arXiv subjects

S. Havlin

Publications and source records attributed to S. Havlin.

At least 37 records · Page 2Linked to original sources

arXiv2005

Localization transition on complex networks via spectral statistics

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.

cond-mat.mes-hall↗

arXiv2004

Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a certain magnitude M$ in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time $τ_0$. As a consequence, the conditional mean recurrence time $\hat τ(τ_0)$ between two events increases monotonically with $τ_0$. For $τ_0$ well below the average recurrence time $\ovτ, \hatτ(τ_0)$ is smaller than $\ovτ$, while for $τ_0>\ovτ$, $\hatτ(τ_0)$ is greater than $\ovτ$. Also the mean residual time until the next earthquake does not depend only on the elapsed time, but also strongly on $τ_0$. The larger $τ_0$ is, the larger is the mean residual time. The above features should be taken into account in any earthquake prognosis.

physics.geo-ph↗

arXiv2004

Levels of Complexity in Scale-Invariant Neural Signals

Many physical and physiological signals exhibit complex scale-invariant features characterized by $1/f$ scaling and long-range power-law correlations, suggesting a possibly common control mechanism. Specifically, it has been suggested that dynamical processes influenced by inputs and feedback on multiple time scales may be sufficient to give rise to $1/f$ scaling and scale invariance. Two examples of physiologic signals that are the output of hierarchical, multi-scale physiologic systems under neural control are the human heartbeat and human gait. Here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable $1/f$ scaling, they still may belong to different complexity classes. Our analysis of the magnitude series correlations and multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast with the nonlinear multifractal behavior found in healthy heartbeat dynamics, gait time series exhibit less complex, close to monofractal behavior and a low degree of nonlinearity. These findings are of interest because they underscore the limitations of traditional two-point correlation methods in fully characterizing physiologic and physical dynamics. In addition, these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar $1/f$ scaling.

cond-mat.stat-mech↗

arXiv2004

Optimization of Network Robustness to Waves of Targeted and Random Attack

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions $p_t$ and $p_r$ respectively of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction $r$ of the nodes having degree $k_2= (\kav - 1 +r)/r$ and the remainder of the nodes having degree $k_1=1$, where $\kav$ is the average degree of all the nodes. We find that the optimal value of $r$ is of the order of $p_t/p_r$ for $p_t/p_r\ll 1$.

cond-mat.stat-mech↗

arXiv2004

Optimization of Robustness of Complex Networks

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random failure and intentional attack while keeping the cost of the network (which we take to be the average number of links per node) constant. We find optimal parameters for: (i) scale free networks having degree distributions with a single power-law regime, (ii) networks having degree distributions with two power-law regimes, and (iii) networks described by degree distributions containing two peaks. Of these various kinds of distributions we find that the optimal network design is one in which all but one of the nodes have the same degree, $k_1$ (close to the average number of links per node), and one node is of very large degree, $k_2 \sim N^{2/3}$, where $N$ is the number of nodes in the network.

cond-mat.other↗

arXiv2003

On the Tomography of Networks and Multicast Trees

In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show that the nodes degree distribution at each layer is a power law with an exponential cut-off. We obtain similar results for the layers surrounding the root of multicast trees cut from such networks, as well as the Internet. All of our results were obtained both analytically and on empirical Interenet data.

cond-mat↗

arXiv2002

Volatility in atmospheric temperature variability

Using detrended fluctuation analysis (DFA), we study the scaling properties of the volatility time series $V_i=| T_{i+1}-T_i|$ of daily temperatures $T_i$ for ten chosen sites around the globe. We find that the volatility is long range power-law correlated with an e xponent $γ$ close to 0.8 for all sites considered here. We use this result to test the scaling performance of several state-of-the art global climate models and find that the models do not reproduce the observed scaling behavior.

cond-mat.stat-mech↗

arXiv2002

Percolation in Directed Scale-Free Networks

Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and out-degree distributions. We derive a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents. In the first regime we regain the known directed percolation mean field exponents. In contrast, the second and third regimes are characterized by anomalous exponents, which we calculate analytically. In the third regime the network is resilient to random dilution, i.e., the percolation threshold is p_c->1.

cond-mat.dis-nn↗

arXiv2001

Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries

We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Levy flights and Levy walks, respectively. Using fractional differential equations with a Riesz kernel, we find exact analytical expressions for both quantities in the continuous limit. We show that numerical solutions for the discrete Levy processes converge to the continuous approximations in all cases except the case of alpha approaching 2 and the cases of x0 near absorbing boundaries. For alpha larger than 2 when the second moment of the flight length distribution exists, our result is replaced by known results of classical diffusion. We show that if x0 is placed in the vicinity of absorbing boundaries, the average total length has a minimum at alpha=1, corresponding to the Cauchy distribution. We discuss the relevance of this result to the problem of foraging, which has received recent attention in the statistical physics literature.

cond-mat.soft↗

arXiv2001

Decomposition of Heartbeat Time Series: Scaling Analysis of the Sign Sequence

The cardiac interbeat (RR) increment time series can be decomposed into two sub-sequences: a magnitude series and a sign series. We show that the sign sequence, a simple binary representation of the original RR series, retains fundamental scaling properties of the original series, is robust with respect to outliers, and may provide useful information about neuroautonomic control mechanisms.

cond-mat.stat-mech↗

arXiv2001

Structural Properties of Self-Attracting Walks

Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the Θtransition of polymers. We are interested in the structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo simulations, we find that for u u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.

cond-mat↗

arXiv2000

Scale Specific and Scale Independent Measures of Heart Rate Variability as Risk Indicators

We study the Heart Rate Variability (HRV) using scale specific variance and scaling exponents as measures of healthy and cardiac impaired individuals. Our results show that the variance and the scaling exponent are uncorrelated. We find that the variance measure at certain scales is well suited to separate healthy subjects from heart patients. However, for cumulative survival probability the scaling exponents outperform the variance measure. Our risk study is based on a database containing recordings from 428 individuals after myocardial infarct (MI) and on database containing 105 healthy subjects and 11 heart patients. The results have been obtained by applying three recently developed methods (DFA - Detrended Fluctuation Analysis, WAV - Multiresolution Wavelet Analysis, and DTS - Detrended Time Series analysis) which are shown to be highly correlated.

physics.med-ph↗

arXiv2000

Multifractal behavior of linear polymers in disordered media

The scaling behavior of linear polymers in disordered media modelled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p_c is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior, i.e. different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers μ_q and enhancement exponents γ_q, which depend on q. Our numerical results suggest that the relation μ_1 = p_ c μbetween the first moment μ_1 and its regular lattice counterpart μis valid.

cond-mat↗

arXiv2000

Swelling-collapse transition of self-attracting walks

We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence for a transition analogous to the Θtransition of polymers. Above a critical attractive interaction u_c, the walk collapses and the exponents νand k, characterising the scaling with time t of the mean square end-to-end distance ~ t^{2 ν} and the average number of visited sites ~ t^k, are universal and given by ν=1/(d+1) and k=d/(d+1). Below u_c, the walk swells and the exponents are as with no interaction, i.e. ν=1/2 for all d, k=1/2 for d=1 and k=1 for d >= 2. At u_c, the exponents are found to be in a different universality class.

cond-mat↗

arXiv2000

Multifractal Properties of the Random Resistor Network

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/ν$ to d_B.

cond-mat.stat-mech↗

arXiv1999

Quasicrystals in a Monodisperse System

We investigate the formation of a two-dimensional quasicrystal in a monodisperse system, using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. We find that more than one stable crystalline phase can form for certain values of the square-well parameters. Quenching the liquid phase at a very low temperature, we obtain an amorphous phase. By heating this amorphous phase, we obtain a quasicrystalline structure with five-fold symmetry. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, we conclude that the observed quasicrystal phase can be the stable phase in a specific range of temperatures.

cond-mat.soft↗

arXiv1999

Scaling for the Percolation Backbone

We study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance $r$ in a system of size $L$. We find a scaling form for the average backbone mass: $ \sim L^{d_B}G(r/L)$, where $G$ can be well approximated by a power law for $0\le x\le 1$: $G(x)\sim x^ψ$ with $ψ=0.37\pm 0.02$. This result implies that $ \sim L^{d_B-ψ}r^ψ$ for the entire range $0<r<L$. We also propose a scaling form for the probability distribution $P(M_B)$ of backbone mass for a given $r$. For $r\approx L, P(M_B)$ is peaked around $L^{d_B}$, whereas for $r\ll L, P(M_B)$ decreases as a power law, $M_B^{-τ_B}$, with $τ_B\simeq 1.20\pm 0.03$. The exponents $ψ$ and $τ_B$ satisfy the relation $ψ=d_B(τ_B-1)$, and $ψ$ is the codimension of the backbone, $ψ=d-d_B$.

cond-mat.stat-mech↗

arXiv1998

Discrimination between Healthy and Sick Cardiac Autonomic Nervous System by Detrended Heart Rate Variability Analysis

Multiresolution Wavelet Transform and Detrended Fluctuation Analysis have been recently proven as excellent methods in the analysis of Heart Rate Variability, and in distinguishing between healthy subjects and patients with various dysfunctions of the cardiac nervous system. We argue that it is possible to obtain a distinction between healthy subjects/patients of at least similar quality by, first, detrending the time-series of RR-intervals by subtracting a running average based on a local window with a length of around 32 data points, and then, calculating the standard deviation of the detrended time-series. The results presented here indicate that the analysis can be based on very short time-series of RR-data (7-8 minutes), which is a considerable improvement relative to 24-hours Holter recordings.

chao-dyn↗