Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG（H）={α ∈ RG｜αh = hα for all h ∈ H）, which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG（H...Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG（H）={α ∈ RG｜αh = hα for all h ∈ H）, which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG（H） is just the central subalgebra Z（RG） of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG（H）. Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG（H） to CRG（H）, that is, 7（CRG（H）） = CRG（H）.展开更多
In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.
Let U = Tri（fit, M, B） be a triangular ring, where A and B are unital rings, and M is a faithful （A, B）-bimodule. It is shown that an additive map φ on U is centralized at zero point （i.e., ,φ（A）B = A,φ（B）...Let U = Tri（fit, M, B） be a triangular ring, where A and B are unital rings, and M is a faithful （A, B）-bimodule. It is shown that an additive map φ on U is centralized at zero point （i.e., ,φ（A）B = A,φ（B） = 0 whenever AB = 0） if and only if it is a centralizer. Let 5 ： U →U be an additive map. It is also shown that the following four conditions are equivalent： （1） 5 is specially generalized derivable at zero point, i.e., 5（AB） = δ（A）B ＋ AS（B） - Aδ（I）B whenever AB = 0; （2） 5 is generalized derivable at zero point, i.e., there exist additive maps τ1 and τ2 on U derivable at zero point such that δ（AB） = δ（A）B ＋ Aτ1（B） = τ2（A）B ＋ Aδ（B） whenever AB = 0; （3） δ is a special generalized derivation; （4） δ is a generalized derivation. These results are then applied to nest algebras of Banach space展开更多
Traumatic brain injury can be categorized into primary and secondary injuries.Secondary injuries are the main cause of disability following traumatic brain injury,which involves a complex multicellular cascade.Microgl...Traumatic brain injury can be categorized into primary and secondary injuries.Secondary injuries are the main cause of disability following traumatic brain injury,which involves a complex multicellular cascade.Microglia play an important role in secondary injury and can be activated in response to traumatic brain injury.In this article,we review the origin and classification of microglia as well as the dynamic changes of microglia in traumatic brain injury.We also clarify the microglial polarization pathways and the therapeutic drugs targeting activated microglia.We found that regulating the signaling pathways involved in pro-inflammatory and anti-inflammatory microglia,such as the Toll-like receptor 4/nuclear factor-kappa B,mitogen-activated protein kinase,Janus kinase/signal transducer and activator of transcription,phosphoinositide 3-kinase/protein kinase B,Notch,and high mobility group box 1 pathways,can alleviate the inflammatory response triggered by microglia in traumatic brain injury,thereby exerting neuroprotective effects.We also reviewed the strategies developed on the basis of these pathways,such as drug and cell replacement therapies.Drugs that modulate inflammatory factors,such as rosuvastatin,have been shown to promote the polarization of antiinflammatory microglia and reduce the inflammatory response caused by traumatic brain injury.Mesenchymal stem cells possess anti-inflammatory properties,and clinical studies have confirmed their significant efficacy and safety in patients with traumatic brain injury.Additionally,advancements in mesenchymal stem cell-delivery methods—such as combinations of novel biomaterials,genetic engineering,and mesenchymal stem cell exosome therapy—have greatly enhanced the efficiency and therapeutic effects of mesenchymal stem cells in animal models.However,numerous challenges in the application of drug and mesenchymal stem cell treatment strategies remain to be addressed.In the future,new technologies,such as single-cell RNA sequencing and transcriptome analysis,can facilitate further experimental studies.Moreover,research involving non-human primates can help translate these treatment strategies to clinical practice.展开更多
Let H be a Hilbert space with dimH ≥2 and Z ∈ B（H） be an arbitrary but fixed operator. In this paper we show that an additive map （I） ： B（H）→ B（H） satisfies Ф（AB） = Ф（A）B = AФ（B） for any A, B ∈ ...Let H be a Hilbert space with dimH ≥2 and Z ∈ B（H） be an arbitrary but fixed operator. In this paper we show that an additive map （I） ： B（H）→ B（H） satisfies Ф（AB） = Ф（A）B = AФ（B） for any A, B ∈ B（H） with AB = Z if and only if Ф（AB） = Ф（A）B = AФ（B）, A, B ∈ B（H）, that is, （I） is a centralizer. Similar results are obtained for Hilbert space nest algebras. In addition, we show that Ф（A2） = AФ（A） = Ф（A）A for any A ∈ B（H） with A2 = 0 if and only if Ф（A） = AФ（I） = Ф（I）A, A ∈ B（H）, and generalize main results in Linear Algebra and its Application, 450, 243-249 （2014） to infinite dimensional case. New equivalent characterization of centralizers on B（H） is obtained.展开更多
Short-chain fatty acids,metabolites produced by the fermentation of dietary fiber by gut microbiota,have garnered significant attention due to their correlation with neurodegenerative diseases,particularly Parkinson’...Short-chain fatty acids,metabolites produced by the fermentation of dietary fiber by gut microbiota,have garnered significant attention due to their correlation with neurodegenerative diseases,particularly Parkinson’s disease.In this review,we summarize the changes in short-chain fatty acid levels and the abundance of short-chain fatty acid-producing bacteria in various samples from patients with Parkinson’s disease,highlighting the critical role of gut homeostasis imbalance in the pathogenesis and progression of the disease.Focusing on the nervous system,we discuss the molecular mechanisms by which short-chain fatty acids influence the homeostasis of both the enteric nervous system and the central nervous system.We identify key processes,including the activation of G protein-coupled receptors and the inhibition of histone deacetylases by short-chain fatty acids.Importantly,structural or functional disruptions in the enteric nervous system mediated by these fatty acids may lead to abnormalα-synuclein expression and gastrointestinal dysmotility,which could serve as an initiating event in Parkinson’s disease.Furthermore,we propose that short-chain fatty acids help establish communication between the enteric nervous system and the central nervous system via the vagal nerve,immune circulation,and endocrine signaling.This communication may shed light on their potential role in the transmission ofα-synuclein from the gut to the brain.Finally,we elucidate novel treatment strategies for Parkinson’s disease that target short-chain fatty acids and examine the challenges associated with translating short-chain fatty acid-based therapies into clinical practice.In conclusion,this review emphasizes the pivotal role of short-chain fatty acids in regulating gut-brain axis integrity and their significance in the pathogenesis of Parkinson’s disease from the perspective of the nervous system.Moreover,it highlights the potential value of short-chain fatty acids in early intervention for Parkinson’s disease.Future research into the molecular mechanisms of short-chain fatty acids and their synergistic interactions with other gut metabolites is likely to advance the clinical translation of innovative short-chain fatty acid-based therapies for Parkinson’s disease.展开更多
The k-characters are class functions on subsets of G^k called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of CG^k, which we call the k-S-ring of G、and we think of these rings...The k-characters are class functions on subsets of G^k called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of CG^k, which we call the k-S-ring of G、and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes", determine G.展开更多
The concept of an I-matrix in the full 2 × 2 matrix ring M2 （R/I）, where R is an arbitrary UFD and I is a nonzero ideal in R, is introduced. We obtain a concrete description of the centralizer of an/-matrix B i...The concept of an I-matrix in the full 2 × 2 matrix ring M2 （R/I）, where R is an arbitrary UFD and I is a nonzero ideal in R, is introduced. We obtain a concrete description of the centralizer of an/-matrix B in M_2（R/I） as the sum of two subrings ,S_1 and ,S_2 of M_2（R/I）, where S_1 is the image （under the natural epimorphism from M_2（R） to M_2（R/I）） of the centralizer in M_2（R） of a pre-image of B, and the entries in S_2 are intersections of certain annihilators of elements arising from the entries of B. It turns out that if R is a PID, then every matrix in M_2（R/I） is an/-matrix. However, this is not the case if R is a UFD in general. Moreover, for every factor ring R/I with zero divisors and every n ≥ 3, there is a matrix for which the mentioned concrete description is not valid.展开更多
In this paper,we introduce a new concept of expansiveness,similar to the separating property.Specifically,we consider a compact Riemannian manifold M without boundary and a C^(1)vector field X on M,which generates a f...In this paper,we introduce a new concept of expansiveness,similar to the separating property.Specifically,we consider a compact Riemannian manifold M without boundary and a C^(1)vector field X on M,which generates a flowφ_(t)on M.We say that X is rescaling separating on a compact invariant setΛof X if there is a constantδ>0 such that,for any x,y∈Λ,if d(φ_(t)(x),φ_(t)(y))≤δ∥X(φ_(t)(x))∥for all t∈R,then y∈Orb(x).We prove that if X is rescaling separating onΛand every singularity of X inΛis hyperbolic,then any C^(1)vector field Y,whose flow commutes withφ_(t)onΛ,must be collinear to X onΛ.As applications of this result,we show that the centralizer of a rescaling separating C^(1)vector field without nonhyperbolic singularity is quasi-trivial.We also proved that there is an open and dense set u⊂χ^(1)(M)such that for any star vector fieldχ∈u,the centralizer of X is collinear to X on the chain recurrent set of X.展开更多
In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnect...In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.展开更多
Regenerative capacity of the central nervous system(CNS)is unevenly distributed among vertebrates.While most mammalian species including humans elicit limited repair following CNS injury or disease,highly regenerative...Regenerative capacity of the central nervous system(CNS)is unevenly distributed among vertebrates.While most mammalian species including humans elicit limited repair following CNS injury or disease,highly regenerative vertebrates including urodele amphibians and teleost fish spontaneously reverse CNS damage.Teletost zebrafish(danio rerio)are tropical freshwater fish that proved to be an excellent vertebrate model of successful CNS regeneration.Differential neuronal,glial,and immune injury responses underlie disparate injury outcomes between highly regenerative zebrafish and poorly regenerative mammals.This article describes complications associated with neuronal repair following spinal cord injury(SCI)in poorly regenerative mammals and highlights intersecting modes of plasticity and regeneration in highly regenerative zebrafish(Figures 1 and 2).Comparative approaches evaluating immunoglial SCI responses were recently reviewed elsewhere(Reyes and Mokalled,2024).展开更多
In this paper, we investigate the Lie algebra L(A,α,δ) of type L and obtain the respective sufficient conditions for L(A,α,δ δ to be semisimple, and for Z(ω) = Fω as well, where 0 ≠ ω ? L(A, α, δ, δ) and Z...In this paper, we investigate the Lie algebra L(A,α,δ) of type L and obtain the respective sufficient conditions for L(A,α,δ δ to be semisimple, and for Z(ω) = Fω as well, where 0 ≠ ω ? L(A, α, δ, δ) and Z(ω) is the centralizer of ω.展开更多
The mature central nervous system(CNS,composed of the brain,spinal cord,olfactory and optic nerves)is unable to regenerate spontaneously after an insult,both in the cases of neurodegenerative diseases(for example Alzh...The mature central nervous system(CNS,composed of the brain,spinal cord,olfactory and optic nerves)is unable to regenerate spontaneously after an insult,both in the cases of neurodegenerative diseases(for example Alzheimer's or Parkinson's disease)or traumatic injuries(such as spinal cord lesions).In the last 20 years,the field has made significant progress in unlocking axon regrowth.展开更多
Central nervous system(CNS) axons fail to regenerate following brain or spinal cord injury(SCI),which typically leads to permanent neurological deficits.Peripheral nervous system axons,howeve r,can regenerate followin...Central nervous system(CNS) axons fail to regenerate following brain or spinal cord injury(SCI),which typically leads to permanent neurological deficits.Peripheral nervous system axons,howeve r,can regenerate following injury.Understanding the mechanisms that underlie this difference is key to developing treatments for CNS neurological diseases and injuries characterized by axonal damage.To initiate repair after peripheral nerve injury,dorsal root ganglion(DRG) neurons mobilize a pro-regenerative gene expression program,which facilitates axon outgrowth.展开更多
Synapses are key structures involved in transmitting information in the nervous system,and their functions rely on the regulation of various lipids.Lipids play important roles in synapse formation,neurotransmitter rel...Synapses are key structures involved in transmitting information in the nervous system,and their functions rely on the regulation of various lipids.Lipids play important roles in synapse formation,neurotransmitter release,and signal transmission,and dysregulation of lipid metabolism is closely associated with various neurodegenerative diseases.The complex roles of lipids in synaptic function and neurological diseases have recently garnered increasing attention,but their specific mechanisms remain to be fully understood.This review aims to explore how lipids regulate synaptic activity in the central nervous system,focusing on their roles in synapse formation,neurotransmitter release,and signal transmission.Additionally,it discusses the mechanisms by which glial cells modulate synaptic function through lipid regulation.This review shows that within the central nervous system,lipids are essential components of the cell membrane bilayer,playing critical roles in synaptic structure and function.They regulate presynaptic vesicular trafficking,postsynaptic signaling pathways,and glial-neuronal interactions.Cholesterol maintains membrane fluidity and promotes the formation of lipid rafts.Glycerophospholipids contribute to the structural integrity of synaptic membranes and are involved in the release of synaptic vesicles.Sphingolipids interact with synaptic receptors through various mechanisms to regulate their activity and are also involved in cellular processes such as inflammation and apoptosis.Fatty acids are vital for energy metabolism and the synthesis of signaling molecules.Abnormalities in lipid metabolism may lead to impairments in synaptic function,affecting information transmission between neurons and the overall health of the nervous system.Therapeutic strategies targeting lipid metabolism,particularly through cholesterol modulation,show promise for treating these conditions.In neurodegenerative diseases such as Alzheimer’s disease,Parkinson disease,and amyotrophic lateral sclerosis,dysregulation of lipid metabolism is closely linked to synaptic dysfunction.Therefore,lipids are not only key molecules in neural regeneration and synaptic repair but may also contribute to neurodegenerative pathology when metabolic dysregulation occurs.Further research is needed to elucidate the specific mechanisms linking lipid metabolism to synaptic dysfunction and to develop targeted lipid therapies for neurological diseases.展开更多
The mechanistic target of rapamycin(m TOR) is a serine/threonine kinase that plays a pivotal role in cellular growth, proliferation, survival, and metabolism. In the central nervous system(CNS), the mTOR pathway regul...The mechanistic target of rapamycin(m TOR) is a serine/threonine kinase that plays a pivotal role in cellular growth, proliferation, survival, and metabolism. In the central nervous system(CNS), the mTOR pathway regulates diverse aspects of neural development and function. Genetic mutations within the m TOR pathway lead to severe neurodevelopmental disorders, collectively known as “mTORopathies”(Crino, 2020). Dysfunctions of m TOR, including both its hyperactivation and hypoactivation, have also been implicated in a wide spectrum of other neurodevelopmental and neurodegenerative conditions, highlighting its importance in CNS health.展开更多
Microglia are the macrophages that populate the brain parenchyma.Research in the past decades has identified them as both essential guardians of the brain and significant contributors to various neurological diseases....Microglia are the macrophages that populate the brain parenchyma.Research in the past decades has identified them as both essential guardians of the brain and significant contributors to various neurological diseases.A highly versatile cell type,microglia have been shown to fulfill a multitude of critical roles in the central nervous system,including facilitating neurogenesis and myelination,pruning synapses,removing debris and waste,modulating neuronal activity,supporting the blood-brain barrier,repairing tissue damage,and surveilling against microbial invasions under physiological conditions(Prinz et al.,2021;Paolicelli et al.,2022).展开更多
Microglia are the resident macrophages of the central nervous system.They act as the first line of defense against pathogens and play essential roles in neuroinflammation and tissue repair after brain insult or in neu...Microglia are the resident macrophages of the central nervous system.They act as the first line of defense against pathogens and play essential roles in neuroinflammation and tissue repair after brain insult or in neurodegenerative and demyelinating diseases(Borst et al.,2021).Together with infiltrating monocyte-derived macrophages,microglia also play a critical role for brain tumor development,since immunosuppressive interactions between tumor cells and tumor-associated microglia and macrophages(TAM)are linked to malignant progression.This mechanism is of particular relevance in glioblastoma(GB),the deadliest form of brain cancer with a median overall survival of less than 15 months(Khan et al.,2023).Therefore,targeting microglia and macrophage activation is a promising strategy for therapeutic interference in brain disease.展开更多
AIM:To evaluate the therapeutic effects of ranibizumab on optic disc and macular microvascular perfusion in central retinal vein occlusion(CRVO)with macular edema(ME).METHODS:Optical coherence tomography angiology(OCT...AIM:To evaluate the therapeutic effects of ranibizumab on optic disc and macular microvascular perfusion in central retinal vein occlusion(CRVO)with macular edema(ME).METHODS:Optical coherence tomography angiology(OCTA)parameters,including optic disc vessel density(VD;including whole-disc VD,intra-disc VD,and peripapillary VD),superficial/deep capillary plexus(SCP/DCP)VD,and central macular thickness(CMT)were analyzed.Additional assessments included best-corrected visual acuity(BCVA)via Early Treatment Diabetic Retinopathy Study(ETDRS)chart and hemorheological profiling.CRVO patients received monthly intravitreal ranibizumab injections for three consecutive months.Pre-and post-treatment parameters were statistically compared.RESULTS:The study comprised 60 CRVO-ME patients(28 males;32 females),aged 50-78y(mean 63.3±7.6y)and 60 age-/sex-matched healthy controls.As compared with participants exhibiting normal funduscopic findings,CRVO patients demonstrated significantly elevated levels of low-shear-rate whole blood viscosity(LSR-WBV),high-shearrate whole blood viscosity(HSR-WBV),and aggregation index(AI,all P<0.05).In CRVO-affected eyes,vertical cupto-disc(C/D)ratio and optic cup volume were significantly smaller,whereas retinal nerve fiber layer(RNFL)thickness was significantly greater,compared to both unaffected contralateral eyes and normal control eyes(all P<0.05).Following treatment,VD of the entire optic disc(P<0.05),intra-disc VD(P<0.05),and peripapillary VD(P<0.05)all increased significantly relative to baseline.CMT decreased significantly(P<0.05),whereas macular SCP-VD and macular DCP-VD showed non-significant slight reductions(P>0.05).At baseline,BCVA of CRVO eyes correlated with whole-disc VD(r=-0.276,P=0.033),intra-disc VD(r=-0.342,P=0.009),and peripapillary VD(r=-0.335,P=0.007),with intra-disc VD demonstrating the strongest association.Besides,BCVA improvement,after the treatment,correlated positively with whole-disc VD(r=0.342,P=0.008)and intradisc VD(r=0.396,P=0.002).CONCLUSION:Optic disc blood perfusion is more closely associated with visual acuity than macular perfusion,suggesting intra-disc VD may serve as a potential biomarker for monitoring visual acuity changes in CRVO.Multiple ranibizumab injections significantly improve optic disc perfusion but may have exerted detrimental effects on the macula.CRVO patients shows higher hemorheological parameters than those with normal fundi.Reduced vertical C/D ratio and optic cup volume may be linked to CRVO incidence,potentially acting as susceptibility factors.展开更多
基金The NSF(11071155) of Chinathe NSF(2008A03) of Shandong Province
文摘Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG（H）={α ∈ RG｜αh = hα for all h ∈ H）, which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG（H） is just the central subalgebra Z（RG） of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG（H）. Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG（H） to CRG（H）, that is, 7（CRG（H）） = CRG（H）.
基金supported by the National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.
基金supported by National Natural Science Foundation of China (Grant No. 11101250)supported by National Natural Science Foundation of China (Grant No. 11171249)Youth Foundation of Shanxi Province (Grant No. 2012021004)
文摘Let U = Tri（fit, M, B） be a triangular ring, where A and B are unital rings, and M is a faithful （A, B）-bimodule. It is shown that an additive map φ on U is centralized at zero point （i.e., ,φ（A）B = A,φ（B） = 0 whenever AB = 0） if and only if it is a centralizer. Let 5 ： U →U be an additive map. It is also shown that the following four conditions are equivalent： （1） 5 is specially generalized derivable at zero point, i.e., 5（AB） = δ（A）B ＋ AS（B） - Aδ（I）B whenever AB = 0; （2） 5 is generalized derivable at zero point, i.e., there exist additive maps τ1 and τ2 on U derivable at zero point such that δ（AB） = δ（A）B ＋ Aτ1（B） = τ2（A）B ＋ Aδ（B） whenever AB = 0; （3） δ is a special generalized derivation; （4） δ is a generalized derivation. These results are then applied to nest algebras of Banach space
基金supported by the Natural Science Foundation of Yunnan Province,No.202401AS070086(to ZW)the National Key Research and Development Program of China,No.2018YFA0801403(to ZW)+1 种基金Yunnan Science and Technology Talent and Platform Plan,No.202105AC160041(to ZW)the Natural Science Foundation of China,No.31960120(to ZW)。
文摘Traumatic brain injury can be categorized into primary and secondary injuries.Secondary injuries are the main cause of disability following traumatic brain injury,which involves a complex multicellular cascade.Microglia play an important role in secondary injury and can be activated in response to traumatic brain injury.In this article,we review the origin and classification of microglia as well as the dynamic changes of microglia in traumatic brain injury.We also clarify the microglial polarization pathways and the therapeutic drugs targeting activated microglia.We found that regulating the signaling pathways involved in pro-inflammatory and anti-inflammatory microglia,such as the Toll-like receptor 4/nuclear factor-kappa B,mitogen-activated protein kinase,Janus kinase/signal transducer and activator of transcription,phosphoinositide 3-kinase/protein kinase B,Notch,and high mobility group box 1 pathways,can alleviate the inflammatory response triggered by microglia in traumatic brain injury,thereby exerting neuroprotective effects.We also reviewed the strategies developed on the basis of these pathways,such as drug and cell replacement therapies.Drugs that modulate inflammatory factors,such as rosuvastatin,have been shown to promote the polarization of antiinflammatory microglia and reduce the inflammatory response caused by traumatic brain injury.Mesenchymal stem cells possess anti-inflammatory properties,and clinical studies have confirmed their significant efficacy and safety in patients with traumatic brain injury.Additionally,advancements in mesenchymal stem cell-delivery methods—such as combinations of novel biomaterials,genetic engineering,and mesenchymal stem cell exosome therapy—have greatly enhanced the efficiency and therapeutic effects of mesenchymal stem cells in animal models.However,numerous challenges in the application of drug and mesenchymal stem cell treatment strategies remain to be addressed.In the future,new technologies,such as single-cell RNA sequencing and transcriptome analysis,can facilitate further experimental studies.Moreover,research involving non-human primates can help translate these treatment strategies to clinical practice.
基金Supported by National Natural Foundation of China(Grant No.11001194)Provincial International Cooperation Project of Shanxi(Grant No.2014081027–2)
文摘Let H be a Hilbert space with dimH ≥2 and Z ∈ B（H） be an arbitrary but fixed operator. In this paper we show that an additive map （I） ： B（H）→ B（H） satisfies Ф（AB） = Ф（A）B = AФ（B） for any A, B ∈ B（H） with AB = Z if and only if Ф（AB） = Ф（A）B = AФ（B）, A, B ∈ B（H）, that is, （I） is a centralizer. Similar results are obtained for Hilbert space nest algebras. In addition, we show that Ф（A2） = AФ（A） = Ф（A）A for any A ∈ B（H） with A2 = 0 if and only if Ф（A） = AФ（I） = Ф（I）A, A ∈ B（H）, and generalize main results in Linear Algebra and its Application, 450, 243-249 （2014） to infinite dimensional case. New equivalent characterization of centralizers on B（H） is obtained.
基金supported by the National Key R&D Program of China,No.2021YFC2501200(to PC).
文摘Short-chain fatty acids,metabolites produced by the fermentation of dietary fiber by gut microbiota,have garnered significant attention due to their correlation with neurodegenerative diseases,particularly Parkinson’s disease.In this review,we summarize the changes in short-chain fatty acid levels and the abundance of short-chain fatty acid-producing bacteria in various samples from patients with Parkinson’s disease,highlighting the critical role of gut homeostasis imbalance in the pathogenesis and progression of the disease.Focusing on the nervous system,we discuss the molecular mechanisms by which short-chain fatty acids influence the homeostasis of both the enteric nervous system and the central nervous system.We identify key processes,including the activation of G protein-coupled receptors and the inhibition of histone deacetylases by short-chain fatty acids.Importantly,structural or functional disruptions in the enteric nervous system mediated by these fatty acids may lead to abnormalα-synuclein expression and gastrointestinal dysmotility,which could serve as an initiating event in Parkinson’s disease.Furthermore,we propose that short-chain fatty acids help establish communication between the enteric nervous system and the central nervous system via the vagal nerve,immune circulation,and endocrine signaling.This communication may shed light on their potential role in the transmission ofα-synuclein from the gut to the brain.Finally,we elucidate novel treatment strategies for Parkinson’s disease that target short-chain fatty acids and examine the challenges associated with translating short-chain fatty acid-based therapies into clinical practice.In conclusion,this review emphasizes the pivotal role of short-chain fatty acids in regulating gut-brain axis integrity and their significance in the pathogenesis of Parkinson’s disease from the perspective of the nervous system.Moreover,it highlights the potential value of short-chain fatty acids in early intervention for Parkinson’s disease.Future research into the molecular mechanisms of short-chain fatty acids and their synergistic interactions with other gut metabolites is likely to advance the clinical translation of innovative short-chain fatty acid-based therapies for Parkinson’s disease.
文摘The k-characters are class functions on subsets of G^k called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of CG^k, which we call the k-S-ring of G、and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes", determine G.
文摘The concept of an I-matrix in the full 2 × 2 matrix ring M2 （R/I）, where R is an arbitrary UFD and I is a nonzero ideal in R, is introduced. We obtain a concrete description of the centralizer of an/-matrix B in M_2（R/I） as the sum of two subrings ,S_1 and ,S_2 of M_2（R/I）, where S_1 is the image （under the natural epimorphism from M_2（R） to M_2（R/I）） of the centralizer in M_2（R） of a pre-image of B, and the entries in S_2 are intersections of certain annihilators of elements arising from the entries of B. It turns out that if R is a PID, then every matrix in M_2（R/I） is an/-matrix. However, this is not the case if R is a UFD in general. Moreover, for every factor ring R/I with zero divisors and every n ≥ 3, there is a matrix for which the mentioned concrete description is not valid.
基金Supported by National Key R&D Program of China(Grant No.2022YFA1005801)National Natural Science Foundation of China(Grant No.12071018)the Fundamental Research Funds for the Central Universities。
文摘In this paper,we introduce a new concept of expansiveness,similar to the separating property.Specifically,we consider a compact Riemannian manifold M without boundary and a C^(1)vector field X on M,which generates a flowφ_(t)on M.We say that X is rescaling separating on a compact invariant setΛof X if there is a constantδ>0 such that,for any x,y∈Λ,if d(φ_(t)(x),φ_(t)(y))≤δ∥X(φ_(t)(x))∥for all t∈R,then y∈Orb(x).We prove that if X is rescaling separating onΛand every singularity of X inΛis hyperbolic,then any C^(1)vector field Y,whose flow commutes withφ_(t)onΛ,must be collinear to X onΛ.As applications of this result,we show that the centralizer of a rescaling separating C^(1)vector field without nonhyperbolic singularity is quasi-trivial.We also proved that there is an open and dense set u⊂χ^(1)(M)such that for any star vector fieldχ∈u,the centralizer of X is collinear to X on the chain recurrent set of X.
文摘In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.
文摘Regenerative capacity of the central nervous system(CNS)is unevenly distributed among vertebrates.While most mammalian species including humans elicit limited repair following CNS injury or disease,highly regenerative vertebrates including urodele amphibians and teleost fish spontaneously reverse CNS damage.Teletost zebrafish(danio rerio)are tropical freshwater fish that proved to be an excellent vertebrate model of successful CNS regeneration.Differential neuronal,glial,and immune injury responses underlie disparate injury outcomes between highly regenerative zebrafish and poorly regenerative mammals.This article describes complications associated with neuronal repair following spinal cord injury(SCI)in poorly regenerative mammals and highlights intersecting modes of plasticity and regeneration in highly regenerative zebrafish(Figures 1 and 2).Comparative approaches evaluating immunoglial SCI responses were recently reviewed elsewhere(Reyes and Mokalled,2024).
基金This work was supported by the National Natural Science Foundation of China(Grant No.10271081)a Fund from Educational Department of Beijing(Grant No.2002KJ-100).
文摘In this paper, we investigate the Lie algebra L(A,α,δ) of type L and obtain the respective sufficient conditions for L(A,α,δ δ to be semisimple, and for Z(ω) = Fω as well, where 0 ≠ ω ? L(A, α, δ, δ) and Z(ω) is the centralizer of ω.
基金supported by ANR(ANR-21CE16-0008-01)ANR(ANR-21-CE16-0008-02 and ANR-23CE52-0007)+1 种基金UNADEV(A22018CS)(to HN)UNADEV(A22020CS)(to SB)。
文摘The mature central nervous system(CNS,composed of the brain,spinal cord,olfactory and optic nerves)is unable to regenerate spontaneously after an insult,both in the cases of neurodegenerative diseases(for example Alzheimer's or Parkinson's disease)or traumatic injuries(such as spinal cord lesions).In the last 20 years,the field has made significant progress in unlocking axon regrowth.
基金supported by the Canada Foundation for Innovation (Project#44220)the Natural Sciences and Engineering Research Council of Canada (RGPIN-2024-03986)+3 种基金the Michael Smith Foundation for Health Research BCthe financial support of Health Canada,through the Canada Brain Research Fund,an innovative partnership between the Government of Canada (through Health Canada),Brain Canada Foundationthe Azrieli Foundationsupported by a Canadian Institutes of Health Research (CIHR) Canada Graduate Scholarship–Master’s Award。
文摘Central nervous system(CNS) axons fail to regenerate following brain or spinal cord injury(SCI),which typically leads to permanent neurological deficits.Peripheral nervous system axons,howeve r,can regenerate following injury.Understanding the mechanisms that underlie this difference is key to developing treatments for CNS neurological diseases and injuries characterized by axonal damage.To initiate repair after peripheral nerve injury,dorsal root ganglion(DRG) neurons mobilize a pro-regenerative gene expression program,which facilitates axon outgrowth.
基金supported by the National Natural Science Foundation of China,No.82201568(to QQ)Capital’s Funds for Health Improvement and Research,No.2024-2-1031(to QQ)Beijing Nova Program,No.20240484566(to QQ).
文摘Synapses are key structures involved in transmitting information in the nervous system,and their functions rely on the regulation of various lipids.Lipids play important roles in synapse formation,neurotransmitter release,and signal transmission,and dysregulation of lipid metabolism is closely associated with various neurodegenerative diseases.The complex roles of lipids in synaptic function and neurological diseases have recently garnered increasing attention,but their specific mechanisms remain to be fully understood.This review aims to explore how lipids regulate synaptic activity in the central nervous system,focusing on their roles in synapse formation,neurotransmitter release,and signal transmission.Additionally,it discusses the mechanisms by which glial cells modulate synaptic function through lipid regulation.This review shows that within the central nervous system,lipids are essential components of the cell membrane bilayer,playing critical roles in synaptic structure and function.They regulate presynaptic vesicular trafficking,postsynaptic signaling pathways,and glial-neuronal interactions.Cholesterol maintains membrane fluidity and promotes the formation of lipid rafts.Glycerophospholipids contribute to the structural integrity of synaptic membranes and are involved in the release of synaptic vesicles.Sphingolipids interact with synaptic receptors through various mechanisms to regulate their activity and are also involved in cellular processes such as inflammation and apoptosis.Fatty acids are vital for energy metabolism and the synthesis of signaling molecules.Abnormalities in lipid metabolism may lead to impairments in synaptic function,affecting information transmission between neurons and the overall health of the nervous system.Therapeutic strategies targeting lipid metabolism,particularly through cholesterol modulation,show promise for treating these conditions.In neurodegenerative diseases such as Alzheimer’s disease,Parkinson disease,and amyotrophic lateral sclerosis,dysregulation of lipid metabolism is closely linked to synaptic dysfunction.Therefore,lipids are not only key molecules in neural regeneration and synaptic repair but may also contribute to neurodegenerative pathology when metabolic dysregulation occurs.Further research is needed to elucidate the specific mechanisms linking lipid metabolism to synaptic dysfunction and to develop targeted lipid therapies for neurological diseases.
基金supported by grants from Simons Foundation (SFARI 479754),CIHR (PJT-180565)the Scottish Rite Charitable Foundation of Canada (to YL)funding from the Canada Research Chairs program。
文摘The mechanistic target of rapamycin(m TOR) is a serine/threonine kinase that plays a pivotal role in cellular growth, proliferation, survival, and metabolism. In the central nervous system(CNS), the mTOR pathway regulates diverse aspects of neural development and function. Genetic mutations within the m TOR pathway lead to severe neurodevelopmental disorders, collectively known as “mTORopathies”(Crino, 2020). Dysfunctions of m TOR, including both its hyperactivation and hypoactivation, have also been implicated in a wide spectrum of other neurodevelopmental and neurodegenerative conditions, highlighting its importance in CNS health.
基金funded by NIH grants HL154720-03S1, AG057587, AG074283, DK122708-03S1, BrightFocus ADR A20183775Brown Foundation 2020 Healthy Aging Initiative (to WC)
文摘Microglia are the macrophages that populate the brain parenchyma.Research in the past decades has identified them as both essential guardians of the brain and significant contributors to various neurological diseases.A highly versatile cell type,microglia have been shown to fulfill a multitude of critical roles in the central nervous system,including facilitating neurogenesis and myelination,pruning synapses,removing debris and waste,modulating neuronal activity,supporting the blood-brain barrier,repairing tissue damage,and surveilling against microbial invasions under physiological conditions(Prinz et al.,2021;Paolicelli et al.,2022).
基金Deutsche Forschungsgemeinschaft(DFG,German Research Foundation),project numbers 324633948 and 409784463(DFG grants Hi 678/9-3 and Hi 678/10-2,FOR2953)to HHBundesministerium für Bildung und Forschung-BMBF,project number 16LW0463K to HT.
文摘Microglia are the resident macrophages of the central nervous system.They act as the first line of defense against pathogens and play essential roles in neuroinflammation and tissue repair after brain insult or in neurodegenerative and demyelinating diseases(Borst et al.,2021).Together with infiltrating monocyte-derived macrophages,microglia also play a critical role for brain tumor development,since immunosuppressive interactions between tumor cells and tumor-associated microglia and macrophages(TAM)are linked to malignant progression.This mechanism is of particular relevance in glioblastoma(GB),the deadliest form of brain cancer with a median overall survival of less than 15 months(Khan et al.,2023).Therefore,targeting microglia and macrophage activation is a promising strategy for therapeutic interference in brain disease.
基金Central High-Level Traditional Chinese Medicine Hospital Project of Eye Hospital China Academy of Chinese Medical Science(No.GSP5-83,No.GSP4-02No.GSP5-06)+1 种基金Supported by National Natural Science Foundation of China(General ProgramNo.82474582).
文摘AIM:To evaluate the therapeutic effects of ranibizumab on optic disc and macular microvascular perfusion in central retinal vein occlusion(CRVO)with macular edema(ME).METHODS:Optical coherence tomography angiology(OCTA)parameters,including optic disc vessel density(VD;including whole-disc VD,intra-disc VD,and peripapillary VD),superficial/deep capillary plexus(SCP/DCP)VD,and central macular thickness(CMT)were analyzed.Additional assessments included best-corrected visual acuity(BCVA)via Early Treatment Diabetic Retinopathy Study(ETDRS)chart and hemorheological profiling.CRVO patients received monthly intravitreal ranibizumab injections for three consecutive months.Pre-and post-treatment parameters were statistically compared.RESULTS:The study comprised 60 CRVO-ME patients(28 males;32 females),aged 50-78y(mean 63.3±7.6y)and 60 age-/sex-matched healthy controls.As compared with participants exhibiting normal funduscopic findings,CRVO patients demonstrated significantly elevated levels of low-shear-rate whole blood viscosity(LSR-WBV),high-shearrate whole blood viscosity(HSR-WBV),and aggregation index(AI,all P<0.05).In CRVO-affected eyes,vertical cupto-disc(C/D)ratio and optic cup volume were significantly smaller,whereas retinal nerve fiber layer(RNFL)thickness was significantly greater,compared to both unaffected contralateral eyes and normal control eyes(all P<0.05).Following treatment,VD of the entire optic disc(P<0.05),intra-disc VD(P<0.05),and peripapillary VD(P<0.05)all increased significantly relative to baseline.CMT decreased significantly(P<0.05),whereas macular SCP-VD and macular DCP-VD showed non-significant slight reductions(P>0.05).At baseline,BCVA of CRVO eyes correlated with whole-disc VD(r=-0.276,P=0.033),intra-disc VD(r=-0.342,P=0.009),and peripapillary VD(r=-0.335,P=0.007),with intra-disc VD demonstrating the strongest association.Besides,BCVA improvement,after the treatment,correlated positively with whole-disc VD(r=0.342,P=0.008)and intradisc VD(r=0.396,P=0.002).CONCLUSION:Optic disc blood perfusion is more closely associated with visual acuity than macular perfusion,suggesting intra-disc VD may serve as a potential biomarker for monitoring visual acuity changes in CRVO.Multiple ranibizumab injections significantly improve optic disc perfusion but may have exerted detrimental effects on the macula.CRVO patients shows higher hemorheological parameters than those with normal fundi.Reduced vertical C/D ratio and optic cup volume may be linked to CRVO incidence,potentially acting as susceptibility factors.
