Propagation acceleration in reaction diffusion equations with anomalous diffusions

In this paper, we are interested in the properties of solution of the nonlocal equation $$\begin{cases}u_t+(-\Delta)^su=f(u),\quad t>0, \ x\in\mathbb{R}\\ u(0,x)=u_0(x),\quad x\in\mathbb{R}\end{cases}$$ where $0\le u_0<1$ is a Heaviside type function, $\Delta^s$ stands for the fractional Laplacian with $s\in (0,1)$, and $f\in C([0,1],\mathbb{R}^+)$ is a non negative nonlinearity such that $f(0)=f(1)=0$ and $f'(1)<0$. In this context, it is known that the solution $u(t,s)$ converges locally uniformly to 1 and our aim here is to understand how fast this invasion process occur. When $f$ is a Fisher-KPP type nonlinearity and $s \in (0,1)$, it is known that the level set of the solution $u(t,x)$ moves at an exponential speed whereas when $f$ is of ignition type and $s\in \left(\frac{1}{2},1\right)$ then the level set of the solution moves at a constant speed. In this article, for general monostable nonlinearities $f$ and any $s\in (0,1)$ we derive generic estimates on the position of the level sets of the solution $u(t,x)$ which then enable us to describe more precisely the behaviour of this invasion process. In particular, we obtain a algebraic generic upper bound on the "speed" of level set highlighting the delicate interplay of $s$ and $f$ in the existence of an exponential acceleration process. When $s\in\left (0,\frac{1}{2}\right]$ and $f$ is of ignition type, we also complete the known description of the behaviour of $u$ and give a precise asymptotic of the speed of the level set in this context. Notably, we prove that the level sets accelerate when $s\in\left(0,\frac{1}{2}\right)$ and that in the critical case $s=\frac{1}{2}$ although no travelling front can exist, the level sets still move asymptotically at a constant speed. These new results are in sharp contrast with the bistable situation where no such acceleration may occur, highlighting therefore the qualitative difference between the two type of nonlinearities

Effect of Gradually Decreasing Photoperiod on Immune Function in Siberian Hamsters

Animals usually use photoperiod as an important environmental cue to time the year. In terms of the winter immunocompetence enhancement hypothesis, animals in the non-tropical zone would actively enhance their immune function to decrease the negative influence of stressors such as low temperature and food shortage in winter. In the present study, we mimicked the transition from summer to winter by decreasing photoperiod gradually and examined the variations of immune repsonses in Siberian hamsters (Phodopus sungorus)&nbsp; to test this hypothesis. Twenty two female adult hamsters were randomly divided into the control (12h light: 12h dark, Control, n=11) and the gradually decreasing photoperiod group (Experiment, n=11). In the experiment group, day length was decreased from 12 h: 12 h light-dark cycle to 8 h: 16 h light-dark cycle at the pace of half an hour per week. We found that gradually decreasing photoperiod had no effect on body composition (wet carcass mass, subcutaneous, retroperitoneal, mesenteric and total body fat mass) and the masses of the organs detected such as brain, heart, liver and so on in hamsters. Similarly, immunological parameters including immune organs (thymus and spleen), white blood cells and serum bacteria killing capacity indicative of innate immunity were also not influenced by gradually decreasing photoperiod, which did not support the winter immunocompetence enhancement hypothesis. However, gradually decreasing photoperiod increased phytohaemagglutinin response post-24h of PHA challenge, which supported this hypothesis. There was no correlation between cellular, innate immunity and body fat mass, suggesting that body fat was not the reasons of the changes of cellular immunity. In summary, distinct components of immune system respond to gradually decreasing photoperiod differently in Siberian hamsters

Introducing the GEV Activation Function for Highly Unbalanced Data to Develop COVID-19 Diagnostic Models

Fast and accurate diagnosis is essential for the efficient and effective control of the COVID-19 pandemic that is currently disrupting the whole world. Despite the prevalence of the COVID-19 outbreak, relatively few diagnostic images are openly available to develop automatic diagnosis algorithms. Traditional deep learning methods often struggle when data is highly unbalanced with many cases in one class and only a few cases in another; new methods must be developed to overcome this challenge. We propose a novel activation function based on the generalized extreme value (GEV) distribution from extreme value theory, which improves performance over the traditional sigmoid activation function when one class significantly outweighs the other. We demonstrate the proposed activation function on a publicly available dataset and externally validate on a dataset consisting of 1,909 healthy chest X-rays and 84 COVID-19 X-rays. The proposed method achieves an improved area under the receiver operating characteristic (DeLong's p-value < 0.05) compared to the sigmoid activation. Our method is also demonstrated on a dataset of healthy and pneumonia vs. COVID-19 X-rays and a set of computerized tomography images, achieving improved sensitivity. The proposed GEV activation function significantly improves upon the previously used sigmoid activation for binary classification. This new paradigm is expected to play a significant role in the fight against COVID-19 and other diseases, with relatively few training cases available

Assessing Hidden Risks of LLMs: An Empirical Study on Robustness, Consistency, and Credibility

The recent popularity of large language models (LLMs) has brought a significant impact to boundless fields, particularly through their open-ended ecosystem such as the APIs, open-sourced models, and plugins. However, with their widespread deployment, there is a general lack of research that thoroughly discusses and analyzes the potential risks concealed. In that case, we intend to conduct a preliminary but pioneering study covering the robustness, consistency, and credibility of LLMs systems. With most of the related literature in the era of LLM uncharted, we propose an automated workflow that copes with an upscaled number of queries/responses. Overall, we conduct over a million queries to the mainstream LLMs including ChatGPT, LLaMA, and OPT. Core to our workflow consists of a data primitive, followed by an automated interpreter that evaluates these LLMs under different adversarial metrical systems. As a result, we draw several, and perhaps unfortunate, conclusions that are quite uncommon from this trendy community. Briefly, they are: (i)-the minor but inevitable error occurrence in the user-generated query input may, by chance, cause the LLM to respond unexpectedly; (ii)-LLMs possess poor consistency when processing semantically similar query input. In addition, as a side finding, we find that ChatGPT is still capable to yield the correct answer even when the input is polluted at an extreme level. While this phenomenon demonstrates the powerful memorization of the LLMs, it raises serious concerns about using such data for LLM-involved evaluation in academic development. To deal with it, we propose a novel index associated with a dataset that roughly decides the feasibility of using such data for LLM-involved evaluation. Extensive empirical studies are tagged to support the aforementioned claims

Differential Reponses of Hematopoietic Stem and Progenitor Cells to mTOR Inhibition

Abnormal activation of the mammalian target of rapamycin (mTOR) signaling pathway has been observed in a variety of human cancers. Therefore, targeting of the mTOR pathway is an attractive strategy for cancer treatment and several mTOR inhibitors, including AZD8055 (AZD), a novel dual mTORC1/2 inhibitor, are currently in clinical trials. Although bone marrow (BM) suppression is one of the primary side effects of anticancer drugs, it is not known if pharmacological inhibition of dual mTORC1/2 affects BM hematopoietic stem and progenitor cells (HSPCs) function and plasticity. Here we report that dual inhibition of mTORC1/2 by AZD or its analogue (KU-63794) depletes mouse BM Lin − Sca-1 + c-Kit + cells in cultures via the induction of apoptotic cell death. Subsequent colony-forming unit (CFU) assays revealed that inhibition of mTORC1/2 suppresses the clonogenic function of hematopoietic progenitor cells (HPCs) in a dose-dependent manner. Surprisingly, we found that dual inhibition of mTORC1/2 markedly inhibits the growth of day-14 cobblestone area-forming cells (CAFCs) but enhances the generation of day-35 CAFCs. Given the fact that day-14 and day-35 CAFCs are functional surrogates of HPCs and hematopoietic stem cells (HSCs), respectively, these results suggest that dual inhibition of mTORC1/2 may have distinct effects on HPCs versus HSCs

Failure mechanisms and dynamic process control measures of deep buried tunnels in tectonic fracture zones under high in-situ stresses—a case study in Southwestern China

Squeezing deformation in tectonic fracture zones under high in-situ stresses has created great difficulties to deep tunnel construction in Southwestern China. This study reports an investigation on large deformation and failure mechanisms of the Wanhe tunnel on the China-Laos Railway through several field tests including the in-situ stress, loosened zone, deformation monitoring, and internal stresses of steel arches. The dynamic process control method is proposed following the combination principle of stress releasing and support resistance. Further, the dynamic process control measures including the advanced and primary supports, the deep-shallow coupled delayed grouting method, and the double steel arches method were applied on site to resist the deformation development. The results of this study indicate that the rapid growth of the tunnel deformation in the early stage was caused by the squeezing effect, and later the loosening effect led to another growing trend of the vault settlement. The dynamic process control method allows to release the deformation of the surrounding rock in the rapid growth stage. Then, it requires to control the deformation within the reserved range by reinforcing the surrounding rock and increasing the stiffness of supports in the later stage. From the feedback of monitoring results, large deformation of Wanhe tunnel was well released and effectively controlled within the deformation allowance. Thus these countermeasures based on the dynamic process control method can guarantee the construction safety of deep buried tunnels in tectonic fracture zones under high in-situ stresses