Monochromatic Clique Decompositions of Graphs

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa ["Monochromatic $K_r$-decompositions of graphs", Journal of Graph Theory}, 76:89--100, 2014], we solve this problem when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.Comment: 14 pages; to appear in J Graph Theor

P2 purinoceptors signaling in fibroblasts of rat subcutaneous tissue

Mestrado em Biologia Molecular e CelularO tecido conjuntivo parece estar envolvido na génese de diversas condições patológicas. O aumento da rigidez do tecido conjuntivo, resultante da fibrose, pode constituir um factor importante no mecanismo patogénico da dor crónica resistente a fármacos (Langevin & Sherman, 2007). Por outro lado, os nucleótidos extracelulares parecem estar envolvidos na fisiopatologia da dor crónica (Burnstock, 2001). Assim, este estudo teve como objectivo averiguar o efeito dos nucleótidos de adenina e uridina na proliferação e síntese de colagénio tipo I de fibroblastos do tecido subcutâneo de rato em cultura. Os resultados obtidos mostram que a incubação com UTP (0.3-100 M, n=5) induz um aumento da proliferação e da produção de colagénio tipo I, o qual é dependente da concentração. Contrariamente, o agonista selectivo dos receptores P2Y2, o MRS 2768 (10 μM, n=3), não teve qualquer efeito no que se refere à proliferação, mas diminuiu significativamente (P<0.05) a síntese de colagénio tipo I. Uma vez que o aumento da produção de colagénio induzida pelo UTP (100 μM) foi proporcional ao aumento do número de células (proliferação celular),podemos especular que este aumento se deve ao aumento do número de células per si do que a uma maior actividade sintética de cada célula. Assim, ao normalizar os valores do colagénio tipo I em relação aos valores obtidos do MTT para os mesmos momentos/dias, deixamos de observar diferenças estatisticamente significativas entre o controlo e as células expostas ao UTP. Uma vez que os receptores P2Y2 não parecem estar envolvidos nesta resposta do UTP (100 μM), esta poderá estar a ser mediada pela activação dos receptores P2Y4 e/ou P2Y6. Considerando que o RB-2 (10 μM, n=5), um antagonista não selectivo que actua preferencialmente no subtipo de receptores P2Y4, não foi capaz de modificar a resposta induzida pelo UTP (100 μM), os receptores P2Y4 parecem também não estar envolvidos. Por outro lado, o MRS 2578 (100 nM), um antagonista selectivo dos receptores P2Y6, atenuou de forma significativa o aumento induzido pelo UTP (100 μM). A corroborar os nossos resultados, uma análise imunocitoquímica mostrou uma imunorreactividade positiva contra os receptores P2Y2 e P2Y6, mostrando um padrão de marcação citoplasmático/membranar, o qual é típico para este tipo de receptores, ao contrário do padrão nuclear exibido pelo anticorpo contra os receptores P2Y4. Relativamente ao envolvimento dos receptores sensíveis ao ADP, os resultados obtidos mostraram que o ADPβS (10-100 μM, n=3-6), um análogo estável do ADP, não parece induzir efeitos significativamente diferentes (P>0.05) na proliferação celular. Contudo, a sua incubação continuada aumentou a produção de colagénio tipo I de forma dependente da concentração (P<0.05). De modo a identificar os receptores purinérgicos envolvidos neste efeito, testamos o ADPβS (100 μM) na presença do MRS 2179 (0.3 μM), do AR-C 66096 (0.1 μM), e do MRS 2211 (10 μM), os quais antagonizam selectivamente os receptores P2Y1, P2Y12 e P2Y13, respectivamente. O efeito facilitatório induzido pelo ADPβS (100 μM) foi atenuado de forma significativa na presença do antagonista dos receptores P2Y1, o MRS 2179 (0.3 μM, n=3), sem ser afectado pelo antagonista dos receptores P2Y12, o AR- C 66096 (0.1 μM, n=3). Pelo contrário, o MRS 2211 (10 μM, n=2) potenciou o aumento da produção de colagénio induzida pelo ADPβS (100 μM), indicando assim que a síntese de colagénio tipo I induzida pelo receptor P2Y1 pode estar a ser parcialmente influenciada por uma activação síncrona do receptor inibitório P2Y13. Por último, uma análise por imunocitoquímica mostrou que estas células apresentam imunorreactividade positiva para os receptores P2Y1 e P2Y13, exibindo um padrão citoplasmático/membranar, contrariamente ao padrão nuclear dos receptores ostentado pelo anticorpo contra os receptores P2Y12. Concluindo, a remodelação da fáscia superficial induzida pelos fibroblastos parece ser regulada por um balanço entre a activação dos receptores P2Y2 e P2Y6, assim como dos receptores P2Y13 e P2Y1. Clarificar as vias que conduzem ao processo de fibrose pode representar uma oportunidade para esclarecer o seu envolvimento na patogénese da dor crónica musculo-esquelética, bem como ser útil no desenvolvimento de novas estratégias terapêuticas.Connective tissue may be involved in the pathogenesis of a wide variety of disease conditions. Increased connective tissue stiffness due to fibrosis may be an important link to the pathogenic mechanism leading to drug-resistant chronic pain (Langevin & Sherman, 2007). In addition, extracellular nucleotides seem to be involved in the pathophysiology of chronic pain (Burnstock, 2001). Therefore, we aimed at investigating the effect of adenine and uridine nucleotides on the proliferation and synthesis of type I collagen by rat fibroblasts from subcutaneous connective tissue. The results showed that continuous incubation of UTP (0.3-100 M, n=5) concentration-dependently increased fibroblasts proliferation, as also increased the synthesis of type I collagen above the control levels. Conversely, the selective P2Y2 agonist, MRS 2768 (10 μM, n=3), was devoid of effect in what concerns proliferation, but significantly (P<0.05) decreased type I collagen synthesis. Since the increase in type I collagen synthesis induced by UTP (100 μM) was proportional to the increase in the amount of cells in the culture (fibroblasts proliferation), we speculated that such an increase could be related to the increase in the cell number rather than a higher synthetic activity. Thus, we performed a more detailed data analysis, in which we normalized type I collagen production taking into consideration the MTT values obtained at the same time points, and we observed no longer significant differences between control and UTP-exposed cells. Discounting the contribution of MRS 2768-sensitive P2Y2 receptors, UTP (100 μM)-induced increase in cells proliferation could be due to P2Y4 and/or P2Y6 receptor activation. Since RB-2 (10 μM, n=5), a non-selective antagonist that acts preferentially on the P2Y4 subtype, did not modify the effect of UTP (100 μM), P2Y4 does not seem to be involved. In turn, MRS 2578 (100 nM), which is a selective P2Y6 antagonist, significantly attenuated UTP (100 μM)-induced increase. To corroborate our results, an immunocytochemistry analysis showed a positive immunoreactivity against the P2Y2 and P2Y6 receptors exhibiting a cytoplasmic/membrane labeling pattern, which is typical for those receptors in many different cells, conversely to the nuclear labeling pattern exhibited by the antibody against the P2Y4. To investigate the involvement of ADP-sensitive P2 receptors on cell proliferation and extracellular matrix production, fibroblast cultures were continuously incubated with the stable ADP analogue, ADPβS (10-100 μM). Results obtained with ADPβS (10-100 μM, n=3-6) showed no significant (P>0.05) differences in fibroblast cells proliferation. However, a continuous incubation with ADPβS (10-100 μM, n=2-5) concentration-dependently increased type I collagen production by fibroblasts (P<0.05). In order to identify which purinoceptor(s) that could be mediating this effect, we tested ADPβS (100 μM) in the presence of MRS 2179 (0.3 μM), AR-C 66096 (0.1 μM), and MRS 2211 (10 μM), which antagonize selectively ADP-sensitive P2Y1, P2Y12 and P2Y13 receptors, respectively. The facilitatory effect of ADPβS (100 μM) was significantly attenuated in the presence of the P2Y1 antagonist, MRS 2179 (0.3 μM, n=3), without being affected by the P2Y12 antagonist, AR- C 66096 (0.1 μM, n=3). In contrast, MRS 2211 (10 μM, n=2) potentiated the effect of ADPβS (100 μM) on type I collagen synthesis, thus indicating that the P2Y1-receptor-induction of type I collagen synthesis may be partially counteracted by synchronous activation of the inhibitory P2Y13 receptor. Finally, an immunocytochemistry analysis showed that these cells exhibit immunoreactivity to P2Y1 and P2Y13 receptors with a cytoplasmic/membrane staining pattern, conversely to the nuclear pattern of P2Y12. Concluding, a delicate balance between the activation of P2Y2 and P2Y6, as well as P2Y13 and P2Y1 purinoceptors, might regulate fibroblast’s induced superficial fascia remodeling. Targeting the pathways leading to fibrosis may represent an opportunity to clarify its involvement in the pathogenesis of musculoskeletal chronic pain and it may be useful for designing novel therapeutic strategies to overcome this disease

Locally Provided Public Schooling in Brazilian Municipalities

The objective of this paper is to assess the demand for public schooling in the Brazilian municipalities within a median voter framework. The quantile regression and spatial techniques proved to be useful to account for the spatial and marginal effects associated with educational services. The coefficients attached to the main variables – price, income and population – were significant and had the expected sign. The relatively high values for those parameters attest the status for these merit goods as “luxuries”. Last, but no least, the municipal school system in Brazil seems to present increasing returns to scale both, at the school and the municipality level.Public Schooling, Demand, Brazilian municipalities, Median voter

Sharp mixed norm spherical restriction

Let $d\geq 2$ be an integer and let $2d/(d-1) < q \leq \infty$. In this paper we investigate the sharp form of the mixed norm Fourier extension inequality \begin{equation*} \big\|\widehat{f\sigma}\big\|_{L^q_{{\rm rad}}L^2_{{\rm ang}}(\mathbb{R}^d)} \leq {\bf C}_{d,q}\, \|f\|_{L^2(\mathbb{S}^{d-1},{\rm d}\sigma)}, \end{equation*} established by L. Vega in 1988. Letting $\mathcal{A}_d \subset (2d/(d-1), \infty]$ be the set of exponents for which the constant functions on $\mathbb{S}^{d-1}$ are the unique extremizers of this inequality, we show that: (i) $\mathcal{A}_d$ contains the even integers and $\infty$; (ii) $\mathcal{A}_d$ is an open set in the extended topology; (iii) $\mathcal{A}_d$ contains a neighborhood of infinity $(q_0(d), \infty]$ with $q_0(d) \leq \left(\tfrac{1}{2} + o(1)\right) d\log d$. In low dimensions we show that $q_0(2) \leq 6.76\,;\,q_0(3) \leq 5.45 \,;\, q_0(4) \leq 5.53 \,;\, q_0(5) \leq 6.07$. In particular, this breaks for the first time the even exponent barrier in sharp Fourier restriction theory. The crux of the matter in our approach is to establish a hierarchy between certain weighted norms of Bessel functions, a nontrivial question of independent interest within the theory of special functions.Comment: 21 page

Economic Consequences of Low Fertility in Europe

This special issue of the European Journal of Population focuses on possible economic consequences of low fertility in Europe. This introduction reviews the history of falling fertility in Europe and the literature that explores its causes, its potential implications, and possible policy responses. It also summarizes the evolution of thinking about the relationship between population growth and economic development, with attention to recent work on the mechanisms through which fertility decline can spur economic growth if the necessary supporting conditions are met. The introduction also identifies some of the challenges of population aging that are associated with low fertility and suggests that there may be less reason for alarm than has been suggested by some observers. The papers that appear in this special issue are also summarized.Economic consequences, low fertility, Europe

Economic consequences of low fertility in Europe

This paper focuses on possible economic consequences of low fertility in Europe. It summarizes a selection of papers that were presented at a conference at the University of St. Gallen in April 2008. This introduction also reviews the history of falling fertility in Europe and the literature that explores its causes, its potential implications, and possible policy responses. It summarizes the evolution of thinking about the relationship between population growth and economic development, with attention to recent work on the mechanisms through which fertility decline can spur economic growth if the necessary supporting conditions are met. The paper also identifies some of the challenges of population aging that are associated with low fertility and suggests that there may be less reason for alarm than has been suggested by some observers. --