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
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
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
Freezing of gait is a significant and debilitating motor symptom often observed in individuals with Parkinson's disease.Resting-state functional magnetic resonance imaging,along with its multi-level feature indice...Freezing of gait is a significant and debilitating motor symptom often observed in individuals with Parkinson's disease.Resting-state functional magnetic resonance imaging,along with its multi-level feature indices,has provided a fresh perspective and valuable insight into the study of freezing of gait in Parkinson's disease.It has been revealed that Parkinson's disease is accompanied by widespread irregularities in inherent brain network activity.However,the effective integration of the multi-level indices of resting-state functional magnetic resonance imaging into clinical settings for the diagnosis of freezing of gait in Parkinson's disease remains a challenge.Although previous studies have demonstrated that radiomics can extract optimal features as biomarkers to identify or predict diseases,a knowledge gap still exists in the field of freezing of gait in Parkinson's disease.This cross-sectional study aimed to evaluate the ability of radiomics features based on multi-level indices of resting-state functional magnetic resonance imaging,along with clinical features,to distinguish between Parkinson's disease patients with and without freezing of gait.We recruited 28 patients with Parkinson's disease who had freezing of gait(15 men and 13 women,average age 63 years)and 30 patients with Parkinson's disease who had no freezing of gait(16 men and 14 women,average age 64 years).Magnetic resonance imaging scans were obtained using a 3.0T scanner to extract the mean amplitude of low-frequency fluctuations,mean regional homogeneity,and degree centrality.Neurological and clinical characteristics were also evaluated.We used the least absolute shrinkage and selection operator algorithm to extract features and established feedforward neural network models based solely on resting-state functional magnetic resonance imaging indicators.We then performed predictive analysis of three distinct groups based on resting-state functional magnetic resonance imaging indicators indicators combined with clinical features.Subsequently,we conducted 100 additional five-fold cross-validations to determine the most effective model for each classification task and evaluated the performance of the model using the area under the receiver operating characteristic curve.The results showed that when differentiating patients with Parkinson's disease who had freezing of gait from those who did not have freezing of gait,or from healthy controls,the models using only the mean regional homogeneity values achieved the highest area under the receiver operating characteristic curve values of 0.750(with an accuracy of 70.9%)and 0.759(with an accuracy of 65.3%),respectively.When classifying patients with Parkinson's disease who had freezing of gait from those who had no freezing of gait,the model using the mean amplitude of low-frequency fluctuation values combined with two clinical features achieved the highest area under the receiver operating characteristic curve of 0.847(with an accuracy of 74.3%).The most significant features for patients with Parkinson's disease who had freezing of gait were amplitude of low-frequency fluctuation alterations in the left parahippocampal gyrus and two clinical characteristics:Montreal Cognitive Assessment and Hamilton Depression Scale scores.Our findings suggest that radiomics features derived from resting-state functional magnetic resonance imaging indices and clinical information can serve as valuable indices for the identification of freezing of gait in 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
The South Central Axis in Beijing showcases China’s image and highlights its cultural confidence.THE Central Axis is the centerpiece of the Chinese capital’s urban spatial layout.The southern extended section of the...The South Central Axis in Beijing showcases China’s image and highlights its cultural confidence.THE Central Axis is the centerpiece of the Chinese capital’s urban spatial layout.The southern extended section of the Central Axis,or the South Central Axis,stretches from the Yongdingmen Gate Tower in the north to the South Fifth Ring Road in the south.While being a strategic transport link facilitating the coordinated development of the Beijing-Tianjin-Hebei region,it also showcases China’s vision for the future and highlights its cultural confidence.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
Myelination in the central nervous system(CNS)is a highly intricate process,exclusive to vertebrates,that relies on the coordinated interaction between oligodendrocytes(OLs)and neurons.In addition to their role in for...Myelination in the central nervous system(CNS)is a highly intricate process,exclusive to vertebrates,that relies on the coordinated interaction between oligodendrocytes(OLs)and neurons.In addition to their role in forming myelin,accumulating evidence indicates that OLs provide crucial trophic support to axons,contributing to normal CNS function.Notably,OL injury and loss are observed in a variety of human conditions,including stroke,traumatic injuries of the brain and spinal cord,as well as neurodegenerative disorders such as multiple sclerosis(MS).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 optimal development,function,and maintenance of the central nervous system(CNS)are determined by the dynamic and continuous crosstalk between its components.Neurons and glial cells,the cellular constituents of the...The optimal development,function,and maintenance of the central nervous system(CNS)are determined by the dynamic and continuous crosstalk between its components.Neurons and glial cells,the cellular constituents of the CNS,orchestrate a wide range of essential activities(Allen and Lyons,2018).Notably,glial cells,which outnumber neurons,constitute the major population within the CNS.This population comprises astrocytes,microglia,oligodendrocytes,and ependymal cells,each fulfilling specialized functions that contribute to neural homeostasis and overall CNS integrity.Astrocytes are pivotal in preserving structural and functional integrity through the regulation of synaptic function,the clearance of neurotransmitters,and ion balance.Moreover,they provide metabolic support to neurons.展开更多
China Outlines 2026 Economic Agenda with Focus on Demand and Reform Fol lowing the an nual Cent ral Economic Work Conference in December,multiple Chinese government depar tments rolled out key priorities for 2026.The ...China Outlines 2026 Economic Agenda with Focus on Demand and Reform Fol lowing the an nual Cent ral Economic Work Conference in December,multiple Chinese government depar tments rolled out key priorities for 2026.The National Development and Reform Commission(NDRC)pledged measures to stabilize investment growth,including leveraging government funds and increasing central budget investment.展开更多
Cells of the central nervous system(CNS)are privileged in lying behind the blood-brain barrier(BBB).Unlike blood vessels in other organs,CNS blood vessels are unique in displaying high electrical resistance and low pe...Cells of the central nervous system(CNS)are privileged in lying behind the blood-brain barrier(BBB).Unlike blood vessels in other organs,CNS blood vessels are unique in displaying high electrical resistance and low permeability.With this unique structure and function,the BBB prevents potentially harmful blood components such as serum proteins,inflammatory cytokines,and inflammatory leukocytes from entering the hallowed space of the CNS and wreaking havoc.In addition to these“tightness”properties,the BBB has an array of specialized transporters designed to import essential nutrients.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 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.
基金supported by the National Natural Science Foundation of China,No.82071909(to GF)the Natural Science Foundation of Liaoning Province,No.2023-MS-07(to HL)。
文摘Freezing of gait is a significant and debilitating motor symptom often observed in individuals with Parkinson's disease.Resting-state functional magnetic resonance imaging,along with its multi-level feature indices,has provided a fresh perspective and valuable insight into the study of freezing of gait in Parkinson's disease.It has been revealed that Parkinson's disease is accompanied by widespread irregularities in inherent brain network activity.However,the effective integration of the multi-level indices of resting-state functional magnetic resonance imaging into clinical settings for the diagnosis of freezing of gait in Parkinson's disease remains a challenge.Although previous studies have demonstrated that radiomics can extract optimal features as biomarkers to identify or predict diseases,a knowledge gap still exists in the field of freezing of gait in Parkinson's disease.This cross-sectional study aimed to evaluate the ability of radiomics features based on multi-level indices of resting-state functional magnetic resonance imaging,along with clinical features,to distinguish between Parkinson's disease patients with and without freezing of gait.We recruited 28 patients with Parkinson's disease who had freezing of gait(15 men and 13 women,average age 63 years)and 30 patients with Parkinson's disease who had no freezing of gait(16 men and 14 women,average age 64 years).Magnetic resonance imaging scans were obtained using a 3.0T scanner to extract the mean amplitude of low-frequency fluctuations,mean regional homogeneity,and degree centrality.Neurological and clinical characteristics were also evaluated.We used the least absolute shrinkage and selection operator algorithm to extract features and established feedforward neural network models based solely on resting-state functional magnetic resonance imaging indicators.We then performed predictive analysis of three distinct groups based on resting-state functional magnetic resonance imaging indicators indicators combined with clinical features.Subsequently,we conducted 100 additional five-fold cross-validations to determine the most effective model for each classification task and evaluated the performance of the model using the area under the receiver operating characteristic curve.The results showed that when differentiating patients with Parkinson's disease who had freezing of gait from those who did not have freezing of gait,or from healthy controls,the models using only the mean regional homogeneity values achieved the highest area under the receiver operating characteristic curve values of 0.750(with an accuracy of 70.9%)and 0.759(with an accuracy of 65.3%),respectively.When classifying patients with Parkinson's disease who had freezing of gait from those who had no freezing of gait,the model using the mean amplitude of low-frequency fluctuation values combined with two clinical features achieved the highest area under the receiver operating characteristic curve of 0.847(with an accuracy of 74.3%).The most significant features for patients with Parkinson's disease who had freezing of gait were amplitude of low-frequency fluctuation alterations in the left parahippocampal gyrus and two clinical characteristics:Montreal Cognitive Assessment and Hamilton Depression Scale scores.Our findings suggest that radiomics features derived from resting-state functional magnetic resonance imaging indices and clinical information can serve as valuable indices for the identification of freezing of gait in 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The South Central Axis in Beijing showcases China’s image and highlights its cultural confidence.THE Central Axis is the centerpiece of the Chinese capital’s urban spatial layout.The southern extended section of the Central Axis,or the South Central Axis,stretches from the Yongdingmen Gate Tower in the north to the South Fifth Ring Road in the south.While being a strategic transport link facilitating the coordinated development of the Beijing-Tianjin-Hebei region,it also showcases China’s vision for the future and highlights its cultural confidence.
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Myelination in the central nervous system(CNS)is a highly intricate process,exclusive to vertebrates,that relies on the coordinated interaction between oligodendrocytes(OLs)and neurons.In addition to their role in forming myelin,accumulating evidence indicates that OLs provide crucial trophic support to axons,contributing to normal CNS function.Notably,OL injury and loss are observed in a variety of human conditions,including stroke,traumatic injuries of the brain and spinal cord,as well as neurodegenerative disorders such as multiple sclerosis(MS).
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 Linea D.1.2023-24 UniversitàCattolica del S.Cuore(to MTV).
文摘The optimal development,function,and maintenance of the central nervous system(CNS)are determined by the dynamic and continuous crosstalk between its components.Neurons and glial cells,the cellular constituents of the CNS,orchestrate a wide range of essential activities(Allen and Lyons,2018).Notably,glial cells,which outnumber neurons,constitute the major population within the CNS.This population comprises astrocytes,microglia,oligodendrocytes,and ependymal cells,each fulfilling specialized functions that contribute to neural homeostasis and overall CNS integrity.Astrocytes are pivotal in preserving structural and functional integrity through the regulation of synaptic function,the clearance of neurotransmitters,and ion balance.Moreover,they provide metabolic support to neurons.
文摘China Outlines 2026 Economic Agenda with Focus on Demand and Reform Fol lowing the an nual Cent ral Economic Work Conference in December,multiple Chinese government depar tments rolled out key priorities for 2026.The National Development and Reform Commission(NDRC)pledged measures to stabilize investment growth,including leveraging government funds and increasing central budget investment.
基金supported by the NIH RF1 grant NS119477 jointly funded by NINDS and NIA(to RM).
文摘Cells of the central nervous system(CNS)are privileged in lying behind the blood-brain barrier(BBB).Unlike blood vessels in other organs,CNS blood vessels are unique in displaying high electrical resistance and low permeability.With this unique structure and function,the BBB prevents potentially harmful blood components such as serum proteins,inflammatory cytokines,and inflammatory leukocytes from entering the hallowed space of the CNS and wreaking havoc.In addition to these“tightness”properties,the BBB has an array of specialized transporters designed to import essential nutrients.
