On the optimal linear convergence factor of the relaxed proximal point algorithm for monotone inclusion problems

Finding a zero of a maximal monotone operator is fundamental in convex optimization and monotone operator theory, and \emph{proximal point algorithm} (PPA) is a primary method for solving this problem. PPA converges not only globally under fairly mild conditions but also asymptotically at a fast linear rate provided that the underlying inverse operator is Lipschitz continuous at the origin. These nice convergence properties are preserved by a relaxed variant of PPA. Recently, a linear convergence bound was established in [M. Tao, and X. M. Yuan, J. Sci. Comput., 74 (2018), pp. 826-850] for the relaxed PPA, and it was shown that the bound is optimal when the relaxation factor $\gamma$ lies in $[1,2)$. However, for other choices of $\gamma$, the bound obtained by Tao and Yuan is suboptimal. In this paper, we establish tight linear convergence bounds for any choice of $\gamma\in(0,2)$ and make the whole picture about optimal linear convergence bounds clear. These results sharpen our understandings to the asymptotic behavior of the relaxed PPA.Comment: 9 pages and 1 figur

3D Wavelet-Based Video Codec with Human Perceptual Model

This thesis explores the use of a human perceptual model in video compression, channel coding, error concealment and subjective image quality measurement. The perceptual distortion model just-noticeable-distortion (JND) is investigated. A video encoding/decoding scheme based on 3D wavelet decomposition and the human perceptual model is implemented. It provides a prior compression quality control which is distinct from the conventional video coding system. JND is applied in quantizer design to improve the subjective quality ofcompressed video. The 3D wavelet decomposition helps to remove spatial and temporal redundancy and provides scalability of video quality. In order to conceal the errors that may occur under bad wireless channel conditions, a slicing method and a joint source channel coding scenario that combines RCPC with CRC and uses the distortion information toallocate convolutional coding rates are proposed. A new subjective quality index based on JND is proposed and used to evaluate the overall performance at different signal to noise ratios (SNR) and at different compression ratios.Due to the wide use of arithmetic coding (AC) in data compression, we consider it as a readily available unit in the video codec system for broadcasting. A new scheme for conditional access (CA) sub-system is designed based on the cryptographic property of arithmetic coding. Itsperformance is analyzed along with its application in a multi-resolution video compression system. This scheme simplifies the conditional access sub-system and provides satisfactory system reliability

Molecular Docking Improvement: Coefficient Adaptive Genetic Algorithms for Multiple Scoring Functions

In this paper, a coefficient adaptive scoring method of molecular docking is presented to improve the docking accuracy with multiple available scoring functions. Based on force-field scoring function, we considered hydrophobic and deformation as well in the proposed method, Instead of simple combination with fixed weights, coefficients of each factor are adaptive in searching procedure. In order to improve the docking accuracy and stability, knowledge-based scoring function is used as another scoring factor. Genetic algorithm with the multi-population evolution and entropy-based searching technique with narrowing down space is used to solve the optimization model for molecular docking. To evaluate the method, we carried out a numerical experiment with 134 protein- ligand complexes of the publicly available GOLD test set. The results validated that it improved the docking accuracy over the individual force-field scoring. In addition, analyses were given to show the disadvantage of individual scoring model. Through the comparison with other popular docking software, the proposed method showed higher accuracy. Among more than 77% of the complexes, the docked results were within 1.0 Å according to Root- Mean-Square Deviation (RMSD) of the X-ray structure. The average computing time obtained here is 563.9 s

Design, Implementation and Modeling of Flooding Disaster-Oriented USV

Although there exist some unmanned surface platforms, and parts of them have been applied in flooding disaster relief, the autonomy of these platforms is still so weak that most of them can only work under the control of operators. The primary reason is the difficulty of obtaining a dynamical model that is sufficient rich for model-based control and sufficient simple for model parameters identification. This makes them difficult to be used to achieve some high-performance autonomous control, such as robust control with respect to disturbances and unknown dynamics and trajectory tracking control in complicated and dynamical surroundings. In this chapter, a flooding disaster-oriented unmanned surface vehicle (USV) designed and implemented by Shenyang Institute of Automation, Chinese Academy of Sciences (SIA, CAS) is introduced first, including the hardware and software structures. Then, we propose a quasi-linear parameter varying (qLPV) model to approach the dynamics of the USV system. We first apply this to solve a structured modeling problem and then introduce model error to solve an unstructured modeling problem. Subsequently, the qLPV model identification results are analyzed and the superiority compared to two linear models is demonstrated. At last, extensive application experiments, including rescuing rope throwing using an automatic pneumatic and water sampling in a 2.5 m radius circle, are described in detail to show the performance of course keeping control and GPS point tracking control based on the proposed model

X-ray emission of contact binary variables within 1 kpc

By assembling the largest sample to date of X-ray emitting EW-type binaries (EWXs), we carried out correlation analyses for the X-ray luminosity log$L_{\textrm{X}}$, and X-ray activity level log($L_{\textrm{X}}$/$L_{\textrm{bol}}$) versus the orbital period $P$ and effective temperature $T_{\rm eff}$. We find strong $P$-log$L_{\textrm{X}}$ and $P$-log($L_{\textrm{X}}$/$L_{\textrm{bol}}$) correlations for EWXs with $P$ < 0.44 days and we provide the linear parametrizations for these relations, on the basis of which the orbital period can be treated as a good predictor for log$L_{\textrm{X}}$ and log($L_{\textrm{X}}$/$L_{\textrm{bol}}$). The aforementioned binary stellar parameters are all correlated with log$L_{\textrm{X}}$, while only $T_{\rm eff}$ exhibits a strong correlation with log($L_{\textrm{X}}$/$L_{\textrm{bol}}$). Then, EWXs with higher temperature show lower X-ray activity level, which could indicate the thinning of the convective area related to the magnetic dynamo mechanism. The total X-ray luminosity of an EWX is essentially consistent with that of an X-ray saturated main sequence star with the same mass as its primary, which may imply that the primary star dominates the X-ray emission. The monotonically decreasing $P$-log($L_{\textrm{X}}$/$L_{\textrm{bol}}$) relation and the short orbital periods indicate that EWXs could all be in the X-ray saturated state, and they may inherit the changing trend of the saturated X-ray luminosities along with the mass shown by single stars. For EWXs, the orbital period, mass, and effective temperature increase in concordance. We demonstrate that the period $P=0.44$ days corresponds to the primary mass of $\sim1.1 \rm M_\odot$, beyond which the saturated X-ray luminosity of single stars will not continue to increase with mass. This explains the break in the positive $P$-log$L_{\textrm{X}}$ relation for EWXs with $P>0.44$ days.Comment: 16 pages, 7 figures and 8 tables; accepted for publication in A&