Computing the minimal covering set

We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm draws upon a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set–the minimal upward covering set and the minimal downward covering set–unless P equals NP. Finally, we observe a strong relationship between von Neumann–Morgenstern stable sets and upward covering on the one hand, and the Banks set and downward covering on the other.     

Minimal mechanisms for school formation in self-propelled particles

In the context of social organisms, a school refers to a cohesive group of organisms that share a common speed and direction of motion, as well as a common axis of body alignment or polarization. Schools are also noted for the relatively fixed nearest-neighbour distances between individuals. The rules of interaction that lead to the formation and maintenance of a school structure have been explored experimentally, analytically, and by simulation. Interest in biological examples, and non-biological “self-propelled particles” such as robots, vehicles, or autonomous agents leads to the question of what are the simplest possible sets of rules that can assure the formation and the stability of the “perfect school”: an aggregate in which the nearest-neighbour distances and speeds are identical.Here we explore mechanisms that lead to a perfect school structure in one and two dimensions. We consider distance-detection as well as velocity-detection between the interacting pairs of self-propelled particles. We construct interaction forces and formulate schooling equations. In the simplest cases, these equations have analytic solutions. In many cases, the stability of the perfect school can be explored. We then investigate how these structures form and evolve over time from various initial configurations using simulations. We study the relationship between the assumed interaction forces and the school patterns that emerge. While true biological schools are far from perfect, the insights gained from this investigation can help to understand some properties of real schools, and to suggest the appropriate properties of artificial schools where coordinated motion is desired.     

Compromise and synchronization in opinion dynamics

We discuss two models of opinion dynamics. We first present a brief review of the Hegselmann and Krause (HK) compromise model in two dimensions, showing that it is possible to simulate the dynamics in the limit of an infinite number of agents by solving numerically a rate equation for a continuum distribution of opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows to study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find the agreement. In the context of the this model, consensus is viewed as a synchronization process.     

Effective mechanism for social recommendation of news

Recommender systems represent an important tool for news distribution on the Internet. In this work we modify a recently proposed social recommendation model in order to deal with no explicit ratings of users on news. The model consists of a network of users which continually adapts in order to achieve an efficient news traffic. To optimize the network’s topology we propose different stochastic algorithms that are scalable with respect to the network’s size. Agent-based simulations reveal the features and the performance of these algorithms. To overcome the resultant drawbacks of each method we introduce two improved algorithms and show that they can optimize the network’s topology almost as fast and effectively as other not-scalable methods that make use of much more information.     

Stochastic nonlinear dynamics of interpersonal and romantic relationships

Current theories from biosocial (e.g., the role of neurotransmitters in behavioral features), ecological (e.g., cultural, political, and institutional conditions), and interpersonal (e.g., attachment) perspectives have grounded interpersonal and romantic relationships in normative social experiences. However, these theories have not been developed to the point of providing a solid theoretical understanding of the dynamics present in interpersonal and romantic relationships, and integrative theories are still lacking. In this paper, mathematical models are used to investigate the dynamics of interpersonal and romantic relationships, via ordinary and stochastic differential equations, in order to provide insight into the behaviors of love. The analysis starts with a deterministic model and progresses to nonlinear stochastic models capturing the stochastic rates and factors (e.g., ecological factors, such as historical, cultural and community conditions) that affect proximal experiences and shape the patterns of relationship. Numerical examples are given to illustrate various dynamics of interpersonal and romantic behaviors with particular emphases placed on sustained oscillations and transitions between locally stable equilibria that are observable in stochastic models (closely related to real interpersonal dynamics), but absent in deterministic models.     

The co-evolution of cultures,social network communities,and agent locations in an extension of Axelrod’s model of cultural dissemination

We introduce a variant of the Axelrod model of cultural dissemination in which agents change their physical locations, social links, and cultures. Numerical simulations are used to investigate the evolution of social network communities and the cultural diversity within and between these communities. An analysis of the simulation results shows that an initial peak in the cultural diversity within network communities is evident before agents segregate into a final configuration of culturally homogeneous communities. Larger long-range interaction probabilities facilitate the initial emergence of culturally diverse network communities, which leads to a more pronounced initial peak in cultural diversity within communities. At equilibrium, the number of communities, and hence cultures, increases when the initial cultural diversity increases. However, the number of communities decreases when the lattice size or population density increases. A phase transition between two regimes of initial cultural diversity is evident. For initial diversities below a critical value, a single network community and culture emerges that dominates the population. For initial diversities above the critical value, multiple culturally homogeneous communities emerge. The critical value of initial diversity at which this transition occurs increases with increasing lattice size and population density and generally with increasing absolute population size. We conclude that larger initial diversities promote cultural heterogenization, while larger lattice sizes, population densities, and in fact absolute population sizes promote homogenization.     

Identifying the greatest team and captain—A complex network approach to cricket matches

We consider all Test matches played between 1877 and 2010 and One Day International (ODI) matches played between 1971 and 2010. We form directed and weighted networks of teams and also of their captains. The success of a team (or captain) is determined by the ‘quality’ of the wins, not simply by the number of wins. We apply the diffusion-based PageRank algorithm to the networks to assess the importance of the wins, and rank the respective teams and captains. Our analysis identifies Australia as the best team in both forms of cricket, Test and ODI. Steve Waugh is identified as the best captain in Test cricket and Ricky Ponting is the best captain in the ODI format. We also compare our ranking scheme with an existing ranking scheme, the Reliance ICC ranking. Our method does not depend on ‘external’ criteria in the ranking of teams (captains). The purpose of this paper is to introduce a revised ranking of cricket teams and to quantify the success of the captains.     

The Forbes 400, the Pareto power-law and efficient markets

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.     

Fritz Reiche and the Emergency Committee in Aid of Displaced Foreign Scholars

I discuss the family background and early life of the German theoretical physicist Fritz Reiche (1883–1969) in Berlin; his higher education at the University of Berlin under Max Planck (1858–1947); his subsequent work at the University of Breslau with Otto Lummer (1860–1925); his return to Berlin in 1911, where he completed his Habilitation thesis in 1913, married Bertha Ochs the following year, became a friend of Albert Einstein (1879–1955), and worked during and immediately after the Great War. In 1921 he was appointed as ordentlicher Professor of Theoretical Physics at the University of Breslau and worked there until he was dismissed in 1933. He spent the academic year 1934–1935 as a visiting professor at the German University in Prague and then returned to Berlin, where he remained until, with the crucial help of his friend Rudolf Ladenburg (1882–1952) and vital assistance of the Emergency Committee in Aid of Displaced Foreign Scholars, he, his wife Bertha, and their daughter Eve were able to emigrate to the United States in 1941 (their son Hans had already emigrated to England in 1939).From 1941–1946 he held appointments at the New School for Social Research in New York, the City College of New York, and Union College in Schenectady, New York, and then was appointed as an Adjunct Professor of Physics at New York University, where his contract was renewed year-by-year until his retirement in 1958.