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Marian Boguna

Publications and source records attributed to Marian Boguna.

At least 19 recordsLinked to original sources
arXiv2024

Measuring spatial distances in causal sets via causal overlaps

Causal set theory is perhaps the most minimalistic approach to quantum gravity, in the sense that it makes next to zero assumptions about the structure of spacetime below the Planck scale. Yet even with this minimalism, the continuum limit is still a major challenge in causal sets. One aspect of this challenge is the measurement of distances in causal sets. While the definition and estimation of time-like distances is relatively straightforward, dealing with space-like distances is much more problematic. Here we introduce an approach to measure distances between space-like separated events based on their causal overlap. We show that the distance estimation errors in this approach vanish in the continuum limit even for smallest distances of the order of the Planck length. These results are expected to inform the causal set geometrogenesis in general, and in particular the development of evolving causal set models in which space emerges from causal dynamics.

gr-qc↗
arXiv2023

Non-Markovian epidemic spreading on temporal networks

Many empirical studies have revealed that the occurrences of contacts associated with human activities are non-Markovian temporal processes with a heavy tailed inter-event time distribution. Besides, there has been increasing empirical evidence that the infection and recovery rates are time-dependent. However, we lack a comprehensive framework to analyze and understand non-Markovian contact and spreading processes on temporal networks. In this paper, we propose a general formalism to study non-Markovian dynamics on non-Markovian temporal networks. We find that, under certain conditions, non-Markovian dynamics on temporal networks are equivalent to Markovian dynamics on static networks. Interestingly, this result is independent of the underlying network topology.

physics.soc-ph↗
arXiv2021

Detecting the ultra low dimensionality of real networks

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging but necessary to generate efficient embeddings to be used in a multitude of downstream tasks. Here, we propose a method to infer the dimensionality of networks without the need for any a priori spatial embedding. Due to the ability of hyperbolic geometry to capture the complex connectivity of real networks, we detect ultra low dimensionality far below values reported using other approaches. We applied our method to real networks from different domains and found unexpected regularities, including: tissue-specific biomolecular networks being extremely low dimensional; brain connectomes being close to the three dimensions of their anatomical embedding; and social networks and the Internet requiring slightly higher dimensionality. Beyond paving the way towards an ultra efficient dimensional reduction, our findings help address fundamental issues that hinge on dimensionality, such as universality in critical behavior.

physics.soc-ph↗
arXiv2020

Network Geometry

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are all intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale-invariance, self-similarity, and other forms of fundamental symmetries in networks. Network geometry is also of great utility in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet. Here, we review the most important theoretical and practical developments dealing with these approaches to network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.

physics.soc-ph↗
arXiv2019

Small worlds and clustering in spatial networks

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current surge of activity in graph embedding. In the vast realm of spatial network models, only a few reproduce even the most basic properties of real-world networks. Here, we focus on three such properties--sparsity, small worldness, and clustering--and identify the general subclass of spatial homogeneous and heterogeneous network models that are sparse small worlds and that have nonzero clustering in the thermodynamic limit. We rely on the maximum entropy approach where network links correspond to noninteracting fermions whose energy dependence on spatial distances determines network small worldness and clustering.

physics.soc-ph↗
arXiv2017

Dynamical properties of the herding voter model with and without noise

Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion formation model, we show that, in the herding phase, a group of agents become effectively the leaders of the dynamics while the rest of the population follow blindly their opinion. Interestingly, in some cases such herding dynamics accelerates the time to consensus, which then become size independent or, on the contrary, makes the consensus nearly impossible. These new behaviors have important consequences when an external noise is added to the system that makes consensus (absorbing) states to disappear. We analyze this new model which shows an interesting phase diagram, with a purely diffusive phase, a herding (or two-states) phase, and mixed phases where both behaviors are possible.

physics.soc-ph↗
arXiv2017

Hidden geometric correlations in real multiplex networks

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the individual layers. We find that these correlations are strong in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate: (i) the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers; (ii) accurate trans-layer link prediction, where connections in one layer can be predicted by observing the hidden geometric space of another layer; and (iii) efficient targeted navigation in the multilayer system using only local knowledge, which outperforms navigation in the single layers only if the geometric correlations are sufficiently strong. Our findings uncover fundamental organizing principles behind real multiplexes and can have important applications in diverse domains.

physics.soc-ph↗
arXiv2016

Competition between global and local online social networks

The overwhelming success of online social networks, the key actors in the Web 2.0 cosmos, has reshaped human interactions globally. To help understand the fundamental mechanisms which determine the fate of online social networks at the system level, we describe the digital world as a complex ecosystem of interacting networks. In this paper, we study the impact of heterogeneity in network fitnesses on the competition between an international network, such as Facebook, and local services. The higher fitness of international networks is induced by their ability to attract users from all over the world, which can then establish social interactions without the limitations of local networks. In other words, inter-country social ties lead to increased fitness of the international network. To study the competition between an international network and local ones, we construct a 1:1000 scale model of the digital world, consisting of the 80 countries with the most Internet users. Under certain conditions, this leads to the extinction of local networks; whereas under different conditions, local networks can persist and even dominate completely. In particular, our model suggests that, with the parameters that best reproduce the empirical overtake of Facebook, this overtake could have not taken place with a significant probability.

physics.soc-ph↗
arXiv2015

How small are building blocks of complex networks

Network motifs are small building blocks of complex networks. Statistically significant motifs often perform network-specific functions. However, the precise nature of the connection between motifs and the global structure and function of networks remains elusive. Here we show that the global structure of some real networks is statistically determined by the probability of connections within motifs of size at most 3, once this probability accounts for node degrees. The connectivity profiles of node triples in these networks capture all their local and global properties. This finding impacts methods relying on motif statistical significance, and enriches our understanding of the elementary forces that shape the structure of complex networks.

physics.soc-ph↗
arXiv2015

Escaping the avalanche collapse in self-similar multiplexes

We deduce and discuss the implications of self-similarity for the stability in terms of robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the stability properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary stability attributes of noninteracting networks. We confirm these results with numerical simulations.

physics.soc-ph↗
arXiv2015

Emergence of Soft Communities from Geometric Preferential Attachment

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed.

physics.soc-ph↗
arXiv2014

Follow the Leader: Herding Behavior in Heterogeneous Populations

Here we study the emergence of spontaneous leadership in large populations. In standard models of opinion dynamics, herding behavior is only obeyed at the local scale due to the interaction of single agents with their neighbors; while at the global scale, such models are governed by purely diffusive processes. Surprisingly, in this paper we show that the combination of a strong separation of time scales within the population and a hierarchical organization of the influences of some agents on the others induces a phase transition between a purely diffusive phase, as in the standard case, and a herding phase where a fraction of the agents self-organize and lead the global opinion of the whole population.

physics.soc-ph↗
arXiv2014

Cosmological networks

Networks often represent systems that do not have a long history of studies in traditional fields of physics, albeit there are some notable exceptions such as energy landscapes and quantum gravity. Here we consider networks that naturally arise in cosmology. Nodes in these networks are stationary observers uniformly distributed in an expanding open FLRW universe with any scale factor, and two observers are connected if one can causally influence the other. We show that these networks are growing Lorentz-invariant graphs with power-law distributions of node degrees. These networks encode maximum information about the observable universe available to a given observer.

gr-qc↗
arXiv2014

Simulating non-Markovian stochastic processes

We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general as it can be implemented very easily in cases, like for delays coupled to the evolution of the system, where other algorithms do not work or need adapted versions, less efficient in computational terms.

cond-mat.dis-nn↗
arXiv2014

The complex architecture of primes and natural numbers

Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.

math.NT↗
arXiv2014

Double percolation phase transition in clustered complex networks

The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most common topological characteristic observed in many real networked systems. In this paper, we report an extensive numerical study on the effects of clustering on the structural properties of complex networks. Strong clustering in heterogeneous networks induces the emergence of a core-periphery organization that has a critical effect on the percolation properties of the networks. We observe a novel double phase transition with an intermediate phase in which only the core of the network is percolated and a final phase in which the periphery percolates regardless of the core. This result implies breaking of the same symmetry at two different values of the control parameter, in stark contrast to the modern theory of continuous phase transitions. Inspired by this core-periphery organization, we introduce a simple model that allows us to analytically prove that such an anomalous phase transition is in fact possible.

physics.soc-ph↗
arXiv2014

Evolution of the digital society reveals balance between viral and mass media influence

Online social networks (OSNs) enable researchers to study the social universe at a previously unattainable scale. The worldwide impact and the necessity to sustain their rapid growth emphasize the importance to unravel the laws governing their evolution. We present a quantitative two-parameter model which reproduces the entire topological evolution of a quasi-isolated OSN with unprecedented precision from the birth of the network. This allows us to precisely gauge the fundamental macroscopic and microscopic mechanisms involved. Our findings suggest that the coupling between the real pre-existing underlying social structure, a viral spreading mechanism, and mass media influence govern the evolution of OSNs. The empirical validation of our model, on a macroscopic scale, reveals that virality is four to five times stronger than mass media influence and, on a microscopic scale, individuals have a higher subscription probability if invited by weaker social contacts, in agreement with the "strength of weak ties" paradigm.

physics.soc-ph↗