Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual mod...Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual models. These geometries have been built by moving real toric manifolds over real bases. Using topological changing behaviors, we unveil certain data associated with gauge sectors relying on affine lie symmetries.展开更多
A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) ...A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.展开更多
We present a proof of the Strominger-Yau-Zaslow (SYZ) conjecture by demonstrating that mirror symmetry fundamentally represents an equivalence of computational structures between Calabi-Yau manifolds. Through developm...We present a proof of the Strominger-Yau-Zaslow (SYZ) conjecture by demonstrating that mirror symmetry fundamentally represents an equivalence of computational structures between Calabi-Yau manifolds. Through development of a rigorous quantum complexity operator formalism, we show that mirror pairs must have equivalent complexity spectra and that the SYZ fibration naturally preserves these computational invariants while implementing the required geometric transformations. Our proof proceeds by first establishing a precise mathematical framework connecting quantum complexity with geometric structures, then demonstrating that the special Lagrangian torus fibration preserves computational complexity at both local and global levels, and finally proving that this preservation necessarily implies the geometric correspondences required by the SYZ conjecture. This approach not only resolves the conjecture but reveals deeper insights about the relationship between computation and geometry in string theory. We introduce new complexity-based invariants for studying mirror symmetry and demonstrate how our framework extends naturally to related geometric structures.展开更多
Primary biliary cholangitis(PBC)is a chronic autoimmune cholestatic liver disease characterized by progressive bile duct destruction,leading to fibrosis,cirrhosis,and eventual liver failure.Over the past two decades,s...Primary biliary cholangitis(PBC)is a chronic autoimmune cholestatic liver disease characterized by progressive bile duct destruction,leading to fibrosis,cirrhosis,and eventual liver failure.Over the past two decades,significant advancements have paved the way for novel therapeutic strategies.Ursodeoxycholic acid(UDCA)has been the cornerstone of PBC management,improving survival and delaying disease progression in most patients.However,up to 40%of patients demonstrate an inadequate response to UDCA,necessitating additional treatment options.Obeticholic acid(OCA),a farnesoid X receptor agonist,has emerged as a second-line therapy,showing efficacy in reducing alkaline phosphatase levels and improving liver biochemistry.Beyond UDCA and OCA,a new wave of therapeutic agents are reshaping the PBC landscape.These include fibrates,peroxisome proliferator-activated receptor agonists and novel immunomodulatory drugs aimed at reducing autoimmune-mediated liver injury.Bile acid transport inhibitors,anti-fibrotic agents,and gut microbiome-targeted therapies are also under investigation,offering hope for personalized treatment approaches.This review highlights the evolution of PBC therapy,emphasizing the unmet needs of patients with refractory disease and the potential of emerging therapies to improve outcomes.As the therapeutic landscape continues to expand,optimizing treatment strategies through precision medicine holds the promise of transforming the management of PBC.展开更多
In this article,we present characterizations of the concavity property of minimal L^(2) integrals degenerating to linearity in the case of fibrations over products of open Riemann surfaces.As applications,we obtain ch...In this article,we present characterizations of the concavity property of minimal L^(2) integrals degenerating to linearity in the case of fibrations over products of open Riemann surfaces.As applications,we obtain characterizations of the holding of the equality in the optimal jets L^(2) extension problem from fibers over products of analytic subsets to fibrations over products of open Riemann surfaces,which implies characterizations of the equality parts of the Suita conjecture and the extended Suita conjecture for fibrations over products of open Riemann surfaces.展开更多
文摘Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual models. These geometries have been built by moving real toric manifolds over real bases. Using topological changing behaviors, we unveil certain data associated with gauge sectors relying on affine lie symmetries.
文摘A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.
文摘We present a proof of the Strominger-Yau-Zaslow (SYZ) conjecture by demonstrating that mirror symmetry fundamentally represents an equivalence of computational structures between Calabi-Yau manifolds. Through development of a rigorous quantum complexity operator formalism, we show that mirror pairs must have equivalent complexity spectra and that the SYZ fibration naturally preserves these computational invariants while implementing the required geometric transformations. Our proof proceeds by first establishing a precise mathematical framework connecting quantum complexity with geometric structures, then demonstrating that the special Lagrangian torus fibration preserves computational complexity at both local and global levels, and finally proving that this preservation necessarily implies the geometric correspondences required by the SYZ conjecture. This approach not only resolves the conjecture but reveals deeper insights about the relationship between computation and geometry in string theory. We introduce new complexity-based invariants for studying mirror symmetry and demonstrate how our framework extends naturally to related geometric structures.
文摘Primary biliary cholangitis(PBC)is a chronic autoimmune cholestatic liver disease characterized by progressive bile duct destruction,leading to fibrosis,cirrhosis,and eventual liver failure.Over the past two decades,significant advancements have paved the way for novel therapeutic strategies.Ursodeoxycholic acid(UDCA)has been the cornerstone of PBC management,improving survival and delaying disease progression in most patients.However,up to 40%of patients demonstrate an inadequate response to UDCA,necessitating additional treatment options.Obeticholic acid(OCA),a farnesoid X receptor agonist,has emerged as a second-line therapy,showing efficacy in reducing alkaline phosphatase levels and improving liver biochemistry.Beyond UDCA and OCA,a new wave of therapeutic agents are reshaping the PBC landscape.These include fibrates,peroxisome proliferator-activated receptor agonists and novel immunomodulatory drugs aimed at reducing autoimmune-mediated liver injury.Bile acid transport inhibitors,anti-fibrotic agents,and gut microbiome-targeted therapies are also under investigation,offering hope for personalized treatment approaches.This review highlights the evolution of PBC therapy,emphasizing the unmet needs of patients with refractory disease and the potential of emerging therapies to improve outcomes.As the therapeutic landscape continues to expand,optimizing treatment strategies through precision medicine holds the promise of transforming the management of PBC.
基金supported by National Key R&D Program of China(Grant No.2021YFA1003100)National Natural Science Foundation of China(Grant Nos.12425101,11825101,11522101 and 11431013)supported by China Postdoctoral Science Foundation(Grant Nos.BX20230402 and 2023M743719).
文摘In this article,we present characterizations of the concavity property of minimal L^(2) integrals degenerating to linearity in the case of fibrations over products of open Riemann surfaces.As applications,we obtain characterizations of the holding of the equality in the optimal jets L^(2) extension problem from fibers over products of analytic subsets to fibrations over products of open Riemann surfaces,which implies characterizations of the equality parts of the Suita conjecture and the extended Suita conjecture for fibrations over products of open Riemann surfaces.
文摘目的探讨致纤维化细胞因子和炎症细胞因子在冻结肩发生中的可能作用。方法 2014年9月至2016年4月,20例冻结肩患者接受肩关节镜手术,其中原发性冻结肩10例(A组),继发性冻结肩10例(B组)。以同期接受肩关节镜手术的10例非冻结肩患者作为对照(C组)。q PCR检测肩关节滑膜组织中基质金属蛋白酶1(MMP1)、MMP3、肿瘤坏死因子-α(TNF-α)、白细胞介素-1(IL-1)、IL-6、IL-8、粒细胞巨噬细胞集落刺激因子(GM-CSF)和巨噬细胞集落刺激因子(M-CSF)m RNA表达水平。结果 A组和B组MMP1和MMP3 m RNA表达高于C组(P<0.05),TNF-α、IL-1、IL-6、IL-8、GM-CSF和M-CSF m RNA显著高于C组(P<0.001),A组和B组间各因子m RNA表达无显著性差异(P>0.05)。结论冻结肩的发生可能与患者关节滑膜组织中致纤维化细胞因子和炎症细胞因子的高表达有关。
