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Most state-of-the-art instance-level human parsing models adopt two-stage anchor-based detectors and, therefore, cannot avoid the heuristic anchor box design and the lack of analysis on a pixel level. To address these two issues, we have designed an instance-level human parsing network which is anchor-free and solvable on a pixel level. It consists of two simple sub-networks: an anchor-free detection head for bounding box predictions and an edge-guided parsing head for human segmentation. The anchor-free detector head inherits the pixel-like merits and effectively avoids the sensitivity of hyper-parameters as proved in object detection applications. By introducing the part-aware boundary clue, the edge-guided parsing head is capable to distinguish adjacent human parts from among each other up to 58 parts in a single human instance, even overlapping instances. Meanwhile, a refinement head integrating box-level score and part-level parsing quality is exploited to improve the quality of the parsing results. Experiments on two multiple human parsing datasets (i.e., CIHP and LV-MHP-v2.0) and one video instance-level human parsing dataset (i.e., VIP) show that our method achieves the best global-level and instance-level performance over state-of-the-art one-stage top-down alternatives., Comment: Accepted by IEEE Transactions on Image Processing (TIP)

In this paper, we consider the mixed ratcheting-periodic dividend strategies for spectrally negative L\'{e}vy risk model, in which dividend payments can both be made continuously without falling and discretely at the jump times of an independent Poisson process. The expected net present value(NPV) of dividends paid up to ruin and the Laplace transform of the ruin time are obtained by using L\'{e}vy fluctuation theory. All the results are expressed in terms of scale functions. Finally, numerical results for Brownian motion with drift are given., Comment: 25 pages, 5 figures

An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques (NST+HT+FB). The main contribution of this article is the accelerated convergence analysis and proofs with a variable/adaptive index selection and different feedback principles at each iteration. These convergence analysis require no longer a priori sparsity information $s$ of a signal. %key theory in this paper is the concept that the number of indices selected at each iteration should be considered in order to speed up the convergence. It is shown that uniform recovery of all $s$-sparse signals from given linear measurements can be achieved under reasonable (preconditioned) restricted isometry conditions. Accelerated convergence rate and improved convergence conditions are obtained by selecting an appropriate size of the index support per iteration. The theoretical findings are sufficiently demonstrated and confirmed by extensive numerical experiments. It is also observed that the proposed algorithms have a clearly advantageous balance of efficiency, adaptivity and accuracy compared with all other state-of-the-art greedy iterative algorithms.

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be computationally expensive and/or prohibitive. The null space tuning algorithm with hard thresholding and feedbacks (NST+HT+FB) has a mean to expedite its procedure by a suboptimal feedback, in which sub-matrix inversion is replaced by an eigenvalue-based approximation. The resulting suboptimal feedback scheme becomes exceedingly effective for large system recovery problems. An adaptive algorithm based on thresholding, suboptimal feedback and null space tuning (AdptNST+HT+subOptFB) without a prior knowledge of the sparsity level is also proposed and analyzed. Convergence analysis is the focus of this article. Numerical simulations are also carried out to demonstrate the superior efficiency of the algorithm compared with state-of-the-art iterative thresholding algorithms at the same level of recovery accuracy, particularly for large systems.

Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely many steps under a (preconditioned) restricted isometry condition. In this paper, we present a new perspective to analyze the algorithm, which turns out that the efficiency of the algorithm can be further elaborated by an estimate of the number of iterations for the guaranteed convergence. The convergence condition of NST+HT+FB is also improved. Moreover, an adaptive scheme (AdptNST+HT+FB) without the knowledge of the sparsity level is proposed with its convergence guarantee. The number of iterations for the finite step of convergence of the AdptNST+HT+FB scheme is also derived. It is further shown that the number of iterations can be significantly reduced by exploiting the structure of the specific sparse signal or the random measurement matrix.