Non-Local Product Rules for Percolation

Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The distinctive scaling properties of the model at criticality, however, strongly suggest that it should belong to a different universality class than ordinary percolation. Here we introduce a generalization of the product rule that reveals the effect of non-locality on the critical behavior of the percolation process. Precisely, pairs of unoccupied bonds are chosen according to a probability that decays as a power-law of their Manhattan distance, and only that bond connecting clusters whose product of their sizes is the smallest, becomes occupied. Interestingly, our results for two-dimensional lattices at criticality shows that the power-law exponent of the product rule has a significant influence on the finite-size scaling exponents for the spanning cluster, the conducting backbone, and the cutting bonds of the system. In all three cases, we observe a continuous variation from ordinary to (non-local) explosive percolation exponents.Comment: 5 pages, 4 figure

How dense can one pack spheres of arbitrary size distribution?

We present the first systematic algorithm to estimate the maximum packing density of spheres when the grain sizes are drawn from an arbitrary size distribution. With an Apollonian filling rule, we implement our technique for disks in 2d and spheres in 3d. As expected, the densest packing is achieved with power-law size distributions. We also test the method on homogeneous and on empirical real distributions, and we propose a scheme to obtain experimentally accessible distributions of grain sizes with low porosity. Our method should be helpful in the development of ultra-strong ceramics and high performance concrete.Comment: 5 pages, 5 figure

Dynamics of Racial Residential Segregation and Gentrification in New York City

Racial residential segregation is interconnected with several other phenomena such as income inequalities, property values inequalities, and racial disparities in health and education. Furthermore, recent literature suggests the phenomenon of gentrification as a cause of perpetuation or increase of racial residential segregation in some American cities. In this paper, we analyze the dynamics of racial residential segregation for white, black, Asian, and Hispanic citizens in New York City in 1990, 2000, and 2010. It was possible to observe that segregation between white and Hispanic citizens and between white and Asian ones has grown, while segregation between white and black is relatively stable. Furthermore, we analyzed the per capita income and the Gini coefficient in each segregated zone, showing that the highest inequalities occur in the zones where there is an overlap of high-density zones of pair of races. Focusing on the changing of the density of population across the city during these 20 years, and by analyzing white and black people's segregation, our analysis reveals that a positive flux of white (black) people is associated with a substantial increase (decrease) of the property values, as compared with the city mean. Furthermore, by clustering the region with the higher density of black citizens, we measured the variation of area and displacement of the four most significant clusters from 1990 to 2010. The large displacements ( & AP; 1.6 k m ) observed for two of these clusters, namely, one in the neighborhood of Harlem and the other inside the borough of Brooklyn, led to the emergence of typically gentrified regions

Origins of power-law degree distribution in the heterogeneity of human activity in social networks

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.Comment: 23 pages, 5 figure

The price of a vote: Diseconomy in proportional elections

The increasing cost of electoral campaigns raises the need for effective campaign planning and a precise understanding of the return of such investment. Interestingly, despite the strong impact of elections on our daily lives, how this investment is translated into votes is still unknown. By performing data analysis and modeling, we show that top candidates spend more money per vote than the less successful and poorer candidates, a relation that discloses a diseconomy of scale. We demonstrate that such electoral diseconomy arises from the competition between candidates due to inefficient campaign expenditure. Our approach succeeds in two important tests. First, it reveals that the statistical pattern in the vote distribution of candidates can be explained in terms of the independently conceived, but similarly skewed distribution of money campaign. Second, using a heuristic argument, we are able to explain the observed turnout percentage for a given election of approximately 63% in average. This result is in good agreement with the average turnout rate obtained from real data. Due to its generality, we expect that our approach can be applied to a wide range of problems concerning the adoption process in marketing campaigns

Circuits with broken fibration symmetries perform core logic computations in biological networks

We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits, ubiquitous across species, that are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops. These canonical variants serve fundamental operations of synchronization and clocks (in their symmetric states) and memory storage (in their broken symmetry states). These conclusions introduce a theoretically principled strategy to search for computational building blocks in biological networks, and present a systematic route to design synthetic biological circuits

How does public opinion become extreme?

We investigate the emergence of extreme opinion trends in society by employing statistical physics modeling and analysis on polls that inquire about a wide range of issues such as religion, economics, politics, abortion, extramarital sex, books, movies, and electoral vote. The surveys lay out a clear indicator of the rise of extreme views. The precursor is a nonlinear relation between the fraction of individuals holding a certain extreme view and the fraction of individuals that includes also moderates, e.g., in politics, those who are “very conservative” versus “moderate to very conservative” ones. We propose an activation model of opinion dynamics with interaction rules based on the existence of individual “stubbornness” that mimics empirical observations. According to our modeling, the onset of nonlinearity can be associated to an abrupt bootstrap-percolation transition with cascades of extreme views through society. Therefore, it represents an early-warning signal to forecast the transition from moderate to extreme views. Moreover, by means of a phase diagram we can classify societies according to the percolative regime they belong to, in terms of critical fractions of extremists and people’s ties

Avoiding catastrophic failure in correlated networks of networks

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in two independent experiments of functional brain networks (in task- and resting states) which show that brain networks are connected with a topology that maximizes stability according to the theory.Comment: 40 pages, 7 figure