Ramification Index Research Articles

Locomotor and gait changes in the LPS model of neuroinflammation are correlated with inflammatory cytokines in blood and brain.

Lipopolysaccharide (LPS) challenge in mice has been used to identify the mechanisms and therapeutics for neuroinflammation. In this study, we aimed to comprehensively evaluate the behavioral changes including locomotion, exploration, and memory, correlating them with a panel of thirteen inflammatory cytokines in both blood and brain.We found that acute LPS administration (0.83 mg/Kg i.p.) reduced body weight, food intake, and glucose levels compared to the saline-injected mice, concomitant with decreased activity in home cage monitoring. Locomotion was significantly reduced in Open Field, Introduced Object, and Y-Maze tests. Decreased exploratory behavior in the Y-Maze and Introduced Object tests was noticed, by measuring the number of arms explored and object interaction time, respectively. Additionally, in rotarod, LPS administration led to a significant decrease in the distance achieved, while in the MouseWalker, LPS led to a reduction in average velocity.LPS induced a decrease in microglia ramification index in the motor cortex and the striatum, while surprisingly a reduction in microglia number was observed in the motor cortex.The concentrations of thirteen cytokines in the blood were significantly altered, while only CXCL1, CCL22, CCL17, G-CSF, and IL-12p40 were changed in the brain. Correlations between cytokine levels in blood and brain were found, most notably for CCL17 and CCL22. TGFβ was the only one with negative correlations to other cytokines. Correlations between cytokines and behavior changes were also disclosed, especially for CCL17, CCL22, G-CSF, and IL-6 and negatively for TGFβ and IL-10.In summary, our study employing acute LPS challenge in mice has revealed a comprehensive profile of behavioral alterations alongside significant changes in inflammatory cytokine levels, both in peripheral blood and brain tissue. These findings contribute to a deeper understanding of the interplay between inflammation and behavior, with possible implications for identifying prognostics and therapeutic targets for neuroinflammatory conditions.

Sex-dependent astrocyte reactivity: Unveiling chronic stress-induced morphological changes across multiple brain regions

Chronic stress is a major precursor to various neuropsychiatric disorders and is linked with increased inflammation in the brain. However, the bidirectional association between inflammation and chronic stress has yet to be fully understood. Astrocytes are one of the key inflammatory regulators in the brain, and the morphological change in reactive astrocytes serves as an important indicator of inflammation. In this study, we evaluated the sex-specific astrocyte response to chronic stress or systemic inflammation in key brain regions associated with mood disorders. We conducted the unpredictable chronic mild stress (UCMS) paradigm to model chronic stress, or lipopolysaccharide (LPS) injection to model systemic inflammation. To evaluate stress-induced morphological changes in astrocyte complexity, we measured GFAP fluorescent intensity for astrocyte expression, branch bifurcation by quantifying branch points and terminal points, branch arborization by conducting Sholl analysis, and calculated the ramification index. Our analysis indicated that chronic stress-induced morphological changes in astrocytes in all brain regions investigated. The effects of chronic stress were region and sex specific. Notably, females had greater stress or inflammation-induced astrocyte activation in the hypothalamus (HYPO), CA1, CA3, and amygdala (AMY) than males. These findings indicate that chronic stress induces astrocyte activation that may drive sex and region-specific effects in females, potentially contributing to sex-dependent mechanisms of disease.

Chronic inflammation with microglia senescence at basal forebrain: impact on cholinergic deficit in Alzheimer's brain haemodynamics.

Cholinergic innervation in the brain is involved in modulating neurovascular function including cerebral blood flow haemodynamics in response to neuronal activity. Cholinergic deficit is associated with pathophysiology in Alzheimer's disease, albeit the aetiology remains to be clarified. In the current study, neocortex cerebral blood flow response to acetylcholine was evaluated by Laser-Doppler Flowmetry (LDF) in 3xTgAD Alzheimer's disease model) and wild-type mice of two age groups. The peak of cerebral blood flow to acetylcholine (i.v.) from baseline levels (% ΔrCBF) was higher in young 3xTgAD versus in wild-type mice (48.35; 95% CI:27.03-69.67 versus 22.70; CI:15.5-29.91, P < 0.05); this was reversed in old 3xTgAD mice (21.44; CI:2.52-40.35 versus 23.25; CI:23.25-39). Choline acetyltransferase protein was reduced in neocortex, while cerebrovascular reactivity to acetylcholine was preserved in young 3×TgAD mice. This suggests endogenous acetylcholine deficit and possible cholinergic denervation from selected cholinergic nuclei within the basal forebrain. The early deposition of tauopathy moieties (mutant hTau and pTau181) and its coincidence in cholinergic cell clusters (occasionaly), were observed at the basal forebrain of 3xTgAD mice including substantia innominate, nucleus Basalis of Meynert and nucleus of horizontal limb diagonal band of Broca. A prominent feature was microglia interacting tauopathy and demonstrated a variety of morphology changes particularly when located in proximity to tauopathy. The microglia ramified phenotype was reduced as evaluated by the ramification index and Fractal analysis. Increased microglia senescence, identified as SASP (senescence-associated secretory phenotype), was colocalization with p16Ink4ɑ, a marker of irreversible cell-cycle arrest in old 3xTgAD versus wild-type mice (P = 0.001). The p16Ink4ɑ was also observed in neuronal cells bearing tauopathy within the basal forebrain of 3xTgAD mice. TNF-ɑ, the pro-inflammatory cytokine elevated persistently in microglia (Pearson's correlation coefficient = 0.62) and the loss of cholinergic cells in vulnerable basal forebrain environment, was indicated by image analysis in 3xTgAD mice, which linked to the cholinergic deficits in neocortex rCBF haemodynamics. Our study revealed the early change of CBF haemodynamics to acetylcholine in 3xTgAD model. As a major effector of brain innate immune activation, microglia SASP with age-related disease progression is indicative of immune cell senescence, which contributes to chronic inflammation and cholinergic deficits at the basal forebrain. Targeting neuroinflammation and senescence may mitigate cholinergic pathophysiology in Alzheimer's disease.

Construction of even-level representations of [formula omitted] with residue field of characteristic two

We construct the finite-dimensional continuous complex representations of SL2 over compact discrete valuation rings of even residual characteristic, assuming the level is large enough compared to the ramification index, in the mixed characteristic case. We also prove that the complex group algebras of SL2 over finite quotient rings of such compact discrete valuation rings depend on the characteristic of the ring. In particular, we prove that the group algebras C[SL2(Z/2rZ)] and C[SL2(F2[t]/(tr))] are not isomorphic for any r≥4.

Ferulic Acid reduces amyloid beta mediated neuroinflammation through modulation of Nurr1 expression in microglial cells.

Microglial cells (MGCs) serve as the resident macrophages in the brain and spinal cord, acting as the first line of immune defense against pathological changes. With various phenotypes, they can shift from a homeostatic state to a reactive state or transit from a reactive to a non-inflammatory reactive state (alternative homeostatic). A well-timed transit is crucial in limiting excessive microglial reaction and promoting the healing process. Studies indicate that increased Nurr1 expression promotes anti-neuroinflammatory responses in the brain. In this study, we investigated the possible role of ferulic acid (FA) in facilitating microglia transition due to its anti-inflammatory and Nurr1-inducing effects. MGCs were extracted from the brains of male NMRI mice at postnatal day 2 (P2) and cultured with or without FA and beta-amyloid (Aβ). Real-time qRT-PCR was conducted to measure the expressions of Nurr1, IL-1β, and IL-10 genes. Immunostaining was performed to determine the number of NURR1-positive cells, and the ramification index (RI) of MGCs was calculated using Image J software. Treating MGCs with FA (50 μg/ml) induced Nurr1 and IL-10 expressions, while reducing the level of IL-1β in the absence of Aβ-stress. Further assessments on cells under Aβ-stress showed that FA treatment restored the IL-10 and Nurr1 levels, increased the RI of cells, and the number of NURR1-positive cells. Morphological assessments and measurements of the RI revealed that FA treatment reversed amoeboid and rod-like cells to a ramified state, which is specific morphology for non-inflammatory reactive microglia. To conclude, FA can provide potential alternative homeostatic transition in Aβ-reactive microglia by recruiting the NURR1 dependent anti-inflammatory responses. This makes it a promising therapeutic candidate for suppressing Aβ-induced neuroinflammatory responses in MGCs. Furthermore, given that FA has the ability to increase NURR1 levels in homeostatic microglia, it could be utilized as a preventative medication.

Different Methods for Evaluating Microglial Activation Using Anti-Ionized Calcium-Binding Adaptor Protein-1 Immunohistochemistry in the Cuprizone Model.

Microglia play an important role in the pathology of various central nervous system disorders, including multiple sclerosis (MS). While different methods exist to evaluate the extent of microglia activation, comparative studies investigating the sensitivity of these methods are missing for most models. In this study, we systematically evaluated which of the three commonly used histological methods (id est, quantification of microglia density, densitometrically evaluated staining intensity, or cellular morphology based on the determination of a ramification index, all measured in anti-ionized calcium-binding adaptor protein-1 (IBA1) immunohistochemical stains) is the most sensitive method to detect subtle changes in the microglia activation status in the context of MS. To this end, we used the toxin-induced cuprizone model which allows the experimental induction of a highly reproducible demyelination in several central nervous system regions, paralleled by early microglia activation. In this study, we showed that after 3 weeks of cuprizone intoxication, all methods reveal a significant microglia activation in the white matter corpus callosum. In contrast, in the affected neocortical grey matter, the evaluation of anti-IBA1 cell morphologies was the most sensitive method to detect subtle changes of microglial activation. The results of this study provide a useful guide for future immunohistochemical evaluations in the cuprizone and other neurodegenerative models.

Essential finite generation of valuation rings in characteristic zero algebraic function fields

Let $K$ be a characteristic zero algebraic function field with a valuation $\nu$. Let $L$ be a finite extension of $K$ and $\omega$ be an extension of $\nu$ to $L$. We establish that the valuation ring $V_{\omega}$ of $\omega$ is essentially finitely generated over the valuation ring $V_{\nu}$ of $\nu$ if and only if the initial index $\epsilon(\omega|\nu)$ is equal to the ramification index $e(\omega|\nu)$ of the extension. This gives a positive answer, for characteristic zero algebraic function fields, to a question posed by Hagen Knaf.

Integral $p$-adic Hodge filtrations in low dimension and ramification

Given an integral p -adic variety, we observe that if the integral Hodge–de Rham spectral sequence behaves nicely, then the special fiber knows the Hodge numbers of the generic fiber. Applying recent advancements of integral p -adic Hodge theory, we show that such a nice behavior is guaranteed if the p -adic variety can be lifted to an analogue of second Witt vectors and satisfies some bound on dimension and ramification index. This is a (ramified) mixed characteristic analogue of results due to Deligne–Illusie, Fontaine–Messing, and Kato. Lastly, we discuss an example illustrating the necessity of the aforementioned lifting condition, which is of independent interest.

Hyperelliptic $$\mathcal {S}_7$$-curves of prime conductor

An abelian threefold $$A_{/{\mathbb {Q}}}$$ of prime conductor N is favorable if its 2-division field F is an $${\mathcal {S}}_7$$ -extension over $${\mathbb {Q}}$$ with ramification index 7 over $${\mathbb {Q}}_2$$ . Let A be favorable and let B be a semistable abelian variety of conductor $$N^d$$ with B[2] filtered by d copies of A[2]. We obtain a class field theoretic criterion on F to guarantee that B is isogenous to $$A^d$$ and a fortiori, A is unique up to isogeny.

Diversity and complexity of the cavotricuspid isthmus in rabbits: A novel scheme for classification and geometrical transformation of anatomical structures.

The aim of this study was to describe the morphology of the cavotricuspid isthmus (CTI) in detail and introduce a comprehensive scheme to describe the topology of this region based on functional considerations. This may lead to a better understanding of isthmus-dependent flutter and fibrillation and to improved intervention strategies. We used images of the cavotricuspid isthmus from 52 rabbits of both sexes with a median weight of 3.40 ± 0.93 kg. The area of the CTI was 124.25 ± 42.14 mm2 with 53.28 ± 21.13 mm2 covered by pectinate muscles connecting the terminal crest and the vestibule. Isthmus length decreased from inferolateral (13.09 ±2.14 mm) to central (9.85 ± 2.14 mm) to paraseptal (4.88 ± 1.96 mm) resembling the overall human geometry. Ramification sites of pectinate muscles were identified and six levels dividing the CTI from posterior to anterior were introduced. This allowed the classification of pectinate muscle segments based on the connected ramification level. To account for the high inter-individual variations in size and shape, the CTI was projected onto a normalized reference frame using bilinear transformation. Furthermore, two measures of complexity were introduced: (i) the ramification index, which reflects the total number of muscle segments connected to a ramification site and (ii) the complexity index, which reflects the type of ramification (branching or merging site). Topological analysis showed that the complexity of the pectinate muscle network decreases from inferolateral to paraseptal and that the number of electrically uncoupled parallel pathways increases in the central section between the terminal crest and the vestibule which introduces potential reentry pathways.

A simple formula for the computation of branches and asymptotes of curves and some applications

In this paper, we obtain a simple formula based on the computation of some derivatives for determining the branches and the asymptotes of curves that are defined by a parametrization. For this purpose, we use some previous results and notions presented in Blasco and Pérez-Díaz (2014a,b, 2015, 2020). From these results, we show how the generalized asymptotes of the input curve can be easily computed and we present some applications related to the ramification index and degree of the asymptote, the infinity form and the multiplicity of the infinity points. Furthermore, we show how to construct all the families of parametric curves having some given asymptotes. We develop this method for the plane case but it can be trivially adapted for dealing with rational curves in n-dimensional space. In addition, the formulaes presented can be similarly obtained for curves defined by a parametrization not necessarily rational.

Mitigation Effects of Selenium Nanoparticles on Depression-Like Behavior Induced by Fluoride in Mice via the JAK2-STAT3 Pathway.

Depression is a mental health problem with typically high levels of distress and dysfunction, and 150 mg/L fluoride (F) can induce depression-like behavior. The development of depression is correlated with neuronal atrophy, insufficient secretion of monoamine neurotransmitters, extreme deviations from the normal microglial activation status, and immune-inflammatory response. Studies found that Se supplementation was related to the improvement of depression. In this study, we applied selenium nanoparticles (SeNPs) for F-induced depression disease mitigation by regulating the histopathology, metabolic index, genes, and protein expression related to the JAK2-STAT3 signaling pathway in vivo. Results showed that F and 2 mg Se/kg BW/day SeNPs lowered the dopamine (DA) content (P < 0.05), altered the microglial morphology, ramification index as well as solidity, and triggered the microglial neuroinflammatory response by increasing the p-STAT3 nuclear translocation (P < 0.01). Furthermore, F reduced the cortical Se content and the number of surviving neurons (P < 0.05), increasing the protein expressions of p-JAK2/JAK2 and p-STAT3/STAT3 of the cortex (P < 0.01), accompanied by the depression-like behavior. Importantly, 1 mg Se/kg BW/day SeNPs alleviated the microglial ramification index as well as solidity changes and decreased the interleukin-1β secretion induced by F by suppressing the p-STAT3 nuclear translocation (P < 0.01). Likewise, 1 mg Se/kg BW/day SeNPs restored the F-disturbed dopamine and noradrenaline secretion, increased the number of cortical surviving neurons, and reduced the vacuolation area, ultimately suppressing the occurrence of depression-like behavior through inhibiting the JAK2-STAT3 pathway activation. In conclusion, 1 mg Se/kg BW/day SeNPs have mitigation effects on the F-induced depression-like behavior. The mechanism of how SeNPs repair neural functions will benefit depression mitigation. This study also indicates that inhibiting the JAK/STAT pathway can be a promising novel treatment for depressive disorders.

Higher criteria for the regularity of a one-dimensional local field

The concept of irregularity of formal modules in one-dimensional local fields is considered. A connection is obtained between the irregularity of all unramified extensions M/L and the ramification index e_(L/K) for a sufficiently wide class of formal groups. The notion of s-irregularity for natural s is introduced (generalization of the notion of irregularity to the case of roots [π^s]), and similar criteria for irregularity are proved for it for the case of generalized and relative formal Lubin—Tate modules.

Resolvent Trace Formula and Determinants of n Laplacians on Orbifold Riemann Surfaces

For $n$ a nonnegative integer, we consider the $n$-Laplacian $\Delta_n$ acting on the space of $n$-differentials on a confinite Riemann surface $X$ which has ramification points. The trace formula for the resolvent kernel is developed along the line \`a la Selberg. Using the trace formula, we compute the regularized determinant of $\Delta_n+s(s+2n-1)$, from which we deduce the regularized determinant of $\Delta_n$, denoted by $\det\!'\Delta_n$. Taking into account the contribution from the absolutely continuous spectrum, $\det\!'\Delta_n$ is equal to a constant $\mathcal{C}_n$ times $Z(n)$ when $n\geq 2$. Here $Z(s)$ is the Selberg zeta function of $X$. When $n=0$ or $n=1$, $Z(n)$ is replaced by the leading coefficient of the Taylor expansion of $Z(s)$ around $s=0$ and $s=1$ respectively. The constants $\mathcal{C}_n$ are calculated explicitly. They depend on the genus, the number of cusps, as well as the ramification indices, but is independent of the moduli parameters.

Purity for Barsotti–Tate groups in some mixed characteristic situations

Let $p$ be a prime. Let $R$ be a regular local ring of dimension $d\ge 2$ whose completion is isomorphic to $C(k)[[x_1,\ldots,x_d]]/(h)$, with $C(k)$ a Cohen ring with the same residue field $k$ as $R$ and with $h\in C(k)[[x_1,\ldots,x_d]]$ such that its reduction modulo $p$ does not belong to the ideal $(x_1^p,\ldots,x_d^p)+(x_1,\ldots,x_d)^{2p-2}$ of $k[[x_1,\ldots,x_d]]$. We extend a result of Vasiu-Zink (for $d=2$) to show that each Barsotti-Tate group over $\text{Frac}(R)$ which extends to every local ring of $\text{Spec}(R)$ of dimension $1$, extends uniquely to a Barsotti-Tate group over $R$. This result corrects in many cases several errors in the literature. As an application, we get that if $Y$ is a regular integral scheme such that the completion of each local ring of $Y$ of residue characteristic $p$ is a formal power series ring over some complete discrete valuation ring of absolute ramification index $e\le p-1$, then each Barsotti-Tate group over the generic point of $Y$ which extends to every local ring of $Y$ of dimension $1$, extends uniquely to a Barsotti-Tate group over $Y$.

Early postnatal allergic airway inflammation induces dystrophic microglia leading to excitatory postsynaptic surplus and autism-like behavior

Microglia play key roles in synaptic pruning, which primarily occurs from the postnatal period to adolescence. Synaptic pruning is essential for normal brain development and its impairment is implicated in neuropsychiatric developmental diseases such as autism spectrum disorders (ASD). Recent epidemiological surveys reported a strong link between ASD and atopic/allergic diseases. However, few studies have experimentally investigated the relationship between allergy and ASD-like manifestations, particularly in the early postnatal period, when allergic disorders occur frequently. Therefore, we aimed to characterize how allergic inflammation in the early postnatal period influences microglia and behavior using mouse models of short- and long-term airway allergy. Male mice were immunized by an intraperitoneal injection of aluminum hydroxide and ovalbumin (OVA) or phosphate-buffered saline (control) on postnatal days (P) 3, 7, and 11, followed by intranasal challenge with OVA or phosphate-buffered saline solution twice a week until P30 or P70. In the hippocampus, Iba-1-positive areas, the size of Iba-1-positive microglial cell bodies, and the ramification index of microglia by Sholl analysis were significantly smaller in the OVA group than in the control group on P30 and P70, although Iba-1-positive microglia numbers did not differ significantly between the two groups. In Iba-1-positive cells, postsynaptic density protein 95 (PSD95)-occupied areas and CD68-occupied areas were significantly decreased on P30 and P70, respectively, in the OVA group compared with the control group. Immunoblotting using hippocampal tissues demonstrated that amounts of PSD95, α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor 2, and N-methyl-D-aspartate (NMDA) receptor 2B were significantly increased in the OVA group compared with the control group on P70, and a similar increasing trend for PSD95 was observed on P30. Neurogenesis was not significantly different between the two groups on P30 or P70 by doublecortin immunohistochemistry. The social preference index was significantly lower in the three chamber test and the number of buried marbles was significantly higher in the OVA group than in the control group on P70 but not on P30, whereas locomotion and anxiety were not different between the two groups. Compared with the control group, serum basal corticosterone levels were significantly elevated and hippocampal glucocorticoid receptor (GR) amounts and nuclear GR translocation in microglia, but not in neurons or astrocytes, were significantly decreased in the OVA group on P70 but not on P30. Gene set enrichment analysis of isolated microglia revealed that genes related to immune responses including Toll-like receptor signaling and chemokine signaling pathways, senescence, and glucocorticoid signaling were significantly upregulated in the OVA group compared with the control group on P30 and P70. These findings suggest that early postnatal allergic airway inflammation induces dystrophic microglia that exhibit defective synaptic pruning upon short- and long-term allergen exposure. Furthermore, long-term allergen exposure induced excitatory postsynaptic surplus and ASD-like behavior. Hypothalamo-pituitary-adrenal axis activation and the compensatory downregulation of microglial GR during long-term allergic airway inflammation may also facilitate these changes.

English

Let K be a number field defined by an irreducible polynomial F(X) ∈ ℤ[X] and ℤK its ring of integers. For every prime integer p, we give sufficient and necessary conditions on F(X) that guarantee the existence of exactly r prime ideals of ℤK lying above p, where $$\overline F \left( X \right)$$ factors into powers of r monic irreducible polynomials in $${\mathbb{F}_p}\left[ X \right]$$ . The given result presents a weaker condition than that given by S. K. Khanduja and M. Kumar (2010), which guarantees the existence of exactly r prime ideals of ℤK lying above p. We further specify for every prime ideal of ℤK lying above p, the ramification index, the residue degree, and a p-generator.

Spectral maps associated to semialgebraic branched coverings

In this article we prove that a semialgebraic map \(\pi :M\rightarrow N\) is a branched covering if and only if its associated spectral map is a branched covering. In addition, such spectral map has a neat behavior with respect to the branching locus, the ramification set and the ramification index. A crucial fact to prove the preceding result is the characterization of the prime ideals whose fibers under the previous spectral map are singletons.

On the structure of certain valued fields

In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields K1 and K2 of mixed characteristic with perfect residue fields, we show that if the n-th residue rings are isomorphic for each n≥1, then K1 and K2 are isometric and isomorphic. More generally, for n1≥1, there is n2 depending only on the ramification indices of K1 and K2 such that any homomorphism from the n1-th residue ring of K1 to the n2-th residue ring of K2 can be lifted to a homomorphism between the valuation rings. Moreover, we get a functor from the category of certain principal Artinian local rings of length n to the category of certain complete discrete valuation rings of mixed characteristic with perfect residue fields, which naturally generalizes the functorial property of unramified complete discrete valuation rings. Our lifting result improves Basarab's relative completeness theorem for finitely ramified henselian valued fields, which solves a question posed by Basarab, in the case of perfect residue fields.

Comparison of Classifications of Two-Dimensional Local Type II Fields

The paper contributes to the theory of the elimination of wild ramification for two-dimensional fields and continues the research related to the classification of fields introduced in the work of Masato Kurihara. We consider two-dimensional mixed-characteristic local fields with the characteristic of the finite residue field not equal to 2. The structure of fields that are weakly unramified over their constant subfield, i.e., the so-called standard fields, is well known. It is also known that any field can be extended into the standard one by a finite extension of its constants subfield. In the general case, the question of the minimum degree of this extension remains open. In Kurihara’s paper, two-dimensional fields are subdivided into two types as follows. A linear relation between the differentials of local parameters is considered. If the valuation of the coefficient at the uniformizer is less than that before the second local parameter, the field belongs to type I; otherwise it belongs to type II. This paper is devoted to the fields of type II. For them, we consider an improved Kurihara invariant: for each field, we introduce a quantity Δ equal to the difference between the valuations of the coefficients in the relation for the differentials of the local parameters. The degree of the constant extension that eliminates the ramification is not less for any field than the ramification index over the constant subfield. However, not all the fields have an extension of this degree. It is proved that in order that the extension of the least possible degree may exist, it suffices for the absolute values of Δ to be sufficiently large. The corresponding estimate for Δ depends on the ramification index of the field over its constant subfield.