Different models of social influence have explored the dynamics of social contagion, imitation, and diffusion of different types of traits, opinions, and conducts. However, few behavioral data indicating social influence dynamics have been obtained f
rom direct observation in `natural social contexts. The present research provides that kind of evidence in the case of the public expression of political preferences in the city of Barcelona, where thousands of citizens supporting the secession of Catalonia from Spain have placed a Catalan flag in their balconies. We present two different studies. 1) In July 2013 we registered the number of flags in 26% of the the city. We find that there is a large dispersion in the density of flags in districts with similar density of pro-independence voters. However, we find that the density of flags tends to be fostered in those electoral district where there is a clear majority of pro-independence vote, while it is inhibited in the opposite cases. 2) During 17 days around Catalonias 2013 National Holiday we observed the position at balcony resolution of the flags displayed in the facades of 82 blocks. We compare the clustering of flags on the facades observed each day to equivalent random distributions and find that successive hangings of flags are not independent events but that a local influence mechanism is favoring their clustering. We also find that except for the National Holiday day the density of flags tends to be fostered in those facades where there is a clear majority of pro-independence vote.
We derive a semi-empirical galactic initial mass function (IMF) from observational constraints. We assume that the star formation rate in a galaxy can be expressed as the product of the IMF, $psi (m)$, which is a smooth function of mass $m$ (in units
of msun), and a time- and space-dependent total rate of star formation per unit area of galactic disk. The mass dependence of the proposed IMF is determined by five parameters: the low-mass slope $gamma$, the high-mass slope $-Gamma$, the characteristic mass $m_{ch}$ (which is close to the mass $m_{rm peak}$ at which the IMF turns over), and the lower and upper limits on the mass, $m_l$ (taken to be 0.004) and $m_u$ (taken to be 120). The star formation rate in terms of number of stars per unit area of galactic disk per unit logarithmic mass interval, is proportional to $m^{-Gamma} left{1-expleft[{-(m/m_{ch})^{gamma +Gamma}}right]right}$, where $cal N_*$ is the number of stars, $m_l<m<m_u$ is the range of stellar masses. The values of $gamma$ and $emch$ are derived from two integral constraints: i) the ratio of the number density of stars in the range $m=0.1-0.6$ to that in the range $m=0.6-0.8$ as inferred from the mass distribution of field stars in the local neighborhood, and ii) the ratio of the number of stars in the range $m=0.08 - 1$ to the number of brown dwarfs in the range $m=0.03-0.08$ in young clusters. The IMF satisfying the above constraints is characterized by the parameters $gamma=0.51$ and $emch=0.35$ (which corresponds to $m_{rm peak}=0.27$). This IMF agrees quite well with the Chabrier (2005) IMF for the entire mass range over which we have compared with data, but predicts significantly more stars with masses $< 0.03, M_odot$; we also compare with other IMFs in current use.
