Epidemic Spreading in Random Rectangular Networks

The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarios -like in the analysis of a disease propagating through plants- the shape of the plots and fields where the host of the disease is located may play a fundamental role on the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots/fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph (RRG) and we consider a lower bound for the epidemic threshold of a Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot/field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots/fields of the same area and different shapes.Comment: Version 4, 13 pages, 6 figures, 44 ref

Mechanisms of Action and Targets of Nitric Oxide in the Oculomotor System

Nitric oxide (NO) production by neurons in the prepositus hypoglossi (PH) nucleus is necessary for the normal performance of eye movements in alert animals. In this study, the mechanism(s) of action of NO in the oculomotor system has been investigated. Spontaneous and vestibularly induced eye movements were recorded in alert cats before and after microinjections in the PH nucleus of drugs affecting the NO–cGMP pathway. The cellular sources and targets of NO were also studied by immunohistochemical detection of neuronal NO synthase (NOS) and NO-sensitive guanylyl cyclase, respectively. Injections of NOS inhibitors produced alterations of eye velocity, but not of eye position, for both spontaneous and vestibularly induced eye movements, suggesting that NO produced by PH neurons is involved in the processing of velocity signals but not in the eye position generation. The effect of neuronal NO is probably exerted on a rich cGMP-producing neuropil dorsal to the nitrergic somas in the PH nucleus. On the other hand, local injections of NO donors or 8-Br-cGMP produced alterations of eye velocity during both spontaneous eye movements and vestibulo-ocular reflex (VOR), as well as changes in eye position generation exclusively during spontaneous eye movements. The target of this additional effect of exogenous NO is probably a well defined group of NO-sensitive cGMP-producing neurons located between the PH and the medial vestibular nuclei. These cells could be involved in the generation of eye position signals during spontaneous eye movements but not during the VOR.Fondo de Investigación Sanitaria Grants 94/0388 and 97/2054Comunidad Autónoma de Madrid Grant 08.5/0019/1997Dirección General de Investigación Científica y Technológica Grant PB 93–117

Unfinished Bridges between Eastern Europe and Latin America : Mexico-Romania Cultural Diplomacy and Nation Branding Experiences

Se analiza el concepto de diplomacia pública y se deconstruye en diplomacia cultural y marca país. Se aborda el contexto histórico de las relaciones México-Rumania, los puntos de coincidencia en temas globales y los temas actuales de la agenda bilateral. Finalmente, se establece una propuesta para llevar la relación a otro nivel a través de la diplomacia cultural y los intentos de marca país.México. Programa de Formación de Alto Nivel para la Administración Pública FederalTrabajo de investigació

The k-metric dimension of a graph

As a generalization of the concept of a metric basis, this article introduces the notion of $k$-metric basis in graphs. Given a connected graph $G=(V,E)$, a set $S\subseteq V$ is said to be a $k$-metric generator for $G$ if the elements of any pair of different vertices of $G$ are distinguished by at least $k$ elements of $S$, i.e., for any two different vertices $u,v\in V$, there exist at least $k$ vertices $w_1,w_2,...,w_k\in S$ such that $d_G(u,w_i)\ne d_G(v,w_i)$ for every $i\in \{1,...,k\}$. A metric generator of minimum cardinality is called a $k$-metric basis and its cardinality the $k$-metric dimension of $G$. A connected graph $G$ is $k$-metric dimensional if $k$ is the largest integer such that there exists a $k$-metric basis for $G$. We give a necessary and sufficient condition for a graph to be $k$-metric dimensional and we obtain several results on the $k$-metric dimension