The ternary Goldbach problem with the Piatetski-Shapiro primes

With the help of the transference principle, we prove that for any $c_1,c_2,c_3\in(1,73/64)$, every sufficiently large odd $n$ can be represented as the sum of three primes $p_1$, $p_2$ and $p_3$, where for each $1\leq i\leq 3$, $p_i$ is of the form $\lfloor n^{c_i}\rfloor$.Comment: This is a very preliminary manuscript, which maybe contains some mistake

Enhancing Representation in Radiography-Reports Foundation Model: A Granular Alignment Algorithm Using Masked Contrastive Learning

Recently, multi-modal vision-language foundation models have gained significant attention in the medical field. While these models offer great opportunities, they still face a number of challenges, such as the requirement for fine-grained knowledge understanding in computer-aided diagnosis and capability of utilizing very limited or no task-specific labeled data in real-world clinical applications. In this study, we present MaCo, a novel multi-modal medical foundation model that explores masked contrastive learning to achieve granular alignment and zero-shot learning for a variety of medical imaging tasks. MaCo incorporates a correlation weighting mechanism to adjust the correlation between masked image patches and their corresponding reports, thereby enhancing the representation learning capabilities. We evaluate MaCo on six well-known open-source X-ray datasets, and the experimental results show it outperforms seven state-of-the-art approaches for classification, segmentation, and zero-shot phase grounding, demonstrating its great potential to promote a wide range of medical image analysis tasks

Addressless: A New Internet Server Model to Prevent Network Scanning

Eliminating unnecessary exposure is a principle of server security. The huge IPv6 address space enhances security by making scanning infeasible, however, with recent advances of IPv6 scanning technologies, network scanning is again threatening server security. In this paper, we propose a new model named addressless server, which separates the server into an entrance module and a main service module, and assigns an IPv6 prefix instead of an IPv6 address to the main service module. The entrance module generates a legitimate IPv6 address under this prefix by encrypting the client address, so that the client can access the main server on a destination address that is different in each connection. In this way, the model provides isolation to the main server, prevents network scanning, and minimizes exposure. Moreover it provides a novel framework that supports flexible load balancing, high-availability, and other desirable features. The model is simple and does not require any modification to the client or the network. We implement a prototype and experiments show that our model can prevent the main server from being scanned at a slight performance cost

CLCI-Net: Cross-Level fusion and Context Inference Networks for Lesion Segmentation of Chronic Stroke

Segmenting stroke lesions from T1-weighted MR images is of great value for large-scale stroke rehabilitation neuroimaging analyses. Nevertheless, there are great challenges with this task, such as large range of stroke lesion scales and the tissue intensity similarity. The famous encoder-decoder convolutional neural network, which although has made great achievements in medical image segmentation areas, may fail to address these challenges due to the insufficient uses of multi-scale features and context information. To address these challenges, this paper proposes a Cross-Level fusion and Context Inference Network (CLCI-Net) for the chronic stroke lesion segmentation from T1-weighted MR images. Specifically, a Cross-Level feature Fusion (CLF) strategy was developed to make full use of different scale features across different levels; Extending Atrous Spatial Pyramid Pooling (ASPP) with CLF, we have enriched multi-scale features to handle the different lesion sizes; In addition, convolutional long short-term memory (ConvLSTM) is employed to infer context information and thus capture fine structures to address the intensity similarity issue. The proposed approach was evaluated on an open-source dataset, the Anatomical Tracings of Lesions After Stroke (ATLAS) with the results showing that our network outperforms five state-of-the-art methods. We make our code and models available at https://github.com/YH0517/CLCI_Net

Highly enhanced catalytic stability of copper by the synergistic effect of porous hierarchy and alloying for selective hydrogenation reaction

Supported copper has a great potential for replacing the commercial palladium-based catalysts in the field of selective alkynes/alkadienes hydrogenation due to its excellent alkene selectivity and relatively high activity. However, fatally, it has a low catalytic stability owing to the rapid oligomerization of alkenes on the copper surface. In this study, 2.5 wt% Cu catalysts with various Cu:Zn ratios and supported on hierarchically porous alumina (HA) were designed and synthesized by deposition–precipitation with urea. Macropores (with diameters of 1 μm) and mesopores (with diameters of 3.5 nm) were introduced by the hydrolysis of metal alkoxides. After in situ activation at 350 °C, the catalytic stability of Cu was highly enhanced, with a limited effect on the catalytic activity and alkene selectivity. The time needed for losing 10% butadiene conversion for Cu1Zn3/HA was ~40 h, which is 20 times higher than that found for Cu/HA (~2 h), and 160 times higher than that found for Cu/bulky alumina (0.25 h). It was found that this type of enhancement in catalytic stability was mainly due to the rapid mass transportation in hierarchically porous structure (i.e., four times higher than that in bulky commercial alumina) and the well-dispersed copper active site modified by Zn, with identification by STEM–HAADF coupled with EDX. This study offers a universal way to optimize the catalytic stability of selective hydrogenation reactions