Structural preferential attachment: stochastic process for the growth of scale-free, modular, and self-similar

Laurent Hébert-Dufresne1, Antoine Allard, Vincent Marceau

  • 1Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec, Canada G1V 0A6.

Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Attachment Styles01:24

Attachment Styles

Jeffrey Simpson's attachment theory suggests that early caregiver relationships shape lasting patterns of behavior and emotional regulation, known as attachment styles. These patterns are organized along two key dimensions: self-esteem and interpersonal trust. The intersection of these dimensions produces four primary attachment styles that typically persist throughout life and significantly influence how individuals form and maintain relationships.Secure Attachment StyleIndividuals with a...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Factors Influencing Attraction III: Similarity01:23

Factors Influencing Attraction III: Similarity

The similarity hypothesis suggests that individuals are more likely to form relationships with others who share similar attitudes, beliefs, values, and interests. This concept has been widely studied in social psychology, demonstrating that perceived similarity fosters interpersonal attraction. In an experiment supporting this hypothesis, participants were presented with fabricated information indicating that strangers held attitudes similar to their own. The results showed that participants...
Relationship Formation02:12

Relationship Formation

What do you think is the single most influential factor in determining with whom you become friends and whom you form romantic relationships? You might be surprised to learn that the answer is simple: the people with whom you have the most contact. This most important factor is proximity. You are more likely to be friends with people you have regular contact with. For example, there are decades of research that shows that you are more likely to become friends with people who live in your dorm,...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...