Diffusion-Based Density-Equalizing Maps: an Interdisciplinary Approach to Visualizing Homicide Rates and Other Georeferenced Statistical Data

In every country, public and private agencies allocate extensive funding to collect large-scale statistical data, which in turn are studied and analyzed in order to determine local, regional, national, and international policies regarding all aspects relevant to the welfare of society. One important aspect of that process is the visualization of statistical data with embedded geographical information, which most often relies on archaic methods such as maps colored according to graded scales. In this work, we apply non-standard visualization techniques based on physical principles. We illustrate the method with recent statistics on homicide rates in Brazil and their correlation to other publicly available data. This physics-based approach provides a novel tool that can be used by interdisciplinary teams investigating statistics and model projections in a variety of fields such as economics and gross domestic product research, public health and epidemiology, socio-demographics, political science, business and marketing, and many others.Comment: 16 pages, 7 figures. To appear in Vol. 42 of Braz. J. Phy

Modeling Active Cell Movement With the Potts Model

In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time

Effects of Mass Media and Cultural Drift in a Model for Social Influence

In the context of an extension of Axelrod's model for social influence, we study the interplay and competition between the cultural drift, represented as random perturbations, and mass media, introduced by means of an external homogeneous field. Unlike previous studies [J. C. Gonz\'alez-Avella {\it et al}, Phys. Rev. E {\bf 72}, 065102(R) (2005)], the mass media coupling proposed here is capable of affecting the cultural traits of any individual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (culturally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external field is found to induce cultural ordering, a behavior opposite to that reported in previous studies using a different prescription for the mass media interaction. We compare the predictions of this model to statistical data measuring the impact of a mass media vasectomy promotion campaign in Brazil.Comment: 10 pages, 3 figures; minor changes; added references. To appear in IJMP

Mass Media Influence Spreading in Social Networks with Community Structure

We study an extension of Axelrod's model for social influence, in which cultural drift is represented as random perturbations, while mass media are introduced by means of an external field. In this scenario, we investigate how the modular structure of social networks affects the propagation of mass media messages across the society. The community structure of social networks is represented by coupled random networks, in which two random graphs are connected by intercommunity links. Considering inhomogeneous mass media fields, we study the conditions for successful message spreading and find a novel phase diagram in the multidimensional parameter space. These findings show that social modularity effects are of paramount importance in order to design successful, cost-effective advertising campaigns.Comment: 21 pages, 9 figures. To appear in JSTA

Alternating regimes of motion in cell motility models

Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra and extra-cellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we consider a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolves according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In the first case, the next orientation of the driving field depends on the previous direction of the field. In the second case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction coefficient and cell density dependent manner. Furthermore, we observe alternating regimes in the mean square displacement, with normal and anomalous diffusion. The crossovers between superdiffusive and diffusive regimes, are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement decreases the duration of the diffusive regime, in particular for high density cultures.Centro Regional de Estudios Genómico

Video_1_Modeling Active Cell Movement With the Potts Model.MOV

<p>In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.</p

Presentation_1_Modeling Active Cell Movement With the Potts Model.PDF

<p>In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.</p

Video_2_Modeling Active Cell Movement With the Potts Model.AVI

<p>In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.</p