Joint Optimization for on-Demand Deployment of UAVs and Spectrum Allocation in UAVs-Assisted Communication

To improve the efficiency and fairness of the spectrum allocation for ground communication assisted by unmanned aerial vehicles(UAVs),a joint optimization method for on-demand deployment and spectrum allocation of UAVs is proposed,which is modeled as a mixed-integer non-convex optimization problem(MINCOP).An algorithm to estimate the minimum number of required UAVs is firstly proposed based on the pre-estimation and simulated annealing.The MINCOP is then decomposed into three sub-problems based on the block coordinate descent method,including the spectrum allocation of UAVs,the association between UAVs and ground users,and the deployment of UAVs.Specifically,the optimal spectrum allocation is derived based on the interference mitigation and channel reuse.The association between UAVs and ground users is optimized based on local iterated optimization.A particle-based optimization algorithm is proposed to resolve the subproblem of the UAVs deployment.Simulation results show that the proposed method could effectively improve the minimum transmission rate of UAVs as well as user fairness of spectrum allocation.

Interseismic slip distribution and locking characteristics of the mid-southern segment of the Tanlu fault zone

We employ the block negative dislocation model to invert the distribution of fault coupling and slip rate deficit on the different segments of the Tanlu(Tancheng-Lujiang) fault zone, according to the GPS horizontal velocity field from 1991 to 2007(the first phase) and 2013 to 2018(the second phase). By comparing the deformation characteristics results, we discuss the relationship between the deformation characteristics with the M earthquake in Japan. The results showed that the fault coupling rate of the northern section of Tancheng in the second phase reduced compared with that in the first phase. However, the results of the two phases showed that the northern section of Juxian still has a high coupling rate, a deep blocking depth, and a dextral compressive deficit, which is the enrapture section of the 1668 Tancheng earthquake. At the same time, the area strain results show that the strain rate of the central and eastern regions of the second phase is obviously enhanced compared with that of the first phase. The occurrence of the great earthquake in Japan has played a specific role in alleviating the strain accumulation in the middle and south sections of the Tanlu fault zone. The results of the maximum shear strain show that the shear strain in the middle section of the Tanlu fault zone in the second phase is weaker than that in the first phase, and the maximum shear strain in the southern section is stronger than that in the first phase. The fault coupling coefficient of the south Sihong to Jiashan section is high, and it is also the unruptured section of historical earthquakes. At the same time, small earthquakes in this area are not active and accumulate stress easily, so the future earthquake risk deserves attention.

A gradually descent method for discrete global optimization

In this paper, a new method named as the gradually descent method was proposed to solve the discrete global optimization problem. With the aid of an auxiliary function, this method enables to convert the problem of finding one discrete minimizer of the objective function f to that of finding another at each cycle. The auxiliary function can ensure that a point, except a prescribed point, is not its integer stationary point if the value of objective function at the point is greater than the scalar which is chosen properly. This property leads to a better minimizer of f found more easily by some classical local search methods. The computational results show that this algorithm is quite efficient and reliable for solving nonlinear integer programming problems.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

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.

Designing fuzzy inference system based on improved gradient descent method

The distribution of sampling data influences completeness of rule base so that extrapolating missing rules is very difficult. Based on data mining, a self-learning method is developed for identifying fuzzy model and extrapolating missing rules, by means of confidence measure and the improved gradient descent method. The proposed approach can not only identify fuzzy model, update its parameters and determine optimal output fuzzy sets simultaneously, but also resolve the uncontrollable problem led by the regions that data do not cover. The simulation results show the effectiveness and accuracy of the proposed approach with the classical truck backer-upper control problem verifying.

EFFICIENT GRADIENT DESCENT METHOD OFRBF NEURAL ENTWORKS WITHADAPTIVE LEARNING RATE

A new algorithm to exploit the learning rates of gradient descent method is presented, based on the second-order Taylor expansion of the error energy function with respect to learning rate, at some values decided by "award-punish" strategy. Detailed deduction of the algorithm applied to RBF networks is given. Simulation studies show that this algorithm can increase the rate of convergence and improve the performance of the gradient descent method.

A Convolutional Neural Network Classifier VGG-19 Architecture for Lesion Detection and Grading in Diabetic Retinopathy Based on Deep Learning

Diabetic Retinopathy(DR)is a type of disease in eyes as a result of a diabetic condition that ends up damaging the retina,leading to blindness or loss of vision.Morphological and physiological retinal variations involving slowdown of blood flow in the retina,elevation of leukocyte cohesion,basement membrane dystrophy,and decline of pericyte cells,develop.As DR in its initial stage has no symptoms,early detection and automated diagnosis can prevent further visual damage.In this research,using a Deep Neural Network(DNN),segmentation methods are proposed to detect the retinal defects such as exudates,hemorrhages,microaneurysms from digital fundus images and then the conditions are classified accurately to identify the grades as mild,moderate,severe,no PDR,PDR in DR.Initially,saliency detection is applied on color images to detect maximum salient foreground objects from the background.Next,structure tensor is applied powerfully to enhance the local patterns of edge elements and intensity changes that occur on edges of the object.Finally,active contours approximation is performed using gradient descent to segment the lesions from the images.Afterwards,the output images from the proposed segmentation process are subjected to evaluate the ratio between the total contour area and the total true contour arc length to label the classes as mild,moderate,severe,No PDR and PDR.Based on the computed ratio obtained from segmented images,the severity levels were identified.Meanwhile,statistical parameters like the mean and the standard deviation of pixel intensities,mean of hue,saturation and deviation clustering,are estimated through K-means,which are computed as features from the output images of the proposed segmentation process.Using these derived feature sets as input to the classifier,the classification of DR was performed.Finally,a VGG-19 deep neural network was trained and tested using the derived feature sets from the KAGGLE fundus image dataset containing 35,126 images in total.The VGG-19 is trained with features extracted from 20,000 images and tested with features extracted from 5,000 images to achieve a sensitivity of 82%and an accuracy of 96%.The proposed system was able to label and classify DR grades automatically.

Rupture model of the 2013 M_W 6.6 Lushan (China) earthquake constrained by a new GPS data set and its effects on potential seismic hazard

Vertical records are critically important when determining the rupture model of an earthquake, especially a thrust earthquake. Due to the relatively low fitness level of near-field vertical displacements, the precision of previous rupture models is relatively low, and the seismic hazard evaluated thereafter should be further updated. In this study, we applied three-component displacement records from GPS stations in and around the source region of the 2013 MW6.6 Lushan earthquake to re-investigate the rupture model.To improve the resolution of the rupture model, records from both continuous and campaign GPS stations were gathered, and secular deformations of the GPS movements were removed from the records of the campaign stations to ensure their reliability. The rupture model was derived by the steepest descent method（SDM）, which is based on a layered velocity structure. The peak slip value was about 0.75 m, with a seismic moment release of 9.89 × 1018 N·m, which was equivalent to an MW6.6 event. The inferred fault geometry coincided well with the aftershock distribution of the Lushan earthquake. Unlike previous rupture models, a secondary slip asperity existed at a shallow depth and even touched the ground surface. Based on the distribution of the co-seismic ruptures of the Lushan and Wenchuan earthquakes, post-seismic relaxation of the Wenchuan earthquake, and tectonic loading process, we proposed that the seismic hazard is quite high and still needs special attention in the seismic gap between the two earthquakes.

Full waveform inversion with spectral conjugategradient method

Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.

A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells

In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar cells.We formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random surfaces.The optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are investigated.To evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the computation.The stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost significantly.Various numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random structures.We also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.

A Gradient Descent Method for Estimating the Markov Chain Choice Model

In this paper,we propose a gradient descent method to estimate the parameters in a Markov chain choice model.Particularly,we derive closed-form formula for the gradient of the log-likelihood function and show the convergence of the algorithm.Numerical experiments verify the efficiency of our approach by comparing with the expectation-maximization algorithm.We show that the similar result can be extended to a more general case that one does not have observation of the no-purchase data.

Numerical Fitting of Planar Photographic Images with Spherical Voronoi Diagrams

There are many phenomena that generate polygonal tessellations on surfaces of 3D objects. One interesting example is the jackfruit, a multiple fruit found in the tropics. A recent study found the best-fit spherical Voronoi diagram from a photo of jackfruit skin, but the optimization was relative to the radius of the sphere and the height of the spikes. In this study, we propose a method for adjusting the position of the center of the sphere in addition to these parameters. Experiments were conducted using both ideal and real data. However, convergence with real data has not been confirmed due to relaxation of the convergence condition.

Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation.With the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions:soliton resolution via the mixed■-Riemann-Hilbert problem

In this paper,we investigate the Cauchy problem of the Sasa-Satsuma(SS)equation with initial data belonging to the Schwartz space.The SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3×3 Lax representation.With the aid of the■nonlinear steepest descent method of the mixed■-Riemann-Hilbert problem,we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

New Results in Cooperative Adaptive Optimal Output Regulation

This paper investigates the cooperative adaptive optimal output regulation problem of continuous-time linear multi-agent systems.As the multi-agent system dynamics are uncertain,solving regulator equations and the corresponding algebraic Riccati equations is challenging,especially for high-order systems.In this paper,a novel method is proposed to approximate the solution of regulator equations,i.e.,gradient descent method.It is worth noting that this method obtains gradients through online data rather than model information.A data-driven distributed adaptive suboptimal controller is developed by adaptive dynamic programming,so that each follower can achieve asymptotic tracking and disturbance rejection.Finally,the effectiveness of the proposed control method is validated by simulations.

Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem:without Solitons

In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation.Furthermore,using the approach of Deift-Zhou nonlinear steepest descent,the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived.For the reverse space-time nonlocal Hirota equation,since the symmetries of its scattering matrix are different with the local Hirota equation,the v(λ_(i))(i=0,1)would like to be imaginary,which results in theδ_(λi)^(0)contains an increasing t(±Imv(λ_(i)))/2,and then the asymptotic behavior for nonlocal Hirota equation becomes differently.

Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method

We introduce the fractional-order global optimal backpropagation machine,which is trained by an improved fractionalorder steepest descent method(FSDM).This is a fractional-order backpropagation neural network(FBPNN),a state-of-the-art fractional-order branch of the family of backpropagation neural networks(BPNNs),different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method.The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error.First,the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically.Then,the mathematical proof of fractional-order global optimal convergence,an assumption of the structure,and fractional-order multi-scale global optimization of the FBPNN are analyzed in detail.Finally,we perform three(types of)experiments to compare the performances of an FBPNN and a classic first-order BPNN,i.e.,example function approximation,fractional-order multi-scale global optimization,and comparison of global search and error fitting abilities with real data.The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.

A GLOBALLY DERIVTIVE-FREE DESCENT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.

Numerical partitioning of components for four-modal sedimentary grain-size distribution based on gradient descent method

The gradient descent(GD)method is used to fit the measured data(i.e.,the laser grain-size distribution of the sediments)with a sum of four weighted lognormal functions.The method is calibrated by a series of ideal numerical experiments.The numerical results indicate that the GD method not only is easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily.The method is applied to numerical partitioning of laser grain-size components of a series of Garzêloess samples and three bottom sedimentary samples of submarine turbidity currents modeled in an open channel laboratory flume.The overall fitting results are satisfactory.As a new approach of data fitting,the GD method could also be adapted to solve other optimization problems.