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.

Velocity bunching in travelling wave accelerator with low acceleration gradient

We present the analytical and simulated results of our study of the influence of the acceleration gradient in the velocity bunching process, which is a bunch compression scheme that uses a travelling wave accelerating structure as a compressor. Our study shows that the bunch compression application with low acceleration gradient is more tolerant to phase jitter and more successful in obtaining a compressed electron beam with symmetrical longitudinal distribution and low energy spread. We also present a transverse emittance compensation scheme to compensate the emittance growth caused by the increase of the space charge force in the compressing process, which is easy to adjust for different compression factors.

一种基于稀疏优化和Nesterov动量策略的模型剪枝算法

随着深度学习快速发展,模型的参数量和计算复杂度爆炸式增长,在移动终端上部署面临挑战,模型剪枝成为深度学习模型落地应用的关键。目前,基于正则化的剪枝方法通常采用L2正则化并结合基于数量级的重要性标准,是一种经验性的方法,缺乏理论依据,精度难以保证。受Proximal梯度方法求解稀疏优化问题的启发,本文提出一种能够在深度神经网络上直接产生稀疏解的Prox⁃NAG优化方法,并设计了与之配套的迭代剪枝算法。该方法基于L1正则化,利用Nesterov动量求解优化问题,克服了原有正则化剪枝方法对L2正则化和数量级标准的依赖,是稀疏优化从传统机器学习向深度学习的自然推广。在CIFAR10数据集上对ResNet系列模型进行剪枝实验,实验结果证明Prox⁃NAG剪枝算法较原有剪枝算法性能有所提升。

On-chip ultrafast stackable dielectric laser positron accelerator

We present a first on-chip positron accelerator based on dielectric laser acceleration.This innovative approach significantly reduces the physical dimensions of the positron acceleration apparatus,enhancing its feasibility for diverse applications.By utilizing a stacked acceleration structure and far-infrared laser technology,we are able to achieve a seven-stage acceleration structure that surpasses the distance and energy gain of using the previous dielectric laser acceleration methods.Additionally,we are able to compress the positron beam to an ultrafast sub-femtosecond scale during the acceleration process,compared with the traditional methods,the positron beam is compressed to a greater extent.We also demonstrate the robustness of the stacked acceleration structure through the successful acceleration of the positron beam.

Ultrahigh accelerating gradient and quality factor of CEPC 650 MHz superconducting radio-frequency cavity

Two 650 MHz single-cell superconducting radio-frequency(SRF)cavities used for the Circular Electron Positron Collider(CEPC)were studied to achieve a high accelerating gradient(E_(acc))and high intrinsic quality factor(Q_(0)).The 650 MHz single-cell cavities were subjected to a combination of buffered chemical polishing(BCP)and electropolishing(EP),and their E_(acc) exceeded40 MV/m.Such a high E_(acc) may result from the cold EP with more uniform removal.BCP is easy,cheap,and rough,whereas EP is complicated,expensive,and precise Therefore,the combination of BCP and EP investigated in this study is suitable for surface treatments of mass SRF cavities.Medium temperature(mid-T)furnace baking was also conducted,which demonstrated an ultrahigh Q_(0) of 8×10^(10) at 22 MV/m for both cavities,and an extremely low BCS resistance(R_(BCS))of~1.0 nΩwas achieved a2.0 K.

Structure and material study of dielectric laser accelerators based on the inverse Cherenkov effect

Dielectric laser accelerators(DLAs)are considered promising candidates for on-chip particle accelerators that can achieve high acceleration gradients.This study explores various combinations of dielectric materials and accelerated structures based on the inverse Cherenkov effect.The designs utilize conventional processing methods and laser parameters currently in use.We optimize the structural model to enhance the gradient of acceleration and the electron energy gain.To achieve higher acceleration gradients and energy gains,the selection of materials and structures should be based on the initial electron energy.Furthermore,we observed that the variation of the acceleration gradient of the material is different at different initial electron energies.These findings suggest that on-chip accelerators are feasible with the help of these structures and materials.

An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.

Nitrogen doping/infusion of 650 MHz cavities for CEPC

The nitrogen doping/infusion of 650 MHz cavities for the circular electron positron collider(CEPC)is investigated in this study.Two 650 MHz 1-cell cavities are first treated via buffered chemical polishing(BCP),followed by nitrogen doping.A"2/6"condition is adopted,similar to that for 1.3 GHz cavities of Linear Coherent Light Source II.The quality factor of both cavities improved to 7×10^(10)in low fields,i.e.,higher than that obtained from the baseline test.One 650 MHz two-cell cavity is nitrogen infused at 165℃for 48 h with a BCP surface base.The intrinsic quality factor(Q0)reached6×10^(10)at 22 MV/m in the vertical test,and the maximum gradient is 25 MV/m,which exceeds the specification of the CEPC(4×10^(10)at 22 MV/m).

Convergence of Gradient Algorithms for Nonconvex C^(1+α) Cost Functions

This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting.A class of stochastic momentum methods,including stochastic gradient descent,heavy ball and Nesterov’s accelerated gradient,is analyzed in a general framework under mild assumptions.Based on the convergence result of expected gradients,the authors prove the almost sure convergence by a detailed discussion of the effects of momentum and the number of upcrossings.It is worth noting that there are not additional restrictions imposed on the objective function and stepsize.Another improvement over previous results is that the existing Lipschitz condition of the gradient is relaxed into the condition of H?lder continuity.As a byproduct,the authors apply a localization procedure to extend the results to stochastic stepsizes.

Gradient Structured Copper by Rotationally Accelerated Shot Peening

A new technology-rotationally accelerated shot peening（RASP）, was developed to prepare gradient structured materials. By using centrifugal acceleration principle and large steel balls, the RASP technology can produce much higher impact energy compared to conventional shot peening. As a proof-of-concept demonstration, the RASP was utilized to refine the surface layer in pure copper（Cu） with an average grain size of 85 nm. The grain size increases largely from surface downwards the bulk, forming an800 ？m thick gradient-structured surface layer and consequently a micro-hardness gradient. The difference between the RASP technology and other established techniques in preparing gradient structured materials is discussed. The RASP technology exhibits a promoting future for large-scale manufacturing of gradient materials.

Scalable Distributed Optimization Combining Conic Projection and Linear Programming for Energy Community Scheduling

In this paper, a new method to address the scheduling problem of a renewable energy community while considering network constraints and users' privacy preservation is proposed. The method decouples the optimization solution into two interacting procedures: conic projection(CP) and linear programming(LP) optimization. A new optimal CP method is proposed based on local computations and on the calculation of the roots of a fourth-order polynomial for which a closed-form solution is known. Computational tests conducted on both 14-bus and 84-bus distribution networks demonstrate the effectiveness of the proposed method in obtaining the same quality of solutions compared with that by a centralized solver. The proposed method is scalable and has features that can be implemented on microcontrollers since both LP and CP procedures require only simple matrix-vector multiplications.

Researches on Large Grain SC Cavities at Peking University

Researches on large grain superconducting cavities are carried out at SRF laboratory of Peking University. A 1.3GHz TESLA type single cell cavity and a 1.3GHz 2-cell cavity made of large grain niobium were fabricated by Peking University.With the collaboration of Jlab,the measured Eacc of the single-cell cavity reached 43.5MV/m after BCP,baking and high temperature heat treatment.

Recent Progress on RF Superconductivity and ERL

RF superconducting cavities can work in CW mode or long pulse mode.RF superconducting technology is widely used in particle accelerators.The development of RF superconductivity is limited by the material,surface treatment and installation.SRF technology is improved greatly after dozens of years'researches.Lots of techniques and experiences have been accumulated by running superconducting accelerators.In recent years,researches and developments have been carried out for future large scientific project.New cavity shape and superconducting cavities made of large grain niobium are the hot frontiers in SRF field.Energy Recovery Linacs have been developed in recent years.ERLs has many advantages such as high efficiency,energy saving,good stability,low radiation level,etc.ERLs are more and more used in advanced light sources and free electron laser facilities.

Beam transport design for a 1 MeV prototype dielectric wall accelerator

The beam transport design of a novel proton dielectric wall accelerator is introduced in this paper. The protons will be accelerated from 40 keV to nearly 1 MeV under an accelerating gradient that is as high as 20 MV/m. A consideration of the beam line as well as the transport simulation is presented. The influences of the injection timing jitter and the accelerating pulse timing jitter are also discussed.

Approximately orthogonal nonnegative Tucker decomposition for flexible multiway clustering

High-order tensor data are prevalent in real-world applications, and multiway clustering is one of the most important techniques for exploratory data mining and compression of multiway data. However, existing multiway clustering is based on the K-means procedure and is incapable of addressing the issue of crossed membership degrees. To overcome this limitation, we propose a flexible multiway clustering model called approximately orthogonal nonnegative Tucker decomposition(AONTD). The new model provides extra flexibility to handle crossed memberships while fully exploiting the multilinear property of tensor data.The accelerated proximal gradient method and the low-rank compression tricks are adopted to optimize the cost function. The experimental results on both synthetic data and real-world cases illustrate that the proposed AONTD model outperforms the benchmark clustering methods by significantly improving the interpretability and robustness.

Geometry dependent multipacting of a superconducting quarter-wave resonator at PKU

A superconducting quarter-wave resonator （QWR） of frequency=162.5 MHz andβ=0.085 （β=v/c） has been designed at Peking University. The multipacting （MP） simulation and analysis for the QWR with CST Particle Studio has been performed. The simulation results reveal that there is no sign of MP with its normal operating accelerating gradients in the range of 6-8 MV/m. The accelerating gradient range that may incur MP is from about 1.4 to 3.2 MV/m, and the places where MP may be encountered are mainly located at the top part of the QWR. So the effect of different top geometries on MP has also been studied in depth. Our results show that an inward convex round roof is better than other round roofs, and plane roofs have an advantage over round roofs on the suppression of MP in general. While considering the optimization of its electromagnetic （EM） design, our initial designed model is also acceptable.

ACCELERATED OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS

We develop a generalization of Nesterov’s accelerated gradient descent method which is designed to deal with orthogonality constraints.To demonstrate the effectiveness of our method,we perform numerical experiments which demonstrate that the number of iterations scales with the square root of the condition number,and also compare with existing state-of-the-art quasi-Newton methods on the Stiefel manifold.Our experiments show that our method outperforms existing state-of-the-art quasi-Newton methods on some large,ill-conditioned problems.

Recent progress on RF superconducting cavities

RF superconducting （SRF） cavities can work in continuous wave mode or long pulse mode. SRF technology has been developing rapidly since the end of the last century. RF superconducting technology is widely used in particle accelerators around the world. As the key elements, research on superconducting cavities is carried out worldwide. Besides Europe, the United States and Japan, many countries have already started SRF projects, such as Canada, India, Korea, etc. Great improvements on SRF technology have been made in China in recent years. Progress in SRF cavities is introduced in this paper.

An untuned MA-loaded cavity for HIRFL-CSR

In order to realize high energy density physics and plasma physics research at HIRFL-CSR, a magnetic alloy （MA）-loaded cavity has been studied. According to the theoretical calculation and simulation for the MA-loaded cavity, we achieved a better result. The MA-loaded cavity had a higher μQf value, with a higher shunt impedance and a higher accelerating gradient. The accelerating gradient was about 95 kV/m at 1.8003 MHz, 130 kV/m at 0.9000 MHz. Compared with the ferrite-loaded cavities that are used at HIRFL-CSR, with about 10 kV/m accelerating gradient, the MA-loaded cavity obviously has an advantage. The results of the theoretical calculation and the simulation, which meet the design requirements are in good agreement.