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At least 685 records · Page 38Linked to original sources
arXiv2013

Inducing Effect on the Percolation Transition in Complex Networks

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.

cond-mat.stat-mech↗
arXiv2013

Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain

Assemblies of interacting quantum particles often surprise us with properties that are difficult to predict. One of the simplest quantum many-body systems is the spin 1/2 Heisenberg antiferromagnetic chain, a linear array of interacting magnetic moments. Its exact ground state is a macroscopic singlet entangling all spins in the chain. Its elementary excitations, called spinons, are fractional spin 1/2 quasiparticles; they are created and detected in pairs by neutron scattering. Theoretical predictions show that two-spinon states exhaust only 71% of the spectral weight while higher-order spinon states, yet to be experimentally located, are predicted to participate in the remaining. Here, by accurate absolute normalization of our inelastic neutron scattering data on a compound realizing the model, we account for the full spectral weight to within 99(8)%. Our data thus establish and quantify the existence of higher-order spinon states. The observation that within error bars, the entire weight is confined within the boundaries of the two-spinon continuum, and that the lineshape resembles a rescaled two-spinon one, allow us to develop a simple physical picture for understanding multi-spinon excitations.

cond-mat.str-el↗
arXiv2013

Abrupt transition in the structural formation of interconnected networks

Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated networks. While examples of such "dissimilar" properties are becoming more abundant, for example diffusion, robustness and competition, it is not yet clear where these differences are rooted in. Here we show that the composition of independent networks into an interconnected network of networks undergoes a structurally sharp transition as the interconnections are formed. Depending of the relative importance of inter and intra-layer connections, we find that the entire interdependent system can be tuned between two regimes: in one regime, the various layers are structurally decoupled and they act as independent entities; in the other regime, network layers are indistinguishable and the whole system behave as a single-level network. We analytically show that the transition between the two regimes is discontinuous even for finite size networks. Thus, any real-world interconnected system is potentially at risk of abrupt changes in its structure that may reflect in new dynamical properties.

physics.soc-ph↗
arXiv2017

Multiscale unfolding of real networks by geometric renormalization

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group for complex networks and use the technique to investigate networks as viewed at different scales. We find that real networks embedded in a hidden metric space show geometric scaling, in agreement with the renormalizability of the underlying geometric model. This allows us to unfold real scale-free networks in a self-similar multilayer shell which unveils the coexisting scales and their interplay. The multiscale unfolding offers a basis for a new approach to explore critical phenomena and universality in complex networks, and affords us immediate practical applications, like high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space which boosts the success of single-layer versions.

cond-mat.dis-nn↗
arXiv2013

Towards designing robust coupled networks

Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failure. Mitigating the risk by partial disconnection endangers their functionality. Here we propose a systematic strategy of selecting a minimum number of autonomous nodes that guarantee a smooth transition in robustness. Our method which is based on betweenness is tested on various examples including the famous 2003 electrical blackout of Italy. We show that, with this strategy, the necessary number of autonomous nodes can be reduced by a factor of five compared to a random choice. We also find that the transition to abrupt collapse follows tricritical scaling characterized by a set of exponents which is independent on the protection strategy.

cond-mat.stat-mech↗
arXiv2013

Exploring the limits of community detection strategies in complex networks

The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem in the field. We performed here a highly detailed evaluation of community detection algorithms, which has two main novelties: 1) using complex closed benchmarks, which provide precise ways to assess whether the solutions generated by the algorithms are optimal; and, 2) A novel type of analysis, based on hierarchically clustering the solutions suggested by multiple community detection algorithms, which allows to easily visualize how different are those solutions. Surprise, a global parameter that evaluates the quality of a partition, confirms the power of these analyses. We show that none of the community detection algorithms tested provide consistently optimal results in all networks and that Surprise maximization, obtained by combining multiple algorithms, obtains quasi-optimal performances in these difficult benchmarks.

physics.soc-ph↗
arXiv2013

The Anatomy of a Scientific Rumor

The announcement of the discovery of a Higgs boson-like particle at CERN will be remembered as one of the milestones of the scientific endeavor of the 21st century. In this paper we present a study of information spreading processes on Twitter before, during and after the announcement of the discovery of a new particle with the features of the elusive Higgs boson on 4th July 2012. We report evidence for non-trivial spatio-temporal patterns in user activities at individual and global level, such as tweeting, re-tweeting and replying to existing tweets. We provide a possible explanation for the observed time-varying dynamics of user activities during the spreading of this scientific "rumor". We model the information spreading in the corresponding network of individuals who posted a tweet related to the Higgs boson discovery. Finally, we show that we are able to reproduce the global behavior of about 500,000 individuals with remarkable accuracy.

physics.soc-ph↗
arXiv2013

Quantifying the effect of temporal resolution on time-varying networks

Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of static networks, each aggregating all edges and nodes present in a time interval of size Δt. In this work we quantify the impact of an arbitrary Δt on the description of a dynamical process taking place upon a time-varying network. We focus on the elementary random walk, and put forth a simple mathematical framework that well describes the behavior observed on real datasets. The analytical description of the bias introduced by time integrating techniques represents a step forward in the correct characterization of dynamical processes on time-varying graphs.

cond-mat.stat-mech↗
arXiv2013

Cellular network entropy as the energy potential in Waddington's differentiation landscape

Differentiation is a key cellular process in normal tissue development that is significantly altered in cancer. Although molecular signatures characterising pluripotency and multipotency exist, there is, as yet, no single quantitative mark of a cellular sample's position in the global differentiation hierarchy. Here we adopt a systems view and consider the sample's network entropy, a measure of signaling pathway promiscuity, computable from a sample's genome-wide expression profile. We demonstrate that network entropy provides a quantitative, in-silico, readout of the average undifferentiated state of the profiled cells, recapitulating the known hierarchy of pluripotent, multipotent and differentiated cell types. Network entropy further exhibits dynamic changes in time course differentiation data, and in line with a sample's differentiation stage. In disease, network entropy predicts a higher level of cellular plasticity in cancer stem cell populations compared to ordinary cancer cells. Importantly, network entropy also allows identification of key differentiation pathways. Our results are consistent with the view that pluripotency is a statistical property defined at the cellular population level, correlating with intra-sample heterogeneity, and driven by the degree of signaling promiscuity in cells. In summary, network entropy provides a quantitative measure of a cell's undifferentiated state, defining its elevation in Waddington's landscape.

q-bio.MN↗
arXiv2013

Single-Neuron Criticality Optimizes Analog Dendritic Computation

Neurons are thought of as the building blocks of excitable brain tissue. However, at the single neuron level, the neuronal membrane, the dendritic arbor and the axonal projections can also be considered an extended active medium. Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions, despite several proposals, remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. By using a probabilistic cellular automaton approach, we model the input-output response of large active dendritic arbors subjected to complex spatio-temporal inputs and exhibiting non-stereotyped dendritic spikes. We find that, if dendritic spikes have a non-deterministic duration, the dendritic arbor can undergo a continuous phase transition from a quiescent to an active state, thereby exhibiting spontaneous and self-sustained localized activity as suggested by experiments. Analogously to the critical brain hypothesis, which states that neuronal networks self-organize near a phase transition to take advantage of specific properties of the critical state, here we propose that neurons with large dendritic arbors optimize their capacity to distinguish incoming stimuli at the critical state. We suggest that "computation at the edge of a phase transition" is more compatible with the view that dendritic arbors perform an analog rather than a digital dendritic computation.

q-bio.NC↗
arXiv2013

Breathing synchronization in interconnected networks

Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillators with a time delay between networks and analyze the dynamics as a function of the couplings and communication lag. We discover a new breathing synchronization regime, where two groups appear in each network synchronized at different frequencies. Each group has a counterpart in the opposite network, one group is in phase and the other in anti-phase with their counterpart. For strong couplings, instead, networks are internally synchronized but a phase shift between them might occur. The implications of our findings on several socio-technical and biological systems are discussed.

nlin.AO↗
arXiv2013

Nonequilibrium Kinetic Study of Sintering of Dispersed Nanoparticles

Kinetic Monte Carlo approach is developed to study aspects of sintering of dispersed nanoparticles of bimodal size distributions. We explore mechanisms of neck development when sintering is initiated at elevated temperatures for nanosize crystalline surfaces of particles of different sizes. Specifically, the role of smaller particles fitting between larger particles, on the sintering of the latter is considered. Formation of stable necks bridging particles at the nanoscale was found to be governed by layering or clustering mechanisms at the facing surfaces, with clustering leading to a much faster formation of the bridging structure. Temperature, particle sizes and local arrangement, as well as other geometrical factors were found to have a profound effect on sintering mediated by a smaller particle placed in a void between larger particles.

cond-mat.mtrl-sci↗
arXiv2013

Stability of jammed packings II: the transverse length scale

As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions provided it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. We find that the stability of such modes be understood in terms of a competition between plane waves and the anomalous vibrational modes associated with the jamming transition; infinitesimal boundary perturbations become irrelevant for systems that are larger than a length scale that characterizes the transverse excitations. This previously identified length diverges at the jamming transition.

cond-mat.soft↗
arXiv2013

Phase diagram of hard board like colloids from computer simulations

The rich mesophase polymorhism and the phase sequence of board-like colloids depends critically on their shape anisometry. Implementing extensive Monte Carlo simulations, we calculated the full phase diagram of sterically interacting board-like particles, for a range of experimentally accessible molecular dimensions/anisometries of colloids of this shape. A variety of self organized mesophases including uniaxial and biaxial nematics, smectic, cubatic and columnar phases have been identified. Our results demonstrate clearly that the molecular anisometry influences critically not only the structure and the symmetry of the mesophases but also, and perhaps more interestingly, the phase sequence among them. New classes of phase sequences such as nematic-nematic and, for the first time, a direct transition from a discotic and a biaxial nematic to an orthogonal smectic A phase have been identified. The molecular geometry requirements for such a phase behavior have been located.

cond-mat.soft↗
arXiv2010

Phase behaviour of polydisperse spheres: simulation strategies and an application to the freezing transition

The statistical mechanics of phase transitions in dense systems of polydisperse particles presents distinctive challenges to computer simulation and analytical theory alike. The core difficulty, namely dealing correctly with particle size fractionation between coexisting phases, is set out in the context of a critique of previous simulation work on such systems. Specialized Monte Carlo simulation techniques and moment free energy method calculations, capable of treating fractionation exactly, are then described and deployed to study the fluid-solid transition of an assembly of repulsive spherical particles described by a top-hat "parent" distribution of particle sizes. The cloud curve delineating the solid-fluid coexistence region is mapped as a function of the degree of polydispersity $δ$, and the properties of the incipient "shadow" phases are presented. The coexistence region is found to shift to higher densities as $δ$ increases, but does not exhibit the sharp narrowing predicted by many theories and some simulations.

cond-mat.soft↗
arXiv2011

Ordering of anisotropic polarizable polymer chains on the full many-body level

We study the effect of dielectric anisotropy of polymers on their equilibrium ordering within mean-field theory but with a formalism that takes into account the full n-body nature of van der Waals forces. Dielectric anisotropy within polymers is to be expected as the electronic properties of the polymer will typically be different along the polymer than across its cross section. It is therefore physically intuitive that larger charge fluctuations can be induced along the chain than perpendicular to it. We show that this dielectric anisotropy leads to n-body interactions which can induce an isotropic--nematic transition. The two body and three body components of the full van der Waals interaction are extracted and it is shown how the two body term behaves like the phenomenological self-aligning-pairwise nematic interaction. At the three body interaction level we see that the nematic phase that is energetically favorable is discotic, however on the full n-body interaction level we find that the normal axial nematic phase is always the stable ordered phase. The n-body nature of our approach also shows that the key parameter driving the nematic-isotropic transition is the bare persistence length of the polymer chain.

cond-mat.soft↗
arXiv2012

A macroscopic model that connects the molar excess entropy of a deeply supercooled liquid near its glass transition temperature to its viscosity

For a deeply supercooled liquid near its glass transition temperature, we suggest a possible way to connect the temperature dependence of its molar excess entropy to that of its viscosity by constructing a macroscopic model, where the deeply supercooled liquid is assumed to be a mixture of solid-like and liquid-like micro regions. In this model, we assume that the mole fraction x of the liquid-like micro regions tends to zero as the temperature T of the liquid is decreased and extrapolated to a temperature Tg*, which we assume to be below but close to the lowest glass transition temperature Tg attainable with the slowest possible cooling rate for the liquid. Without referring to any specific microscopic nature of the solid-like and liquid-like micro regions, we also assume that near Tg, the molar enthalpy of the solid-like micro regions is lower than that of the liquid-like micro regions. We then show that the temperature dependence of x is directly related to that of the molar excess entropy. Close to Tg, we assume that an activated motion of the solid-like micro regions controls the viscosity and that this activated motion is a collective motion involving practically all of the solid-like micro-regions so that the molar activation free energy for the activated motion is proportional to the mole fraction, 1-x, of the solid-like micro regions. The temperature dependence of the viscosity is thus connected to that of the molar excess entropy through the temperature dependence of the mole fraction x. As an example, we apply our model to a class of glass formers for which the molar excess entropy at temperatures near Tg is proportional to 1-T/TK with TK < Tg \sim Tg* and find their viscosities to be well approximated by the Vogel-Fulcher-Tamman equation for temperatures very close to Tg. We estimate the values of three parameters in our model for three glass formers in this class.

cond-mat.stat-mech↗