Can simple models explain Zipf’s law for all exponents?

H. Simon proposed a simple stochastic process for explaining Zipf’s law for word frequencies. Here we introduce two similar generalizations of Simon’s model that cover the same range of exponents as the standard Simon model. The mathematical approach followed minimizes the amount of mathematical background needed for deriving the exponent, compared to previous approaches to the standard Simon’s model. Reviewing what is known from other simple explanations of Zipf’s law, we conclude there is no single radically simple explanation covering the whole range of variation of the exponent of Zipf’s law in humans. The meaningfulness of Zipf’s law for word frequencies remains an open question.Peer ReviewedPostprint (published version

Opinion dynamics with disagreement and modulated information

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals' opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions' overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices

Molecular Dynamics Simulation of Vascular Network Formation

Endothelial cells are responsible for the formation of the capillary blood vessel network. We describe a system of endothelial cells by means of two-dimensional molecular dynamics simulations of point-like particles. Cells' motion is governed by the gradient of the concentration of a chemical substance that they produce (chemotaxis). The typical time of degradation of the chemical substance introduces a characteristic length in the system. We show that point-like model cells form network resembling structures tuned by this characteristic length, before collapsing altogether. Successively, we improve the non-realistic point-like model cells by introducing an isotropic strong repulsive force between them and a velocity dependent force mimicking the observed peculiarity of endothelial cells to preserve the direction of their motion (persistence). This more realistic model does not show a clear network formation. We ascribe this partial fault in reproducing the experiments to the static geometry of our model cells that, in reality, change their shapes by elongating toward neighboring cells.Comment: 10 pages, 3 figures, 2 of which composite with 8 pictures each. Accepted on J.Stat.Mech. (2009). Appeared at the poster session of StatPhys23, Genoa, Italy, July 13 (2007

Complex delay dynamics on railway networks: from universal laws to realistic modelling

Railways are a key infrastructure for any modern country. The reliability and resilience of this peculiar transportation system may be challenged by different shocks such as disruptions, strikes and adverse weather conditions. These events compromise the correct functioning of the system and trigger the spreading of delays into the railway network on a daily basis. Despite their importance, a general theoretical understanding of the underlying causes of these disruptions is still lacking. In this work, we analyse the Italian and German railway networks by leveraging on the train schedules and actual delay data retrieved during the year 2015. We use {these} data to infer simple statistical laws ruling the emergence of localized delays in different areas of the network and we model the spreading of these delays throughout the network by exploiting a framework inspired by epidemic spreading models. Our model offers a fast and easy tool for the preliminary assessment of the {effectiveness of} traffic handling policies, and of the railway {network} criticalities.Comment: 32 pages (with appendix), 28 Figures (with appendix), 2 Table

Measuring Marginal q

Using asset prices I estimate the marginal value of capital in a dynamic stochastic economy under general assumptions about technology and preferences. The state-space measure of marginal q relies on the joint measurability of the value function, i.e. firm market value, and its underlying firm state variables. Unlike existing methodologies, the state-space marginal q requires only general restrictions on the stochastic discount factor and the firm investment technology, and it uses simple linear estimation methods. Consistently with a large class of neoclassical investment models, I construct the state-space marginal q using the firm capital stock and profitability shocks. I show that this new measure of real investment opportunities is substantially different from the conventional Tobin\u27s Q, it yields more plausible and robust estimates of capital adjustment costs, it increases the correlation with investment and the sensitivity of investment to fundamentals

Irreversible Investment and the Cross-Section of Stock Returns in General Equilibrium

A general equilibrium production economy with heterogeneous firms and irreversible investment generates the value premium. Investment irreversibility prevents unprofitable value firms from optimally scaling down their capital stock. In contrast, profitable and fast growing - growth - firms can optimally use investment to provide consumption insurance. Value firms are riskier and have higher expected returns than growth firms, especially in bad times when consumption volatility is high. The value premium is larger for small stocks as small value firms are more severely affected by irreversibility. Firms’ investment and capital predict the cross-section of stock returns much like book-to-market and market equity both in the model and data. The model can replicate the failure of the unconditional CAPM. Multifactor models, including the Fama and French (1993) factor model, and to a lesser extent, conditional versions of the CAPM, outperform the unconditional CAPM