4,370 research outputs found
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
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