Free cyclic actions on surfaces and the Borsuk-Ulam theorem

Let $M$ and $N$ be topological spaces, let $G$ be a group, and let $\tau \colon\thinspace G \times M \to M$ be a proper free action of $G$. In this paper, we define a Borsuk-Ulam-type property for homotopy classes of maps from $M$ to $N$ with respect to the pair $(G,\tau)$ that generalises the classical antipodal Borsuk-Ulam theorem of maps from the $n$-sphere $\mathbb{S}^n$ to $\mathbb{R}^n$. In the cases where $M$ is a finite pathwise-connected CW-complex, $G$ is a finite, non-trivial Abelian group, $\tau$ is a proper free cellular action, and $N$ is either $\mathbb{R}^2$ or a compact surface without boundary different of $\mathbb{S}^2$ and $\mathbb{RP}^2$, we give an algebraic criterion involving braid groups to decide whether a free homotopy class $\beta \in [M,N]$ has the Borsuk-Ulam property. As an application of this criterion, we consider the case where $M$ is a compact surface without boundary equipped with a free action $\tau$ of the finite cyclic group $\mathbb{Z}_n$. In terms of the orientability of the orbit space $M_\tau$ of $M$ by the action $\tau$, the value of $n$ modulo $4$ and a certain algebraic condition involving the first homology group of $M_\tau$, we are able to determine if the single homotopy class of maps from $M$ to $\mathbb{R}^2$ possesses the Borsuk-Ulam property with respect to $(\mathbb{Z}_n,\tau)$. Finally, we give some examples of surfaces on which the symmetric group acts, and for these cases, we obtain some partial results regarding the Borsuk-Ulam property for maps whose target is $\mathbb{R}^2$.Comment: 18 pages, 2 figure

The Borsuk-Ulam property for homotopy classes on bundles, parametrized braids groups and applications for surfaces bundles

Let $M$ and $N$ be fiber bundles over the same base $B$, where $M$ is endowed with a free involution $\tau$ over $B$. A homotopy class $\delta \in [M,N]_{B}$ (over $B$) is said to have the Borsuk-Ulam property with respect to $\tau$ if for every fiber-preserving map $f\colon M \to N$ over $B$ which represents $\delta$ there exists a point $x \in M$ such that $f(\tau(x)) = f(x)$. In the cases that $B$ is a $K(\pi ,1)$-space and the fibers of the projections $M \to B$ and $N \to B$ are $K(\pi,1)$ closed surfaces $S_M$ and $S_N$, respectively, we show that the problem of decide if a homotopy class of a fiber-preserving map $f\colon M \to N$ over $B$ has the Borsuk-Ulam property is equivalent of an algebraic problem involving the fundamental groups of $M$, the orbit space of $M$ by $\tau$ and a type of generalized braid groups of $N$ that we call parametrized braid groups. As an application, we determine the homotopy classes of self fiber-preserving maps of some 2-torus bundles over $\mathbb{S}^1$ that satisfy the Borsuk-Ulam property with respect to certain involutions $\tau$ over $\mathbb{S}^1$

Industrialización de un absorbedor modular de vibraciones

Se trata de la industrialización de un absorbedor modular de vibraciones basado en la tecnología TMD (Tuned Mass Damper) a través de la construcción de una maqueta digital parametrizada con el objetivo de crear una gama de producto que pueda ser comercializada. La evolución de este producto, partiendo de un prototipo inicial, presenta mejoras tecnológicas las cuales hacen que nuestro producto se diferencie de otros TMD. Cada producto concreto se define mediante una hoja de cálculo donde obtendremos como salida los valores de los parámetros del modelo TMD de CATIA, en función de los datos de entrada que nos ofrece el cliente. La hoja de cálculo fue construida empleando una hoja EXCEL donde presentamos todas las ecuaciones que rigen el TMD. Finalmente, se presentará el prototipo de TMD construido en el laboratorio de estructuras, el cual fue empleado para testar las nuevas soluciones tecnológicas implementadas en la maqueta digital ofrecida a los clientes.It is about the industrialization of a modular absorber of vibrations using the TMD’s technologies (Tuned Mass Damper) through the construction of a parametric digital mock-up with the goal of creating a range of this product that could be marketable. The evolution of this product, based on an initial prototype, provides some technological improvements which make our product different from other TMDs. The different models of this product are based on a spreadsheet where we obtain the parameter´s values of the TMD model of CATIA, depending on the input data offered by the client. The spreadsheet was developed using an EXCEL sheet where we show all TMD’s equations. Finally, both the digital mock-up and the mockup of the prototype are presented. They were built in the laboratory of structures and the mockup of the prototype was used to test these new solutions.Departamento de Construcciones Arquitectónicas, Ingeniería del Terreno y Mecánica de los Medios Continuos y Teoría de EstructurasMáster en Ingeniería Industria

First evidence of borings in calamitean stems and other plant-arthropod interactions from the late Pennsylvanian of the Saale Basin

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The probiotic Escherichia coli strain Nissle 1917 (EcN) stops acute diarrhoea in infants and toddlers

In most cases, acute diarrhoea will become self-limiting during the first few days after onset. For young children, however, health risks may develop when the disease lasts longer than 3 days. The purpose of the present trial was to determine whether the stool frequency of infants and toddlers suffering from acute diarrhoea could be normalised more quickly by administering the probiotic Escherichia coli Nissle 1917 (EcN) solution than by administering a placebo. The safety of EcN were also assessed. A total of 113 children (aged 2–47 months) with acute diarrhoea (> three watery or loose stools in 24 h) were randomised to either a group receiving the probiotic EcN suspension (n = 55) or a group receiving the placebo suspension (n = 58) in a confirmative, double-blind clinical trial. Depending on the age of patients, 1–3 ml per day of verum suspension (10(8) viable EcN cells per millilitre) or placebo were administered orally. The causes of the diarrhoea were viral rather than bacterial, but they were mainly unspecific infections. The median onset of treatment response (reduction of daily stool frequency to ≤ three watery or loose stools over at least 2 consecutive days) occurred more rapidly in the children receiving the EcN solution (2.5 days) than in those receiving the placebo (4.8 days), a significant difference (2.3 days; p = 0.0007). The number of patients showing a response was clearly higher (p < 0.0001) in the EcN group (52/55; 94.5%) than in the placebo group (39/58; 67.2%). EcN was found to be safe and well-tolerated, and it showed a significant superiority compared to the placebo in the treatment of acute diarrhoea in infants and toddlers. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:http://dx.doi.org/10.1007/s00431-007-0419-x) contains supplementary material, which is available to authorized users

Identification of chitinase-3-like protein 1 as a novel neutrophil antigenic target in Crohn’s disease

Background and Aims There is an increasing incidence of inflammatory bowel disease [IBD]. Autoimmune responses are involved in the pathophysiology of IBD, but their underlying pathways and target antigens have not yet been fully elucidated. Methods Autoantigenic targets in IBD were identified after separation of whole cell proteins isolated from neutrophils using two-dimensional electrophoresis and matrix assisted laser desorption ionization – time of flight mass spectrometry-based protein identification of the spots that displayed Western blotting signals with anti-neutrophil cytoplasmic antibody-positive sera. The prevalence of IgG, IgA and secretory IgA [sIgA] to chitinase 3-like protein 1 [CHI3L1] was analysed by enzyme-linked immunosorbent assays using recombinant CHI3L1 in 110 patients with Crohn’s disease [CD], 95 with ulcerative colitis [UC], 126 with coeliac disease [CeD] and 86 healthy controls [HCs]. Results The 18-glycosylhydrolase family member CHI3L1 was identified as a neutrophil autoantigenic target. CD patients displayed significantly higher levels of IgG to CHI3L1 than patients with UC and CeD (p < 0.0001, respectively). IgA and sIgA to CHI3L1 was significantly higher in CD than in UC, CeD and HCs [p < 0.0001, respectively]. IgA and sIgA to CHI3L1 demonstrated the highest prevalence in CD [25.5%, 28/110; and 41.8%%, 46/110] compared to HCs [2.3%, 2/86; and 4.7%%, 4/86; p = 0.0015 and p < 0.0001] and are associated with a more complicated progression of CD. Conclusion CHI3L1 is a novel neutrophil autoantigenic target in CD. IgA and sIgA to CHI3L1 may serve as novel markers for CD and may facilitate the serological diagnosis of IBD

PR3-ANCAs Detected by Third-Generation ELISA Predicts Severe Disease and Poor Survival in Primary Sclerosing Cholangitis

A highly sensitive detection of anti-neutrophil cytoplasmic antibodies to serine proteinase-3 (PR3-ANCAs) aids in the serological diagnosis of autoimmune liver disorders and the prediction of severity in primary sclerosing cholangitis (PSC). Here, we evaluate a novel thirdgeneration ELISA for the detection of PR3-ANCAs. In total, 309 patients with PSC, 51 with primary biliary cholangitis (PBC), and 120 healthy blood donors (BD) were analyzed. For the survival analysis in PSC, the outcome was defined as liver-transplantation-free survival during the followup. Positive PR3-ANCA levels were found in 74/309 (24.0%) of patients with PSC. No BDs and one patient with PBC demonstrated PR3-ANCA positivity. PR3-ANCAs were revealed as independent predictors for a poor PSC outcome (study endpoint: liver transplantation/death, log-rank test, p = 0.02). PR3-ANCA positivity, lower albumin levels, and higher bilirubin concentrations were independent risks of a poor survival (Cox proportional-hazards regression analysis, p < 0.05). The Mayo risk score for PSC was associated with PR3-ANCA positivity (p = 0.01) and the disease severity assessed with a model of end-stage liver disease (MELD) and extended MELD-Na (p < 0.05). PR3-ANCAs detected by a third-generation ELISA are diagnostic and prognostic markers for PSC. Their wider use could help to identify patients who are at-risk of a more severe disease