Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow

We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new Harnack inequalities extend the previous differential Harnack inequalities for linear heat equations with potentials under the Ricci flow.Comment: 17 pages. New explanations added; Final versio

Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation

Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where $(x,t) \in M^N \times (-\infty, \infty)$ and $\alpha$ is an arbitrary constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities for positive bounded solutions.Comment: 18 page

Carthamus tinctorius Enhances the Antitumor Activity of Dendritic Cell Vaccines via Polarization toward Th1 Cytokines and Increase of Cytotoxic T Lymphocytes

Carthamus tinctorius (CT), also named safflower, is a traditional Chinese medicine widely used to improve blood circulation. CT also has been studied for its antitumor activity in certain cancers. To investigate the effects of CT on the dendritic cell (DC)-based vaccine in cancer treatment, cytokine secretion of mouse splenic T lymphocytes and the maturation of DCs in response to CT were analyzed. To assess the antitumor activity of CT extract on mouse CD117+ (c-kit)-derived DCs pulsed with JC mammal tumor antigens, the JC tumor was challenged by the CT-treated DC vaccine in vivo. CT stimulated IFN-γ and IL-10 secretion of splenic T lymphocytes and enhanced the maturation of DCs by enhancing immunological molecule expression. When DC vaccine was pulsed with tumor antigens along with CT extract, the levels of TNF-α and IL-1β were dramatically increased with a dose-dependent response and more immunologic and co-stimulatory molecules were expressed on the DC surface. In addition, CT-treated tumor lysate-pulsed DC vaccine reduced the tumor weight in tumor-bearing mice by 15.3% more than tumor lysate-pulsed DC vaccine without CT treatment. CT polarized cytokine secretion toward the Th1 pathway and also increased the population of cytotoxic T lymphocytes ex vivo. In conclusion, CT activates DCs might promote the recognition of antigens and facilitate antigen presentation to Th1 immune responses

Demethoxycurcumin Retards Cell Growth and Induces Apoptosis in Human Brain Malignant Glioma GBM 8401 Cells

Demethoxycurcumin (DMC; a curcumin-related demethoxy compound) has been recently shown to display antioxidant and antitumor activities. It has also produced a potent chemopreventive action against cancer. In the present study, the antiproliferation (using the MTT assay, DMC was found to have cytotoxic activities against GBM 8401 cell with IC50 values at 22.71 μM) and induced apoptosis effects of DMC have been investigated in human brain malignant glioma GBM 8401 cells. We have studied the mitochondrial membrane potential (MMP), DNA fragmentation, caspase activation, and NF-κB transcriptional factor activity. By these approaches, our results indicated that DMC has produced an inhibition of cell proliferation as well as the activation of apoptosis in GBM 8401 cells. Both effects were observed to increase in proportion with the dosage of DMC treatment, and the apoptosis was induced by DMC in human brain malignant glioma GBM 8401 cells via mitochondria- and caspase-dependent pathways

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau gradient estimate method has been moved to the appendix. The new proof is simple and direc

Precise dd excitations and commensurate intersite Coulomb interactions in the dissimilar cuprate YBa_2Cu_3O_(7-x) and La_(2-x)Sr_xCuO_4

Using high-resolution extreme ultraviolet resonant inelastic X-ray scattering (EUVRIXS) spectroscopy at Cu M-edge, we observed the doping dependent spectral shifts of inter-orbital (dd) excitations of YBa_2Cu_3O_(7-x) and La_(2-x)Sr_xCuO_4. With increasing hole doping level from undoped to optimally doped superconducting compositions, the leading edge of dd excitations is found to shift towards lower energy loss in a roughly linear trend that is irrespective to the cuprate species. The magnitude of energy shift can be explained by including a 0.15 eV Coulomb attraction between Cu 3d_(x^2-y^2) electrons and the doped holes on the surrounding oxygens in the atomic multiplet calculations. The consistent energy shift between distinct cuprate families suggests that this inter-site Coulomb interaction energy scale is relatively material-independent, and provides an important reference point for understanding charge density wave phenomena in the cuprate phase diagram.Comment: 29 pages; 8 figures. Physical Review B, in press. This paper reveals a Cu 3d-O 2p intersite interaction energy for the first time experimentally. It also explains why Tc of YBCO is higher than that of LSC

MetaGPT: Meta Programming for Multi-Agent Collaborative Framework

Recently, remarkable progress has been made in automated task-solving through the use of multi-agents driven by large language models (LLMs). However, existing works primarily focuses on simple tasks lacking exploration and investigation in complicated tasks mainly due to the hallucination problem. This kind of hallucination gets amplified infinitely as multiple intelligent agents interact with each other, resulting in failures when tackling complicated problems.Therefore, we introduce MetaGPT, an innovative framework that infuses effective human workflows as a meta programming approach into LLM-driven multi-agent collaboration. In particular, MetaGPT first encodes Standardized Operating Procedures (SOPs) into prompts, fostering structured coordination. And then, it further mandates modular outputs, bestowing agents with domain expertise paralleling human professionals to validate outputs and reduce compounded errors. In this way, MetaGPT leverages the assembly line work model to assign diverse roles to various agents, thus establishing a framework that can effectively and cohesively deconstruct complex multi-agent collaborative problems. Our experiments conducted on collaborative software engineering tasks illustrate MetaGPT's capability in producing comprehensive solutions with higher coherence relative to existing conversational and chat-based multi-agent systems. This underscores the potential of incorporating human domain knowledge into multi-agents, thus opening up novel avenues for grappling with intricate real-world challenges. The GitHub repository of this project is made publicly available on: https://github.com/geekan/MetaGP

Elimination of head and neck cancer initiating cells through targeting glucose regulated protein78 signaling

<p>Abstract</p> <p>Background</p> <p>Head and neck squamous cell carcinoma (HNSCC) is a highly lethal cancer that contains cellular and functional heterogeneity. Previously, we enriched a subpopulation of highly tumorigenic head and neck cancer initiating cells (HN-CICs) from HNSCC. However, the molecular mechanisms by which to govern the characteristics of HN-CICs remain unclear. GRP78, a stress-inducible endoplasmic reticulum chaperone, has been reported to play a crucial role in the maintenance of embryonic stem cells, but the role of GRP78 in CICs has not been elucidated.</p> <p>Results</p> <p>Initially, we recognized GRP78 as a putative candidate on mediating the stemness and tumorigenic properties of HN-CICs by differential systemic analyses. Subsequently, cells with GRP78 anchored at the plasma membrane (^memGRP78⁺) exerted cancer stemness properties of self-renewal, differentiation and radioresistance. Of note, xenotransplantation assay indicated merely 100 ^memGRP78⁺HNSCCs resulted in tumor growth. Moreover, knockdown of GRP78 significantly reduced the self-renewal ability, side population cells and expression of stemness genes, but inversely promoted cell differentiation and apoptosis in HN-CICs. Targeting GRP78 also lessened tumorigenicity of HN-CICs both <it>in vitro </it>and <it>in vivo</it>. Clinically, co-expression of GRP78 and Nanog predicted the worse survival prognosis of HNSCC patients by immunohistochemical analyses. Finally, depletion of GRP78 in HN-CICs induced the expression of Bax, Caspase 3, and PTEN.</p> <p>Conclusions</p> <p>In summary, ^memGRP78 should be a novel surface marker for isolation of HN-CICs, and targeting GRP78 signaling might be a potential therapeutic strategy for HNSCC through eliminating HN-CICs.</p

Group A Streptococcus Subcutaneous Infection-Induced Central Nervous System Inflammation Is Attenuated by Blocking Peripheral TNF

Group A streptococcus (GAS) infection causes a strong inflammatory response associated with cytokine storms, leading to multiorgan failure, which is characterized as streptococcal toxic shock syndrome. However, little is known about GAS subcutaneous infection-mediated brain inflammation. Therefore, we used a bioluminescent GAS strain and reporter mice carrying firefly luciferase under transcriptional control of the nuclear factor-kappa B (NF-κB) promoter to concurrently monitor the host immune response and bacterial burden in a single mouse. Notably, in addition to the subcutaneous inoculation locus at the back of mice, we detected strong luminescence signals from NF-κB activation and increased inflammatory cytokine production in the brain, implying the existence of central nervous system inflammation after GAS subcutaneous infection. The inflamed brain exhibited an increased expression of glial fibrillary acidic protein and nicotinamide adenine dinucleotide phosphate oxidase components and greater microglial activation and blood–brain barrier (BBB) disruption. Furthermore, Fluoro-Jade C positive cells increased in the brain, indicating that neurons underwent degeneration. Peripheral tumor necrosis factor (TNF), which contributes to pathology in brain injury, was elevated in the circulation, and the expression of its receptor was also increased in the inflamed brain. Blockage of peripheral TNF effectively reduced brain inflammation and injury, thereby preventing BBB disruption and improving survival. Our study provides new insights into GAS-induced central nervous system inflammation, such as encephalopathy, which can be attenuated by circulating TNF blockage