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Homological Perturbation Theory and Mirror symmetry

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Acta Mathematica sinica,English series 2003年第4期19卷 695-714页

作者： jianzhou DepartmentofMathematicalsciences TsinghuaUniversityBeijing100084P.R.China

We explain how deformation theories of geometric objects such as complexstructures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaberor Poisson algebras. We use homological perturbation theory to construct A_∞ algebra structures onthe cohomology, and their canonically defined deformation. such constructions are used to formulatea version of A_∞ algebraic mirror symmetry.

关键词： homological perturbation theory mirror symmetry

Quadratic Recursion Relations of Hodge Integrals via Localization

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Acta Mathematica sinica,English series 2003年第2期19卷 209-232页

作者： GangTIAN jianzhou DepartmentofMathematics MassachusettsInstituteofTechonlogyCambridgeMA02139UAS DepartmentofMathematicalsciences TsinghuaUniversityBeijing100084P.R.China

We derive some quadratic recursion relations for some Hodge integrals by virtual localization and obtain many closed formulas. We apply our formulas to the local geometry of toric Fano surfaces in a Calabi-Yau threefo... 详细信息

关键词： Localization Hodge integrals BPs numbers

New solution bounds of the continuous algebraic Riccati equation and their applications in redundant control input systems

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science China(Information sciences) 2019年第10期62卷 69-85页

作者： jianzhou LIU Li WANG school of Mathematics and Computational science Xiangtan University school of Mathematics and Computational science Hunan University of Science and Technology

Redundant control inputs have wide applications in engineering, and have significant effects in quadratic performance optimal control, Hcontrol, tracking control, and many uncertain systems. In this paper, using some properties related to the inequality of the special matrix and the transformation of the matrix equation, we present new bounds of the solution of the continuous algebraic Riccati equation. The new bounds are more precise than those proposed in some existing studies on this topic. subsequently, two lower bounds are presented for the optimal controller gain of the system(1), and a new upper bound is obtained for the optimal controller gain of the extended control system(3). several examples are provided to demonstrate that our bounds of the optimal controller gain are superior to some previous results. subsequently, we provide the applications of the new bounds in relevant redundant control problems and obtain good results. Finally,the corresponding numerical examples are provided to illustrate the effectiveness of our results and to compare them with the existing results.

关键词： Riccati equation bounds redundant control input controller gain inequality

Revisiting cerebral endothelial cells in Alzheimer’s disease

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Neural Regeneration Research 2025年第10期20卷 2911-2912页

作者： Amira s.Hanafy Department of Neurosurgery University Hospital BonnBonnGermany

Alzheimer’s disease(AD)is the most common neurodegenerative disorder characterized by slow and progressive decline of cognitive and memory *** only approximately 5%of the cases,AD is familial,as often predisposed by genetic mutations(Hoogmartens et al.,2021),while sporadic AD accounts for approximately 95%of the *** amyloid cascade hypothesis is one of the fundamental hypotheses put out to explain AD pathogenesis as dysregulated homeostasis of amyloid-β(Aβ)peptides that leads to the accumulation of Aβplaques in the parenchyma,an anatomical hallmark of AD.

关键词： Alzheimer Aβ cerebral

A systematic review of progenitor survival and maturation in Parkinsonian models

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Neural Regeneration Research 2025年第11期20卷 3172-3178页

作者： Giulia Comini Eilís Dowd Pharmacology&Therapeutics and Galway Neuroscience Center University of GalwayGalwayIreland

stem cell-based brain repair is a promising emergent therapy for Parkinson's disease based on years of foundational research using human fetal donors as a cell *** current therapeutic options for patients,this approach has the potential to provide longterm stem cell–derived reconstruction and restoration of the dopaminergic input to denervated regions of the brain allowing for restoration of certain functions to *** ultimate clinical success of stem cell–derived brain repair will depend on both the safety and efficacy of the approach and the latter is dependent on the ability of the transplanted cells to survive and differentiate into functional dopaminergic neurons in the Parkinsonian *** the pre-clinical literature suggests that there is considerable variability in survival and differentiation between studies,the aim of this systematic review was to assess these parameters in human stem cell-derived dopaminergic progenitor transplant studies in animal models of Parkinson's disease.A defined systematic search of the PubMed database was completed to identify relevant studies published up to March *** screening,76 articles were included in the analysis from which 178 separate transplant studies were *** these,graft survival could be assessed in 52 studies and differentiation in 129 ***,we found that graft survival ranged froms transplanted,with a median of 51%of transplanted cells surviving in the brain;while dopaminergic differentiation of the cells ranged from 0% to 46% of cells transplanted with a median of 3%.This systematic review suggests that there is considerable scope for improvement in the differentiation of stem cell-derived dopaminergic progenitors to maximize the therapeutic potential of this approach for patients.

关键词： cell replacement therapy differentiation embryonic stem cells graft induced pluripotent stem cells Parkinson's disease survival transplant

Critical Property of the Geometric Phase in the Dicke Model with the Dipole-dipole Interactions

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Journal of Materials science & Technology 2008年第6期24卷 960-962页

作者： Yunfeng WU Ping ZHANG jianzhou ZHENG College of science Dalian Nationalities University Dalian 116600 China

We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field was derived with the time-dependent unitary transformation. It is shown that dipole-dipole interactions have a deep influence on scaled behavior of the geometric phase at the critical point.

关键词： Geometric phases Quantum phase transition Dipole-dipole interactions

Deciphering the mechanobiology of microglia in traumatic brain injury with advanced microsystems

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Neural Regeneration Research 2025年第8期20卷 2304-2306页

作者： Anthony Procès sylvain Gabriele Univ.Grenoble Alpes InsermU1216Grenoble Institut des NeurosciencesGrenobleFrance Mechanobiology&Biomaterials Group CIRMAPResearch Institute for BiosciencesUniversity of MonsMonsBelgium

Advanced microsystems in traumatic brain injury research:Traumatic brain injury(TBI)results from a mechanical insult to the brain,leading to neuronal and axonal damage and subsequently causing a secondary *** minutes ... 详细信息

关键词： traumatic injury damage

Emerging structures and dynamic mechanisms ofγ-secretase for Alzheimer’s disease

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Neural Regeneration Research 2025年第1期20卷 174-180页

作者： Yinglong Miao Michael s.Wolfe Computational Medicine Program and Department of Pharmacology University of North Carolina–Chapel HillChapel HillNCUSA Department of Medicinal Chemistry University of KansasLawrenceKSUSA

γ-secretase,called“the proteasome of the membrane,”is a membrane-embedded protease complex that cleaves 150+peptide substrates with central roles in biology and medicine,including amyloid precursor protein and the Notch family of cell-surface *** inγ-secretase and amyloid precursor protein lead to early-onset familial Alzheimer’s disease.γ-secretase has thus served as a critical drug target for treating familial Alzheimer’s disease and the more common late-onset Alzheimer’s disease as ***,critical gaps remain in understanding the mechanisms of processive proteolysis of substrates,the effects of familial Alzheimer’s disease mutations,and allosteric modulation of substrate cleavage byγ-*** this review,we focus on recent studies of structural dynamic mechanisms ofγ-*** mechanisms,including the“Fit-stay-Trim,”“sliding-Unwinding,”and“Tilting-Unwinding,”have been proposed for substrate proteolysis of amyloid precursor protein byγ-secretase based on all-atom molecular dynamics *** an incorrect registry of the Notch1 substrate was identified in the cryo-electron microscopy structure of Notch1-boundγ-secretase,molecular dynamics simulations on a resolved model of Notch1-boundγ-secretase that was reconstructed using the amyloid precursor protein-boundγ-secretase as a template successfully capturedγ-secretase activation for proper cleavages of both wildtype and mutant Notch,being consistent with biochemical experimental *** approach could be potentially applied to decipher the processing mechanisms of various substrates byγ-*** addition,controversy over the effects of familial Alzheimer’s disease mutations,particularly the issue of whether they stabilize or destabilizeγ-secretase-substrate complexes,is ***,an outlook is provided for future studies ofγ-secretase,including pathways of substrate binding and product release,effects of modulators on familial Alzheimer’s disease mutations

关键词： Alzheimer’s disease amyloid precursor protein cryo-EM structures drug design intramembrane proteolysis molecular dynamics Notch

The Disc Theorem for the schur Complement of Two Class submatrices with γ-Diagonally Dominant Properties

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Numerical Mathematics(Theory,Methods and Applications) 2017年第1期10卷 84-97页

作者： Guangqi Li jianzhou Liu Juan Zhang Department of Mathematics and Computational science Xiangtan UniversityXiangtanHunan 411105China College of science National University of Defense TechnologyChangshaHunan 410073China

The distribution for eigenvalues of schur complement of matrices plays an important role in many mathematical *** this paper,we firstly present some criteria for *** as application,for two class matrices whose sub-matrices areγ-diagonally dominant and productγ-diagonally dominant,we show that the eigenvalues of the schur complement are located in the Gersgorin discs and the Ostrowski discs of the original matrices under certain conditions.

关键词： schur complement Gersgorin Theorem Ostrowski Theorem H-matrix