L_(1)-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection

Brain tumors come in various types,each with distinct characteristics and treatment approaches,making manual detection a time-consuming and potentially ambiguous process.Brain tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment outcomes.Machine learning models have become key players in automating brain tumor detection.Gradient descent methods are the mainstream algorithms for solving machine learning models.In this paper,we propose a novel distributed proximal stochastic gradient descent approach to solve the L_(1)-Smooth Support Vector Machine(SVM)classifier for brain tumor detection.Firstly,the smooth hinge loss is introduced to be used as the loss function of SVM.It avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent optimization.Secondly,the L_(1) regularization method is employed to sparsify features and enhance the robustness of the model.Finally,adaptive proximal stochastic gradient descent(PGD)with momentum,and distributed adaptive PGDwithmomentum(DPGD)are proposed and applied to the L_(1)-Smooth SVM.Distributed computing is crucial in large-scale data analysis,with its value manifested in extending algorithms to distributed clusters,thus enabling more efficient processing ofmassive amounts of data.The DPGD algorithm leverages Spark,enabling full utilization of the computer’s multi-core resources.Due to its sparsity induced by L_(1) regularization on parameters,it exhibits significantly accelerated convergence speed.From the perspective of loss reduction,DPGD converges faster than PGD.The experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor detection.Frompre-trained models,both the PGD andDPGD outperform other models,boasting an accuracy of 95.21%.

On the spreading behavior of a droplet on a circular cylinder using the lattice Boltzmann method

The study of a droplet spreading on a circular cylinder under gravity was carried out using the pseudo-potential lattice Boltzmann high-density ratios multiphase model with a non-ideal Peng–Robinson equation of state. The calculation results indicate that the motion of the droplet on the cylinder can be divided into three stages: spreading, sliding, and aggregating.The contact length and contact time of a droplet on a cylindrical surface can be affected by factors such as the wettability gradient of the cylindrical wall, the Bond number, and droplet size. Furthermore, phase diagrams showing the relationship between Bond number, cylinder wall wettability gradient, and contact time as well as maximum contact length for three different droplet sizes are given. A theoretical foundation for additional research into the heat and mass transfer process between the droplet and the cylinder can be established by comprehending the variable rules of maximum contact length and contact time.

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.

Anderson Acceleration of Gradient Methods with Energy for Optimization Problems

Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.

Fractional Gradient Descent RBFNN for Active Fault-Tolerant Control of Plant Protection UAVs

With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Gradient Recovery Based Two-Grid Finite Element Method for Parabolic Integro-Differential Optimal Control Problems

In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.

A Methodology to Reduce Thermal Gradients Due to the Exothermic Reactions in Resin Transfer Molding Applications

Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can cause thermal gradients in the composite,potentially leading to undesired residual stresses which can cause shrinkage and warpage.In the present numerical study of these processes,a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization;the effect of some parameters on the thermal gradient is then analyzed,namely:the fiber nature,the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation.The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.

Selecting the optimum location of the corner using gravity gradient method

The conventional gravity gradient method to plot the geologic body location is fuzzy. When the depth is large and the geologic body is small, the Vzz and Vzx derivative errors are also large. We describe that using the status distinguishing factor to optimally determine the comer location is more accurate than the conventional higher-order derivative method. Thus, a better small geologic body and fault resolution is obtained by using the gravity gradient method and trial theoretical model calculation. The actual data is better processed, providing a better basis for prospecting and determination of subsurface geologic structure.

One-step green method to prepare progressive burning gun propellant through gradient denitration strategy

Gradiently denitrated gun propellant(GDGP)prepared by a“gradient denitration”strategy is obviously superior in progressive burning performance to the traditional deterred gun propellant.Currently,the preparation of GDGP employed a tedious two-step method involving organic solvents,which hinders the large-scale preparation of GDGP.In this paper,GDGP was successfully prepared via a novelty and environmentally friendly one-step method.The obtained samples were characterized by FT-IR,Raman,SEM and XPS.The results showed that the content of nitrate groups gradiently increased from the surface to the core in the surface layer of GDGP and the surface layer of GDGP exhibited a higher compaction than that of raw gun propellant,with a well-preserved nitrocellulose structure.The denitration process enabled the propellant surface with regressive energy density and good progressive burning performance,as confirmed by oxygen bomb and closed bomb test.At the same time,the effects of different solvents on the component loss of propellant were compared.The result showed that water caused the least component loss.Finally,the stability of GDGP was confirmed by methyl-violet test.This work not only provided environmentally friendly,simple and economic preparation of GDGP,but also confirmed the stability of GDGP prepared by this method.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

A modified three–term conjugate gradient method with sufficient descent property

A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.

Rockburst Intensity Grade Prediction Model Based on Batch Gradient Descent and Multi-Scale Residual Deep Neural Network

Rockburst is a phenomenon in which free surfaces are formed during excavation,which subsequently causes the sudden release of energy in the construction of mines and tunnels.Light rockburst only peels off rock slices without ejection,while severe rockburst causes casualties and property loss.The frequency and degree of rockburst damage increases with the excavation depth.Moreover,rockburst is the leading engineering geological hazard in the excavation process,and thus the prediction of its intensity grade is of great significance to the development of geotechnical engineering.Therefore,the prediction of rockburst intensity grade is one problem that needs to be solved urgently.By comprehensively considering the occurrence mechanism of rockburst,this paper selects the stress index(σθ/σc),brittleness index(σ_(c)/σ_(t)),and rock elastic energy index(Wet)as the rockburst evaluation indexes through the Spearman coefficient method.This overcomes the low accuracy problem of a single evaluation index prediction method.Following this,the BGD-MSR-DNN rockburst intensity grade prediction model based on batch gradient descent and a multi-scale residual deep neural network is proposed.The batch gradient descent(BGD)module is used to replace the gradient descent algorithm,which effectively improves the efficiency of the network and reduces the model training time.Moreover,the multi-scale residual(MSR)module solves the problem of network degradation when there are too many hidden layers of the deep neural network(DNN),thus improving the model prediction accuracy.The experimental results reveal the BGDMSR-DNN model accuracy to reach 97.1%,outperforming other comparable models.Finally,actual projects such as Qinling Tunnel and Daxiangling Tunnel,reached an accuracy of 100%.The model can be applied in mines and tunnel engineering to realize the accurate and rapid prediction of rockburst intensity grade.

A review of the wave gradiometry method for seismic imaging

As dense seismic arrays at different scales are deployed,the techniques to make full use of array data with low computing cost become increasingly needed.The wave gradiometry method(WGM)is a new branch in seismic tomography,which utilizes the spatial gradients of the wavefield to determine the phase velocity,wave propagation direction,geometrical spreading,and radiation pattern.Seismic wave propagation parameters obtained using the WGM can be further applied to invert 3D velocity models,Q values,and anisotropy at lithospheric(crust and/or mantle)and smaller scales(e.g.,industrial oilfield or fault zone).Herein,we review the theoretical foundation,technical development,and major applications of the WGM,and compared the WGM with other commonly used major array imaging methods.Future development of the WGM is also discussed.

AN ASYMPTOTIC METHOD FOR ANALYZING THE STRESS IN A FUNCTIONALLY GRADIENT MATERIAL LAYER ON A SURFACE OF A STRUCTURAL COMPONENT

A simple and effective method for analyzing the stress distribution in a Functionally Gradient Material(FGM) layer on the su;face of a structural component is proposed in this paper. Generally, the FGM layer is very thin compared with the characteristic length of the structural component, and the nonhomogeneity exists only in the thin layer. Based on these features, by choosing a small parameter I which characterizes the stiffness of the layer relative to the component, and expanding the stresses and displacements on the two sides of the interface according to the parameter lambda, then asymptotically using the continuity conditions of the stresses and displacements on the interface, a decoupling computing process of the coupling control equations of the layer and the structural component is realized. Finally, two examples are given to illustrate the application of the method proposed.

A Study on the Convergence of Gradient Method with Momentum for Sigma-Pi-Sigma Neural Networks

In this paper, a gradient method with momentum for sigma-pi-sigma neural networks (SPSNN) is considered in order to accelerate the convergence of the learning procedure for the network weights. The momentum coefficient is chosen in an adaptive manner, and the corresponding weak convergence and strong convergence results are proved.

Ionospheric forecasting model using fuzzy logic-based gradient descent method

Space weather phenomena cause satellite to ground or satellite to aircraft transmission outages over the VHF to L-band frequency range, particularly in the low latitude region. Global Positioning System （GPS） is primarily susceptible to this form of space weather. Faulty GPS signals are attributed to ionospheric error, which is a function of Total Electron Content （TEC）. Importantly, precise forecasts of space weather conditions and appropriate hazard observant cautions required for ionospheric space weather obser- vations are limited. In this paper, a fuzzy logic-based gradient descent method has been proposed to forecast the ionospheric TEC values. In this technique, membership functions have been tuned based on the gradient descent estimated values. The proposed algorithm has been tested with the TEC data of two geomagnetic storms in the low latitude station of KL University, Guntur, India （16.44°N, 80.62°E）. It has been found that the gradient descent method performs well and the predicted TEC values are close to the original TEC measurements.

Effect of nitrogen introduction methods on the microstructure and properties of gradient cemented carbides

Gradient cemented carbides with the surface depleted in cubic phases were prepared following normal powder metallurgical pro-cedures.Gradient zone formation and the influence of nitrogen introduction methods on the microstructure and performance of the alloys were investigated.The results show that the simple one-step vacuum sintering technique is doable for producing gradient cemented carbides.Gradient structure formation is attributed to the gradient in nitrogen activity during sintering,but is independent from nitrogen introduced methods.A uniform carbon distribution is found throughout the materials.Moreover,the transverse rupture strength of the cemented carbides can be increased by a gradient layer.Different nitrogen carriers give the alloys distinguishing microstructure and mechanical properties,and a gradient alloy with ultrafine-TiC0.5N0.5 is found optimal.

Gradient Step Method to Predict the Ozone Solubility in Water

In this work it presents a strategy to obtain the ozone solubility in water by gradient step method. In this methodology, the ozone in mixture with oxygen is bubbling in a reactor with distilled water at 21℃ and pH 7. The ozone concentration on gas phase is continually increased after the saturation is reached. The method proposed is faster than conventional method （isocratic method）. The solubility from the gradient method is compared with that values obtained from correlations founded in the literature.

An Efficient Energy Routing Protocol Based on Gradient Descent Method in WSNs

In a wireless sensor network[1],the operation of a node depends on the battery power it carries.Because of the environmental reasons,the node cannot replace the battery.In order to improve the life cycle of the network,energy becomes one of the key problems in the design of the wireless sensor network(WSN)routing protocol[2].This paper proposes a routing protocol ERGD based on the method of gradient descent that can minimizes the consumption of energy.Within the communication radius of the current node,the distance between the current node and the next hop node is assumed that can generate a projected energy at the distance from the current node to the base station(BS),this projected energy and the remaining energy of the next hop node is the key factor in finding the next hop node.The simulation results show that the proposed protocol effectively extends the life cycle of the network and improves the reliability and fault tolerance of the system.