A stochastic coordinate descent splitting primal-dual fixed point algorithm and applications to large-scale composite optimization

We consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators, which is is inspired by recent results of Chen, Huang and Zhang. With the idea of coordinate descent, we design a stochastic coordinate descent splitting primal- dual fixed point algorithm. Based on randomized krasnosel'skii mann iterations and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1407.0898 by other authors; substantial text overlap with arXiv:1604.0417

A stochastic coordinate descent inertial primal-dual algorithm for large-scale composite optimization

We consider an inertial primal-dual algorithm to compute the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a stochastic coordinate descent inertial primal-dual splitting algorithm. Moreover, in order to prove the convergence of the proposed inertial algorithm, we formulate first the inertial version of the randomized Krasnosel'skii-Mann iterations algorithm for approximating the set of fixed points of a nonexpansive operator and investigate its convergence properties. Then the convergence of stochastic coordinate descent inertial primal-dual splitting algorithm is derived by applying the inertial version of the randomized Krasnosel'skii-Mann iterations to the composition of the proximity operator.Comment: arXiv admin note: substantial text overlap with arXiv:1604.04172, arXiv:1604.04282; substantial text overlap with arXiv:1407.0898 by other author

An inertial primal-dual fixed point algorithm for composite optimization problems

We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their proximity operators. The convergence of the IPDFP is obtained by reformulating the Problem (1.1) to the sum of three convex functions. This work brings together and notably extends several classical splitting schemes, like the primaldual method proposed by Chambolle and Pock, and the recent proximity algorithms of Charles A. et al designed for the L1/TV image denoising model. The iterative algorithm is used for solving nondifferentiable convex optimization problems arising in image processing. The experimental results indicate that the proposed IPDFP iterative algorithm performs well with respect to state-of-the-art methods.Comment: arXiv admin note: text overlap with arXiv:1604.04845, arXiv:1604.04172; text overlap with arXiv:1403.3522, arXiv:1407.0898 by other author

Electromagnetic Response for High-Frequency Gravitational Waves in the GHz to THz Band

We consider the electromagnetic (EM) response of a Gaussian beam passing through a static magnetic field to be the high-frequency gravitational waves (HFGW) as generated by several devices discussed at this conference. It is found that under the synchroresonance condition, the first-order perturbative EM power fluxes will contain a ''left circular wave'' and a ''right circular wave'' around the symmetrical axis of the Gaussian beam. However, the perturbative effects produced by the states of + polarization and \times polarization of the GW have a different physical behavior. For the HFGW of $\nu_{g}=3GHz$, $h=10^{-30}$ (which corresponds to the power flux density $~ 10^{-6} W m^{-2}$) to $\nu_{g}=1.3THz$, $h=10^{-28}$ (which corresponds to the power flux density $~10^{3} W m^{-2}$) expected by the HFGW generators described at this conference, the corresponding perturbative photon fluxes passing through a surface region of $10^{-2} m^{2}$ would be expected to be $10^{3} s^{-1} - 10^{4} s^{-1}$. They are the orders of magnitude of the perturbative photon flux we estimated using typical laboratory parameters that could lead to the development of sensitive HFGW receivers. Moreover, we will also discuss the relative background noise problems and the possibility of displaying the HFGW. A laboratory test bed for juxtaposed HFGW generators and our detecting scheme is explored and discussed.Comment: 19 pages, 3 figure

Electromagnetic response of a Gaussian beam to high-frequency relic gravitational waves in quintessential inflationary models

Maximal signal and peak of high-frequency relic gravitational waves (GW's), recently expected by quintessential inflationary models, may be firmly localized in the GHz region, the energy density of the relic gravitons in critical units (i.e., $h_0^2 \Omega_{GW}$) is of the order $10^{-6}$, roughly eight orders of magnitude larger than in ordinary inflationary models. This is just right best frequency band of the electromagnetic (EM) response to the high-frequency GW's in smaller EM detecting systems. We consider the EM response of a Gaussian beam passing through a static magnetic field to a high-frequency relic GW. It is found that under the synchroresonance condition, the first-order perturbative EM power fluxes will contain "left circular wave" and "right circular wave" around the symmetrical axis of the Gaussian beam, but the perturbative effects produced by the states of + polarization and $\times$ polarization of the relic GW have different properties, and the perturbations on behavior are obviously different from that of the background EM fields in the local regions. For the high-frequency relic GW with the typical parameters $\nu_g = 10^{10}Hz$, $h = 10^{- 30}$ in the quintessential inflationary models, the corresponding perturbative photon flux passing through the region $10^{- 2} m^{2}$ would be expected to be $10^{3}s^{-1}$. This is largest perturbative photon flux we recently analyzed and estimated using the typical laboratory parameters. In addition, we also discuss geometrical phase shift generated by the high-frequency relic GW in the Gaussian beam and estimate possible physical effects.Comment: 36 pages, 5 figure

Mismatch study of C-ADS main linac

The ADS accelerator in China is a CW (Continuous-Wave) proton linac with 1.5 GeV in beam energy, 10 mA in beam current, and 15 MW in beam power. To meet the extremely low beam loss rate requirement and high reliability, it is very important to study the beam halo caused by beam mismatch, which is one major source of beam loss. To avoid the envelope instability, the phase advances per period are all smaller than 90 degree in the main linac design. In this paper, the results of the emittance growth and the envelope oscillations caused by mismatch in the main linac section are presented. To meet the emittance growth requirement, the transverse and longitudinal mismatch factors should be smaller than 0.4 and 0.3, respectively.Comment: 6 pages, 9 figure

A splitting primal-dual proximity algorithm for solving composite optimization problems

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encountered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Further, we propose a preconditioned method, of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography (CT) image reconstruction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality.Comment: 22 pages, 3 figure

Neural Machine Translation with External Phrase Memory

In this paper, we propose phraseNet, a neural machine translator with a phrase memory which stores phrase pairs in symbolic form, mined from corpus or specified by human experts. For any given source sentence, phraseNet scans the phrase memory to determine the candidate phrase pairs and integrates tagging information in the representation of source sentence accordingly. The decoder utilizes a mixture of word-generating component and phrase-generating component, with a specifically designed strategy to generate a sequence of multiple words all at once. The phraseNet not only approaches one step towards incorporating external knowledge into neural machine translation, but also makes an effort to extend the word-by-word generation mechanism of recurrent neural network. Our empirical study on Chinese-to-English translation shows that, with carefully-chosen phrase table in memory, phraseNet yields 3.45 BLEU improvement over the generic neural machine translator.Comment: 8 figures, 9 page

Position reconstruction in fission fragment detection using the low pressure MWPC technique for the JLab experiment E02-017

When a lambda hyperon was embedded in a nucleus, it can form a hypernucleus. The lifetime and its mass dependence of stable hypernuclei provide information about the weak decay of lambda hyperon inside nuclear medium. This work will introduce the Jefferson Lab experiment (E02-017) which aims to study the lifetime of the heavy hypernuclei using a specially developed fission fragment detection technique, a multi-wire proportional chamber operated under low gas pressure (LPMWPC). Presented here are the method and performance of the reconstruction of fission position on the target foil, the separation of target materials at different regions and the comparison and verification with the Mote Carlo simulation.Comment: 10 page

Learning Acoustic Scattering Fields for Dynamic Interactive Sound Propagation

We present a novel hybrid sound propagation algorithm for interactive applications. Our approach is designed for dynamic scenes and uses a neural network-based learned scattered field representation along with ray tracing to generate specular, diffuse, diffraction, and occlusion effects efficiently. We use geometric deep learning to approximate the acoustic scattering field using spherical harmonics. We use a large 3D dataset for training, and compare its accuracy with the ground truth generated using an accurate wave-based solver. The additional overhead of computing the learned scattered field at runtime is small and we demonstrate its interactive performance by generating plausible sound effects in dynamic scenes with diffraction and occlusion effects. We demonstrate the perceptual benefits of our approach based on an audio-visual user study