Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

RUMOR PROCESSES ON N

We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumor. The appetite for spreading or hearing the rumor is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand-based on the distribution of the random variables-whether the probability of having an infinite set of individuals knowing the rumor is positive or not.

Osteoblastlike Cell Adhesion on Titanium Surfaces Modified by Plasma Nitriding

Purpose: The aim of this study was to evaluate the characteristics of various titanium surfaces modified by cold plasma nitriding in terms of adhesion and proliferation of rat osteoblastlike cells. Materials and Methods: Samples of grade 2 titanium were subjected to three different surface modification processes: polishing, nit riding by plasma direct current, and nitriding by cathodic cage discharge. To evaluate the effect of the surface treatment on the cellular response, the adhesion and proliferation of osteoblastlike cells (MC3T3) were quantified and the results were analyzed by Kruskal-Wallis and Friedman statistical tests. Cellular morphology was observed by scanning electron microscopy. Results: There was more MC3T3 cell attachment on the rougher surfaces produced by cathodic cage discharge compared with polished samples (P < .05). Conclusions: Plasma nitriding improves titanium surface roughness and wettability, leading to osteoblastlike cell adhesion. INT J ORAL MAXILLOFAC IMPLANTS 2011;26:237-244