Optimal Control of Brownian Inventory Models with Convex Inventory Cost: Discounted Cost Case

We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a three-step lower-bound approach to solving the optimal control problem under a discounted cost criterion. In addition, we prove that a four-parameter control band policy is optimal among all feasible policies. A key step is the constructive proof of the existence of a unique solution to the free boundary problem. The proof leads naturally to an algorithm to compute the four parameters of the optimal control band policy

Chinese Medicine in Transformation: Learning, Practice, and the Participation of Ordinary People in Contemporary Chinese Society

早稲田大学博士(学術)早大学位記番号:新9369doctoral thesi

Identification of an Immune Signature Predicting Prognosis Risk and Lymphocyte Infiltration in Colon Cancer

Increasing studies have highlighted the effects of the tumor immune micro-environment (TIM) on colon cancer (CC) tumorigenesis, prognosis, and metastasis. However, there is no reliable molecular marker that can effectively estimate the immune infiltration and predict the CC relapse risk. Here, we leveraged the gene expression profile and clinical characteristics from 1430 samples, including four gene expression omnibus database (GEO) databases and the cancer genome atlas (TCGA) database, to construct an immune risk signature that could be used as a predictor of survival outcome and immune activity. A risk model consisting of 10 immune-related genes were screened out in the Lasso-Cox model and were then aggregated to generate the immune risk signature based on the regression coefficients. The signature demonstrated robust prognostic ability in discovery and validation datasets, and this association remained significant in the multivariate analysis after controlling for age, gender, clinical stage, or microsatellite instability status. Leukocyte subpopulation analysis indicated that the low-risk signature was enriched with cytotoxic cells (activated CD4/CD8(+)T cell and NK cell) and depleted of myeloid-derived suppressor cells (MDSC) and regulatory T cells. Further analysis indicated patients with a low-risk signature harbored higher tumor mutation loads and lower mutational frequencies in significantly mutated genes ofAPCandFBXW7. Together, our constructed signature could predict prognosis and represent the TIM of CC, which promotes individualized treatment and provides a promising novel molecular marker for immunotherapy

Towards Mixture Proportion Estimation without Irreducibility

\textit{Mixture proportion estimation} (MPE) is a fundamental problem of practical significance, where we are given data from only a \textit{mixture} and one of its two \textit{components} to identify the proportion of each component. All existing MPE methods that are distribution-independent explicitly or implicitly rely on the \textit{irreducible} assumption---the unobserved component is not a mixture containing the observable component. If this is not satisfied, those methods will lead to a critical estimation bias. In this paper, we propose \textit{Regrouping-MPE} that works without irreducible assumption: it builds a new irreducible MPE problem and solves the new problem. It is worthwhile to change the problem: we prove that if the assumption holds, our method will not affect anything; if the assumption does not hold, the bias from problem changing is less than the bias from violation of the irreducible assumption in the original problem. Experiments show that our method outperforms all state-of-the-art MPE methods on various real-world datasets

PNT-Edge: Towards Robust Edge Detection with Noisy Labels by Learning Pixel-level Noise Transitions

Relying on large-scale training data with pixel-level labels, previous edge detection methods have achieved high performance. However, it is hard to manually label edges accurately, especially for large datasets, and thus the datasets inevitably contain noisy labels. This label-noise issue has been studied extensively for classification, while still remaining under-explored for edge detection. To address the label-noise issue for edge detection, this paper proposes to learn Pixel-level NoiseTransitions to model the label-corruption process. To achieve it, we develop a novel Pixel-wise Shift Learning (PSL) module to estimate the transition from clean to noisy labels as a displacement field. Exploiting the estimated noise transitions, our model, named PNT-Edge, is able to fit the prediction to clean labels. In addition, a local edge density regularization term is devised to exploit local structure information for better transition learning. This term encourages learning large shifts for the edges with complex local structures. Experiments on SBD and Cityscapes demonstrate the effectiveness of our method in relieving the impact of label noise. Codes are available at https://github.com/DREAMXFAR/PNT-Edge.Comment: Accepted by ACM-MM 202