Key polynomials for simple extensions of valued fields

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with a valuation $\nu$ of rank 1. That is, we assume given a rank 1 valuation $\nu$ of $K$ and its extension $\nu'$ to $L$. Let $(R_\nu,M_\nu,k_\nu)$ denote the valuation ring of $\nu$. The purpose of this paper is to present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo. Namely, we associate to $\iota$ a countable well ordered set $$\mathbf{Q}=\{Q_i\}_{i\in\Lambda}\subset K[x];$$ the $Q_i$ are called {\bf key polynomials}. Key polynomials $Q_i$ which have no immediate predecessor are called {\bf limit key polynomials}. Let $\beta_i=\nu'(Q_i)$. We give an explicit description of the limit key polynomials (which may be viewed as a generalization of the Artin--Schreier polynomials). We also give an upper bound on the order type of the set of key polynomials. Namely, we show that if $\operatorname{char}\ k_\nu=0$ then the set of key polynomials has order type at most $\omega$, while in the case $\operatorname{char}\ k_\nu=p>0$ this order type is bounded above by $\omega\times\omega$, where $\omega$ stands for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519

Rank one discrete valuations of power series fields

In this paper we study the rank one discrete valuations of the field $k((X_1,..., X_n))$ whose center in k\lcor\X\rcor is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in section 5. The constructions given in these sections are not effective in the general case, because we need either to use the Zorn's lemma or to know explicitly a section $\sigma$ of the natural homomorphism R_v\to\d between the ring and the residue field of the valuation $v$. However, as a consequence of this construction, in section 7, we prove that k((\X)) can be embedded into a field L((\Y)), where $L$ is an algebraic extension of $k$ and the {\em ``extended valuation'' is as close as possible to the usual order function}

Efectos del entrenamiento de fuerza integrado dos veces por semana en jóvenes

La aptitud física es uno de los factores más importante para prevenir las enfermedades cardiovasculares La fuerza es uno de los componentes más influyentes sobre la aptitud física. Objetivo: Se estudió un grupo de 21 varones (V) y 11 mujeres (M) jóvenes, al cual se aplicó un programa de entrenamiento de fuerza integrado durante 7 semanas, con una frecuencia de 2 días semanales. Método: Se evaluó la fuerza máxima a través de una repetición máxima (1RM) en los ejercicios de press de banca (PB) y ¿ sentadilla (SEN). El entrenamiento consistió en aplicar intensidades del 45 al 90% y volúmenes de 10 a 18 repeticiones por ejercicio, saltos y pliometría. Resultados: Se encontraron diferencias significativas p< 0.01 pre y post entrenamiento, PB en V 57.9 + 7.2 vs 65 + 8.2 Kg; SEN en V 84.1 + 15.3 vs 101.1 + 16.1 Kg; PB en M 38.5 + 8.6 vs 47.4 + 6.7 Kg SEN en M 61.8 + 15.1 vs 80.3 + 13.7 Kg. Conclusión: El entrenamiento de dos veces a la semana con un programa de fuerza integrado, durante 7 semanas incrementa la fuerza en forma significativa en jóvenes sanos de ambos

Benefit-risk assessment of sonidegib and vismodegib in the treatment of locally advanced basal cell carcinoma

Sonidegib and vismodegib are Hedgehog pathway inhibitors (HhIs) that play a relevant role in the management of locally advanced basal cell carcinoma (laBCC). This study compared the efficacy and safety of both HhIs based on their available data using effect size measures such as number needed to treat (NNT), number needed to harm (NNH), and likelihood to be helped or harmed (LHH)

The whole-brain pattern of magnetic susceptibility perturbations in Parkinson's disease

Although iron-mediated oxidative stress has been proposed as a potential pathomechanism in Parkinson's disease, the global distribution of iron accumulation in Parkinson's disease has not yet been elucidated. This study used a new magnetic resonance imaging contrast, quantitative susceptibility mapping, and state-of-the-art methods to map for the first time the whole-brain landscape of magnetostatic alterations as a surrogate for iron level changes in n = 25 patients with idiopathic Parkinson's disease versus n = 50 matched controls. In addition to whole-brain analysis, a regional study including sub-segmentation of the substantia nigra into dorsal and ventral regions and qualitative assessment of susceptibility maps in single subjects were also performed. The most remarkable basal ganglia effect was an apparent magnetic susceptibility increase-consistent with iron deposition-in the dorsal substantia nigra, though an effect was also observed in ventral regions. Increased bulk susceptibility, additionally, was detected in rostral pontine areas and in a cortical pattern tightly concordant with known Parkinson's disease distributions of α-synuclein pathology. In contrast, the normally iron-rich cerebellar dentate nucleus returned a susceptibility reduction suggesting decreased iron content. These results are in agreement with previous post-mortem studies in which iron content was evaluated in specific regions of interest; however, extensive neocortical and cerebellar changes constitute a far more complex pattern of iron dysregulation than was anticipated. Such findings also stand in stark contrast to the lack of statistically significant group change using conventional magnetic resonance imaging methods namely voxel-based morphometry, cortical thickness analysis, subcortical volumetry and tract-based diffusion tensor analysis; confirming the potential of whole-brain quantitative susceptibility mapping as an in vivo biomarker in Parkinson's disease

Vimentin and heat shock protein expression are induced in the kidney by angiotensin and by nitric oxide inhibition

Vimentin and heat shock protein expression are induced in the kidney by angiotensin and by nitric oxide inhibition.BackgroundAngiotensin II (Ang II) infusion and nitric oxide synthesis (NOS) inhibition with Nω-nitro-L-arginine-methyl-ester (L-NAME) are experimental models of hypertension associated with renal inflammation and oxidative stress. To gain insight into the nature of the tubulointerstitial injury induced in these models, we studied lectin-binding specificities, vimentin expression, and heat shock protein (HSP) 60 and 70 in these experimental models.MethodsSprague-Dawley rats received Ang II infusion (435 ng/kg/min) for 2 weeks by subcutaneous minipumps (Ang II group, N = 5) or L-NAME in the drinking water (70 mg/100 mL) for 3 weeks (L-NAME group N = 7). The control group consisted of 10 rats. Systolic blood pressure (tail-cuff plethysmography), serum creatinine, and proteinuria were determined weekly. At the end of the treatment period, rats were sacrificed and kidneys studied. Binding specificities of fluorescein-labeled lectins were examined in frozen sections, and cellular infiltrates were identified by immunohistology and expression of vimentin and HSP 60 and 70 with immunohistochemistry and computer image analysis.ResultsTubulointerstitial accumulation of macrophages, lymphocytes, and Ang II–positive cells were present in the Ang II group and L-NAME group. Vimentin, HSP 60, and HSP 70 were increased 8 to 20 times in the cortex of the rats of the Ang II group and the L-NAME groups. Neoexpression of vimentin and HSPs was found primarily in proximal tubular cells.ConclusionAng II infusion and NOS inhibition induce tubular injury with epithelial cell transdifferentiation and expression of stress proteins. The role of these changes in the accumulation and activation of the interstitial inflammatory infiltrate merits further investigation

Influence of a Concurrent Exercise Training Intervention during Pregnancy on Maternal and Arterial and Venous Cord Serum Cytokines: The GESTAFIT Project

The aim of the present study was to analyze the influence of a supervised concurrent exercise-training program, from the 17th gestational week until delivery, on cytokines in maternal (at 17th and 35th gestational week, and at delivery) and arterial and venous cord serum. Fifty-eight Caucasian pregnant women (age: 33.5 +/- 4.7 years old, body mass index: 23.6 +/- 4.1kg/m(2)) from the GESTAFIT Project (exercise (n = 37) and control (n = 21) groups) participated in this quasi-experimental study (per-protocol basis). The exercise group followed a 60-min 3 days/week concurrent (aerobic-resistance) exercise-training from the 17th gestational week to delivery. Maternal and arterial and venous cord serum cytokines (fractalkine, interleukin (IL)-1 beta, IL-6, IL-8, IL-10, interferon (IFN)-gamma, and tumor necrosis factor (TNF)-alpha) were assessed using Luminex xMAP technology. In maternal serum (after adjusting for the baseline values of cytokines), the exercise group decreased TNF-alpha (from baseline to 35th week, p = 0.02), and increased less IL-1 beta (from baseline to delivery, p = 0.03) concentrations than controls. When adjusting for other potential confounders, these differences became non-significant. In cord blood, the exercise group showed reduced arterial IL-6 and venous TNF-alpha (p = 0.03 and p = 0.001, respectively) and higher concentrations of arterial IL-1 beta (p = 0.03) compared to controls. The application of concurrent exercise-training programs could be a strategy to modulate immune responses in pregnant women and their fetuses. However, future research is needed to better understand the origin and clearance of these cytokines, their role in the maternal-placental-fetus crosstalk, and the influence of exercise interventions on them