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
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
Using operator algebras,we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.Quantum computation is usually implemented on finite discrete sets,and the pu...Using operator algebras,we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.Quantum computation is usually implemented on finite discrete sets,and the purpose of this study is to extend this to theories on arbitrary sets.The conventional theory of quantum computers can be viewed as a simplified algebraic geometry theory in which the action of SU(2)is defined on each point of a discrete set.In this study,we extend this in general as a theory of quantum fibrations in which the action of the von Neumann algebra is defined on an arbitrary topological space.The quantum channel is then naturally extended as a net of von Neumann algebras.This allows for a more mathematically rigorous discussion of general theories,including physics and chemistry,which are defined on sets that are not necessarily discrete,from the perspective of quantum computer science.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
In the study of the collapsed manifolds with bounded sectional curvature,the following two results provide basic tools:a(singular)fibration theorem by K.Fukaya[J.Differential Gcom.,1987.25(1):139156]and J.Cheeger,K.Fu...In the study of the collapsed manifolds with bounded sectional curvature,the following two results provide basic tools:a(singular)fibration theorem by K.Fukaya[J.Differential Gcom.,1987.25(1):139156]and J.Cheeger,K.Fukaya,and M.Gromov[J.Airier.Math.Soc.,1992.5(2):327372],and the stability for isometric compact Lie group actions on manifolds by R.S.Palais[Bull.Amer.Math.Soc.,1961,67(4):362364]and K.Grove and H.Karcher[Math.Z..1973,132:1120].The main results in this paper(partially)generalize the two results to manifolds with local bounded Ricci covering geometry.展开更多
This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smoo...This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].展开更多
On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly buil...On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.展开更多
In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of nume...In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of numerical Campedelli surfaces with fibrations of genus 2.展开更多
We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space ...We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space is isomorphic to a quotient of the projective space. We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.展开更多
This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the var...This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the variety ∑ cannot be smooth on this fibre. Moreover, two examples are given to show the occurrence of such cases.展开更多
K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split...K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split fibration of categories L: H_b → H_B and H_b possesses some construction as in H_B.展开更多
Let f : X → B be a generic ordinary proper fibration over a complete curve in positive characteristics, we prove that the dual of higher direct image sheaf R^1 f_*O_X is nef. As a corollary, we show that f_*ω_(S/B) ...Let f : X → B be a generic ordinary proper fibration over a complete curve in positive characteristics, we prove that the dual of higher direct image sheaf R^1 f_*O_X is nef. As a corollary, we show that f_*ω_(S/B) is nef, if f : S → B is a fibration from a surface to a curve with generic ordinary fibres.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 the medical and dental field, the importance and need for the study of materials and drugs for use as bone grafts or regeneration in injured areas due to the presence of fractures, infections or tumors that cause e...In the medical and dental field, the importance and need for the study of materials and drugs for use as bone grafts or regeneration in injured areas due to the presence of fractures, infections or tumors that cause extensive loss of bone tissue is observed. Bone is a specialized, vascularized and dynamic connective tissue that changes throughout the life of the organism. When injured, it has a unique ability to regenerate and repair without the presence of scars, but in some situations, due to the size of the defect, the bone tissue does not regenerate completely. Thus, due to its importance, there is a great development in therapeutic approaches for the treatment of bone defects through studies that include autografts, allografts and artificial materials used alone or in association with bone grafts. Pharmaceuticals composed of biomaterials and osteogenic active substances have been extensively studied because they provide potential for tissue regeneration and new strategies for the treatment of bone defects. Statins work as specific inhibitors of 3-hydroxy-3-methyl-glutaryl coenzyme A reductase (HMG-CoAreductase). They represent efficient drugs in lowering cholesterol, as they reduce platelet aggregation and thrombus deposition;in addition, they promote angiogenesis, reduce the β-amyloid peptide related to Alzheimer’s disease and suppress the activation of T lymphocytes. Furthermore, these substances have been used in the treatment of hypercholesterolemia and coronary artery disease. By inhibiting HMG-CoAreductase, statins not only inhibit cholesterol synthesis, but also exhibit several other beneficial pleiotropic effects. Therefore, there has been increasing interest in researching the effects of statins, including Simvastatin, on bone and osteometabolic diseases. However, statins in high doses cause inflammation in bone defects and inhibit osteoblastic differentiation, negatively contributing to bone repair. Thus, different types of studies with different concentrations of statins have been studied to positively or negatively correlate this drug with bone regeneration. In this review we will address the positive, negative or neutral effects of statins in relation to bone defects providing a comprehensive understanding of their application. Finally, we will discuss a variety of statin-based drugs and the ideal dose through a theoretical basis with preclinical, clinical and laboratory work in order to promote the repair of bone defects.展开更多
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.
基金supported by Pacific Institute for the Mathematical Science(PIMS)postdoctoral fellowship award and by the U.S.Department of Energy,Office of Science,National Quantum Information Science Research Centers,Co-design Center for Quantum Advantage(C2QA)under Contract No.DESC0012704。
文摘Using operator algebras,we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.Quantum computation is usually implemented on finite discrete sets,and the purpose of this study is to extend this to theories on arbitrary sets.The conventional theory of quantum computers can be viewed as a simplified algebraic geometry theory in which the action of SU(2)is defined on each point of a discrete set.In this study,we extend this in general as a theory of quantum fibrations in which the action of the von Neumann algebra is defined on an arbitrary topological space.The quantum channel is then naturally extended as a net of von Neumann algebras.This allows for a more mathematically rigorous discussion of general theories,including physics and chemistry,which are defined on sets that are not necessarily discrete,from the perspective of quantum computer science.
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In the study of the collapsed manifolds with bounded sectional curvature,the following two results provide basic tools:a(singular)fibration theorem by K.Fukaya[J.Differential Gcom.,1987.25(1):139156]and J.Cheeger,K.Fukaya,and M.Gromov[J.Airier.Math.Soc.,1992.5(2):327372],and the stability for isometric compact Lie group actions on manifolds by R.S.Palais[Bull.Amer.Math.Soc.,1961,67(4):362364]and K.Grove and H.Karcher[Math.Z..1973,132:1120].The main results in this paper(partially)generalize the two results to manifolds with local bounded Ricci covering geometry.
基金Project supported by the DGICYT Grant (No. MTM2007-60016)the Junta de Andalucía Grant(No. P07-FQM-2863)
文摘This paper presents a definition of residue formulas for the Euler class ot eohomology-oriented sphere fibrations ε. If the base of ε is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].
基金This work was supported by the National Natural Science Foundation of China(Grant No.10101004).
文摘On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.
文摘In this series of papers, surfaces of general-type with X(O_s)=1 and fibrations of genus 2 are classified completely, and some new surfaces with invariant p_8=0 are constructed This paper will set up two kinds of numerical Campedelli surfaces with fibrations of genus 2.
基金supported by Japan Society for Promotion of Sciences(Grant No.18684001)
文摘We consider base spaces of Lagrangian fibrations from singular symplectic varieties. After defining cohomologically irreducible symplectic varieties, we construct an example of Lagrar, gian fibration whose base space is isomorphic to a quotient of the projective space. We also prove that the base space of Lagrangian fibration from a cohomologically symplectic variety is isomorphic to the projective space provided that the base space is smooth.
文摘This paper investigates the relative 1-canonical images of non-hyperelliptic fibrations of genus 4. It is proved that if a fibre of the relative 1-canonical image ∑ is not a complete intersection in 3 , then the variety ∑ cannot be smooth on this fibre. Moreover, two examples are given to show the occurrence of such cases.
基金Supported by National Natural Science Foundation of Chinathe Doctoral Foundation of the National Educational Committee of China
文摘K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed spare B ([5]). This paper extends H_B to the track homotopy category H_b over a fixed map b: B → , such that there exists a split fibration of categories L: H_b → H_B and H_b possesses some construction as in H_B.
基金supported by National Natural Science Foundation of China(Grant Nos.11231003 and 11321101)
文摘Let f : X → B be a generic ordinary proper fibration over a complete curve in positive characteristics, we prove that the dual of higher direct image sheaf R^1 f_*O_X is nef. As a corollary, we show that f_*ω_(S/B) is nef, if f : S → B is a fibration from a surface to a curve with generic ordinary fibres.
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.
文摘In the medical and dental field, the importance and need for the study of materials and drugs for use as bone grafts or regeneration in injured areas due to the presence of fractures, infections or tumors that cause extensive loss of bone tissue is observed. Bone is a specialized, vascularized and dynamic connective tissue that changes throughout the life of the organism. When injured, it has a unique ability to regenerate and repair without the presence of scars, but in some situations, due to the size of the defect, the bone tissue does not regenerate completely. Thus, due to its importance, there is a great development in therapeutic approaches for the treatment of bone defects through studies that include autografts, allografts and artificial materials used alone or in association with bone grafts. Pharmaceuticals composed of biomaterials and osteogenic active substances have been extensively studied because they provide potential for tissue regeneration and new strategies for the treatment of bone defects. Statins work as specific inhibitors of 3-hydroxy-3-methyl-glutaryl coenzyme A reductase (HMG-CoAreductase). They represent efficient drugs in lowering cholesterol, as they reduce platelet aggregation and thrombus deposition;in addition, they promote angiogenesis, reduce the β-amyloid peptide related to Alzheimer’s disease and suppress the activation of T lymphocytes. Furthermore, these substances have been used in the treatment of hypercholesterolemia and coronary artery disease. By inhibiting HMG-CoAreductase, statins not only inhibit cholesterol synthesis, but also exhibit several other beneficial pleiotropic effects. Therefore, there has been increasing interest in researching the effects of statins, including Simvastatin, on bone and osteometabolic diseases. However, statins in high doses cause inflammation in bone defects and inhibit osteoblastic differentiation, negatively contributing to bone repair. Thus, different types of studies with different concentrations of statins have been studied to positively or negatively correlate this drug with bone regeneration. In this review we will address the positive, negative or neutral effects of statins in relation to bone defects providing a comprehensive understanding of their application. Finally, we will discuss a variety of statin-based drugs and the ideal dose through a theoretical basis with preclinical, clinical and laboratory work in order to promote the repair of bone defects.
