Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics

We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.Comment: 12 pages, 7 figure

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

Interpolation of bilinear operators and compactness

The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\rho$ method.Comment: This work was published at "Nonlinear Analysis: Theory, Methods and Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some gaps in the original proof of Theorem 4.3, Here we give a new proof. For this, we change the Lemma 4.

Environmental problems and opportunities of the peri-urban interface and their impact upon the poor

The objective of this document is to provide an overview of the problems and opportunities of the peri-urban interface (PUI) with regard to the broad concerns of environmentalsustainability and poverty

Graded identities of block-triangular matrices

Let $F$ be an infinite field and $UT(d_1,\dots, d_n)$ be the algebra of upper block-triangular matrices over $F$. In this paper we describe a basis for the $G$-graded polynomial identities of $UT(d_1,\dots, d_n)$, with an elementary grading induced by an $n$-tuple of elements of a group $G$ such that the neutral component corresponds to the diagonal of $UT(d_1,\dots,d_n)$. In particular, we prove that the monomial identities of such algebra follow from the ones of degree up to $2n-1$. Our results generalize for infinite fields of arbitrary characteristic, previous results in the literature which were obtained for fields of characteristic zero and for particular $G$-gradings. In the characteristic zero case we also generalize results for the algebra $UT(d_1,\dots, d_n)\otimes C$ with a tensor product grading, where $C$ is a color commutative algebra generating the variety of all color commutative algebras.Comment: 24 pages and 39 references. We have added section 5 in the text about tensor products by color commutative superalgebra

Oxygen clamps in gold nanowires

We investigate how the insertion of an oxygen atom in an atomically thin gold nanowire can affect its rupture. We find, using ab initio total energy density functional theory calculations, that O atoms when inserted in gold nanowires form not only stable but also very strong bonds, in such a way that they can extract atoms from a stable tip, serving in this way as a clamp that could be used to pull a string of gold atoms.Comment: 4 pages; 4 figure