On Ellipsoids Attached to Root Systems

For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.

Tumor-targeted self-assembled micelles reducing PD-L1 expression combined with ICIs to enhance chemo-immunotherapy of TNBC

Immune checkpoint inhibitors(ICIs)therapy targeting programmed cell death ligand 1(PD-L1)and programmed death protein 1(PD-1)had exhibited significant clinical benefits for cancer treatment such as triple negative breast cancer(TNBC).However,the relatively low anti-tumor immune response rate and ICIs drug resistance highlight the necessity of developing ICIs combination therapy strategies to improve the anti-tumor effect of immunotherapy.Herein,the immunomodulator epigallocatechin gallate palmitate(PEGCG)and the immunoadjuvant metformin(MET)self-assembled into tumor-targeted micelles via hydrogen bond and electrostatic interaction,which encapsulated the therapeutic agents doxorubicin(DOX)-loaded PEGCG-MET micelles(PMD)and combined with ICIs(anti-PD-1 antibody)as therapeutic strategy to reduce the endogenous expression of PD-L1 and improve the tumor immunosuppressive microenvironment.The results presented that PMD integrated chemotherapy and immunotherapy to enhance antitumor efficacy in vitro and in vivo,compared with DOX or anti-PD-1 antibody for the therapy of TNBC.PMD micelles might be a potential candidate,which could remedy the shortcomings of antibody-based ICIs and provide synergistic effect to enhance the antitumor effects of ICIs in tumor therapy.