Fullerenes with the maximum Clar number

The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2. We find that there are no fullerenes whose order n is congruent to 2 modulo 6 attaining this bound. In other words, the Clar number for a fullerene whose order n is congruent to 2 modulo 6 is bounded above by [n/6]-3. Moreover, we show that two experimentally produced fullerenes C80:1 (D5d) and C80:2 (D2) attain this bound. Finally, we present a graph-theoretical characterization for fullerenes, whose order n is congruent to 2 (respectively, 4) modulo 6, achieving the maximum Clar number [n/6]-3 (respectively, [n/6]-2)

Uncertainty-Guided Lung Nodule Segmentation with Feature-Aware Attention

Since radiologists have different training and clinical experiences, they may provide various segmentation annotations for a lung nodule. Conventional studies choose a single annotation as the learning target by default, but they waste valuable information of consensus or disagreements ingrained in the multiple annotations. This paper proposes an Uncertainty-Guided Segmentation Network (UGS-Net), which learns the rich visual features from the regions that may cause segmentation uncertainty and contributes to a better segmentation result. With an Uncertainty-Aware Module, this network can provide a Multi-Confidence Mask (MCM), pointing out regions with different segmentation uncertainty levels. Moreover, this paper introduces a Feature-Aware Attention Module to enhance the learning of the nodule boundary and density differences. Experimental results show that our method can predict the nodule regions with different uncertainty levels and achieve superior performance in LIDC-IDRI dataset.Comment: 10 pages, 4 figures, 30 reference

The minimum degree of minimal kk-factor-critical claw-free graphs*

A graph $G$ of order $n$ is said to be $k$-factor-critical for integers $1\leq k< n$, if the removal of any $k$ vertices results in a graph with a perfect matching. A $k$-factor-critical graph is minimal if for every edge, the deletion of it results in a graph that is not $k$-factor-critical. In 1998, O. Favaron and M. Shi conjectured that every minimal $k$-factor-critical graph has minimum degree $k+1$. In this paper, we confirm the conjecture for minimal $k$-factor-critical claw-free graphs. Moreover, we show that every minimal $k$-factor-critical claw-free graph $G$ has at least $\frac{k-1}{2k}|V(G)|$ vertices of degree $k+1$ in the case of $(k+1)$-connected, yielding further evidence for S. Norine and R. Thomas' conjecture on the minimum degree of minimal bricks when $k=2$.Comment: 17 pages, 12 figure

Metallothioneins Are Required for Formation of Cross-Adaptation Response to Neurobehavioral Toxicity from Lead and Mercury Exposure in Nematodes

Metallothioneins (MTs) are small, cysteine-rich polypeptides, but the role of MTs in inducing the formation of adaptive response is still largely unknown. We investigated the roles of metallothionein genes (mtl-1 and mtl-2) in the formation of cross-adaptation response to neurobehavioral toxicity from metal exposure in Caenorhabditis elegans. Pre-treatment with mild heat-shock at L2-larva stage effectively prevented the formation of the neurobehavioral defects and the activation of severe stress response in metal exposed nematodes at concentrations of 50 and 100 µM, but pre-treatment with mild heat-shock did not prevent the formation of neurobehavioral defects in 200 µM of metal exposed nematodes. During the formation of cross-adaptation response, the induction of mtl-1 and mtl-2 promoter activity and subsequent GFP gene expression were sharply increased in 50 µM or 100 µM of metal exposed Pmtl-1::GFP and Pmtl-2::GFP transgenic adult animals after mild heat-shock treatment compared with those treated with mild heat-shock or metal exposure alone. Moreover, after pre-treatment with mild heat-shock, no noticeable increase of locomotion behaviors could be observed in metal exposed mtl-1 or mtl-2 mutant nematodes compared to those without mild heat-shock pre-treatment. The defects of adaptive response to neurobehavioral toxicity induced by metal exposure formed in mtl-1 and mtl-2 mutants could be completely rescued by the expression of mtl-1 and mtl-2 with the aid of their native promoters. Furthermore, over-expression of MTL-1 and MTL-2 at the L2-larval stage significantly suppressed the toxicity on locomotion behaviors from metal exposure at all examined concentrations. Therefore, the normal formation of cross-adaptation response to neurobehavioral toxicity induced by metal exposure may need the enough accumulation of MTs protein in animal tissues

Lung Nodule Segmentation and Uncertain Region Prediction with an Uncertainty-Aware Attention Mechanism

Radiologists possess diverse training and clinical experiences, leading to variations in the segmentation annotations of lung nodules and resulting in segmentation uncertainty.Conventional methods typically select a single annotation as the learning target or attempt to learn a latent space comprising multiple annotations. However, these approaches fail to leverage the valuable information inherent in the consensus and disagreements among the multiple annotations. In this paper, we propose an Uncertainty-Aware Attention Mechanism (UAAM) that utilizes consensus and disagreements among multiple annotations to facilitate better segmentation. To this end, we introduce the Multi-Confidence Mask (MCM), which combines a Low-Confidence (LC) Mask and a High-Confidence (HC) Mask.The LC mask indicates regions with low segmentation confidence, where radiologists may have different segmentation choices. Following UAAM, we further design an Uncertainty-Guide Multi-Confidence Segmentation Network (UGMCS-Net), which contains three modules: a Feature Extracting Module that captures a general feature of a lung nodule, an Uncertainty-Aware Module that produces three features for the the annotations' union, intersection, and annotation set, and an Intersection-Union Constraining Module that uses distances between the three features to balance the predictions of final segmentation and MCM. To comprehensively demonstrate the performance of our method, we propose a Complex Nodule Validation on LIDC-IDRI, which tests UGMCS-Net's segmentation performance on lung nodules that are difficult to segment using common methods. Experimental results demonstrate that our method can significantly improve the segmentation performance on nodules that are difficult to segment using conventional methods.Comment: 10 pages, 10 figures. We have reported a preliminary version of this work in MICCAI 202

Unified Multi-Modal Image Synthesis for Missing Modality Imputation

Multi-modal medical images provide complementary soft-tissue characteristics that aid in the screening and diagnosis of diseases. However, limited scanning time, image corruption and various imaging protocols often result in incomplete multi-modal images, thus limiting the usage of multi-modal data for clinical purposes. To address this issue, in this paper, we propose a novel unified multi-modal image synthesis method for missing modality imputation. Our method overall takes a generative adversarial architecture, which aims to synthesize missing modalities from any combination of available ones with a single model. To this end, we specifically design a Commonality- and Discrepancy-Sensitive Encoder for the generator to exploit both modality-invariant and specific information contained in input modalities. The incorporation of both types of information facilitates the generation of images with consistent anatomy and realistic details of the desired distribution. Besides, we propose a Dynamic Feature Unification Module to integrate information from a varying number of available modalities, which enables the network to be robust to random missing modalities. The module performs both hard integration and soft integration, ensuring the effectiveness of feature combination while avoiding information loss. Verified on two public multi-modal magnetic resonance datasets, the proposed method is effective in handling various synthesis tasks and shows superior performance compared to previous methods.Comment: 10 pages, 9 figure

Identification of novel somatic fusions of ERG-VEGFA, TMPRSS2-ERG, and VEGFA-TMPRSS2 in prostate cancer treated with anlotinib and androgen deprivation therapy: A case report

The TMPRSS2-ERG fusion gene has frequently been found in prostate cancer and is associated with malignancy. Identifying novel fusions will help to stratify patients and establish patient-tailored therapies. A 78-year-old man presented to our hospital with severe symptoms of urinary urgency and frequency for 2 years, as well as severe bone pain for 1 year. He was diagnosed with metastatic prostate cancer with a Gleason score of 5 + 5. Three gene fusions, ERG_VEGFA, TMPRSS2_ERG, and VEGFA_TMPRSS2, were identified in the patient\u27s prostate cancer tissue. Notably, administration of the tyrosine kinase inhibitor, anlotinib, in combination with a gonadotropin-releasing hormone agonist (GnRHa) and abiraterone, reduced the patient\u27s bone pain and also stabilized his prostate cancer for more than 2 years. This is the first report of somatic fusions among the VEGFA, ERG, and TMPRSS2 genes in cancer tissues from a patient with prostate cancer who responded well to antiangiogenic treatment combined with a GnRHa and abiraterone