Jixin Wang

Philip A. Ernst, Alexander L. Stolyar, Jixin Wang

We revisit a classical problem in dynamic storage allocation. Items arrive in a linear storage medium, modeled as a half-axis, at a Poisson rate $r$ and depart after an independent exponentially distributed unit mean service time. The arriving item sizes (lengths) are assumed to be independent and identically distributed (i.i.d.) from a common distribution $H$. A widely employed algorithm for allocating the items is the "first-fit" discipline, namely, each arriving item is placed in the left-most vacant interval large enough to accommodate it. In a seminal 1985 paper, Coffman, Kadota, and Shepp ([6]) proved that in the special case of unit length items (i.e. degenerate $H$), as $r$ tends towards infinity, the first-fit algorithm is asymptotically optimal in the following sense: the steady-state ratio of expected "empty space" (gaps between items) to expected occupied space tends towards $0$. In a sequel to [6], Coffman, Kadota, and Shepp ([5]) conjectured that the first-fit discipline is also asymptotically optimal for non-degenerate $H$. In this paper we provide the first proof of first-fit asymptotic optimality for non-degenerate distributions $H$ of item sizes. Our main result is for the case when $H$ is concentrated on countably many positive real sizes forming an increasing sequence that is either finite or goes to infinity, with the average item size being finite. We prove that under the first-fit discipline, as $r$ tends towards infinity, the steady-state packing configuration (scaled down by $r$) converges in distribution to the limiting packing configuration with smaller items on the left, larger items on the right, and with no gaps between. In particular, this proves asymptotic optimality of first-fit in the sense that in steady-state the empty space (scaled down by $r$) vanishes.

Jixin Wang, Sanping Zhou, Chaowei Fang et al.

Deep neural networks have achieved satisfactory performance in piles of medical image analysis tasks. However the training of deep neural network requires a large amount of samples with high-quality annotations. In medical image segmentation, it is very laborious and expensive to acquire precise pixel-level annotations. Aiming at training deep segmentation models on datasets with probably corrupted annotations, we propose a novel Meta Corrupted Pixels Mining (MCPM) method based on a simple meta mask network. Our method is targeted at automatically estimate a weighting map to evaluate the importance of every pixel in the learning of segmentation network. The meta mask network which regards the loss value map of the predicted segmentation results as input, is capable of identifying out corrupted layers and allocating small weights to them. An alternative algorithm is adopted to train the segmentation network and the meta mask network, simultaneously. Extensive experimental results on LIDC-IDRI and LiTS datasets show that our method outperforms state-of-the-art approaches which are devised for coping with corrupted annotations.