52 research outputs found
Quantum Navigation and Ranking in Complex Networks
Complex networks are formal frameworks capturing the interdependencies
between the elements of large systems and databases. This formalism allows to
use network navigation methods to rank the importance that each constituent has
on the global organization of the system. A key example is Pagerank navigation
which is at the core of the most used search engine of the World Wide Web.
Inspired in this classical algorithm, we define a quantum navigation method
providing a unique ranking of the elements of a network. We analyze the
convergence of quantum navigation to the stationary rank of networks and show
that quantumness decreases the number of navigation steps before convergence.
In addition, we show that quantum navigation allows to solve degeneracies found
in classical ranks. By implementing the quantum algorithm in real networks, we
confirm these improvements and show that quantum coherence unveils new
hierarchical features about the global organization of complex systems.Comment: title changed, more real networks analyzed, version published in
scientific report
Evolutionary dynamics of group interactions on structured populations: a review
Interactions among living organisms, from bacteria colonies to human
societies, are inherently more complex than interactions among particles
and non-living matter. Group interactions are a particularly important and
widespread class, representative of which is the public goods game. In
addition, methods of statistical physics have proved valuable for studying
pattern formation, equilibrium selection and self-organization in evolution-
ary games. Here, we review recent advances in the study of evolutionary
dynamics of group interactions on top of structured populations, including
lattices, complex networks and coevolutionary models. We also compare
these results with those obtained on well-mixed populations. The review
particularly highlights that the study of the dynamics of group interactions,
like several other important equilibrium and non-equilibrium dynamical
processes in biological, economical and social sciences, benefits from the
synergy between statistical physics, network science and evolutionary
game theory
On a Class of Spatial Discretizations of Equations of the Nonlinear Schrodinger Type
We demonstrate the systematic derivation of a class of discretizations of
nonlinear Schr{\"o}dinger (NLS) equations for general polynomial nonlinearity
whose stationary solutions can be found from a reduced two-point algebraic
condition. We then focus on the cubic problem and illustrate how our class of
models compares with the well-known discretizations such as the standard
discrete NLS equation, or the integrable variant thereof. We also discuss the
conservation laws of the derived generalizations of the cubic case, such as the
lattice momentum or mass and the connection with their corresponding continuum
siblings.Comment: Submitted for publication in a journal on October 14, 200
Collective behavior of "electronic fireflies"
A simple system composed of electronic oscillators capable of emitting and
detecting light-pulses is studied. The oscillators are biologically inspired,
their behavior is designed for keeping a desired light intensity, W, in the
system. From another perspective, the system behaves like modified integrate
and fire type neurons that are pulse-coupled with inhibitory type interactions:
the firing of one oscillator delays the firing of all the others. Experimental
and computational studies reveal that although no driving force favoring
synchronization is considered, for a given interval of W phase-locking appears.
This weak synchronization is sometimes accompanied by complex dynamical
patterns in the flashing sequence of the oscillators.Comment: 4 pages, 4 figures include
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems
A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems. \ud
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Modeling Abnormal Priming in Alzheimer's Patients with a Free Association Network
Alzheimer's Disease irremediably alters the proficiency of word search and retrieval processes even at its early stages. Such disruption can sometimes be paradoxical in specific language tasks, for example semantic priming. Here we focus in the striking side-effect of hyperpriming in Alzheimer's Disease patients, which has been well-established in the literature for a long time. Previous studies have evidenced that modern network theory can become a powerful complementary tool to gain insight in cognitive phenomena. Here, we first show that network modeling is an appropriate approach to account for semantic priming in normal subjects. Then we turn to priming in degraded cognition: hyperpriming can be readily understood in the scope of a progressive degradation of the semantic network structure. We compare our simulation results with previous empirical observations in diseased patients finding a qualitative agreement. The network approach presented here can be used to accommodate current theories about impaired cognition, and towards a better understanding of lexical organization in healthy and diseased patients
The Kuramoto model in complex networks
181 pages, 48 figures. In Press, Accepted Manuscript, Physics Reports 2015 Acknowledgments We are indebted with B. Sonnenschein, E. R. dos Santos, P. Schultz, C. Grabow, M. Ha and C. Choi for insightful and helpful discussions. T.P. acknowledges FAPESP (No. 2012/22160-7 and No. 2015/02486-3) and IRTG 1740. P.J. thanks founding from the China Scholarship Council (CSC). F.A.R. acknowledges CNPq (Grant No. 305940/2010-4) and FAPESP (Grants No. 2011/50761-2 and No. 2013/26416-9) for financial support. J.K. would like to acknowledge IRTG 1740 (DFG and FAPESP).Peer reviewedPreprin
Statistical physics of vaccination
Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination–one of the most important preventive measures of modern times–is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research
Synchrony-optimized networks of non-identical Kuramoto oscillators
In this Letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling network to its synchronizability. These relations were previously only established from a linear stability analysis of the identical oscillator case. We further demonstrate that the heterogeneity in the oscillator population produces heterogeneity in the optimal coupling network as well. Two rules for enhancing the synchronizability of a given network by a suitable placement of oscillators are given: (i) native frequencies of adjacent oscillators must be anti-correlated and (ii) frequency magnitudes should positively correlate with the degree of the node they are placed at
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