Mathematical analysis of Markov models for social processes

We present Markov models for two social processes: the spread of rumors and the change in the spatial distribution of a population over time. For the spread of rumors, we present two models. The first is for the situation in which all particles are identical but one initially knows the rumor. The second is for a situation in which there are two kinds of particles: spreaders, who can spread the rumor, and ordinary particles, who only can learn the rumor. We find that the limiting distribution for the first model is the convolution of two double exponential distributions and for the second model is a double exponential distribution. The stochastic dynamics for our model of the change in the spatial distribution of a population over time include the four basic demographic processes: birth, death, migration, and immigration. We allow interaction between particles only inasmuch as the immigration rate can depend on the existing configuration of particles. We focus on the critical case of constant mean density, under the conditions of long jumps migration, immigration in which distant particles have a positive effect, or both. We prove, under these conditions, the existence of ergodic limiting behavior: the point process is stationary in space and time. Without the strong mixing due to these conditions, the population vanishes due to infinite clusterization

Exploring the Reasons for the Seasons Using Google Earth, 3D Models, and Plots

Public understanding of climate and climate change is of broad societal importance. However, misconceptions regarding reasons for the seasons abound amongst students, teachers, and the public, many of whom believe that seasonality is caused by large variations in Earth\u27s distance from the Sun. Misconceptions may be reinforced by textbook illustrations that exaggerate eccentricity or show an inclined view of Earth\u27s near-circular orbit. Textbook explanations that omit multiple factors influencing seasons, that do not mesh with students\u27 experiences, or that are erroneous, hinder scientifically valid reasoning. Studies show that many teachers share their students\u27 misconceptions, and even when they understand basic concepts, teachers may fail to appreciate the range of factors contributing to seasonal change, or their relative importance. We have therefore developed a learning resource using Google Earth, a virtual globe with other useful, weather- and climate-related visualizations. A classroom test of 27 undergraduates in a public research university showed that 15 improved their test scores after the Google Earth-based laboratory class, whereas 5 disimproved. Mean correct answers rose from 4.7/10 to 6/10, giving a paired t-test value of 0.21. After using Google Earth, students are helped to segue to a heliocentric view

The Paradox of Power in CSR: A Case Study on Implementation

Purpose Although current literature assumes positive outcomes for stakeholders resulting from an increase in power associated with CSR, this research suggests that this increase can lead to conflict within organizations, resulting in almost complete inactivity on CSR. Methods A single in-depth case study, focusing on power as an embedded concept. Results Empirical evidence is used to demonstrate how some actors use CSR to improve their own positions within an organization. Resource dependence theory is used to highlight why this may be a more significant concern for CSR. Conclusions Increasing power for CSR has the potential to offer actors associated with it increased personal power, and thus can attract opportunistic actors with little interest in realizing the benefits of CSR for the company and its stakeholders. Thus power can be an impediment to furthering CSR strategy and activities at the individual and organizational level