Nonexistence of solutions to fractional parabolic problem with general nonlinearities

In this content, we investigate a class of fractional parabolic equation with general nonlinearities ∂z(x, t) ∂t − ( + λ) β 2 z(x, t) = a(x1) f (z), where a and f are nondecreasing functions. We first prove that the monotone increasing property of the positive solutions in x1 direction. Based on this, nonexistence of the solutions are obtained by using a contradiction argument. We believe these new ideas we introduced will be applied to solve more fractional parabolic problemsThe research of Zhang has been partially supported by National Natural Science Foun dation of China(No. 12001344) and the Graduate Education and Teaching Innovation Project of Shanxi, China (No. 2022YJJG124), the research of Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain under Grant PID2020-113275GB-I00, cofinanced by the European Community fund FEDER, as well as Xunta de Galicia grant ED431C 2019/02 for Competitive Reference Research Groups (2019–22) and the research of Wang has been partially supported by Natural Science Foundation of Shanxi Province, China(No. 20210302123339)S

RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM

ABSTRACT The paper evaluates the radiation damping associated with shallow foundations sitting on linear or nonlinear soil medium. The study was motivated by the need to develop macroscopic foundation models that can realistically capture the nonlinear behaviour and energy dissipation mechanism of shallow foundations. Such model is essential to simulate the complex behaviour of structure components (e.g. shear walls, columns etc.) sitting on flexible foundations due to soil-structure interaction effects. In this study, the dynamic response of an infinitely long strip foundation resting on an elastic and inelastic half-space is investigated. The numerical analysis results presented here reveal that dynamic responses of shallow foundations strongly depend on amplitude and frequency of the input motion. In particular, the radiation damping of the system is affected by soil nonlinearity, foundation geometry and excitation frequency. The yielding of soil reduces the energy dissipation through the out going waves. As a result, the radiation damping of nonlinear soil medium is significantly lower than the elastic soil counterpart. The effects of initial elastic stiffness, yielding stress and excitation amplitude are incorporated in a nonlinearity indicator, which has shown strong correspondence to the radiation damping of the system

Peripheral blood T Regulatory cell counts may not predict transplant rejection

<p>Abstract</p> <p>Background</p> <p>Recent evidence shows that allograft survival rates show a positive correlation with the number of circulating T regulatory cells (Tregs). This study investigated both the number and the cytokine profiles exhibited by Foxp3⁺Tregs in blood, spleen and lymph nodes of Lewis rat recipients of BN rat cardiac allografts after a single-dose of Rapamycin (RAPA).</p> <p>Results</p> <p>Rats were divided into three groups: control group (containing healthy control and acute rejection group), and recipients treated with a single dose of RAPA on either Day 1 (1D group)or Day 3 (3D group) post-transplant. We analyzed the number of Foxp3+Tregs and the expression of Foxp3 and cytokines in the peripheral blood and the peripheral lymphoid tissues. No difference was found in the numbers of circulating Foxp3+ Tregs between these three groups. RAPA administration significantly increased Foxp3 expression in peripheral lymphoid tissues after a single dose of RAPA on Day 3 post-transplant. Foxp3+Tregs inhibited the activity of effector T cells (T_eff) via the secretion of TGF-β1.</p> <p>Conclusion</p> <p>The number of Tregs in the recipient's blood may not be a good predictor of transplant rejection. Foxp3+Tregs inhibit the activity of T_effcells mainly in the peripheral lymphoid tissues.</p

Enhancing the General Agent Capabilities of Low-Parameter LLMs through Tuning and Multi-Branch Reasoning

Open-source pre-trained Large Language Models (LLMs) exhibit strong language understanding and generation capabilities, making them highly successful in a variety of tasks. However, when used as agents for dealing with complex problems in the real world, their performance is far inferior to large commercial models such as ChatGPT and GPT-4. As intelligent agents, LLMs need to have the capabilities of task planning, long-term memory, and the ability to leverage external tools to achieve satisfactory performance. Various methods have been proposed to enhance the agent capabilities of LLMs. On the one hand, methods involve constructing agent-specific data and fine-tuning the models. On the other hand, some methods focus on designing prompts that effectively activate the reasoning abilities of the LLMs. We explore both strategies on the 7B and 13B models. We propose a comprehensive method for constructing agent-specific data using GPT-4. Through supervised fine-tuning with constructed data, we find that for these models with a relatively small number of parameters, supervised fine-tuning can significantly reduce hallucination outputs and formatting errors in agent tasks. Furthermore, techniques such as multi-path reasoning and task decomposition can effectively decrease problem complexity and enhance the performance of LLMs as agents. We evaluate our method on five agent tasks of AgentBench and achieve satisfactory results.Comment: To appear at NAACL 202