.43%, 87.42%, and 87.62% for the Vgg16, AlexNet, and GoogLeNet models, respectively. The performance of our optimizer is compared with existing approaches, namely stochastic gradient descent with momentum (SGDM), adaptive momentum estimation (ADAM), the original cuckoo search algorithm (CSA), Caputo fractional gradient descent (CFGD), beetle antenna search with ADAM (BASADAM), and CSA with ADAM (CSA-ADAM). Evaluation criteria encompass accuracy, robustness, consistency, and convergence speed. Comparative results highlight significant enhancements across all metrics, showcasing the potential of deep learning techniques with the proposed optimizer for accurately identifying ocular tumors. This research contributes significantly to the development of computer-aided diagnosis systems for ocular tumors, emphasizing the benefits of the proposed optimizer in medical image classification domains.

Clinical Outcomes of Urgent or Emergency Transcatheter Aortic Valve Implantation - Insights From the Nationwide Registry of Japan Transcatheter Valve Therapies.

Limited data are available for clinical outcomes in patients who underwent urgent or emergency transcatheter aortic valve implantation (TAVI). This study investigated in-hospital and 1-year outcomes and explored prognostic covariates in urgent/emergency TAVI using nationwide registry data.Methods and Results: Among 26,775 patients who underwent TAVI between August 2013 and December 2019, 25,495 with 1-year follow-up information were analyzed in this study. Baseline and procedural characteristics, as well as clinical adverse events, were compared between the urgent/emergency and elective TAVI groups. The primary outcome was all-cause mortality within 1 year after TAVI. Multivariable Cox regression models were constructed to identify independent predictors after urgent or emergency TAVI. Urgent or emergency TAVI was performed in 578 (2.3%) patients. The Society of Thoracic Surgeons score was significantly higher in the urgent/emergency than elective TAVI group (13.3% vs. 6.0%; P<0.001). Device success rate was comparable between the 2 groups. All-cause death-free survival within 1 year was lower in the urgent/emergency than elective TAVI group (77.2% vs. 92.2%; log rank P<0.001). Malignancy, albumin and creatinine concentrations, ejection fraction, and mean pressure gradient were associated with 1-year mortality in the urgent/emergency TAVI group. Despite higher surgical risk and more comorbidities, the procedure was successfully performed in patients undergoing urgent/emergency TAVI, although it should be noted that prognosis was worse than for elective TAVI.

Fractional gradient system and generalized Birkhoff system

Fractional gradient system and generalized Birkhoff system

Implementation of Caputo type fractional derivative chain rule on back propagation algorithm

Fractional gradient computation is a challenging task for neural networks. In this study, the brief history of fractional derivation is abstracted, and the core framework of the Faà di Bruno formula is implemented to the fractional gradient computation problem. As an analytical approach to solve the chain rule problem of fractional derivatives, the use of the Faà di Bruno formula for the Caputo-type fractional derivative is proposed. When the fractional gradient is calculated using the proposed approach, the problem of determining the bounds of the formula for calculating the Caputo derivative is addressed. As a consequence, the fundamental problem with the fractional back-propagation algorithm is solved analytically, paving the way for the use of any differentiable and integrable activation function in case they are stable. The development of the algorithm and its practical implementation on the photovoltaic fault detection data-set is investigated. The reliability of the neural network metrics is also investigated using analysis of variance (ANOVA), the results are then presented to decide which are the best metrics and the best fractional order. Ordinary back-propagation, fractional back-propagation with and without L2 regularization and momentum are presented in the results to show the advantages of using L2 regularization and momentum in fractional order gradient. Consequently, the test metrics are reliable but cannot be separated from each other. By changing the batch size from 2 to full batches, the proposed system performs better with bigger batches, but adaptive moment estimation (ADAM) performs better with small batches. The cross validation shows the performance of back propagate ion neural networks have better performance than the ordinary neural networks. It is interesting that the best order for a specific data-set cannot be determined because it depends on the batch size, number of epochs and the cross-validation folds .

Impact of left ventricular ejection fraction and aortic valve gradient on mortality following transcatheter aortic valve intervention

BackgroundData regarding the impact of reduced left ventricular ejection fraction (LVEF) and/or reduced mean aortic valve gradient (AVG) on outcomes following transcatheter aortic valve intervention (TAVI) have been conflicting. We sought to assess the relationship between LVEF, AVG, and 1-year mortality in patients undergoing TAVI. MethodsWe prospectively evaluated 298 consecutive adults undergoing TAVI from 2015 to 2018 at an academic tertiary medical center. Patients were categorized according to LVEF and mean AVG. The primary outcome of interest was all-cause mortality at 1 year. ResultsOf 298 adults undergoing TAVI, 66 (22.1%) had baseline LVEF ≤45% while 232 (77.9%) had baseline LVEF >45%; 173 (58.1%) had baseline AVG < 40mmHg while 125 (41.9%) had baseline AVG ≥ 40mmHg. Rates of 1-year all-cause mortality were significantly higher in patients with LVEF ≤45% (28.8% vs 12.1%, p = 0.001) and those with AVG < 40mmHg (19.7% vs 10.4%, p = 0.031) compared to those with LVEF >45% and AVG ≥ 40mmHg respectively. In multivariable analysis, higher AVG (per mmHg) (OR 0.97, 95% CI 0.94–0.99, p = 0.026) was noted to be independently associated with lower rates of 1-year mortality, while LVEF was not (OR 0.98, 95% CI 0.96–1.01). ConclusionsIn this prospective, contemporary registry of adults undergoing TAVI, while 1-year unadjusted mortality rates are significantly higher in patients with reduced LVEF and reduced AVG, risk-adjusted mortality at 1 year is only higher in those with reduced AVG – not in those with reduced LVEF.

Leveraging bioanalytical characterization of fractionated monoclonal antibody pools to identify aggregation-prone and less filterable proteoforms during virus filtration.

Monoclonal antibodies (mAbs) are an essential class of biotherapeutics. A platform process is used for mAb development to ensure clinically safe and stable molecules. Regulatory authorities ensure that mAb production processes include sufficient viral clearance steps to achieve less than one virus particle per million doses of product. Virus filtration is used for size-based removal of enveloped and nonenveloped viruses during downstream processing of mAbs. Process development in mAb purification relies on empirical approaches and often includes adsorptive prefiltration to mitigate virus filter fouling. Opportunities for molecular-level prediction of mAb filterability are needed to plug the existing knowledge gap in downstream processing. A molecular-level approach to understanding the factors influencing mAb filterability may reduce process development time, material loss, and processing costs due to oversized virus filters. In this work, pH step gradient fractionation was applied on polished bulk mAb feed to obtain concentrated pools of fractionated mAb variants. Biophysical properties and quality attributes of fractionated pools, including oligomeric state (size), isoelectric point profile, diffusion interaction parameters, and glycoform profile, were determined using bioanalytical methods. Filterability (loading and throughput) of fractionated pools were evaluated. Statistical methods were used to obtain correlations between quality attributes of mAb fractions and filterability on the Viresolve Pro virus filter.

Global existence for nonlocal quasilinear diffusion systems in nonisotropic nondivergence form

AbstractWe consider the quasilinear diffusion problem of for an open set , , for , and any . Here, denotes an operator which may involve the distributional Riesz fractional gradient of order , with , the classical gradient or/and nonlocal derivatives , with . We show global existence results for various quasilinear diffusion systems in nondivergence form for linear elliptic operators , including classical elliptic systems, anisotropic fractional equations and systems, and anisotropic local and nonlocal operators of the following type: for coercive, invertible matrices and suitable vectorial functions .

Parallel Fractional Stochastic Gradient Descent With Adaptive Learning for Recommender Systems

The structural change toward the digital transformation of online sales elevates the importance of parallel processing techniques in recommender systems, particularly in the pandemic and post-pandemic era. Matrix factorization (MF) is a popular and scalable approach in collaborative filtering (CF) to predict user preferences in recommender systems. Researchers apply Stochastic Gradient Descent (SGD) as one of the most famous optimization techniques for MF. Paralleling SGD methods help address Big Data challenges due to the wide range of products and the sparsity in user ratings. However, these methods&#x2019; convergence rate and accuracy are affected by the dependency between the user and item latent factors, specifically in large-scale problems. Besides, the performance is sensitive to the applied learning rates. This paper proposes a new parallel method to remove dependencies and boost speed-up by using fractional calculus to improve accuracy and convergence rate. We also apply adaptive learning rates to enhance the performance of our proposed method. The proposed method is based on Compute Unified Device Architecture (CUDA) platform. We evaluate the performance of our proposed method using real-world data and compare the results with the close baselines. The results show that our method can obtain high accuracy and convergence rate in addition to high parallelism.

A Baring Fault Diagnosis Method under Small Sample Conditions Based on the Fractional Order Siamese Deep Residual Shrinkage Network

A bearing fault is one of the major causes of rotating machinery faults. However, in real industrial scenarios, the harsh and complex environment makes it very difficult to collect sufficient fault data. Due to this limitation, most of the current methods cannot accurately identify the fault type in cases with limited data, so timely maintenance cannot be conducted. In order to solve this problem, a bearing fault diagnosis method based on the fractional order Siamese deep residual shrinkage network (FO-SDRSN) is proposed in this paper. After data collection, all kinds of vibration data are first converted into two-dimensional time series feature maps, and these feature maps are divided into the same or different types of fault sample pairs. Then, a Siamese network based on the deep residual shrinkage network (DRSN) is used to extract the features of the fault sample pairs, and the fault type is determined according to the features. After that, the contrastive loss function and diagnostic loss function of the sample pairs are combined, and the network parameters are continuously optimized using the fractional order momentum gradient descent method to reduce the loss function. This improves the accuracy of fault diagnosis with a small sample training dataset. Finally, four small sample datasets are used to verify the effectiveness of the proposed method. The results show that the FO-SDRSN method is superior to other advanced methods in terms of training accuracy and stability under small sample conditions.

The impact of concomitant chronic total occlusion on clinical outcomes in patients undergoing transcatheter aortic valve replacement: a large single-center analysis.

Coronary artery disease (CAD) is a common finding in patients with severe aortic stenosis undergoing transcatheter aortic valve replacement (TAVR). However, the impact on prognosis of chronic total occlusions (CTOs), a drastic expression of CAD, remains unclear. We retrospectively reviewed 1,487 consecutive TAVR cases performed at a single tertiary care medical center. Pre-TAVR angiograms were analyzed for the presence of a CTO. At the time of TAVR, 11.2% (n = 167) patients had a CTO. There was no significant association between the presence of a CTO and in-hospital or 30-day mortality. There was also no difference in long-term survival. LV ejection fraction and mean aortic gradients were lower in the CTO group. Our analysis suggests that concomitant CTO lesions in patients undergoing TAVR differ in their risk profile and clinical findings to patients without CTO. CTO lesion per se were not associated with increased mortality, nevertheless CTOs which supply non-viable myocardium in TAVR population were associated with increased risk of death. Additional research is needed to evaluate the prognostic significance of CTO lesions in TAVR patients.

Finite element based dynamic analysis of a porous exponentially graded shaft system subjected to thermal gradients

Abstract In modern applications, demand for the rotor shafts made of FGM has increased in aerospace, gas turbine and turbo jet engines due to its improved dynamic characteristics at elevated temperatures. The dynamic vibration response of a functionally graded Jeffcott rotor-bearing system with induced porosities has been studied for non-uniform porosity distributions. The functionally graded (FG) shaft’s radial direction exhibits continuous variation in the material qualities. The FG rotor’s cross-sectional material properties have been graded using the exponential law. The temperature gradients have been considered to be varied across the cross-section based on exponential temperature distribution. For the first time, using the FE method, it has been possible to study the impact of induced porosities on the free vibration frequencies and steady-state vibration responses of the functionally graded rotor-bearing system. This has led to the development of a two-node porous functionally graded rotor element with uneven porosity distributions using the Timoshenko beam theory. It has been observed that the free vibration frequencies and the FG rotor-bearing system critical speeds are affected by increased porosity and thermal gradients. The frequency responses demonstrate that as temperature gradient and volume fraction of porosity rise, the FG rotor-bearing system’s critical speeds shift to the left.

Analysis of the Mouse Hepatic Peroxisome Proteome-Identification of Novel Protein Constituents Using a Semi-Quantitative SWATH-MS Approach.

Ongoing technical and bioinformatics improvements in mass spectrometry (MS) allow for the identifying and quantifying of the enrichment of increasingly less-abundant proteins in individual fractions. Accordingly, this study reassessed the proteome of mouse liver peroxisomes by the parallel isolation of peroxisomes from a mitochondria- and a microsome-enriched prefraction, combining density-gradient centrifugation with a semi-quantitative SWATH-MS proteomics approach to unveil novel peroxisomal or peroxisome-associated proteins. In total, 1071 proteins were identified using MS and assessed in terms of their distribution in either high-density peroxisomal or low-density gradient fractions, containing the bulk of organelle material. Combining the data from both fractionation approaches allowed for the identification of specific protein profiles characteristic of mitochondria, the ER and peroxisomes. Among the proteins significantly enriched in the peroxisomal cluster were several novel peroxisomal candidates. Five of those were validated by colocalization in peroxisomes, using confocal microscopy. The peroxisomal import of HTATIP2 and PAFAH2, which contain a peroxisome-targeting sequence 1 (PTS1), could be confirmed by overexpression in HepG2 cells. The candidates SAR1B and PDCD6, which are known ER-exit-site proteins, did not directly colocalize with peroxisomes, but resided at ER sites, which frequently surrounded peroxisomes. Hence, both proteins might concentrate at presumably co-purified peroxisome-ER membrane contacts. Intriguingly, the fifth candidate, OCIA domain-containing protein 1, was previously described as decreasing mitochondrial network formation. In this work, we confirmed its peroxisomal localization and further observed a reduction in peroxisome numbers in response to OCIAD1 overexpression. Hence, OCIAD1 appears to be a novel protein, which has an impact on both mitochondrial and peroxisomal maintenance.

A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations

A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations

Superior Yield Strength and High‐Tensile‐Toughness Matching of Medium‐Mn Steel with Gradient Structure Developed by Cyclic Torsion

A multiphase‐gradient‐structured medium‐Mn steel with dislocation/stacking fault (SF) density gradient, austenite fraction gradient, and grain size gradient is designed and fabricated by cyclic torsion. It exhibits higher yield strength (YS) (942 MPa), ultimate tensile strength (1295 MPa), and tensile toughness (290 mJ mm−3) than its homogeneous counterpart (672, 1273 MPa, and 278 mJ mm−3, respectively). High‐density‐interlaced SFs are generated at the surface region because of the change in strain path and stress state during cyclic torsion. These massive interactive SFs promote the persistent martensite transformation of the retained austenite in the surface region within the entire uniform strain range. Therefore, in addition to the central layer, the surface region in the gradient structures provides strong strain hardening. Moreover, the continuous martensite transformation in the surface region allows the gradient structure to be retained even after tensile failure, which is beneficial for improving the heterogeneous‐deformation‐induced (HDI) hardening of the gradient‐structured sample during tensile deformation. Thus, the combination of active and persistent transformation‐induced plasticity effect and HDI hardening contributes to its excellent tensile toughness and ductility. Quantitative analysis indicates that HDI strengthening and dislocation strengthening play a dominant role in the sample's ultrahigh YS.

A novel gradient descent optimizer based on fractional order scheduler and its application in deep neural networks

To improve convergence speed of deep neural network trained by gradient descent methods (GDMs), this paper proposed a novel fractional order gradient descent optimizer (FOAdam) based on Caputo operator and Adam algorithm, and analyzed the impact of fractional order on convergence performance using optimization theory and simulation. Furthermore, to address the trade-off between convergence speed and precision under fixed-order conditions, a fractional order scheduler (FOS) was designed based on the Connections Cloud Model (CCM). Numerical experiments conducted on MNIST and CIFAR-10 datasets showed that FOS-FOAdam outperformed other mainstream GDMs in terms of convergence speed and precision. Finally, FOS-FOAdam was applied in recognizing and classifying image datasets of cuttings and cores at the logging site, demonstrating good prospects for practical engineering applications.

An Improved Prioritized DDPG Based on Fractional-Order Learning Scheme.

Although deep deterministic policy gradient (DDPG) algorithm gets widespread attention as a result of its powerful functionality and applicability for large-scale continuous control, it cannot be denied that DDPG has problems such as low sample utilization efficiency and insufficient exploration. Therefore, an improved DDPG is presented to overcome these challenges in this article. Firstly, an optimizer based on fractional gradient is introduced into the algorithm network, which is conductive to increase the speed and accuracy of training convergence. On this basis, high-value experience replay based on weight-changed priority is proposed to improve sample utilization efficiency, and aiming to have a stronger exploration of the environment, an optimized exploration strategy for boundary action space is adopted. Finally, our proposed method is tested through the experiments of gym and pybullet platform. According to the results, our method speeds up the learning process, obtains higher average rewards in comparison with other algorithms.

Adaptive fixed-time proximal gradient method for non-smooth optimization: the fractional approach

Non-smooth optimization has now played an important role in many fields, such as l1-regulation problem and sparse recovery problem. In this paper, a novel fractional fixed-time proximal gradient method is proposed for solving the composite optimization problems with non-smooth terms. At first, according to the distribution of zeroes of Mittag-Leffler functions, a novel fixed-time convergence theory with a fractional adaptive gain is proposed. Based on the optimal condition analysis of the transformed problem using the augmented Lagrangian function, a novel fixed-time proximal gradient method is then proposed and the fixed-time convergence property is rigorously proven. Furthermore, the proposed algorithm is applied to solve the sparse recovery problem in compressive sensing, and the restricted isometry condition required for the application of the algorithm is analyzed to achieve fixed-time recovery of the signal. Finally, simulation examples are provided to validate all the results.

Comparison of Evolut-R 34 mm Valve and Smaller Evolut-R Valves in Patients Undergoing Transcatheter Aortic Valve Implantation and Determination of Mild Paravalvular Leak Predictors.

The main purpose of this study was to evaluate and compare the in-hospital, 1-month and 1-year post-procedure outcomes of patients treated with Evolut-R 34 mm and Evolut-R 23/26/29 mm devices. Additionally, the study aimed to identify factors that could predict the occurrence of ≥ mild paravalvular leaks (PVL). Between April 2015 and May 2022, 269 consecutive patients who underwent transcatheter aortic valve implantation (TAVI) with Evolut-R 34 mm (n = 66, 24.5%) and Evolut-R 23/26/29 mm (n = 203, 75.5%) devices in a single center were retrospectively analyzed. Patients in the Evolut-R 34 mm group had a lower female sex ratio (16.7% vs. 66.5%, P <.001, respectively), ejection fraction (50.7 ± 10.1% vs. 54.5 ± 9.3%, P =.016, respectively), and mean aortic gradient (7.4 ± 3.3 vs. 9.2 ± 5.0, P =.026, respectively) compared to the Evolut-R 23/26/29 mm group. The groups did not exhibit any statistically significant distinctions with regard to technical success, the need for a permanent pacemaker, occurrences of stroke, major vascular complications, PVL, major adverse cardiovascular and cerebrovascular events, or mortality. Peak velocity was confirmed as a significant predictor of ≥mild PVL in both patient groups in the receiver operating characteristic curve analysis. In logistic regression analysis; In patients with Evolut-R 34 mm valve, pre-TAVI aortic valve peak velocity (odds ratio (OR) = 23.202; P =.019) and calcium volume 800 Hounsfield Units (mm3) (OR = 1.017; P <.001) were independent predictors of ≥mild PVL. The Evolut-R 34 mm valve has shown comparable in-hospital results with smaller valve sizes. Pre-TAVI aortic valve peak velocity and calcium volume predicted ≥ mild PVL in Evolut-R 34 mm patients.

Evaluation of soil texture classification from orthodox interpolation and machine learning techniques

The current investigation examines the effectiveness of various approaches in predicting the soil texture class (clay, silt, and sand contents) of the Rawalpindi district, Punjab province, Pakistan. The employed techniques included artificial neural networks (ANNs), kriging, co-kriging, and inverse distance weighting (IDW). A total of 44 soil specimens from depths of 10–15 cm were gathered, and then the hydrometer method was adopted to measure their texture. The map of soil grain sets was formulated in the ArcGIS environment, utilizing distinct interpolation approaches. The MATLAB software was used to evaluate soil texture. The gradient fraction, latitude and longitude, elevation, and soil texture fragments of points were proposed to an ANN. Several statistical values, such as correlation coefficient (R), geometric mean error ratios (GMER), and root mean square error (RMSE), were utilized to evaluate the precision of the intended techniques. In assessing grain size and spatial dissemination of clay, silt, and sand, the effectiveness and precision of ANN were superior compared to kriging, co-kriging, and inverse distance weighting. Still, less than a 50% correlation was observed using the ANN. In this examination, the IDW had inferior precision compared to the other approaches. The results demonstrated that the practices produced acceptable results and can be used for future research. Soil texture is among the most central variables that can manipulate agriculture plans. The prepared maps exhibiting the soil texture groups are imperative for crop yield and pastoral scheduling.

Eringen’s model via linearization of nonlocal hyperelasticity

We consider Riesz’ fractional gradient and a truncated version of it. The equations of nonlocal nonlinear elasticity based on those gradients are known. We perform a formal linearization and arrive at the equations of linear elasticity based on those nonlocal operators. We prove the existence of solutions of the linear equations, notably, by a nonlocal version of Korn’s inequality. Finally, we show that the linearizations obtained are particular cases of Eringen’s model with singular kernels.