Global and Quadratic Convergence of Newton Hard-Thresholding Pursuit

Algorithms based on the hard thresholding principle have been well studied with sounding theoretical guarantees in the compressed sensing and more general sparsity-constrained optimization. It is widely observed in existing empirical studies that when a restricted Newton step was used (as the debiasing step), the hard-thresholding algorithms tend to meet halting conditions in a significantly low number of iterations and are very efficient. Hence, the thus obtained Newton hard-thresholding algorithms call for stronger theoretical guarantees than for their simple hard-thresholding counterparts. This paper provides a theoretical justification for the use of the restricted Newton step. We build our theory and algorithm, Newton Hard-Thresholding Pursuit (NHTP), for the sparsity-constrained optimization. Our main result shows that NHTP is quadratically convergent under the standard assumption of restricted strong convexity and smoothness. We also establish its global convergence to a stationary point under a weaker assumption. In the special case of the compressive sensing, NHTP effectively reduces to some of the existing hard-thresholding algorithms with a Newton step. Consequently, our fast convergence result justifies why those algorithms perform better than without the Newton step. The efficiency of NHTP was demonstrated on both synthetic and real data in compressed sensing and sparse logistic regression

A semismooth newton method for the nearest Euclidean distance matrix problem

The Nearest Euclidean distance matrix problem (NEDM) is a fundamentalcomputational problem in applications such asmultidimensional scaling and molecularconformation from nuclear magnetic resonance data in computational chemistry.Especially in the latter application, the problem is often large scale with the number ofatoms ranging from a few hundreds to a few thousands.In this paper, we introduce asemismooth Newton method that solves the dual problem of (NEDM). We prove that themethod is quadratically convergent.We then present an application of the Newton method to NEDM with $H$-weights.We demonstrate the superior performance of the Newton method over existing methodsincluding the latest quadratic semi-definite programming solver.This research also opens a new avenue towards efficient solution methods for the molecularembedding problem

Dynamic model and ADRC of a novel water-air unmanned vehicle for water entry with in-ground effect

The class of vehicles that can move both in the air and underwater has been of great interest for decades. A novel water-air unmanned vehicle with double quadrotor structure is designed in this study. The air power mechanism works when the vehicle flies in the air, whereas the water power mechanism works when it moves underwater. The water entry process of water-air unmanned vehicle requires accurate attitude and height control, or the vehicle may bounce off or overturn. However, a force resisting its descent known as in-ground effect will affect its stability. The in-ground effect formula of the water entry process is derived by experiments, and the water entry dynamic model is improved at the same time. An active disturbance rejection controller (ADRC) is designed for the control of water entry attitude and height. Experimental results obtained from the comparison of the ADRC and a proportional-integral-derivative (PID) controller show that the ADRC designed in this study is more robust than the PID controller for the internal coupling and external disturbance on the vehicle. Moreover, the ADRC can meet the requirements of rapid attitude adjustment and accurate height control

The motion characteristics of a cylinder vehicle in the oblique water-exit process

The hydrodynamic model of a vehicle exiting the water surface obliquely has been analyzed. The analyzed object is a cylinder vehicle and its motion characteristics. Two methods have been used to simulate the water-exit process under the same conditions: Numerical Simulation Method (NSM) and Theoretical Model Solution Method (TMSM). The comparison results of the two methods can validate the hydrodynamic model founded in this paper. Different initial angles and different initial velocities have been simulated by this hydrodynamic model and the numerical simulation has been analyzed. The analysis reveals the rule of change of altitude and position of the vehicle in the water-exit process, and its motion after it exits the water surface. This paper explains why it is more difficult for the vehicle to exit the water obliquely than vertically. The results show that the hydrodynamic model of the water exiting vehicle can be used to research the exiting water motion characteristics. The models simulate the physics of motion realistically and this hydrodynamic model can be used as a foundation for the future research of the stability and control of a vehicle exiting the water

Minimum Thrust of a Morphing Unmanned Submersible Aerial Vehicle in the Water-to-Air Motion

This study proposes a new water-to-air motion pattern that combines morphing with power switch. Under the conditions of this pattern, the vehicle needs a certain thrust to avoid falling back after jumping out of the water. The minimum thrust is among the most important design parameters of a vehicle. The water-exit and take-off dynamic models of the vehicle are constructed through the force and motion analysis before and after morphing. The control model of the vehicle is created by analysing the control problem in the take-off motion. The minimum thrust at different initial water-exit angles is computed using the optimum searching algorithm. The following law is then established: the greater the initial water-exit angle, the smaller the minimum thrust required in the air. Such a relationship becomes insignificant when the initial water-exit angle exceeds 40°

catena-Poly[[(dimethyl sulfoxide-κO)zinc(II)]-μ-(E)-2-[(2-oxido-1-naphth­yl)­methyl­eneamino]propanoato-κ4 O 2,N,O 1:O 1′]

In the title coordination polymer, [Zn(C14H11NO3)(C2H6OS)]n, each ZnII ion is five-coordinated in a slightly distorted trigonal–bipyramidal coordination environment, formed by three O atoms from two 2-[(2-oxido-1-naphth­yl)­methyl­eneamino]propanoate ligands, one O atom from a dimethyl sulfoxide mol­ecule and the N atom from the amino­propanoate ligand. The propanoate ligands bridge ZnII ions, forming a zigzag chain parallel to [010]

Flow field interference characteristic of axial ring wing configuration

To analyze the air flow interference between upper and lower wings in axial ring wing configuration, NASA SC(2)-1006 supercritical airfoil is chosen as the basic airfoil. Flow field around the double-wing structure with different relative distances between upper and lower wings is numerically simulated, using SST  turbulence model, and the numerical conclusion about the influence of relative distance D/L on the aerodynamic performance is drawn. It is shown that, at the speed Ma = 0.8, reflection of shockwave between the upper wing and the lower wing has a great negative effect on both lift and drag coefficient. When D/L = 0.1, and the angle of attack AOA = 0°, the resultant lift produced by the two wings is equivalent to that of the single wing, while the resultant drag is 4 times of that of the single wing, which shows a poor aerodynamic characteristic. With the increasing of the relative distance, the intensity of the shockwave between the upper and lower wings is weakened and the negative effect is relieved. Furthermore, the growth of the angle of attack AOA can obscure the negative effect. It could provide helpful reference to the design of axial ring wing aircraft

Green-light p-n Junction Particle Inhomogeneous Phase Enhancement of MgB2 Smart Meta-Superconductor

Improving the critical temperature (TC), critical magnetic field (HC), and critical current (JC) of superconducting materials has always been one of the most significant challenges in the field of superconductivity, but progress has been slow over the years. Based on the concept of injecting energy to enhance electron pairing states, in this study, we have employed a solid-state sintering method to fabricate a series of smart meta-superconductors (SMSCs) consisting of p-n junction nanostructures with a wavelength of 550 nm, doped within an MgB2 matrix. Experimental results demonstrate that compared to pure MgB2 samples, the critical transition temperature (TC) has increased by 1.2 K, the critical current (JC) has increased by 52.8%, and the Meissner effect (HC) shows significant improvement in its diamagnetic properties. This phenomenon of enhanced superconducting performance can be explained by the coupling between superconducting electrons and evanescent waves