THE TALENT VERSUS LUCK MODEL AS AN ENSEMBLE OF ONE-DIMENSIONAL RANDOM WALKS

The role of luck on individual success is hard to be investigated empirically. Simplified mathematical models are often used to shed light on the subtle relations between success and luck. Recently, a simple model called “Talent versus Luck” showed that the most successful individual in a population can be just an average talented individual that is subjected to a very fortunate sequence of events. Here, we modify the framework of the TvL model such that in our model the individuals’ success is modelled as an ensemble of one-dimensional random walks. Our model reproduces the original TvL results and, due to the mathematical simplicity, it shows clearly that the original conclusions of the TvL model are the consequence of two factors: first, the normal distribution of talents with low standard deviation, which creates a large number of average talented individuals; second, the low number of steps considered, which allows the observation of large fluctuations. We also show that the results strongly depend on the relative frequency of good and bad luck events, which defines a critical value for the talent: in the long run, the individuals with high talent end up very successful and those with low talent end up ruined. Last, we considered two variations to illustrate applications of the ensemble of random walks model.

STATISTICAL PROPERTIES OF RANKINGS IN SPORTS AND GAMES

Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a variety of fields. More recently, data availability has allowed us to study rank dynamics: how elements of a ranking change in time. Here, we study the rank distributions and rank dynamics of 12 datasets from different sports and games. To study rank dynamics, we consider measures that we have defined previously: rank diversity, change probability, rank entropy, and rank complexity. We also introduce a new measure that we call “system closure” that reflects how many elements enter or leave the rankings in time. We use a random walk model to reproduce the observed rank dynamics, showing that a simple mechanism can generate similar statistical properties as the ones observed in the datasets. Our results show that while rank distributions vary considerably for different rankings, rank dynamics have similar behaviors, independently of the nature and competitiveness of the sport or game and its ranking method. Our results also suggest that our measures of rank dynamics are general and applicable for complex systems of different natures.

DESIGN OF CONTROLLABLE LEADER–FOLLOWER NETWORKS VIA MEMETIC ALGORITHMS

In many engineered and natural networked systems, there has been great interest in leader selection and/or edge assignment during the optimal design of controllable networks. In this paper, we present our pioneering work in leader–follower network design via memetic algorithms, which focuses on minimizing the number of leaders or the amount of control energy while ensuring network controllability. We consider three problems in this paper: (1) selecting the minimum number of leaders in a pre-defined network with guaranteed network controllability; (2) selecting the leaders in a pre-defined network with the minimum control energy; and (3) assigning edges (interactions) between nodes to form a controllable leader–follower network with the minimum control energy. The proposed framework can be applied in designing signed, unsigned, directed, or undirected networks. It should be noted that this work is the first to apply memetic algorithms in the design of controllable networks. We chose memetic algorithms because they have been shown to be more efficient and more effective than the standard genetic algorithms in solving some optimization problems. Our simulation results provide an additional demonstration of their efficiency and effectiveness.