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The primary objective of Phase I oncology trials is to assess the safety and tolerability of novel therapeutics. Conventional dose escalation methods identify the maximum tolerated dose (MTD) based on dose-limiting toxicity (DLT). However, as cancer therapies have evolved from chemotherapy to targeted therapies, these traditional methods have become problematic. Many targeted therapies rarely produce DLT and are administered over multiple cycles, potentially resulting in the accumulation of lower-grade toxicities, which can lead to intolerance, such as dose reduction or interruption. To address this issue, we proposed dual-criterion designs that find the MTD based on both DLT and non-DLT-caused intolerance. We considered the model-based design and model-assisted design that allow real-time decision-making in the presence of pending data due to long event assessment windows. Compared to DLT-based methods, our approaches exhibit superior operating characteristics when intolerance is the primary driver for determining the MTD and comparable operating characteristics when DLT is the primary driver.

This paper aims to investigate the evolution problem for planar curves with singularities. Motivated by the inverse curvature flow introduced by Li and Wang (Calc. Var. Partial Differ. Equ. 62 (2023), No. 135), we intend to consider the area-preserving and length-preserving inverse curvature flow with nonlocal term for $\ell$-convex Legendre curves. For the area-preserving flow, an $\ell$-convex Legendre curve %of with initial algebraic area $A_0>0$ evolves to a circle of radius $\sqrt{\frac{A_0}{\pi}}$. For the length-preserving flow, an $\ell$-convex Legendre curve %of with initial algebraic length $L_0$ evolves to a circle of radius $\frac{L_0}{2\pi}$. As the by-product, we obtain some geometric inequalities for $\ell$-convex Legendre curves through the length-preserving flow.

The central focus of this paper is the $L_p$ dual Minkowski problem for $C$-compatible sets, where $C$ is a pointed closed convex cone in $\mathbb{R}^n$ with nonempty interior. Such a problem deals with the characterization of the $(p, q)$-th dual curvature measure of a $C$-compatible set. It produces new Monge-Amp\`{e}re equations for unbounded convex hypersurface, often defined over open domains and with non-positive unknown convex functions. Within the family of $C$-determined sets, the $L_p$ dual Minkowski problem is solved for $0\neq p\in \mathbb{R}$ and $q\in \mathbb{R}$; while it is solved for the range of $p\leq 0$ and $p

Automatically extracting Protein-Protein Interactions (PPI) from biomedical literature provides additional support for precision medicine efforts. This paper proposes a novel memory network-based model (MNM) for PPI extraction, which leverages prior knowledge about protein-protein pairs with memory networks. The proposed MNM captures important context clues related to knowledge representations learned from knowledge bases. Both entity embeddings and relation embeddings of prior knowledge are effective in improving the PPI extraction model, leading to a new state-of-the-art performance on the BioCreative VI PPI dataset. The paper also shows that multiple computational layers over an external memory are superior to long short-term memory networks with the local memories., Comment: Published on Database-The Journal of Biological Databases and Curation, 11 pages, 5 figures

Chemical-disease relation (CDR) extraction is significantly important to various areas of biomedical research and health care. Nowadays, many large-scale biomedical knowledge bases (KBs) containing triples about entity pairs and their relations have been built. KBs are important resources for biomedical relation extraction. However, previous research pays little attention to prior knowledge. In addition, the dependency tree contains important syntactic and semantic information, which helps to improve relation extraction. So how to effectively use it is also worth studying. In this paper, we propose a novel convolutional attention network (CAN) for CDR extraction. Firstly, we extract the shortest dependency path (SDP) between chemical and disease pairs in a sentence, which includes a sequence of words, dependency directions, and dependency relation tags. Then the convolution operations are performed on the SDP to produce deep semantic dependency features. After that, an attention mechanism is employed to learn the importance/weight of each semantic dependency vector related to knowledge representations learned from KBs. Finally, in order to combine dependency information and prior knowledge, the concatenation of weighted semantic dependency representations and knowledge representations is fed to the softmax layer for classification. Experiments on the BioCreative V CDR dataset show that our method achieves comparable performance with the state-of-the-art systems, and both dependency information and prior knowledge play important roles in CDR extraction task., Comment: Published on Journal of Biomedical Informatics, 13 pages

Automatically extracting the relationships between chemicals and diseases is significantly important to various areas of biomedical research and health care. Biomedical experts have built many large-scale knowledge bases (KBs) to advance the development of biomedical research. KBs contain huge amounts of structured information about entities and relationships, therefore plays a pivotal role in chemical-disease relation (CDR) extraction. However, previous researches pay less attention to the prior knowledge existing in KBs. This paper proposes a neural network-based attention model (NAM) for CDR extraction, which makes full use of context information in documents and prior knowledge in KBs. For a pair of entities in a document, an attention mechanism is employed to select important context words with respect to the relation representations learned from KBs. Experiments on the BioCreative V CDR dataset show that combining context and knowledge representations through the attention mechanism, could significantly improve the CDR extraction performance while achieve comparable results with state-of-the-art systems., Comment: Published on IEEE/ACM Transactions on Computational Biology and Bioinformatics, 11 pages, 5 figures

In this paper we obtain the extended Green-Osher inequality when two smooth, planar strictly convex bodies are at a dilation position and show the necessary and sufficient condition for the case of equality., Comment: 7 pages

B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski and $L_p$-Brunn-Minkowski inequalities for two convex bodies in $\mathbb{R}^3$., Comment: 11 pages, 2 figures