Degenerate Mean Field Games with H\"ormander diffusion

In this paper, we study a class of degenerate mean field game systems arising from the mean field games with H\"ormander diffusion, where the generic player may have a ``forbidden'' direction at some point. Here we prove the existence and uniqueness of the classical solutions in weighted H\"older spaces for the PDE systems, which describe the Nash equilibria in the games. The degeneracy causes the lack of commutation of vector fields and the fundamental solution which are the main difficulties in the proof of the global Schauder estimate and the weak maximum principle. Based on the idea of the localizing technique and the local homogeneity of degenerate operators, we extend the maximum regularity result and obtain the global Schauder estimates. For the weak maximum principle, we construct a subsolution instead of the fundamental solution of the degenerate operators.Comment: We deeply appreciate your consideration of the manuscript. Thank you very muc

Mean Field Games with infinitely degenerate diffusion and non-coercive Hamiltonian

In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings difficulties to the uniform boundness of the solutions, which is central to the existence and regularity results. First, from the perspective of the value function in the stochastic optimal control problems, we prove the Lipschitz continuity and the semiconcavity for the solutions of the Hamilton-Jacobi equations (HJE). Then the existence of the weak solutions for the degenerate systems is obtained via a vanishing viscosity method. Furthermore, by constructing an auxiliary function, we conclude the regularity of the viscosity solution for the HJE in the almost everywhere sense

Digital twin brain: a bridge between biological intelligence and artificial intelligence

In recent years, advances in neuroscience and artificial intelligence have paved the way for unprecedented opportunities for understanding the complexity of the brain and its emulation by computational systems. Cutting-edge advancements in neuroscience research have revealed the intricate relationship between brain structure and function, while the success of artificial neural networks highlights the importance of network architecture. Now is the time to bring them together to better unravel how intelligence emerges from the brain's multiscale repositories. In this review, we propose the Digital Twin Brain (DTB) as a transformative platform that bridges the gap between biological and artificial intelligence. It consists of three core elements: the brain structure that is fundamental to the twinning process, bottom-layer models to generate brain functions, and its wide spectrum of applications. Crucially, brain atlases provide a vital constraint, preserving the brain's network organization within the DTB. Furthermore, we highlight open questions that invite joint efforts from interdisciplinary fields and emphasize the far-reaching implications of the DTB. The DTB can offer unprecedented insights into the emergence of intelligence and neurological disorders, which holds tremendous promise for advancing our understanding of both biological and artificial intelligence, and ultimately propelling the development of artificial general intelligence and facilitating precision mental healthcare

Overexpression of DBT suppresses the aggressiveness of renal clear cell carcinoma and correlates with immune infiltration

Conventional therapy for kidney renal clear cell carcinoma (KIRC) is unpromising. The tumor microenvironment (TME) is intimately linked to the invasiveness of a variety of tumor forms, including KIRC. The purpose of this research is to establish the prognostic and immune-related significance of dihydrolipoamide branched chain transacylase E2 (DBT) in individuals with KIRC. In this investigation, we discovered that DBT expression was down-regulated in a range of human malignancies, and low DBT expression in KIRC was linked to higher-level clinicopathological characteristics as well as a poor prognosis for KIRC patients. Based on the findings of univariate and multivariate Cox regression analyses, DBT might be employed as an independent prognostic factor in KIRC patients. Furthermore, we developed a nomogram to better investigate DBT’s predictive usefulness. To confirm DBT expression, we examined KIRC cell lines using RT-qPCR and Western blotting. We also examined the role of DBT in KIRC using colony formation, CCK-8, EdU, transwell, and wound healing assays. We discovered that plasmid-mediated overexpression of DBT in KIRC cells slowed cell proliferation and decreased migration and invasion. Multiple enrichment analyses revealed that DBT may be involved in processes and pathways related to immunotherapy and drug metabolism. We computed the immune infiltration score and discovered that the immunological score and the ESTIMATE score were both greater in the DBT low expression group. According to the CIBERSORT algorithm, DBT seems to promote anti-cancer immune responses in KIRC by activating M1 macrophages, mast cells, and dendritic cells while inhibiting regulatory T cells. Finally, in KIRC, DBT expression was found to be highly linked to immunological checkpoints, targeted medicines, and immunotherapeutic agents. Our findings suggest that DBT is a distinct predictive biomarker for KIRC patients, playing a significant role in the TME of KIRC and serving as a reference for the selection of targeted treatment and immunotherapy

Nanoscale dihydroartemisinin@zeolitic imidazolate frameworks for enhanced antigiardial activity and mechanism analysis

An artificial semisynthetic material can be derived from artemisinin (ART) called dihydroartemisinin (DHA). Although DHA has enhanced antigiardial potential, its clinical application is limited because of its poor selectivity and low solubility. The drug’s absorption has a direct impact on the cell, and mechanism research is limited to its destruction of the cytoskeleton. In this study, we used the zeolitic imidazolate framework-8 and loaded it with DHA (DHA@Zif-8) to improve its antigiardial potential. DHA@Zif-8 can enhance cellular uptake, increase antigiardial proliferation and encystation, and expand the endoplasmic reticulum compared with the DHA-treated group. We used RNA sequencing (RNA-seq) to investigate the antigiardial mechanism. We found that 126 genes were downregulated and 123 genes were upregulated. According to the KEGG and GO pathway analysis, the metabolic functions in G. lamblia are affected by DHA@Zif-8 NPs. We used real-time quantitative reverse transcription polymerase chain reaction to verify our results using the RNA-seq data. DHA@Zif-8 NPs significantly enhanced the eradication of the parasite from the stool in vivo. In addition, the intestinal mucosal injury caused by G. lamblia trophozoites markedly improved in the intestine. This research provided the potential of utilizing DHA@Zif-8 to develop an antiprotozoan drug for clinical applications