THE FACTORIZATIONS OF GENERIC FIEDLER MATRIX

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,

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-C: Constructive Algorithms for Canonical Factorizations and a Special Class of Asymptotic Scales

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.

ON ORTHOGONAL (0,f)-FACTORIZATIONS

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.

Rice condition numbers of QR and Cholesky factorizations

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 .

ON(g,f)-FACTORIZATIONS OF GRAPHS

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.

[0, ki ]1m -FACTORIZATIONS ORTHOGONAL TO A SUBGRAPH

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.

Super number roots and factorizations for a kind of polynomial

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.

On the Factorizations of (mg, mf)-graph

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.

Ungraded Matrix Factorizations as Mirrors of Non-orientable Lagrangians

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.

Hypidone hydrochloride(YL-0919)ameliorates functional deficits after traumatic brain injury in mice by activating the sigma-1 receptor for antioxidation

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.

On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices

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.

Factorizations of groups and related topics

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.

Reduced mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor contributes to neurodegeneration in a model of spinal and bulbar muscular atrophy pathology

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.

Functions of nuclear factor Y in nervous system development,function and health

Nuclear factor Y is a ubiquitous heterotrimeric transcription factor complex conserved across eukaryotes that binds to CCAAT boxes,one of the most common motifs found in gene promoters and enhancers.Over the last 30 years,research has revealed that the nuclear factor Y complex controls many aspects of brain development,including differentiation,axon guidance,homeostasis,disease,and most recently regeneration.However,a complete understanding of transcriptional regulatory networks,including how the nuclear factor Y complex binds to specific CCAAT boxes to perform its function remains elusive.In this review,we explore the nuclear factor Y complex’s role and mode of action during brain development,as well as how genomic technologies may expand understanding of this key regulator of gene expression.

Hydrogen sulfide reduces oxidative stress in Huntington's disease via Nrf2

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.

The effects of exercise interventions on brain-derived neurotrophic factor levels in children and adolescents:a meta-analysis

Brain-derived neurotrophic factor is a crucial neurotrophic factor that plays a significant role in brain health. Although the vast majority of meta-analyses have confirmed that exercise interventions can increase brain-derived neurotrophic factor levels in children and adolescents, the effects of specific types of exercise on brain-derived neurotrophic factor levels are still controversial. To address this issue, we used meta-analytic methods to quantitatively evaluate, analyze, and integrate relevant studies. Our goals were to formulate general conclusions regarding the use of exercise interventions, explore the physiological mechanisms by which exercise improves brain health and cognitive ability in children and adolescents, and provide a reliable foundation for follow-up research. We used the Pub Med, Web of Science, Science Direct, Springer, Wiley Online Library, Weipu, Wanfang, and China National Knowledge Infrastructure databases to search for randomized controlled trials examining the influences of exercise interventions on brain-derived neurotrophic factor levels in children and adolescents. The extracted data were analyzed using Review Manager 5.3. According to the inclusion criteria, we assessed randomized controlled trials in which the samples were mainly children and adolescents, and the outcome indicators were measured before and after the intervention. We excluded animal experiments, studies that lacked a control group, and those that did not report quantitative results. The mean difference(MD;before versus after intervention) was used to evaluate the effect of exercise on brain-derived neurotrophic factor levels in children and adolescents. Overall, 531 participants(60 children and 471 adolescents, 10.9–16.1 years) were included from 13 randomized controlled trials. Heterogeneity was evaluated using the Q statistic and I^(2) test provided by Review Manager software. The meta-analysis showed that there was no heterogeneity among the studies(P = 0.67, I^(2) = 0.00%). The combined effect of the interventions was significant(MD = 2.88, 95% CI: 1.53–4.22, P < 0.0001), indicating that the brain-derived neurotrophic factor levels of the children and adolescents in the exercise group were significantly higher than those in the control group. In conclusion, different types of exercise interventions significantly increased brain-derived neurotrophic factor levels in children and adolescents. However, because of the small sample size of this meta-analysis, more high-quality research is needed to verify our conclusions. This metaanalysis was registered at PROSPERO(registration ID: CRD42023439408).

Context-dependent role of sirtuin 2 in inflammation

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.

Telencephalic stab wound injury induces regenerative angiogenesis and neurogenesis in zebrafish:unveiling the role of vascular endothelial growth factor signaling and microglia

After brain damage,regenerative angiogenesis and neurogenesis have been shown to occur simultaneously in mammals,suggesting a close link between these processes.However,the mechanisms by which these processes interact are not well understood.In this work,we aimed to study the correlation between angiogenesis and neurogenesis after a telencephalic stab wound injury.To this end,we used zebrafish as a relevant model of neuroplasticity and brain repair mechanisms.First,using the Tg(fli1:EGFP×mpeg1.1:mCherry)zebrafish line,which enables visualization of blood vessels and microglia respectively,we analyzed regenerative angiogenesis from 1 to 21 days post-lesion.In parallel,we monitored brain cell proliferation in neurogenic niches localized in the ventricular zone by using immunohistochemistry.We found that after brain damage,the blood vessel area and width as well as expression of the fli1 transgene and vascular endothelial growth factor(vegfaa and vegfbb)were increased.At the same time,neural stem cell proliferation was also increased,peaking between 3 and 5 days post-lesion in a manner similar to angiogenesis,along with the recruitment of microglia.Then,through pharmacological manipulation by injecting an anti-angiogenic drug(Tivozanib)or Vegf at the lesion site,we demonstrated that blocking or activating Vegf signaling modulated both angiogenic and neurogenic processes,as well as microglial recruitment.Finally,we showed that inhibition of microglia by clodronate-containing liposome injection or dexamethasone treatment impairs regenerative neurogenesis,as previously described,as well as injury-induced angiogenesis.In conclusion,we have described regenerative angiogenesis in zebrafish for the first time and have highlighted the role of inflammation in this process.In addition,we have shown that both angiogenesis and neurogenesis are involved in brain repair and that microglia and inflammation-dependent mechanisms activated by Vegf signaling are important contributors to these processes.This study paves the way for a better understanding of the effect of Vegf on microglia and for studies aimed at promoting angiogenesis to improve brain plasticity after brain injury.

Recovery of the injured neural system through gene delivery to surviving neurons in Parkinson’s disease

A critical unaddressed problem in Parkinson’s disease is the lack of therapy that slows or hampers neurodegeneration.While medications effectively manage symptoms,they offer no long-term benefit because they fail to address the underlying neuronal loss.This highlights that the elusive goals of halting progression and restoring damaged neurons limit the long-term impact of current approaches.Recent clinical trials using gene therapy have demonstrated the safety of various vector delivery systems,dosages,and transgenes expressed in the central nervous system,signifying tangible and substantial progress in applying gene therapy as a promising Parkinson’s disease treatment.Intriguingly,at diagnosis,many dopamine neurons remain in the substantia nigra,offering a potential window for recovery and survival.We propose that modulating these surviving dopamine neurons and axons in the substantia nigra and striatum using gene therapy offers a potentially more impactful therapeutic approach for future research.Moreover,innovative gene therapies that focus on preserving the remaining elements may have significant potential for enhancing long-term outcomes and the quality of life for patients with Parkinson’s disease.In this review,we provide a perspective on how gene therapy can protect vulnerable elements in the substantia nigra and striatum,offering a novel approach to addressing Parkinson’s disease at its core.

Glucocorticoid receptor signaling in the brain and its involvement in cognitive function

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.