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Mathematical models and the rank optimization method for current Steiner networks are presented in the work. This method is based on the nonlocal minimum condition and on the dynamical decomposition of the current Steiner network in optimized intersecting subnetworks of an equal dimension that follows from it. A computer simulation is presented that shows a sufficient effectiveness of the method in applying it in designing distributive piping networks of water- and gas-supply. [ABSTRACT FROM AUTHOR]

In the real-time bidding (RTB) display advertising ecosystem, when receiving a bid request, Demand-side platform (DSP) needs to predict user response on each ad impression and determines whether to bid and calculates the bid price according to its prediction. When given a fixed advertising budget, in order to maximize the return on investment (ROI), DSP aims to buy in more conversions and then more clicks than non-clicks. In this paper, we consider response prediction problem as a ranking problem for impression chances and propose a triplet-wise comparison based learning optimization which derived from Bayesian personalized ranking (BPR) based on pairwise learning to learn model parameters. Pairwise learning can only employ one type of historical click and conversion information through optimizing the correct order of random pair of a positive and a negative example for binary classification. While triplet-wise learning combines these two kinds of historical response information into the same model through taking into consideration the correct order of the pair of conversion and click-only as well as the pair of click-only and non-click. Since our method accomplishes the click and conversion prediction tasks in the same predicting procedure, our algorithm is good at ranking click impressions higher than non-click ones and conversion impressions higher than click-only ones. In this way, under a fixed budget, biding algorithm would preferentially buy in more conversions than others and then more clicks than non-clicks. Our experiments demonstrate that the improved method not only outperforms both pairwise and MSE schemes on three classes ranking in terms of multi-AUC, NDCG etc., but also, outperforms others on binary classification for click and non-click on the targeted real-world bidding log data owing to the introduction of historical conversion information. [ABSTRACT FROM AUTHOR]

We present an analysis of sets of matrices with rank less than or equal to a specified number s. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank exactly equal to s. The normal cone formula appears to be new. This allows for easy application of prior results guaranteeing local linear convergence of the fundamental alternating projection algorithm between sets, one of which is a rank constraint set. We apply this to show local linear convergence of another fundamental algorithm, approximate steepest descent. Our results apply not only to linear systems with rank constraints, as has been treated extensively in the literature, but also nonconvex systems with rank constraints. [ABSTRACT FROM AUTHOR]

Turbulence mitigation refers to the stabilization of videos with nonuniform deformations due to the influence of optical turbulence. Typical approaches for turbulence mitigation follow averaging or dewarping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects, which can often be of great interest. In this paper, we address the novel problem of simultaneous turbulence mitigation and moving object detection. We propose a novel three-term low-rank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and \ell1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by \ell1 norm. Second, since the object's motion is linear and intrinsically different from the Gaussian-like turbulence, a Gaussian-based turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. [ABSTRACT FROM AUTHOR]