The concept of Fiedler matrices was introduced in [1] by L. Stuart and R.Weaver.In[1], they investigated the factorization of Fiedler matrix into Fiedler matrices and pre-sented some open questions i. e. When is a Fie...The concept of Fiedler matrices was introduced in [1] by L. Stuart and R.Weaver.In[1], they investigated the factorization of Fiedler matrix into Fiedler matrices and pre-sented some open questions i. e. When is a Fiedler matrix factorizable as a product ofFiedler matrices? Are there useful sufficient conditions? If a Fiedler matrix is factorizable,are the factors unique? If not, are the dimensions of the factors unique? In this paper,展开更多
This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting...This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.展开更多
Let G be a graph and f an integer-valued function defined on V(G). It is proved that every (0,mf - m+1)-graph G has a (0,f)-factorization orthogonal to any given subgraph with m edges.
A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition n...A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .展开更多
Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g less than or equal to f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)less ...Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g less than or equal to f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)less than or equal to d(F)(x)less than or equal to f(x) for all x is an element of V(G). If G itself is a (g, f)-factor, then it is said that G is a (g, f)-graph. If the edges of G can be decomposed into some edge disjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, one sufficient condition for a graph to be (g, f)-factorable is given.展开更多
Let G be a graph, k(1), ... , k(m) be positive integers. If the edges of graph G can be decomposed into some edge disjoint [0, k(1)]-factor F-1, ..., [0, k(m)]-factor F-m, then we can say (F) over bar = {F-1, ..., F-m...Let G be a graph, k(1), ... , k(m) be positive integers. If the edges of graph G can be decomposed into some edge disjoint [0, k(1)]-factor F-1, ..., [0, k(m)]-factor F-m, then we can say (F) over bar = {F-1, ..., F-m}, is a [0, k(i)](1)(m) -factorization of G. If H is a subgraph with m edges in graph G and / E (H) boolean AND E(F-i) / = 1 for all 1 less than or equal to i less than or equal to m, then we can call that (F) over bar is orthogonal to H. It is proved that if G is a [0, k(1) + ... + k(m) - m + 1]-graph, H is a subgraph with m edges in G, then graph G has a [0, k(i)](1)(m)-factorization orthogonal to H.展开更多
This paper considers the updating problem of the hyperbolic matrix factorizations. The sufficient conditions for the existence of the updated hyperbolic matrix factorizations are first provided. Then, some differentia...This paper considers the updating problem of the hyperbolic matrix factorizations. The sufficient conditions for the existence of the updated hyperbolic matrix factorizations are first provided. Then, some differential inequalities and first order perturbation expansions for the updated hyperbolic factors are derived. These results generalize the corresponding ones for the updating problem of the classical QR factorization obtained by Jiguang SUN.展开更多
It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 821289...It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.展开更多
Let G be an (mg, mf)-graph, where g and f are integer-valued functions defined on V(G) and such that 0≤g(x)≤f(x) for each x ∈ V(G). It is proved that(1) If Z ≠ , both g and f may be not even, G has a (g, f)-factor...Let G be an (mg, mf)-graph, where g and f are integer-valued functions defined on V(G) and such that 0≤g(x)≤f(x) for each x ∈ V(G). It is proved that(1) If Z ≠ , both g and f may be not even, G has a (g, f)-factorization, where Z = {x ∈ V(G):mf(x)-dG(x)≤t(x) or dG(x)-mg(x)≤ t(x), t(x)=f(x)-g(x)>0}.(2) Let G be an m-regular graph with 2n vertices, m ≥ n. If (P1, P2,..., Pr) is a partition of m, P1 ≡m (mod 2), Pi≡0 (mod 2), i=2,..., r, then the edge set E(G) of G can be parted into r parts E1,E2,..., Er of E(G) such that G[Ei] is a Pi-factor of G.展开更多
Spinal cord injury represents a severe form of central nervous system trauma for which effective treatments remain limited.Microglia is the resident immune cells of the central nervous system,play a critical role in s...Spinal cord injury represents a severe form of central nervous system trauma for which effective treatments remain limited.Microglia is the resident immune cells of the central nervous system,play a critical role in spinal cord injury.Previous studies have shown that microglia can promote neuronal survival by phagocytosing dead cells and debris and by releasing neuroprotective and anti-inflammatory factors.However,excessive activation of microglia can lead to persistent inflammation and contribute to the formation of glial scars,which hinder axonal regeneration.Despite this,the precise role and mechanisms of microglia during the acute phase of spinal cord injury remain controversial and poorly understood.To elucidate the role of microglia in spinal cord injury,we employed the colony-stimulating factor 1 receptor inhibitor PLX5622 to deplete microglia.We observed that sustained depletion of microglia resulted in an expansion of the lesion area,downregulation of brain-derived neurotrophic factor,and impaired functional recovery after spinal cord injury.Next,we generated a transgenic mouse line with conditional overexpression of brain-derived neurotrophic factor specifically in microglia.We found that brain-derived neurotrophic factor overexpression in microglia increased angiogenesis and blood flow following spinal cord injury and facilitated the recovery of hindlimb motor function.Additionally,brain-derived neurotrophic factor overexpression in microglia reduced inflammation and neuronal apoptosis during the acute phase of spinal cord injury.Furthermore,through using specific transgenic mouse lines,TMEM119,and the colony-stimulating factor 1 receptor inhibitor PLX73086,we demonstrated that the neuroprotective effects were predominantly due to brain-derived neurotrophic factor overexpression in microglia rather than macrophages.In conclusion,our findings suggest the critical role of microglia in the formation of protective glial scars.Depleting microglia is detrimental to recovery of spinal cord injury,whereas targeting brain-derived neurotrophic factor overexpression in microglia represents a promising and novel therapeutic strategy to enhance motor function recovery in patients with spinal cord injury.展开更多
In this paper,rank factorizations and factor left prime factorizations are studied.The authors prove that any polynomial matrix with full row rank has factor left prime factorizations.And for a class of polynomial mat...In this paper,rank factorizations and factor left prime factorizations are studied.The authors prove that any polynomial matrix with full row rank has factor left prime factorizations.And for a class of polynomial matrices,the authors give an algorithm to decide whether they have rank factorizations or factor left prime factorizations and compute these factorizations if they exist.展开更多
This is a survey of some recent progress in the theory of groups with factorizations. Some of the methods can be used to obtain information about finite groups in general, nilpotent algebras and nearrings.
Border-associated macrophages are located at the interface between the brain and the periphery, including the perivascular spaces, choroid plexus, and meninges. Until recently, the functions of border-associated macro...Border-associated macrophages are located at the interface between the brain and the periphery, including the perivascular spaces, choroid plexus, and meninges. Until recently, the functions of border-associated macrophages have been poorly understood and largely overlooked. However, a recent study reported that border-associated macrophages participate in stroke-induced inflammation, although many details and the underlying mechanisms remain unclear. In this study, we performed a comprehensive single-cell analysis of mouse border-associated macrophages using sequencing data obtained from the Gene Expression Omnibus(GEO) database(GSE174574 and GSE225948). Differentially expressed genes were identified, and enrichment analysis was performed to identify the transcription profile of border-associated macrophages. CellChat analysis was conducted to determine the cell communication network of border-associated macrophages. Transcription factors were predicted using the ‘pySCENIC' tool. We found that, in response to hypoxia, borderassociated macrophages underwent dynamic transcriptional changes and participated in the regulation of inflammatory-related pathways. Notably, the tumor necrosis factor pathway was activated by border-associated macrophages following ischemic stroke. The pySCENIC analysis indicated that the activity of signal transducer and activator of transcription 3(Stat3) was obviously upregulated in stroke, suggesting that Stat3 inhibition may be a promising strategy for treating border-associated macrophages-induced neuroinflammation. Finally, we constructed an animal model to investigate the effects of border-associated macrophages depletion following a stroke. Treatment with liposomes containing clodronate significantly reduced infarct volume in the animals and improved neurological scores compared with untreated animals. Taken together, our results demonstrate comprehensive changes in border-associated macrophages following a stroke, providing a theoretical basis for targeting border-associated macrophages-induced neuroinflammation in stroke treatment.展开更多
This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of resear...This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of research.In particular,we only touch the great consequences of the fundamental paper of Liebeck,Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations.In each case the reader can find additional references at the end of Section 1.Some of the methods of investigation can be used to obtain information about finite groups in general,nilpotent algebras and related nearrings.展开更多
BACKGROUND Ischemic stroke is one of the leading global causes of disability and death.Despite advances in modern medical technology that improve acute treatment and rehabilitation measures,post-stroke anxiety and dep...BACKGROUND Ischemic stroke is one of the leading global causes of disability and death.Despite advances in modern medical technology that improve acute treatment and rehabilitation measures,post-stroke anxiety and depression(PSD)do not receive sufficient attention.AIM To systematically evaluate risk factors and early identification markers for PSD for more precise screening and intervention strategies in clinical practice.METHODS This retrospective study analyzed clinical data from 112 patients with ischemic stroke admitted between January 2022 and December 2024.Based on assessments using the Hamilton Rating Scale for Anxiety(HAMA)and Hamilton Rating Scale for Depression(HAMD)at 2 weeks(±3 days)post-stroke,patients were classified into the PSD group(HAMA≥7 and/or HAMD≥7)and the non-PSD group(HAMA<7 and HAMD<7).Observation indicators included psychological assessment,demographic and clinical characteristics,stroke-related clinical indicators,neuroimaging assessments,and laboratory biomarkers.Multivariate logistic regression analysis was used to identify independent risk factors for PSD,and receiver operating characteristic curve analysis was used to evaluate the diagnostic value of potential biomarkers.RESULTS Of the 112 patients,46(41.1%)were diagnosed with PSD.Multivariate analysis identified five independent risk factors:Female gender[Odds ratio(OR)=2.32,95%confidence interval(CI):1.56-3.45],history of mental disorders prior to stroke(OR=3.17,95%CI:1.89-5.32),infarct location in the frontal lobe or limbic system(OR=2.86,95%CI:1.73-4.71),stroke severity with National Institutes of Health Stroke Scale≥8 at admission(OR=2.54,95%CI:1.62-3.99),and low social support(Social Support Rating Scale<35,OR=2.18,95%CI:1.42-3.36).Subgroup analysis showed that depression patients more commonly had left hemisphere lesions(68.4%vs 45.2%),while anxiety patients more frequently presented with right hemisphere lesions(59.5%vs 39.5%).The PSD group exhibited larger infarct volumes(8.7 cm^(3) vs 5.3 cm^(3)),more severe white matter hyperintensities,and more pronounced frontal lobe atrophy.Analysis of inflammatory markers showed significantly elevated levels of interleukin-6(7.8 pg/mL vs 4.5 pg/mL)and tumor necrosis factor-alpha(15.6 pg/mL vs 9.8 pg/mL)in the PSD group,while hypothalamicpituitary-adrenal axis function assessment revealed higher cortisol levels(386.5±92.3 nmol/L vs 328.7±75.6 nmol/L)and flattened diurnal rhythm in the PSD group.CONCLUSION PSD is a complex neuropsychiatric consequence of stroke involving disruption of the frontal-limbic circuitry,neuroinflammatory responses,and dysfunction of the hypothalamic-pituitary-adrenal axis.展开更多
Strokes include both ischemic stroke,which is mediated by a blockade or reduction in the blood supply to the brain,and hemorrhagic stroke,which comprises intracerebral hemorrhage and subarachnoid hemorrhage and is cha...Strokes include both ischemic stroke,which is mediated by a blockade or reduction in the blood supply to the brain,and hemorrhagic stroke,which comprises intracerebral hemorrhage and subarachnoid hemorrhage and is characterized by bleeding within the brain.Stroke is a lifethreatening cerebrovascular condition characterized by intricate pathophysiological mechanisms,including oxidative stress,inflammation,mitochondrial dysfunction,and neuronal injury.Critical transcription factors,such as nuclear factor erythroid 2-related factor 2 and nuclear factor kappa B,play central roles in the progression of stroke.Nuclear factor erythroid 2-related factor 2 is sensitive to changes in the cellular redox status and is crucial in protecting cells against oxidative damage,inflammatory responses,and cytotoxic agents.It plays a significant role in post-stroke neuroprotection and repair by influencing mitochondrial function,endoplasmic reticulum stress,and lysosomal activity and regulating metabolic pathways and cytokine expression.Conversely,nuclear factor-kappa B is closely associated with mitochondrial dysfunction,the generation of reactive oxygen species,oxidative stress exacerbation,and inflammation.Nuclear factor-kappa B contributes to neuronal injury,apoptosis,and immune responses following stroke by modulating cell adhesion molecules and inflammatory mediators.The interplay between these pathways,potentially involving crosstalk among various organelles,significantly influences stroke pathophysiology.Advancements in single-cell sequencing and spatial transcriptomics have greatly improved our understanding of stroke pathogenesis and offer new opportunities for the development of targeted,individualized,cell typespecific treatments.In this review,we discuss the mechanisms underlying the involvement of nuclear factor erythroid 2-related factor 2 and nuclear factor-kappa B in both ischemic and hemorrhagic stroke,with an emphasis on their roles in oxidative stress,inflammation,and neuroprotection.展开更多
Nerve trauma commonly results in chronic neuropathic pain. This is by triggering the release of proinflammatory mediators from local and invading cells that induce inflammation and nociceptive neuron hyperexcitability...Nerve trauma commonly results in chronic neuropathic pain. This is by triggering the release of proinflammatory mediators from local and invading cells that induce inflammation and nociceptive neuron hyperexcitability. Even without apparent inflammation, injury sites are associated with increased inflammatory markers. This review focuses on how it might be possible to reduce neuropathic pain by reducing inflammation. Physiologically, pain is resolved by a combination of the out-migration of pro-inflammatory cells from the injury site, the down-regulation of the genes underlying the inflammation, up-regulating genes for anti-inflammatory mediators, and reducing nociceptive neuron hyperexcitability. While various techniques reduce chronic neuropathic pain, the best are effective on < 50% of patients, no technique reliably or permanently eliminates neuropathic pain. This is because most techniques are predominantly aimed at reducing pain, not inflammation. In addition, while single factors reduce pain, increasing evidence indicates significant and longer-lasting pain relief requires multiple factors acting simultaneously. Therefore, it is not surprising that extensive data indicate that the application of platelet-rich plasma provides more significant and longer-lasting pain suppression than other techniques, although its analgesia is neither complete nor permanent. However, several case reports indicate that platelet-rich plasma can induce permanent neuropathic pain elimination when the platelet concentration is significantly increased and is applied to longer nerve lengths. This review examines the primary triggers of the development and maintenance of neuropathic pain and techniques that reduce chronic neuropathic pain. The application of plateletrich plasma holds great promise for providing complete and permanent chronic neuropathic pain elimination.展开更多
BACKGROUND Post-transplant tertiary hyperparathyroidism(PT-tHPT)is a well-recognized complication following kidney transplantation,characterized by persistent excessive secretion of parathyroid hormone(PTH)despite imp...BACKGROUND Post-transplant tertiary hyperparathyroidism(PT-tHPT)is a well-recognized complication following kidney transplantation,characterized by persistent excessive secretion of parathyroid hormone(PTH)despite improved renal function.It is potentially associated with an increased risk of cardiovascular events,renal osteodystrophy,pathologic fractures,graft loss,and mortality.AIM To evaluate the incidence,risk factors,and outcomes of PT-tHPT amongst kidney transplant recipients.METHODS A total of 887 transplant recipients who underwent transplantation between 2000 and 2020 were evaluated.Univariable and multivariable logistic regression was performed to determine the predictors of tertiary hyperparathyroidism.Graft and recipient outcomes were assessed using multivariable Cox regression.A separate multivariable Cox regression was performed to determine the effect of treatment strategies on outcomes.RESULTS PT-tHPT,defined as elevated PTH(>65 ng/L)and persistent hypercalcemia(>2.60 mmol/L),was diagnosed in 14%of recipients.Risk factors for PT-tHPT included older age[odds ratio(OR)=1.36,P<0.001],Asian ethnicity(OR=0.33,P=0.006),total ischemia time(OR=1.03,P=0.048 per hour),pre-transplant serum calcium(OR=1.38,P<0.001)per decile increase,pre-transplant PTH level(OR=1.31,P<0.001)per decile increase,longer dialysis duration(OR=1.12,P=0.002)per year,history of acute rejection(OR=2.37,P=0.012),and slope of estimated glomerular filtration rate change(OR=0.91,P=0.001).There were a 3.4-fold higher risk of death-censored graft loss and a 1.9-fold greater risk of recipient death with PT-tHPT.The three treatment strategies of conservative management,calcimimetic and parathyroidectomy did not significantly change the graft or patient outcome.CONCLUSION Pretransplant elevated calcium and PTH levels,older age and dialysis duration are associated with PT-tHPT.While PT-tHPT significantly affects graft and recipient survival,the treatment strategies did not affect survival.展开更多
BACKGROUND Aseptic loosening remains the leading cause of revision in primary total hip arthroplasty(pTHA).However,the literature demonstrates significant variability regarding the relative contributions of different ...BACKGROUND Aseptic loosening remains the leading cause of revision in primary total hip arthroplasty(pTHA).However,the literature demonstrates significant variability regarding the relative contributions of different factors.AIM To investigate the key determinants of aseptic loosening,we performed a systematic review and meta-analysis.METHODS A comprehensive search of PubMed,Web of Science,EMBASE,and the Cochrane Library was conducted,encompassing studies from database inception to January 1,2025.Meta-analyses were performed to evaluate factors associated with aseptic loosening following pTHA.Inclusion and exclusion criteria were systematically applied at each stage to ensure methodological transparency and reproducibility.Study quality was assessed using standardized categories.Pooled odds ratio(OR)with corresponding 95%confidence interval were calculated with random-or fixed-effects models to generate reliability estimates,and study heterogeneity was visualized using forest plots.Ten factors,categorized into patient-,surgeon-,and device-related domains,were reviewed and meta-analyzed.Funnel plot analysis demonstrated a relatively symmetrical distribution,suggesting minimal publication bias.RESULTS A meta-analysis of 20 studies(520789 participants)found a pooled prevalence of 1.96%.Significant risk factors for aseptic loosening after pTHA included elevated body mass index(OR=1.116,P<0.001),higher Charlson comorbidity index(OR=1.378,P<0.001),prosthesis-related factors(OR=1.497,P<0.001),and adverse lifestyles(OR=2.198,P=0.037).Protective factors were non-white race(OR=0.445,P<0.001)and favorable genetics(OR=0.723,P<0.001).Male sex increased risk(OR=1.232,P=0.016),while age and anatomy were not significant.Surgical expertise showed a slight protective effect(OR=1.048,P<0.001).A comprehensive understanding of the modifiable and non-modifiable factors contributing to aseptic loosening after pTHA requires consideration of patient-related factors,surgical expertise,and prosthesis characteristics.CONCLUSION The identification of these factors is critical for risk mitigation.High-risk patients should receive targeted counseling regarding individualized profiles.Further studies are warranted to establish clearer causal relationships and identify additional contributing factors.展开更多
BACKGROUND Lumbar interbody fusion(LIF)is the primary treatment for lumbar degenerative diseases.Elderly patients are prone to anxiety and depression after undergoing surgery,which affects their postoperative recovery...BACKGROUND Lumbar interbody fusion(LIF)is the primary treatment for lumbar degenerative diseases.Elderly patients are prone to anxiety and depression after undergoing surgery,which affects their postoperative recovery speed and quality of life.Effective prevention of anxiety and depression in elderly patients has become an urgent problem.AIM To investigate the trajectory of anxiety and depression levels in elderly patients after LIF,and the influencing factors.METHODS Random sampling was used to select 239 elderly patients who underwent LIF from January 2020 to December 2024 in Shenzhen Pingle Orthopedic Hospital.General information and surgery-related indices were recorded,and participants completed measures of psychological status,lumbar spine dysfunction,and quality of life.A latent class growth model was used to analyze the post-LIF trajectory of anxiety and depression levels,and unordered multi-categorical logistic regression was used to analyze the influencing factors.RESULTS Three trajectories of change in anxiety level were identified:Increasing anxiety(n=26,10.88%),decreasing anxiety(n=27,11.30%),and stable anxiety(n=186,77.82%).Likewise,three trajectories of change in depression level were identified:Increasing depression(n=30,12.55%),decreasing depression(n=26,10.88%),and stable depression(n=183,76.57%).Regression analysis showed that having no partner,female sex,elevated Oswestry dysfunction index(ODI)scores,and reduced 36-Item Short Form Health Survey scores all contributed to increased anxiety levels,whereas female sex,postoperative opioid use,and elevated ODI scores all contributed to increased depression levels.CONCLUSION During clinical observation,combining factors to predict anxiety and depression in post-LIF elderly patients enables timely intervention,quickens recovery,and enhances quality of life.展开更多
基金This work is supported by the Natural Scientific Research Foundation of Yunnan Province(200A0001--1M)the Scientific Research Foundation of Education Commission of Yunnan Province(9911126)
文摘The concept of Fiedler matrices was introduced in [1] by L. Stuart and R.Weaver.In[1], they investigated the factorization of Fiedler matrix into Fiedler matrices and pre-sented some open questions i. e. When is a Fiedler matrix factorizable as a product ofFiedler matrices? Are there useful sufficient conditions? If a Fiedler matrix is factorizable,are the factors unique? If not, are the dimensions of the factors unique? In this paper,
文摘This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.
文摘Let G be a graph and f an integer-valued function defined on V(G). It is proved that every (0,mf - m+1)-graph G has a (0,f)-factorization orthogonal to any given subgraph with m edges.
文摘A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .
文摘Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g less than or equal to f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)less than or equal to d(F)(x)less than or equal to f(x) for all x is an element of V(G). If G itself is a (g, f)-factor, then it is said that G is a (g, f)-graph. If the edges of G can be decomposed into some edge disjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, one sufficient condition for a graph to be (g, f)-factorable is given.
文摘Let G be a graph, k(1), ... , k(m) be positive integers. If the edges of graph G can be decomposed into some edge disjoint [0, k(1)]-factor F-1, ..., [0, k(m)]-factor F-m, then we can say (F) over bar = {F-1, ..., F-m}, is a [0, k(i)](1)(m) -factorization of G. If H is a subgraph with m edges in graph G and / E (H) boolean AND E(F-i) / = 1 for all 1 less than or equal to i less than or equal to m, then we can call that (F) over bar is orthogonal to H. It is proved that if G is a [0, k(1) + ... + k(m) - m + 1]-graph, H is a subgraph with m edges in G, then graph G has a [0, k(i)](1)(m)-factorization orthogonal to H.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1120150711171361)the Natural Science Foundation Project of CQ CSTC(Grant No.2010BB9215)
文摘This paper considers the updating problem of the hyperbolic matrix factorizations. The sufficient conditions for the existence of the updated hyperbolic matrix factorizations are first provided. Then, some differential inequalities and first order perturbation expansions for the updated hyperbolic factors are derived. These results generalize the corresponding ones for the updating problem of the classical QR factorization obtained by Jiguang SUN.
文摘It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.
基金Foundation item:Hunan Provincial Educational Department (03C496)
文摘Let G be an (mg, mf)-graph, where g and f are integer-valued functions defined on V(G) and such that 0≤g(x)≤f(x) for each x ∈ V(G). It is proved that(1) If Z ≠ , both g and f may be not even, G has a (g, f)-factorization, where Z = {x ∈ V(G):mf(x)-dG(x)≤t(x) or dG(x)-mg(x)≤ t(x), t(x)=f(x)-g(x)>0}.(2) Let G be an m-regular graph with 2n vertices, m ≥ n. If (P1, P2,..., Pr) is a partition of m, P1 ≡m (mod 2), Pi≡0 (mod 2), i=2,..., r, then the edge set E(G) of G can be parted into r parts E1,E2,..., Er of E(G) such that G[Ei] is a Pi-factor of G.
基金supported by the National Natural Science Foundation of China,Nos.82072165 and 82272256(both to XM)the Key Project of Xiangyang Central Hospital,No.2023YZ03(to RM)。
文摘Spinal cord injury represents a severe form of central nervous system trauma for which effective treatments remain limited.Microglia is the resident immune cells of the central nervous system,play a critical role in spinal cord injury.Previous studies have shown that microglia can promote neuronal survival by phagocytosing dead cells and debris and by releasing neuroprotective and anti-inflammatory factors.However,excessive activation of microglia can lead to persistent inflammation and contribute to the formation of glial scars,which hinder axonal regeneration.Despite this,the precise role and mechanisms of microglia during the acute phase of spinal cord injury remain controversial and poorly understood.To elucidate the role of microglia in spinal cord injury,we employed the colony-stimulating factor 1 receptor inhibitor PLX5622 to deplete microglia.We observed that sustained depletion of microglia resulted in an expansion of the lesion area,downregulation of brain-derived neurotrophic factor,and impaired functional recovery after spinal cord injury.Next,we generated a transgenic mouse line with conditional overexpression of brain-derived neurotrophic factor specifically in microglia.We found that brain-derived neurotrophic factor overexpression in microglia increased angiogenesis and blood flow following spinal cord injury and facilitated the recovery of hindlimb motor function.Additionally,brain-derived neurotrophic factor overexpression in microglia reduced inflammation and neuronal apoptosis during the acute phase of spinal cord injury.Furthermore,through using specific transgenic mouse lines,TMEM119,and the colony-stimulating factor 1 receptor inhibitor PLX73086,we demonstrated that the neuroprotective effects were predominantly due to brain-derived neurotrophic factor overexpression in microglia rather than macrophages.In conclusion,our findings suggest the critical role of microglia in the formation of protective glial scars.Depleting microglia is detrimental to recovery of spinal cord injury,whereas targeting brain-derived neurotrophic factor overexpression in microglia represents a promising and novel therapeutic strategy to enhance motor function recovery in patients with spinal cord injury.
基金supported by the National Science Foundation of China under Grant Nos.11371131 and 11501192
文摘In this paper,rank factorizations and factor left prime factorizations are studied.The authors prove that any polynomial matrix with full row rank has factor left prime factorizations.And for a class of polynomial matrices,the authors give an algorithm to decide whether they have rank factorizations or factor left prime factorizations and compute these factorizations if they exist.
文摘This is a survey of some recent progress in the theory of groups with factorizations. Some of the methods can be used to obtain information about finite groups in general, nilpotent algebras and nearrings.
基金supported by Qingdao Key Medical and Health Discipline ProjectThe Intramural Research Program of the Affiliated Hospital of Qingdao University,No. 4910Qingdao West Coast New Area Science and Technology Project,No. 2020-55 (all to SW)。
文摘Border-associated macrophages are located at the interface between the brain and the periphery, including the perivascular spaces, choroid plexus, and meninges. Until recently, the functions of border-associated macrophages have been poorly understood and largely overlooked. However, a recent study reported that border-associated macrophages participate in stroke-induced inflammation, although many details and the underlying mechanisms remain unclear. In this study, we performed a comprehensive single-cell analysis of mouse border-associated macrophages using sequencing data obtained from the Gene Expression Omnibus(GEO) database(GSE174574 and GSE225948). Differentially expressed genes were identified, and enrichment analysis was performed to identify the transcription profile of border-associated macrophages. CellChat analysis was conducted to determine the cell communication network of border-associated macrophages. Transcription factors were predicted using the ‘pySCENIC' tool. We found that, in response to hypoxia, borderassociated macrophages underwent dynamic transcriptional changes and participated in the regulation of inflammatory-related pathways. Notably, the tumor necrosis factor pathway was activated by border-associated macrophages following ischemic stroke. The pySCENIC analysis indicated that the activity of signal transducer and activator of transcription 3(Stat3) was obviously upregulated in stroke, suggesting that Stat3 inhibition may be a promising strategy for treating border-associated macrophages-induced neuroinflammation. Finally, we constructed an animal model to investigate the effects of border-associated macrophages depletion following a stroke. Treatment with liposomes containing clodronate significantly reduced infarct volume in the animals and improved neurological scores compared with untreated animals. Taken together, our results demonstrate comprehensive changes in border-associated macrophages following a stroke, providing a theoretical basis for targeting border-associated macrophages-induced neuroinflammation in stroke treatment.
文摘This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of research.In particular,we only touch the great consequences of the fundamental paper of Liebeck,Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations.In each case the reader can find additional references at the end of Section 1.Some of the methods of investigation can be used to obtain information about finite groups in general,nilpotent algebras and related nearrings.
文摘BACKGROUND Ischemic stroke is one of the leading global causes of disability and death.Despite advances in modern medical technology that improve acute treatment and rehabilitation measures,post-stroke anxiety and depression(PSD)do not receive sufficient attention.AIM To systematically evaluate risk factors and early identification markers for PSD for more precise screening and intervention strategies in clinical practice.METHODS This retrospective study analyzed clinical data from 112 patients with ischemic stroke admitted between January 2022 and December 2024.Based on assessments using the Hamilton Rating Scale for Anxiety(HAMA)and Hamilton Rating Scale for Depression(HAMD)at 2 weeks(±3 days)post-stroke,patients were classified into the PSD group(HAMA≥7 and/or HAMD≥7)and the non-PSD group(HAMA<7 and HAMD<7).Observation indicators included psychological assessment,demographic and clinical characteristics,stroke-related clinical indicators,neuroimaging assessments,and laboratory biomarkers.Multivariate logistic regression analysis was used to identify independent risk factors for PSD,and receiver operating characteristic curve analysis was used to evaluate the diagnostic value of potential biomarkers.RESULTS Of the 112 patients,46(41.1%)were diagnosed with PSD.Multivariate analysis identified five independent risk factors:Female gender[Odds ratio(OR)=2.32,95%confidence interval(CI):1.56-3.45],history of mental disorders prior to stroke(OR=3.17,95%CI:1.89-5.32),infarct location in the frontal lobe or limbic system(OR=2.86,95%CI:1.73-4.71),stroke severity with National Institutes of Health Stroke Scale≥8 at admission(OR=2.54,95%CI:1.62-3.99),and low social support(Social Support Rating Scale<35,OR=2.18,95%CI:1.42-3.36).Subgroup analysis showed that depression patients more commonly had left hemisphere lesions(68.4%vs 45.2%),while anxiety patients more frequently presented with right hemisphere lesions(59.5%vs 39.5%).The PSD group exhibited larger infarct volumes(8.7 cm^(3) vs 5.3 cm^(3)),more severe white matter hyperintensities,and more pronounced frontal lobe atrophy.Analysis of inflammatory markers showed significantly elevated levels of interleukin-6(7.8 pg/mL vs 4.5 pg/mL)and tumor necrosis factor-alpha(15.6 pg/mL vs 9.8 pg/mL)in the PSD group,while hypothalamicpituitary-adrenal axis function assessment revealed higher cortisol levels(386.5±92.3 nmol/L vs 328.7±75.6 nmol/L)and flattened diurnal rhythm in the PSD group.CONCLUSION PSD is a complex neuropsychiatric consequence of stroke involving disruption of the frontal-limbic circuitry,neuroinflammatory responses,and dysfunction of the hypothalamic-pituitary-adrenal axis.
基金supported by grants from the Zhejiang Provincial TCM Science and Technology Plan Project,No.2023ZL156(to YH)Ningbo Top Medical and Health Research Program,No.2022020304(to XG)+1 种基金the Natural Science Foundation of Ningbo,No.2023J019(to YH)Key Laboratory of Precision Medicine for Atherosclerotic Diseases of Zhejiang Province,No.2022E10026(to YH)。
文摘Strokes include both ischemic stroke,which is mediated by a blockade or reduction in the blood supply to the brain,and hemorrhagic stroke,which comprises intracerebral hemorrhage and subarachnoid hemorrhage and is characterized by bleeding within the brain.Stroke is a lifethreatening cerebrovascular condition characterized by intricate pathophysiological mechanisms,including oxidative stress,inflammation,mitochondrial dysfunction,and neuronal injury.Critical transcription factors,such as nuclear factor erythroid 2-related factor 2 and nuclear factor kappa B,play central roles in the progression of stroke.Nuclear factor erythroid 2-related factor 2 is sensitive to changes in the cellular redox status and is crucial in protecting cells against oxidative damage,inflammatory responses,and cytotoxic agents.It plays a significant role in post-stroke neuroprotection and repair by influencing mitochondrial function,endoplasmic reticulum stress,and lysosomal activity and regulating metabolic pathways and cytokine expression.Conversely,nuclear factor-kappa B is closely associated with mitochondrial dysfunction,the generation of reactive oxygen species,oxidative stress exacerbation,and inflammation.Nuclear factor-kappa B contributes to neuronal injury,apoptosis,and immune responses following stroke by modulating cell adhesion molecules and inflammatory mediators.The interplay between these pathways,potentially involving crosstalk among various organelles,significantly influences stroke pathophysiology.Advancements in single-cell sequencing and spatial transcriptomics have greatly improved our understanding of stroke pathogenesis and offer new opportunities for the development of targeted,individualized,cell typespecific treatments.In this review,we discuss the mechanisms underlying the involvement of nuclear factor erythroid 2-related factor 2 and nuclear factor-kappa B in both ischemic and hemorrhagic stroke,with an emphasis on their roles in oxidative stress,inflammation,and neuroprotection.
文摘Nerve trauma commonly results in chronic neuropathic pain. This is by triggering the release of proinflammatory mediators from local and invading cells that induce inflammation and nociceptive neuron hyperexcitability. Even without apparent inflammation, injury sites are associated with increased inflammatory markers. This review focuses on how it might be possible to reduce neuropathic pain by reducing inflammation. Physiologically, pain is resolved by a combination of the out-migration of pro-inflammatory cells from the injury site, the down-regulation of the genes underlying the inflammation, up-regulating genes for anti-inflammatory mediators, and reducing nociceptive neuron hyperexcitability. While various techniques reduce chronic neuropathic pain, the best are effective on < 50% of patients, no technique reliably or permanently eliminates neuropathic pain. This is because most techniques are predominantly aimed at reducing pain, not inflammation. In addition, while single factors reduce pain, increasing evidence indicates significant and longer-lasting pain relief requires multiple factors acting simultaneously. Therefore, it is not surprising that extensive data indicate that the application of platelet-rich plasma provides more significant and longer-lasting pain suppression than other techniques, although its analgesia is neither complete nor permanent. However, several case reports indicate that platelet-rich plasma can induce permanent neuropathic pain elimination when the platelet concentration is significantly increased and is applied to longer nerve lengths. This review examines the primary triggers of the development and maintenance of neuropathic pain and techniques that reduce chronic neuropathic pain. The application of plateletrich plasma holds great promise for providing complete and permanent chronic neuropathic pain elimination.
文摘BACKGROUND Post-transplant tertiary hyperparathyroidism(PT-tHPT)is a well-recognized complication following kidney transplantation,characterized by persistent excessive secretion of parathyroid hormone(PTH)despite improved renal function.It is potentially associated with an increased risk of cardiovascular events,renal osteodystrophy,pathologic fractures,graft loss,and mortality.AIM To evaluate the incidence,risk factors,and outcomes of PT-tHPT amongst kidney transplant recipients.METHODS A total of 887 transplant recipients who underwent transplantation between 2000 and 2020 were evaluated.Univariable and multivariable logistic regression was performed to determine the predictors of tertiary hyperparathyroidism.Graft and recipient outcomes were assessed using multivariable Cox regression.A separate multivariable Cox regression was performed to determine the effect of treatment strategies on outcomes.RESULTS PT-tHPT,defined as elevated PTH(>65 ng/L)and persistent hypercalcemia(>2.60 mmol/L),was diagnosed in 14%of recipients.Risk factors for PT-tHPT included older age[odds ratio(OR)=1.36,P<0.001],Asian ethnicity(OR=0.33,P=0.006),total ischemia time(OR=1.03,P=0.048 per hour),pre-transplant serum calcium(OR=1.38,P<0.001)per decile increase,pre-transplant PTH level(OR=1.31,P<0.001)per decile increase,longer dialysis duration(OR=1.12,P=0.002)per year,history of acute rejection(OR=2.37,P=0.012),and slope of estimated glomerular filtration rate change(OR=0.91,P=0.001).There were a 3.4-fold higher risk of death-censored graft loss and a 1.9-fold greater risk of recipient death with PT-tHPT.The three treatment strategies of conservative management,calcimimetic and parathyroidectomy did not significantly change the graft or patient outcome.CONCLUSION Pretransplant elevated calcium and PTH levels,older age and dialysis duration are associated with PT-tHPT.While PT-tHPT significantly affects graft and recipient survival,the treatment strategies did not affect survival.
基金Supported by the National Natural Science Foundation of China,No.82402789Beijing Jishuitan Hospital Youcai Plan,No.KYYC202402+2 种基金Beijing Jishuitan Research Funding,No.HL202402and Beijing Natural Science Foundation,No.L232062No.L222063.
文摘BACKGROUND Aseptic loosening remains the leading cause of revision in primary total hip arthroplasty(pTHA).However,the literature demonstrates significant variability regarding the relative contributions of different factors.AIM To investigate the key determinants of aseptic loosening,we performed a systematic review and meta-analysis.METHODS A comprehensive search of PubMed,Web of Science,EMBASE,and the Cochrane Library was conducted,encompassing studies from database inception to January 1,2025.Meta-analyses were performed to evaluate factors associated with aseptic loosening following pTHA.Inclusion and exclusion criteria were systematically applied at each stage to ensure methodological transparency and reproducibility.Study quality was assessed using standardized categories.Pooled odds ratio(OR)with corresponding 95%confidence interval were calculated with random-or fixed-effects models to generate reliability estimates,and study heterogeneity was visualized using forest plots.Ten factors,categorized into patient-,surgeon-,and device-related domains,were reviewed and meta-analyzed.Funnel plot analysis demonstrated a relatively symmetrical distribution,suggesting minimal publication bias.RESULTS A meta-analysis of 20 studies(520789 participants)found a pooled prevalence of 1.96%.Significant risk factors for aseptic loosening after pTHA included elevated body mass index(OR=1.116,P<0.001),higher Charlson comorbidity index(OR=1.378,P<0.001),prosthesis-related factors(OR=1.497,P<0.001),and adverse lifestyles(OR=2.198,P=0.037).Protective factors were non-white race(OR=0.445,P<0.001)and favorable genetics(OR=0.723,P<0.001).Male sex increased risk(OR=1.232,P=0.016),while age and anatomy were not significant.Surgical expertise showed a slight protective effect(OR=1.048,P<0.001).A comprehensive understanding of the modifiable and non-modifiable factors contributing to aseptic loosening after pTHA requires consideration of patient-related factors,surgical expertise,and prosthesis characteristics.CONCLUSION The identification of these factors is critical for risk mitigation.High-risk patients should receive targeted counseling regarding individualized profiles.Further studies are warranted to establish clearer causal relationships and identify additional contributing factors.
基金Supported by the Scientific Research Projects of the Health System in Pingshan District,No.2023122.
文摘BACKGROUND Lumbar interbody fusion(LIF)is the primary treatment for lumbar degenerative diseases.Elderly patients are prone to anxiety and depression after undergoing surgery,which affects their postoperative recovery speed and quality of life.Effective prevention of anxiety and depression in elderly patients has become an urgent problem.AIM To investigate the trajectory of anxiety and depression levels in elderly patients after LIF,and the influencing factors.METHODS Random sampling was used to select 239 elderly patients who underwent LIF from January 2020 to December 2024 in Shenzhen Pingle Orthopedic Hospital.General information and surgery-related indices were recorded,and participants completed measures of psychological status,lumbar spine dysfunction,and quality of life.A latent class growth model was used to analyze the post-LIF trajectory of anxiety and depression levels,and unordered multi-categorical logistic regression was used to analyze the influencing factors.RESULTS Three trajectories of change in anxiety level were identified:Increasing anxiety(n=26,10.88%),decreasing anxiety(n=27,11.30%),and stable anxiety(n=186,77.82%).Likewise,three trajectories of change in depression level were identified:Increasing depression(n=30,12.55%),decreasing depression(n=26,10.88%),and stable depression(n=183,76.57%).Regression analysis showed that having no partner,female sex,elevated Oswestry dysfunction index(ODI)scores,and reduced 36-Item Short Form Health Survey scores all contributed to increased anxiety levels,whereas female sex,postoperative opioid use,and elevated ODI scores all contributed to increased depression levels.CONCLUSION During clinical observation,combining factors to predict anxiety and depression in post-LIF elderly patients enables timely intervention,quickens recovery,and enhances quality of life.
