A Study of Nash Equilibrium in Contribution Games for Peer-to-Peer Networks

We consider a stylized model of content contribution in a peer-to-peer network. The model is appealing because it allows for linear-quadratic payoff functions and for very general interaction patterns among agents. Furthermore, when the model has a unique Nash equilibrium (NE) we find that it is defined by a network centrality measure (Bonacich 1987), with L1 and L2 norms of the Bonacich index vector providing aggregate contribution and social welfare. Furthermore, we find that NE are always (even when they are non-unique) computable by solving a linear complementarity problem. We study the network designer's problem of engineering the most efficient equilibrium outcome, proving that maximizing aggregate contribution can be reconciled with maximizing aggregate welfare. We also provide a partial characterization of optimal NE graphs and suggest different approaches for how a network designer can promote more efficient graph structures.Engineering and Applied Science

The Importance of Network Topology in Local Contribution Games

We consider a model of content contribution in peer-to-peer networks with linear quadratic payoffs and very general interaction patterns. We find that Nash equilibria of this game always exist; moreover, they are computable by solving a linear complementarity problem. The equilibrium is unique when goods are strategic complements or weak substitutes and contributions are proportional to a network centrality measure called the Bonacich index. In the case of public goods, the equilibrium is non-unique and characterized by k-order maximal independent sets. The structure of optimal networks is always star-like when the game exhibits strict or weak complements. Under public good scenarios, while star-like networks remain optimal in the best case, they also yield the worst-performing equilibria. We also discuss a network-based policy for improving the equilibrium performance of networks by the exclusion of a single player.Engineering and Applied Science

A logical study of local and global graded similarities

In this work we study the relationship between global and local similarities in the graded framework of fuzzy class theory (FCT), in which there already exists a graded notion of similarity. In FCT we can express the fact that a fuzzy relation is reflexive, symmetric, or transitive up to a certain degree, and similarity is defined as a first-order sentence, which is the fusion of three sentences corresponding to the graded notions of reflexivity, symmetry, and transitivity. This allows us to speak in a natural way of the degree of similarity of a relation. We consider global similarities defined from local similarities using t-norms as aggregation operators, and we obtain some results in the framework of FCT that, adequately interpreted, allow us to say that when we take a t-norm as an aggregation operator, the properties of reflexivity, symmetry, and transitivity of fuzzy binary relations are inherited from the local to the global level, and that the global similarity is a congruence if some of the local similarities are congruence

Obstructive Sleep Apnoea Syndrome, Endothelial Function and Markers of Endothelialization. Changes after CPAP

STUDY OBJECTIVES: This study tries to assess the endothelial function in vivo using flow-mediated dilatation (FMD) and several biomarkers of endothelium formation/restoration and damage in patients with obstructive sleep apnoea (OSA) syndrome at baseline and after three months with CPAP therapy. DESIGN: Observational study, before and after CPAP therapy. SETTING AND PATIENTS: We studied 30 patients with apnoea/hypopnoea index (AHI) >15/h that were compared with themselves after three months of CPAP therapy. FMD was assessed non-invasively in vivo using the Laser-Doppler flowmetry. Circulating cell-free DNA (cf-DNA) and microparticles (MPs) were measured as markers of endothelial damage and the vascular endothelial growth factor (VEGF) was determined as a marker of endothelial restoration process. MEASUREMENTS AND RESULTS: After three month with CPAP, FMD significantly increased (1072.26 ± 483.21 vs. 1604.38 ± 915.69 PU, p< 0.005) cf-DNA and MPs significantly decreased (187.93 ± 115.81 vs. 121.28 ± 78.98 pg/ml, p<0.01, and 69.60 ± 62.60 vs. 39.82 ± 22.14 U/μL, p<0.05, respectively) and VEGF levels increased (585.02 ± 246.06 vs. 641.11 ± 212.69 pg/ml, p<0.05). These changes were higher in patients with more severe disease. There was a relationship between markers of damage (r = -0.53, p<0.005) but not between markers of damage and restoration, thus suggesting that both types of markers should be measured together. CONCLUSIONS: CPAP therapy improves FMD. This improvement may be related to an increase of endothelial restoration process and a decrease of endothelial damage

Some results on homoclinic and heteroclinic connections in planar systems

Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to obtain a sequence of explicit algebraic lower and upper bounds for the bifurcation set ${\Phi(n,b)=0}.$ The method is applied to two quadratic families, one of them is the well-known Bogdanov-Takens system. One of the results that we obtain for this system is the bifurcation curve for small values of $n$, given by $b=\frac5 7 n^{1/2}+{72/2401}n- {30024/45294865}n^{3/2}- {2352961656/11108339166925} n^2+O(n^{5/2})$. We obtain the new three terms from purely algebraic calculations, without evaluating Melnikov functions

Nutrient fluxes through boundaries in the hypolimnion of Sau reservoir : expected patterns and unanticipated processes

By contrast to many natural lakes, the summer hypolimnion in advection-dominated systems like canyon-shaped reservoirs is not isolated from direct inputs from the river. This has important implications in the evolution of limnological features of the hypolimnion through the stratified period, especially if the river water directly plunges as a density current into the hypolimnion as a consequence of temperature differences. Taking the Sau Reservoir (Spain) as a prototype for this kind of systems, we present data from 11 years of monitoring to show how the river water entering the reservoir during summer is the main factor determining hypolimnetic nutrient concentrations. The empirical regression approach used all through the paper also stressed the effect of the improvement in water quality experienced by the river during the studied period on the improvement of the water quality stored in the summer hypolimnion of the reservoir. Since the change in river water quality was the consequence of the implementation of remediation measures at the basin scale, we advocate these solutions to manage reservoir eutrophication problems in this type of systems, which, in addition, had other unexpected benefits for the hypolimnetic water quality in Sau Reservoir.A diferencia de muchos lagos naturales, el hipolimnion que se forma en verano en sistemas dominados por la advección, como los embalses que inundan valles profundos y estrechos, no está aislado de las entradas directas desde el río. Esto tiene importantes implicaciones en la evolución de las características limnológicas del hipolimnion durante el periodo de estratificación, especialmente si el agua del río entra al embalse como una corriente de densidad directamente en el hipolimnion debido a diferencias de temperatura. Tomando el Embalse de Sau (España) como prototipo de este tipo de sistemas, mostramos 11 años de datos de un programa de monitoreo para ejemplificar cómo el agua del río que entra en verano al embalse es el factor determinante de la concentración de nutrientes en el hipolimnion. La aproximación de regresión empírica utilizada en el artículo también puso de manifiesto el efecto de la mejora en la calidad del agua que sufrió el río durante el periodo de estudio en la mejora del agua del agua embalsada en el hipolimnion. Ya que esta mejora en el río fue consecuencia de la implementación de medidas de restauración a nivel de la cuenca, promovemos estas soluciones para la gestión de problemas de eutrofización en este tipo de sistemas, que por otra parte mostraron ventajas inesperadas en el caso del hipolimnion del Embalse de Sau

Phylogeny, distribution and pathogenicity of Lasiodiplodia species associated with dieback of table grape in the main Brazilian exporting region

[EN] Botryosphaeria dieback is an important disease of table grape in the Sao Francisco Valley, the main Brazilian exporting region. The objectives of this study were to identify species of Lasiodiplodia associated with botryosphaeria dieback of table grapes in the Sao Francisco Valley, investigate the prevalence and distribution of the species in the region, and evaluate their pathogenicity and virulence in green shoots of table grape. A total of 112 Lasiodiplodia isolates were obtained from 14 vineyards, located in Casa Nova, Juazeiro and Petrolina. Fungal identifications were made using phylogenetic analysis based on partial sequences of translation elongation factor 1-alpha (EF1-alpha) and internal transcribed spacer (ITS) sequences, in combination with morphometric characteristics of conidia. Eight species of Lasiodiplodia were identified: L. brasiliense, L. crassispora, L. egyptiacae, L. euphorbicola, L. hormozganensis, L. jatrophicola, L. pseudotheobromae and L. theobromae. Except for L. crassispora, L. pseudotheobromae and L. theobromae, all the other species are reported for the first time on grapevine worldwide. The distribution of Lasiodiplodia species differed between the three table grape populations of Sao Francisco Valley. All Lasiodiplodia species isolated in this study were present in the population of Casa Nova and Lasiodiplodia theobromae was the most prevalent. All species of Lasiodiplodia were pathogenic on detached green shoots of grapevine, with L. brasiliense being the most virulent.This study was financed by Fundacao de Amparo a Ciencia e Tecnologia do Estado de Pernambuco (FACEPE APQ 137-5.01/12, IBPG-0674-5.01/09). M.P.S.C. and S.J.M. also acknowledge the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico-CNPq research fellowship. A.J.L.P. thanks Fundacao para a Ciencia e a Tecnologia (Portugal) for financial support through grant PEst-OE/BIA/UI0457/2011.Correia, KC.; Silva, M.; De Morais, M.; Armengol Fortí, J.; Phillips, A.; Camara, M.; Michereff, S. (2016). Phylogeny, distribution and pathogenicity of Lasiodiplodia species associated with dieback of table grape in the main Brazilian exporting region. Plant Pathology. 65(1):92-103. doi:10.1111/ppa.12388S9210365