Physics

The role of statisticians in society is to provide tools, techniques, and guidance with regards to how much to trust data. This role is increasingly more important with more data and more misinformation than ever before. The American Statistical Association recently released two statements on p-values, and provided four guiding principles. We evaluate their claims using these principles and find that they failed to adhere to them. In this age of distrust, we have an opportunity to be role models of trustworthiness, and responsibility to take it.

Lotka's seminal work (A.J. Lotka A., Proc. Natl. Acad. Sci. U.S.A. 6 (1920) 410) "on certain rhythmic relations'' is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It is because non-transitive interactions have paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires deeper understanding of related dynamical processes. In this perspective article we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.

Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to mobility, node or edge failures, and varying traffic loads. Percolation theory quantifies the threshold value of a local control parameter such as a node occupation (resp., deletion) probability or an edge activation (resp., removal) probability above (resp., below) which there exists a giant connected component (GCC), a connected component comprising of a number of occupied nodes and active edges whose size is proportional to the size of the network itself. Any pair of occupied nodes in the GCC is connected via at least one path comprised of active edges and occupied nodes. The mere existence of the GCC itself does not guarantee that the long-range connectivity would be robust, e.g., to random link or node failures due to network dynamics. In this paper, we explore new percolation thresholds that guarantee not only spanning network connectivity, but also robustness. We define and analyze four measures of robust network connectivity, explore their interrelationships, and numerically evaluate the respective robust percolation thresholds for the 2D square lattice.

We consider the privacy of interactions between individuals in a network. For many networks, while nodes are anonymous to outside observers, the existence of a link between individuals implies the possibility of one node revealing identifying information about its neighbor. Moreover, while the identities of the accounts are likely hidden to an observer, the network of interaction between two anonymous accounts is often available. For example, in blockchain cryptocurrencies, transactions between two anonymous accounts are published openly. Here we consider what happens if one (or more) parties in such a network are deanonymized by an outside identity. These compromised individuals could leak information about others with whom they interacted, which could then cascade to more and more nodes' information being revealed. We use a percolation framework to analyze the scenario outlined above and show for different likelihoods of individuals possessing information on their counter-parties, the fraction of accounts that can be identified and the idealized minimum number of steps from a deanonymized node to an anonymous node (a measure of the effort required to deanonymize that individual). We further develop a greedy algorithm to estimate the \emph{actual} number of steps that will be needed to identify a particular node based on the noisy information available to the attacker. We apply our framework to three real-world networks: (1) a blockchain transaction network, (2) a network of interactions on the dark web, and (3) a political conspiracy network. We find that in all three networks, beginning from one compromised individual, it is possible to deanonymize a significant fraction of the network ( >50 %) within less than 5 steps. Overall these results provide guidelines for investigators seeking to identify actors in anonymous networks, as well as for users seeking to maintain their privacy.

In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components composing the complex systems. As a paradigm for random and semi-random connectivity, percolation model plays a key role in the development of network science and its applications. On the one hand, the concepts and analytical methods, such as the emergence of the giant cluster, the finite-size scaling, and the mean-field method, which are intimately related to the percolation theory, are employed to quantify and solve some core problems of networks. On the other hand, the insights into the percolation theory also facilitate the understanding of networked systems, such as robustness, epidemic spreading, vital node identification, and community detection. Meanwhile, network science also brings some new issues to the percolation theory itself, such as percolation of strong heterogeneous systems, topological transition of networks beyond pairwise interactions, and emergence of a giant cluster with mutual connections. So far, the percolation theory has already percolated into the researches of structure analysis and dynamic modeling in network science. Understanding the percolation theory should help the study of many fields in network science, including the still opening questions in the frontiers of networks, such as networks beyond pairwise interactions, temporal networks, and network of networks. The intention of this paper is to offer an overview of these applications, as well as the basic theory of percolation transition on network systems.

We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of microscopic events produced by a self-exciting Hawkes process, and leverage a percolation framework to study the formation of macroscopic bursts of activity as a function of the resolution parameter. We find that the very same process may result in different distributions of avalanche size and duration, which are understood in terms of the competition between the 1D percolation and the branching process universality class. Pure regimes for the individual classes are observed at specific values of the resolution parameter corresponding to the critical points of the percolation diagram. A regime of crossover characterized by a mixture of the two universal behaviors is observed in a wide region of the diagram. The hybrid scaling appears to be a likely outcome for an analysis of the time series based on a reasonably chosen, but not precisely adjusted, value of the resolution parameter.

Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level of the individual. In this work, we ask which factors contribute to a single voter maintaining a long-term statistical bias for one opinion over the other in the face of social influence. To this end, a modified version of the network voter model is proposed, which also incorporates quenched disorder in the interaction strengths between individuals and the possibility of antagonistic relationships. We find that a sparse interaction network and heterogeneity in interaction strengths give rise to the possibility of arbitrarily long-lived individual biases, even when there is no population-averaged bias for one opinion over the other. This is demonstrated by calculating the eigenvalue spectrum of the weighted network Laplacian using the theory of sparse random matrices.

In the wake of the pandemic, the inadequacy of urban sidewalks to comply with social distancing remains untackled in academy. Beyond isolated efforts (from sidewalk widenings to car-free Open Streets), there is a need for a large-scale and quantitative strategy for cities to handle the challenges that COVID-19 poses in the use of public space. The main obstacle is a generalized lack of publicly available data on sidewalk infrastructure worldwide, and thus city governments have not yet benefited from a complex systems approach of treating urban sidewalks as networks. Here, we leverage sidewalk geometries from ten cities in three continents, to first analyze sidewalk and roadbed geometries, and find that cities most often present an arrogant distribution of public space: imbalanced and unfair with respect to pedestrians. Then, we connect these geometries to build a sidewalk network --adjacent, but not assimilable to road networks, so fertile in urban science. In a no-intervention scenario, we apply percolation theory to examine whether the sidewalk infrastructure in cities can withstand the tight pandemic social distancing imposed on our streets. The resulting collapse of sidewalk networks, often at widths below three meters, calls for a cautious strategy, taking into account the interdependencies between a city's sidewalk and road networks, as any improvement for pedestrians comes at a cost for motor transport. With notable success, we propose a shared-effort heuristic that delays the sidewalk connectivity breakdown, while preserving the road network's functionality.

More than one billion students are out of school because of Covid-19, forced to a remote learning that has several drawbacks and has been hurriedly arranged; in addition, most countries are currently uncertain on how to plan school activities for the 2020-2021 school year; all of this makes learning and education some of the biggest world issues of the current pandemic. Unfortunately, due to the length of the incubation period of Covid-19, full opening of schools seems to be impractical till a vaccine is available. In order to support the possibility of some in-person learning, we study a mathematical model of the diffusion of the epidemic due to school opening, and evaluate plans aimed at containing the extra Covid-19 cases due to school activities while ensuring an adequate number of in-class learning periods. We consider a SEAIR model with an external source of infection and a suitable loss function; after a realistic parameter selection, we numerically determine optimal school opening strategies by simulated annealing. It turns out that blended models, with almost periodic alternations of in-class and remote teaching days or weeks, are generally optimal. Besides containing Covid-19 diffusion, these solutions could be pedagogically acceptable, and could also become a driving model for the society at large. In a prototypical example, the optimal strategy results in the school opening 90 days out of 200 with the number of Covid-19 cases among the individuals related to the school increasing by about 66%, instead of the about 250% increase that would have been a consequence of full opening.

We study the effect of polarization in Axelrod's model of cultural dissemination. This is done through the introduction of a cultural feature that takes only two values, while the other features can present a larger number of possible traits. Our numerical results and mean-field approximations show that polarization reduces the characteristic phase transition of the original model to a finite-size effect, since at the thermodynamic limit only the ordered phase is present. Furthermore, for finite system sizes, the stationary state depends on the percolation threshold of the network where the model is implemented: a polarized phase is obtained for percolation thresholds below 1/2, a fragmented multicultural one otherwise.