Hausdorff Moment Transforms and Their Performance

Various methods have been proposed to approximate a solution to the truncated Hausdorff moment problem. In this paper, we establish a method of comparison for the performance of the approximations. Three ways of producing random moment sequences are discussed and applied. Also, some of the approximations have been rewritten as linear transforms and detailed accuracy requirements are analyzed. Our finding shows that the performance of the approximations differs significantly in their convergence properties, accuracy, and numerical complexity, and that the decay type of the moment sequence strongly affects the accuracy requirement

Detection of EGFR and COX-2 Expression by Immunohistochemical Method on a Tissue Microarray Section in Lung Cancer and Biological Significance

Background and objective Epidermal growth factor receptor (EGFR) and cyclooxygenase-2 (COX-2), which can regulate growth, invasion and metastasis of tumor through relevant signaling pathway, have been detected in a variety of solid tumors. The aim of this study is to investigate the biological significance of EGFR and COX-2 expression in lung cancer and the relationship between them. Methods The expression of EGFR and COX-2 was detected in 89 primary lung cancer tissues, 12 premaliganant lesions, 12 lymph node metastases, and 10 normal lung tissues as the control by immunohistochemical method on a tissue microarray section. Results EGFR protein was detectable in 59.6%, 41.7%, and 66.7% of primary lung cancer tissues, premalignant lesions and lymph node metastases, respectively; COX-2 protein was detectable in 52.8%, 41.7%, and 66.7% of primary lung cancer tissues, premalignant lesions and lymph node metastases, respectively, which were significantly higher than those of the control (P < 0.05). The positive ratios and the levels of the expression of EGFR and COX-2 proteins were closely related to histological type, clinical stage and lymph node metastasis of lung cancer (P < 0.05), but not to histological grade, sex and age (P>0.05). COX-2 expression was related to gross type (P < 0.05). A highly positive correlation was observed between EGFR and COX-2 expression (P < 0.01). Conclusion Overexpression of EGFR and COX-2 may play an important role in the tumorgenesis, progression and malignancy of lung cancer. Detection of EGFR and COX-2 expression might be helpful to diagnosis and prognosis of lung cancer

Expression and Significance of gp96 and Immune-related Gene CTLA-4, CD8 in Lung Cancer Tissues

Background and objective It has been proven that gp96 plays an important role in specific cytotoxic immune response which is involved in anti-tumor effect in the body. The aim of this study is to investigate the biological significance of heat shock protein gp96 and immune-related gene CTLA-4, CD8 expressions in lung cancer tissues of different progressive stages. Methods We used Envision immunohistochemistry method to detect the levels of expression of gp96, CTLA-4, CD8 in tissue microarray, which contained 89 primary lung cancer tissues, 12 lymph node metastasis lung cancer tissues, 12 precancerous lesions and 10 normal lung tissues, and analyzed the relationship between their expressions and clinicopathological parameters. Results (1) The positive rate of gp96 in primary lung cancer was remarkably higher than that in precancerous lesion and normal lung tissue (P &lt; 0.05). The positive rate of CTLA-4 in primary lung cancer tissue and precancerous lesion was significantly higher than that in normal lung tissue (P &lt; 0.05). The positive rate of CD8 in primary lung cancer tissue was significantly higher than that in normal lung tissue (P &lt; 0.05). The positive rate of gp96 in CD8-positive lymphocytes in the high expression group was less than that in the low group (P &lt; 0.05). (2) The positive rate of gp96 was closely related to sex, differentiation and clinical stage (P &lt; 0.05), but not to age, gross type, histological type and lymph node metastasis (P &gt; 0.05). The positive rate of CTLA-4 was closely related to age and differentiation (P &lt; 0.05), but not to sex, gross type, histological type, clinical stage and lymph node metastasis (P &gt; 0.05). CD8 expression was related to clinical stage (P &lt; 0.05), but not to sex, age, gross type, histological type, differentiation and lymph node metastasis (P &gt; 0.05). The positive rates of gp96, CTLA-4 were higher than that of CD8 in squamous cell carcinoma and SCLC, respectively. (3) There was positive correlation between gp96 and CTLA-4; there was negative correlation between gp96 and CD8, and there was negative correlation between CD8 and CTLA-4 (P &lt; 0.05). Conclusion Gene expression of PD-L1 on lung cancer cell line can decrease the cytolytic effect of CTL on target cells

Large Language Models as Tool Makers

Recent research has highlighted the potential of large language models (LLMs) to improve their problem-solving capabilities with the aid of suitable external tools. In our work, we further advance this concept by introducing a closed-loop framework, referred to as LLMs A s Tool Makers (LATM), where LLMs create their own reusable tools for problem-solving. Our approach consists of two phases: 1) tool making: an LLM acts as the tool maker that crafts tools for a set of tasks. 2) tool using: another LLM acts as the tool user, which applies the tool built by the tool maker for problem-solving. On the problem-solving server side, tool-making enables continual tool generation and caching as new requests emerge. This framework enables subsequent requests to access cached tools via their corresponding APIs, enhancing the efficiency of task resolution. Recognizing that tool-making requires more sophisticated capabilities, we assign this task to a powerful, albeit resource-intensive, model. Conversely, the simpler tool-using phase is delegated to a lightweight model. This strategic division of labor allows the once-off cost of tool-making to be spread over multiple instances of tool-using, significantly reducing average costs while maintaining strong performance. Furthermore, our method offers a functional cache through the caching and reuse of tools, which stores the functionality of a class of requests instead of the natural language responses from LLMs, thus extending the applicability of the conventional cache mechanism. We evaluate our approach across various complex reasoning tasks, including Big-Bench tasks. With GPT-4 as the tool maker and GPT-3.5 as the tool user, LATM demonstrates performance equivalent to using GPT-4 for both roles, but with a significantly reduced inference cost.Comment: Code available at https://github.com/ctlllll/LLM-ToolMake

DECap: Towards Generalized Explicit Caption Editing via Diffusion Mechanism

Explicit Caption Editing (ECE) -- refining reference image captions through a sequence of explicit edit operations (e.g., KEEP, DETELE) -- has raised significant attention due to its explainable and human-like nature. After training with carefully designed reference and ground-truth caption pairs, state-of-the-art ECE models exhibit limited generalization ability beyond the original training data distribution, i.e., they are tailored to refine content details only in in-domain samples but fail to correct errors in out-of-domain samples. To this end, we propose a new Diffusion-based Explicit Caption editing method: DECap. Specifically, we reformulate the ECE task as a denoising process under the diffusion mechanism, and introduce innovative edit-based noising and denoising processes. Thanks to this design, the noising process can help to eliminate the need for meticulous paired data selection by directly introducing word-level noises for training, learning diverse distribution over input reference caption. The denoising process involves the explicit predictions of edit operations and corresponding content words, refining reference captions through iterative step-wise editing. To further efficiently implement our diffusion process and improve the inference speed, DECap discards the prevalent multi-stage design and directly generates edit operations and content words simultaneously. Extensive ablations have demonstrated the strong generalization ability of DECap in various scenarios. More interestingly, it even shows great potential in improving the quality and controllability of caption generation