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
We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a s...We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.展开更多
The pathophysiology of Huntington's disease involves high levels of the neurotoxin quinolinic acid. Quinolinic acid accumulation results in oxidative stress, which leads to neurotoxicity. However, the molecular an...The pathophysiology of Huntington's disease involves high levels of the neurotoxin quinolinic acid. Quinolinic acid accumulation results in oxidative stress, which leads to neurotoxicity. However, the molecular and cellular mechanisms by which quinolinic acid contributes to Huntington's disease pathology remain unknown. In this study, we established in vitro and in vivo models of Huntington's disease by administering quinolinic acid to the PC12 neuronal cell line and the striatum of mice, respectively. We observed a decrease in the levels of hydrogen sulfide in both PC12 cells and mouse serum, which was accompanied by down-regulation of cystathionine β-synthase, an enzyme responsible for hydrogen sulfide production. However, treatment with NaHS(a hydrogen sulfide donor) increased hydrogen sulfide levels in the neurons and in mouse serum, as well as cystathionine β-synthase expression in the neurons and the mouse striatum, while also improving oxidative imbalance and mitochondrial dysfunction in PC12 cells and the mouse striatum. These beneficial effects correlated with upregulation of nuclear factor erythroid 2-related factor 2 expression. Finally, treatment with the nuclear factor erythroid 2-related factor 2inhibitor ML385 reversed the beneficial impact of exogenous hydrogen sulfide on quinolinic acid-induced oxidative stress. Taken together, our findings show that hydrogen sulfide reduces oxidative stress in Huntington's disease by activating nuclear factor erythroid 2-related factor 2,suggesting that hydrogen sulfide is a novel neuroprotective drug candidate for treating patients with Huntington's disease.展开更多
Spinal and bulbar muscular atrophy is a neurodegenerative disease caused by extended CAG trinucleotide repeats in the androgen receptor gene,which encodes a ligand-dependent transcription facto r.The mutant androgen r...Spinal and bulbar muscular atrophy is a neurodegenerative disease caused by extended CAG trinucleotide repeats in the androgen receptor gene,which encodes a ligand-dependent transcription facto r.The mutant androgen receptor protein,characterized by polyglutamine expansion,is prone to misfolding and forms aggregates in both the nucleus and cytoplasm in the brain in spinal and bulbar muscular atrophy patients.These aggregates alter protein-protein interactions and compromise transcriptional activity.In this study,we reported that in both cultured N2a cells and mouse brain,mutant androgen receptor with polyglutamine expansion causes reduced expression of mesencephalic astrocyte-de rived neurotrophic factor.Overexpressio n of mesencephalic astrocyte-derived neurotrophic factor amelio rated the neurotoxicity of mutant androgen receptor through the inhibition of mutant androgen receptor aggregation.Conversely.knocking down endogenous mesencephalic astrocyte-derived neurotrophic factor in the mouse brain exacerbated neuronal damage and mutant androgen receptor aggregation.Our findings suggest that inhibition of mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor is a potential mechanism underlying neurodegeneration in spinal and bulbar muscular atrophy.展开更多
Sirtuin 2 is a member of the sirtuin family nicotinamide adenine dinucleotide(NAD~+)-dependent deacetylases, known for its regulatory role in different processes, including inflammation. In this context, sirtuin 2 has...Sirtuin 2 is a member of the sirtuin family nicotinamide adenine dinucleotide(NAD~+)-dependent deacetylases, known for its regulatory role in different processes, including inflammation. In this context, sirtuin 2 has been involved in the modulation of key inflammatory signaling pathways and transcription factors by deacetylating specific targets, such as nuclear factor κB and nucleotide-binding oligomerization domain-leucine-rich-repeat and pyrin domain-containing protein 3(NLRP3). However, whether sirtuin 2-mediated pathways induce a pro-or an anti-inflammatory response remains controversial. Sirtuin 2 has been implicated in promoting inflammation in conditions such as asthma and neurodegenerative diseases, suggesting that its inhibition in these conditions could be a potential therapeutic strategy. Conversely, arthritis and type 2 diabetes mellitus studies suggest that sirtuin 2 is essential at the peripheral level and, thus, its inhibition in these pathologies would not be recommended. Overall, the precise role of sirtuin 2 in inflammation appears to be context-dependent, and further investigation is needed to determine the specific molecular mechanisms and downstream targets through which sirtuin 2 influences inflammatory processes in various tissues and pathological conditions. The present review explores the involvement of sirtuin 2 in the inflammation associated with different pathologies to elucidate whether its pharmacological modulation could serve as an effective strategy for treating this prevalent symptom across various diseases.展开更多
Traumatic brain injury involves complex pathophysiological mechanisms,among which oxidative stress significantly contributes to the occurrence of secondary injury.In this study,we evaluated hypidone hydrochloride(YL-0...Traumatic brain injury involves complex pathophysiological mechanisms,among which oxidative stress significantly contributes to the occurrence of secondary injury.In this study,we evaluated hypidone hydrochloride(YL-0919),a self-developed antidepressant with selective sigma-1 receptor agonist properties,and its associated mechanisms and targets in traumatic brain injury.Behavioral experiments to assess functional deficits were followed by assessment of neuronal damage through histological analyses and examination of blood-brain barrier permeability and brain edema.Next,we investigated the antioxidative effects of YL-0919 by assessing the levels of traditional markers of oxidative stress in vivo in mice and in vitro in HT22 cells.Finally,the targeted action of YL-0919 was verified by employing a sigma-1 receptor antagonist(BD-1047).Our findings demonstrated that YL-0919 markedly improved deficits in motor function and spatial cognition on day 3 post traumatic brain injury,while also decreasing neuronal mortality and reversing blood-brain barrier disruption and brain edema.Furthermore,YL-0919 effectively combated oxidative stress both in vivo and in vitro.The protective effects of YL-0919 were partially inhibited by BD-1047.These results indicated that YL-0919 relieved impairments in motor and spatial cognition by restraining oxidative stress,a neuroprotective effect that was partially reversed by the sigma-1 receptor antagonist BD-1047.YL-0919 may have potential as a new treatment for traumatic brain injury.展开更多
The hypothalamic-pituitary-adrenal axis regulates the secretion of glucoco rticoids in response to environmental challenges.In the brain,a nuclear receptor transcription fa ctor,the glucocorticoid recepto r,is an impo...The hypothalamic-pituitary-adrenal axis regulates the secretion of glucoco rticoids in response to environmental challenges.In the brain,a nuclear receptor transcription fa ctor,the glucocorticoid recepto r,is an important component of the hypothalamicpituitary-a d renal axis's negative feedback loop and plays a key role in regulating cognitive equilibrium and neuroplasticity.The glucoco rticoid receptor influences cognitive processes,including glutamate neurotransmission,calcium signaling,and the activation of brain-derived neurotrophic factor-mediated pathways,through a combination of genomic and non-genomic mechanisms.Protein interactions within the central nervous system can alter the expression and activity of the glucocorticoid receptor,there by affecting the hypothalamic-pituitary-a d renal axis and stress-related cognitive functions.An appropriate level of glucocorticoid receptor expression can improve cognitive function,while excessive glucocorticoid receptors or long-term exposure to glucoco rticoids may lead to cognitive impairment.Patients with cognitive impairment-associated diseases,such as Alzheimer's disease,aging,depression,Parkinson's disease,Huntington's disease,stroke,and addiction,often present with dysregulation of the hypothalamic-pituitary-adrenal axis and glucocorticoid receptor expression.This review provides a comprehensive overview of the functions of the glucoco rticoid receptor in the hypothalamic-pituitary-a d renal axis and cognitive activities.It emphasizes that appropriate glucocorticoid receptor signaling fa cilitates learning and memory,while its dysregulation can lead to cognitive impairment.This provides clues about how glucocorticoid receptor signaling can be targeted to ove rcome cognitive disability-related disorders.展开更多
Reperfusion following cerebral ischemia causes both structural and functional damage to brain tissue and could aggravate a patient's condition;this phenomenon is known as cerebral ischemia-reperfusion injury.Curre...Reperfusion following cerebral ischemia causes both structural and functional damage to brain tissue and could aggravate a patient's condition;this phenomenon is known as cerebral ischemia-reperfusion injury.Current studies have elucidated the neuroprotective role of the sirtuin protein family(Sirtuins)in modulating cerebral ischemia-reperfusion injury.However,the potential of utilizing it as a novel intervention target to influence the prognosis of cerebral ischemia-reperfusion injury requires additional exploration.In this review,the origin and research progress of Sirtuins are summarized,suggesting the involvement of Sirtuins in diverse mechanisms that affect cerebral ischemia-reperfusion injury,including inflammation,oxidative stress,blood-brain barrier damage,apoptosis,pyroptosis,and autophagy.The therapeutic avenues related to Sirtuins that may improve the prognosis of cerebral ischemia-reperfusion injury were also investigated by modulating Sirtuins expression and affecting representative pathways,such as nuclear factor-kappa B signaling,oxidative stress mediated by adenosine monophosphate-activated protein kinase,and the forkhead box O.This review also summarizes the potential of endogenous substances,such as RNA and hormones,drugs,dietary supplements,and emerging therapies that regulate Sirtuins expression.This review also reveals that regulating Sirtuins mitigates cerebral ischemia-reperfusion injury when combined with other risk factors.While Sirtuins show promise as a potential target for the treatment of cerebral ischemiareperfusion injury,most recent studies are based on rodent models with circadian rhythms that are distinct from those of humans,potentially influencing the efficacy of Sirtuinstargeting drug therapies.Overall,this review provides new insights into the role of Sirtuins in the pathology and treatment of cerebral ischemia-reperfusion injury.展开更多
BACKGROUND Simulated microgravity environment can lead to gastrointestinal motility disturbance.The pathogenesis of gastrointestinal motility disorders is closely related to the stem cell factor(SCF)/c-kit signaling p...BACKGROUND Simulated microgravity environment can lead to gastrointestinal motility disturbance.The pathogenesis of gastrointestinal motility disorders is closely related to the stem cell factor(SCF)/c-kit signaling pathway associated with intestinal flora and Cajal stromal cells.Moreover,intestinal flora can also affect the regulation of SCF/c-kit signaling pathway,thus affecting the expression of Cajal stromal cells.Cajal cells are the pacemakers of gastrointestinal motility.AIM To investigate the effects of Bifidobacterium lactis(B.lactis)BLa80 on the intestinal flora of rats in simulated microgravity and on the gastrointestinal motility-related SCF/c-kit pathway.METHODS The internationally recognized tail suspension animal model was used to simulate the microgravity environment,and 30 rats were randomly divided into control group,tail suspension group and drug administration tail suspension group with 10 rats in each group for a total of 28 days.The tail group was given B.lactis BLa80 by intragastric administration,and the other two groups were given water intragastric administration,the concentration of intragastric administration was 0.1 g/mL,and each rat was 1 mL/day.Hematoxylin&eosin staining was used to observe the histopathological changes in each segment of the intestine of each group,and the expression levels of SCF,c-kit,extracellular signal-regulated kinase(ERK)and p-ERK in the gastric antrum of each group were detected by Western blotting and PCR.The fecal flora and mucosal flora of rats in each group were detected by 16S rRNA.RESULTS Simulated microgravity resulted in severe exfoliation of villi of duodenum,jejunum and ileum in rats,marked damage,increased space between villi,loose arrangement,shortened columnar epithelium of colon,less folds,narrower mucosal thickness,reduced goblet cell number and crypts,and significant improvement after probiotic intervention.Simulated microgravity reduced the expressions of SCF and c-kit,and increased the expressions of ERK and P-ERK in the gastric antrum of rats.However,after probiotic intervention,the expressions of SCF and ckit were increased,while the expressions of ERK and P-ERK were decreased,with statistical significance(P<0.05).In addition,simulated microgravity can reduce the operational taxonomic unit(OTU)of the overall intestinal flora of rats,B.lactis BLa80 can increase the OTU of rats,simulated microgravity can reduce the overall richness and diversity of stool flora of rats,increase the abundance of firmicutes in stool flora of rats,and reduce the abundance of Bacteroides in stool flora of rats,most of which are mainly beneficial bacteria.Simulated microgravity can increase the overall richness and diversity of mucosal flora,increase the abundance of Bacteroides and Desulphurides in the rat mucosal flora,and decrease the abundance of firmicutes,most of which are proteobacteria.After probiotics intervention,the overall Bacteroidetes trend in simulated microgravity rats was increased.CONCLUSION B.lactis BLa80 can ameliorate intestinal mucosal injury,regulate intestinal flora,inhibit ERK expression,and activate the SCF/c-kit signaling pathway,which may have a facilitating effect on gastrointestinal motility in simulated microgravity rats.展开更多
BACKGROUND Colorectal polyps are commonly observed in patients with chronic liver disease(CLD)and pose a significant clinical concern because of their potential for malignancy.AIM To explore the clinical characteristi...BACKGROUND Colorectal polyps are commonly observed in patients with chronic liver disease(CLD)and pose a significant clinical concern because of their potential for malignancy.AIM To explore the clinical characteristics of colorectal polyps in patients with CLD,a nomogram was established to predict the presence of adenomatous polyps(AP).METHODS Patients with CLD who underwent colonoscopy at Tianjin Second People’s Hospital from January 2020 to May 2023 were evaluated.Clinical data including laboratory results,colonoscopy findings,and pathology reports were collected.Key variables for the nomogram were identified through least absolute shrinkage and selection operator regression,followed by multivariate logistic regression.The performance of the model was evaluated using the area under the receiver area under curve,as well as calibration curves and decision curve analysis.RESULTS The study enrolled 870 participants who underwent colonoscopy,and the detection rate of AP in patients with CLD was 28.6%.Compared to individuals without polyps,six risk factors were identified as predictors for AP occurrence:Age,male sex,body mass index,alcohol consumption,overlapping metabolic dysfunction-associated steatotic liver disease,and serum ferritin levels.The novel nomogram(AP model)demonstrated an area under curve of 0.801(95%confidence interval:0.756-0.845)and 0.785(95%confidence interval:0.712-0.858)in the training and validation groups.Calibration curves indicated good agreement among predicted and actual probabilities(training:χ^(2)=11.860,P=0.157;validation:χ^(2)=7.055,P=0.530).The decision curve analysis underscored the clinical utility of the nomogram for predicting the risk of AP.CONCLUSION The AP model showed reasonable accuracy and provided a clinical foundation for predicting the occurrence of AP in patients with CLD,which has a certain predictive value.展开更多
Retinal aging has been recognized as a significant risk factor for various retinal disorders,including diabetic retinopathy,age-related macular degeneration,and glaucoma,following a growing understanding of the molecu...Retinal aging has been recognized as a significant risk factor for various retinal disorders,including diabetic retinopathy,age-related macular degeneration,and glaucoma,following a growing understanding of the molecular underpinnings of their development.This comprehensive review explores the mechanisms of retinal aging and investigates potential neuroprotective approaches,focusing on the activation of transcription factor EB.Recent meta-analyses have demonstrated promising outcomes of transcription factor EB-targeted strategies,such as exercise,calorie restriction,rapamycin,and metformin,in patients and animal models of these common retinal diseases.The review critically assesses the role of transcription factor EB in retinal biology during aging,its neuroprotective effects,and its therapeutic potential for retinal disorders.The impact of transcription factor EB on retinal aging is cell-specific,influencing metabolic reprogramming and energy homeostasis in retinal neurons through the regulation of mitochondrial quality control and nutrient-sensing pathways.In vascular endothelial cells,transcription factor EB controls important processes,including endothelial cell proliferation,endothelial tube formation,and nitric oxide levels,thereby influencing the inner blood-retinal barrier,angiogenesis,and retinal microvasculature.Additionally,transcription factor EB affects vascular smooth muscle cells,inhibiting vascular calcification and atherogenesis.In retinal pigment epithelial cells,transcription factor EB modulates functions such as autophagy,lysosomal dynamics,and clearance of the aging pigment lipofuscin,thereby promoting photoreceptor survival and regulating vascular endothelial growth factor A expression involved in neovascularization.These cell-specific functions of transcription factor EB significantly impact retinal aging mechanisms encompassing proteostasis,neuronal synapse plasticity,energy metabolism,microvasculature,and inflammation,ultimately offering protection against retinal aging and diseases.The review emphasizes transcription factor EB as a potential therapeutic target for retinal diseases.Therefore,it is imperative to obtain well-controlled direct experimental evidence to confirm the efficacy of transcription factor EB modulation in retinal diseases while minimizing its risk of adverse effects.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 Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(Grant No.2020R1A5A1016126)。
文摘We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.
基金supported by the National Natural Science Foundation of China,Nos.82271327 (to ZW),82072535 (to ZW),81873768 (to ZW),and 82001253 (to TL)。
文摘The pathophysiology of Huntington's disease involves high levels of the neurotoxin quinolinic acid. Quinolinic acid accumulation results in oxidative stress, which leads to neurotoxicity. However, the molecular and cellular mechanisms by which quinolinic acid contributes to Huntington's disease pathology remain unknown. In this study, we established in vitro and in vivo models of Huntington's disease by administering quinolinic acid to the PC12 neuronal cell line and the striatum of mice, respectively. We observed a decrease in the levels of hydrogen sulfide in both PC12 cells and mouse serum, which was accompanied by down-regulation of cystathionine β-synthase, an enzyme responsible for hydrogen sulfide production. However, treatment with NaHS(a hydrogen sulfide donor) increased hydrogen sulfide levels in the neurons and in mouse serum, as well as cystathionine β-synthase expression in the neurons and the mouse striatum, while also improving oxidative imbalance and mitochondrial dysfunction in PC12 cells and the mouse striatum. These beneficial effects correlated with upregulation of nuclear factor erythroid 2-related factor 2 expression. Finally, treatment with the nuclear factor erythroid 2-related factor 2inhibitor ML385 reversed the beneficial impact of exogenous hydrogen sulfide on quinolinic acid-induced oxidative stress. Taken together, our findings show that hydrogen sulfide reduces oxidative stress in Huntington's disease by activating nuclear factor erythroid 2-related factor 2,suggesting that hydrogen sulfide is a novel neuroprotective drug candidate for treating patients with Huntington's disease.
基金supported by the National Key R&D Program of China,No.2021YFA0805200(to SY)the National Natural Science Foundation of China,No.31970954(to SY)two grants from the Department of Science and Technology of Guangdong Province,Nos.2021ZT09Y007,2020B121201006(both to XJL)。
文摘Spinal and bulbar muscular atrophy is a neurodegenerative disease caused by extended CAG trinucleotide repeats in the androgen receptor gene,which encodes a ligand-dependent transcription facto r.The mutant androgen receptor protein,characterized by polyglutamine expansion,is prone to misfolding and forms aggregates in both the nucleus and cytoplasm in the brain in spinal and bulbar muscular atrophy patients.These aggregates alter protein-protein interactions and compromise transcriptional activity.In this study,we reported that in both cultured N2a cells and mouse brain,mutant androgen receptor with polyglutamine expansion causes reduced expression of mesencephalic astrocyte-de rived neurotrophic factor.Overexpressio n of mesencephalic astrocyte-derived neurotrophic factor amelio rated the neurotoxicity of mutant androgen receptor through the inhibition of mutant androgen receptor aggregation.Conversely.knocking down endogenous mesencephalic astrocyte-derived neurotrophic factor in the mouse brain exacerbated neuronal damage and mutant androgen receptor aggregation.Our findings suggest that inhibition of mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor is a potential mechanism underlying neurodegeneration in spinal and bulbar muscular atrophy.
基金funded by FEDER/Ministerio de Ciencia,Innovación y Universidades Agencia Estatal de Investigación/Project(PID2020-119729GB-100,REF/AEI/10.13039/501100011033)(to EP)a predoctoral fellowship from the Spanish Ministry of Universities(FPU)and Amigos de la Universidad de Navarra(to NSS)“Programa MRR Investigo 2023”(to MGB and MMD)。
文摘Sirtuin 2 is a member of the sirtuin family nicotinamide adenine dinucleotide(NAD~+)-dependent deacetylases, known for its regulatory role in different processes, including inflammation. In this context, sirtuin 2 has been involved in the modulation of key inflammatory signaling pathways and transcription factors by deacetylating specific targets, such as nuclear factor κB and nucleotide-binding oligomerization domain-leucine-rich-repeat and pyrin domain-containing protein 3(NLRP3). However, whether sirtuin 2-mediated pathways induce a pro-or an anti-inflammatory response remains controversial. Sirtuin 2 has been implicated in promoting inflammation in conditions such as asthma and neurodegenerative diseases, suggesting that its inhibition in these conditions could be a potential therapeutic strategy. Conversely, arthritis and type 2 diabetes mellitus studies suggest that sirtuin 2 is essential at the peripheral level and, thus, its inhibition in these pathologies would not be recommended. Overall, the precise role of sirtuin 2 in inflammation appears to be context-dependent, and further investigation is needed to determine the specific molecular mechanisms and downstream targets through which sirtuin 2 influences inflammatory processes in various tissues and pathological conditions. The present review explores the involvement of sirtuin 2 in the inflammation associated with different pathologies to elucidate whether its pharmacological modulation could serve as an effective strategy for treating this prevalent symptom across various diseases.
基金supported by the National Natural Science Foundation of China,Nos.82204360(to HM)and 82270411(to GW)National Science and Technology Innovation 2030 Major Program,No.2021ZD0200900(to YL)。
文摘Traumatic brain injury involves complex pathophysiological mechanisms,among which oxidative stress significantly contributes to the occurrence of secondary injury.In this study,we evaluated hypidone hydrochloride(YL-0919),a self-developed antidepressant with selective sigma-1 receptor agonist properties,and its associated mechanisms and targets in traumatic brain injury.Behavioral experiments to assess functional deficits were followed by assessment of neuronal damage through histological analyses and examination of blood-brain barrier permeability and brain edema.Next,we investigated the antioxidative effects of YL-0919 by assessing the levels of traditional markers of oxidative stress in vivo in mice and in vitro in HT22 cells.Finally,the targeted action of YL-0919 was verified by employing a sigma-1 receptor antagonist(BD-1047).Our findings demonstrated that YL-0919 markedly improved deficits in motor function and spatial cognition on day 3 post traumatic brain injury,while also decreasing neuronal mortality and reversing blood-brain barrier disruption and brain edema.Furthermore,YL-0919 effectively combated oxidative stress both in vivo and in vitro.The protective effects of YL-0919 were partially inhibited by BD-1047.These results indicated that YL-0919 relieved impairments in motor and spatial cognition by restraining oxidative stress,a neuroprotective effect that was partially reversed by the sigma-1 receptor antagonist BD-1047.YL-0919 may have potential as a new treatment for traumatic brain injury.
基金supported by the National Natural Science Foundation of China,No.82371444(to YZ)the Natural Science Foundation of Hubei Province,No.2022CFB216(to XC)the Key Research Project of Ministry of Science and Technology of China,No.2022ZD021160(to YZ)。
文摘The hypothalamic-pituitary-adrenal axis regulates the secretion of glucoco rticoids in response to environmental challenges.In the brain,a nuclear receptor transcription fa ctor,the glucocorticoid recepto r,is an important component of the hypothalamicpituitary-a d renal axis's negative feedback loop and plays a key role in regulating cognitive equilibrium and neuroplasticity.The glucoco rticoid receptor influences cognitive processes,including glutamate neurotransmission,calcium signaling,and the activation of brain-derived neurotrophic factor-mediated pathways,through a combination of genomic and non-genomic mechanisms.Protein interactions within the central nervous system can alter the expression and activity of the glucocorticoid receptor,there by affecting the hypothalamic-pituitary-a d renal axis and stress-related cognitive functions.An appropriate level of glucocorticoid receptor expression can improve cognitive function,while excessive glucocorticoid receptors or long-term exposure to glucoco rticoids may lead to cognitive impairment.Patients with cognitive impairment-associated diseases,such as Alzheimer's disease,aging,depression,Parkinson's disease,Huntington's disease,stroke,and addiction,often present with dysregulation of the hypothalamic-pituitary-adrenal axis and glucocorticoid receptor expression.This review provides a comprehensive overview of the functions of the glucoco rticoid receptor in the hypothalamic-pituitary-a d renal axis and cognitive activities.It emphasizes that appropriate glucocorticoid receptor signaling fa cilitates learning and memory,while its dysregulation can lead to cognitive impairment.This provides clues about how glucocorticoid receptor signaling can be targeted to ove rcome cognitive disability-related disorders.
文摘Reperfusion following cerebral ischemia causes both structural and functional damage to brain tissue and could aggravate a patient's condition;this phenomenon is known as cerebral ischemia-reperfusion injury.Current studies have elucidated the neuroprotective role of the sirtuin protein family(Sirtuins)in modulating cerebral ischemia-reperfusion injury.However,the potential of utilizing it as a novel intervention target to influence the prognosis of cerebral ischemia-reperfusion injury requires additional exploration.In this review,the origin and research progress of Sirtuins are summarized,suggesting the involvement of Sirtuins in diverse mechanisms that affect cerebral ischemia-reperfusion injury,including inflammation,oxidative stress,blood-brain barrier damage,apoptosis,pyroptosis,and autophagy.The therapeutic avenues related to Sirtuins that may improve the prognosis of cerebral ischemia-reperfusion injury were also investigated by modulating Sirtuins expression and affecting representative pathways,such as nuclear factor-kappa B signaling,oxidative stress mediated by adenosine monophosphate-activated protein kinase,and the forkhead box O.This review also summarizes the potential of endogenous substances,such as RNA and hormones,drugs,dietary supplements,and emerging therapies that regulate Sirtuins expression.This review also reveals that regulating Sirtuins mitigates cerebral ischemia-reperfusion injury when combined with other risk factors.While Sirtuins show promise as a potential target for the treatment of cerebral ischemiareperfusion injury,most recent studies are based on rodent models with circadian rhythms that are distinct from those of humans,potentially influencing the efficacy of Sirtuinstargeting drug therapies.Overall,this review provides new insights into the role of Sirtuins in the pathology and treatment of cerebral ischemia-reperfusion injury.
文摘BACKGROUND Simulated microgravity environment can lead to gastrointestinal motility disturbance.The pathogenesis of gastrointestinal motility disorders is closely related to the stem cell factor(SCF)/c-kit signaling pathway associated with intestinal flora and Cajal stromal cells.Moreover,intestinal flora can also affect the regulation of SCF/c-kit signaling pathway,thus affecting the expression of Cajal stromal cells.Cajal cells are the pacemakers of gastrointestinal motility.AIM To investigate the effects of Bifidobacterium lactis(B.lactis)BLa80 on the intestinal flora of rats in simulated microgravity and on the gastrointestinal motility-related SCF/c-kit pathway.METHODS The internationally recognized tail suspension animal model was used to simulate the microgravity environment,and 30 rats were randomly divided into control group,tail suspension group and drug administration tail suspension group with 10 rats in each group for a total of 28 days.The tail group was given B.lactis BLa80 by intragastric administration,and the other two groups were given water intragastric administration,the concentration of intragastric administration was 0.1 g/mL,and each rat was 1 mL/day.Hematoxylin&eosin staining was used to observe the histopathological changes in each segment of the intestine of each group,and the expression levels of SCF,c-kit,extracellular signal-regulated kinase(ERK)and p-ERK in the gastric antrum of each group were detected by Western blotting and PCR.The fecal flora and mucosal flora of rats in each group were detected by 16S rRNA.RESULTS Simulated microgravity resulted in severe exfoliation of villi of duodenum,jejunum and ileum in rats,marked damage,increased space between villi,loose arrangement,shortened columnar epithelium of colon,less folds,narrower mucosal thickness,reduced goblet cell number and crypts,and significant improvement after probiotic intervention.Simulated microgravity reduced the expressions of SCF and c-kit,and increased the expressions of ERK and P-ERK in the gastric antrum of rats.However,after probiotic intervention,the expressions of SCF and ckit were increased,while the expressions of ERK and P-ERK were decreased,with statistical significance(P<0.05).In addition,simulated microgravity can reduce the operational taxonomic unit(OTU)of the overall intestinal flora of rats,B.lactis BLa80 can increase the OTU of rats,simulated microgravity can reduce the overall richness and diversity of stool flora of rats,increase the abundance of firmicutes in stool flora of rats,and reduce the abundance of Bacteroides in stool flora of rats,most of which are mainly beneficial bacteria.Simulated microgravity can increase the overall richness and diversity of mucosal flora,increase the abundance of Bacteroides and Desulphurides in the rat mucosal flora,and decrease the abundance of firmicutes,most of which are proteobacteria.After probiotics intervention,the overall Bacteroidetes trend in simulated microgravity rats was increased.CONCLUSION B.lactis BLa80 can ameliorate intestinal mucosal injury,regulate intestinal flora,inhibit ERK expression,and activate the SCF/c-kit signaling pathway,which may have a facilitating effect on gastrointestinal motility in simulated microgravity rats.
基金Supported by the National Natural Science Foundation of China,No.62375202Natural Science Foundation of Tianjin,No.23JCYBJC00950+1 种基金Tianjin Health Science and Technology Project Key Discipline Special,No.TJWJ2022XK034Research Project in Key Areas of Traditional Chinese Medicine in 2024,No.2024022.
文摘BACKGROUND Colorectal polyps are commonly observed in patients with chronic liver disease(CLD)and pose a significant clinical concern because of their potential for malignancy.AIM To explore the clinical characteristics of colorectal polyps in patients with CLD,a nomogram was established to predict the presence of adenomatous polyps(AP).METHODS Patients with CLD who underwent colonoscopy at Tianjin Second People’s Hospital from January 2020 to May 2023 were evaluated.Clinical data including laboratory results,colonoscopy findings,and pathology reports were collected.Key variables for the nomogram were identified through least absolute shrinkage and selection operator regression,followed by multivariate logistic regression.The performance of the model was evaluated using the area under the receiver area under curve,as well as calibration curves and decision curve analysis.RESULTS The study enrolled 870 participants who underwent colonoscopy,and the detection rate of AP in patients with CLD was 28.6%.Compared to individuals without polyps,six risk factors were identified as predictors for AP occurrence:Age,male sex,body mass index,alcohol consumption,overlapping metabolic dysfunction-associated steatotic liver disease,and serum ferritin levels.The novel nomogram(AP model)demonstrated an area under curve of 0.801(95%confidence interval:0.756-0.845)and 0.785(95%confidence interval:0.712-0.858)in the training and validation groups.Calibration curves indicated good agreement among predicted and actual probabilities(training:χ^(2)=11.860,P=0.157;validation:χ^(2)=7.055,P=0.530).The decision curve analysis underscored the clinical utility of the nomogram for predicting the risk of AP.CONCLUSION The AP model showed reasonable accuracy and provided a clinical foundation for predicting the occurrence of AP in patients with CLD,which has a certain predictive value.
基金supported by the Start-up Fund for new faculty from the Hong Kong Polytechnic University(PolyU)(A0043215)(to SA)the General Research Fund and Research Impact Fund from the Hong Kong Research Grants Council(15106018,R5032-18)(to DYT)+1 种基金the Research Center for SHARP Vision in PolyU(P0045843)(to SA)the InnoHK scheme from the Hong Kong Special Administrative Region Government(to DYT).
文摘Retinal aging has been recognized as a significant risk factor for various retinal disorders,including diabetic retinopathy,age-related macular degeneration,and glaucoma,following a growing understanding of the molecular underpinnings of their development.This comprehensive review explores the mechanisms of retinal aging and investigates potential neuroprotective approaches,focusing on the activation of transcription factor EB.Recent meta-analyses have demonstrated promising outcomes of transcription factor EB-targeted strategies,such as exercise,calorie restriction,rapamycin,and metformin,in patients and animal models of these common retinal diseases.The review critically assesses the role of transcription factor EB in retinal biology during aging,its neuroprotective effects,and its therapeutic potential for retinal disorders.The impact of transcription factor EB on retinal aging is cell-specific,influencing metabolic reprogramming and energy homeostasis in retinal neurons through the regulation of mitochondrial quality control and nutrient-sensing pathways.In vascular endothelial cells,transcription factor EB controls important processes,including endothelial cell proliferation,endothelial tube formation,and nitric oxide levels,thereby influencing the inner blood-retinal barrier,angiogenesis,and retinal microvasculature.Additionally,transcription factor EB affects vascular smooth muscle cells,inhibiting vascular calcification and atherogenesis.In retinal pigment epithelial cells,transcription factor EB modulates functions such as autophagy,lysosomal dynamics,and clearance of the aging pigment lipofuscin,thereby promoting photoreceptor survival and regulating vascular endothelial growth factor A expression involved in neovascularization.These cell-specific functions of transcription factor EB significantly impact retinal aging mechanisms encompassing proteostasis,neuronal synapse plasticity,energy metabolism,microvasculature,and inflammation,ultimately offering protection against retinal aging and diseases.The review emphasizes transcription factor EB as a potential therapeutic target for retinal diseases.Therefore,it is imperative to obtain well-controlled direct experimental evidence to confirm the efficacy of transcription factor EB modulation in retinal diseases while minimizing its risk of adverse effects.
