arXiv subjects

Francesca Colaiori

Publications and source records attributed to Francesca Colaiori.

26 records · Page 2Linked to original sources

arXiv2004

Detecting communities in large networks

We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable to the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words and in uncovering mental association patterns.

cond-mat.dis-nn↗

arXiv2004

Average trajectory of returning walks

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For uncorrelated random walks the average shape is semicircular, independently from the single increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations induces non trivial asymmetric shapes, which are studied numerically.

cond-mat.stat-mech↗

arXiv2003

The average shape of a fluctuation: universality in excursions of stochastic processes

We study the average shape of a fluctuation of a time series x(t), that is the average value _T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form _T = T^αf(t/T) is obeyed. The scaling function f(s) is to a large extent independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.

cond-mat.stat-mech↗

arXiv2001

Rayleigh loops in the random-field Ising model on the Bethe lattice

We analyze the demagnetization properties of the random-field Ising model on the Bethe lattice focusing on the beahvior near the disorder induced phase transition. We derive an exact recursion relation for the magnetization and integrate it numerically. Our analysis shows that demagnetization is possible only in the continous high disorder phase, where at low field the loops are described by the Rayleigh law. In the low disorder phase, the saturation loop displays a discontinuity which is reflected by a non vanishing magnetization m_\infty after a series of nested loops. In this case, at low fields the loops are not symmetric and the Rayleigh law does not hold.

cond-mat.stat-mech↗

arXiv2001

Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension

We have studied the Kardar-Parisi-Zhang equation in the strong coupling regime in the mode-coupling approximation. We solved numerically in dimension d=1 for the correlation function at wavevector k. At large times t we found the predicted stretched exponential decay consistent with our previous saddle point analysis in [Phys. Rev. E {\bf 63}, 057103 (2001)], but we also observed that the decay to zero occurred in an unexpected oscillatory way. We have compared the results from mode-coupling for the scaling functions with the recent exact results from Praehofer and Spohn [cond-mat/0101200] for d=1 who also find an oscillatory decay to zero.

cond-mat.stat-mech↗

arXiv2000

Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the correlation function in the long time limit - a limit which is hard to study using simulations. The correlation function at wavevector k in dimension d is found to behave asymptotically at time t as C(k,t)\simeq 1/k^{d+4-2z} (Btk^z)^{γ/z} e^{-(Btk^z)^{1/z}}, with γ=(d-1)/2, A a determined constant and B a scale factor.

cond-mat.stat-mech↗

arXiv2000

Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling approximation for the KPZ equation in the strong coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension d_c=4, and the expansion z=2-(d-4)/4+O((4-d)^2) around d_c. We find the exact z=3/2 value in d=1, and estimate the values 1.62, 1.78 for z, in d=2,3. The result d_c=4 and the expansion around d_c are very robust and can be derived just from a mild assumption on the relative scale on which the response and correlation functions vary as z approaches 2.

cond-mat.stat-mech↗

arXiv1999

Directed Percolation and Generalized Friendly Walkers

We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of m directed random walkers with rather general attractive interactions, when suitably continued to m=0. In 1+1 dimensions, this is dual to a model of interacting steps on a vicinal surface. A similar correspondence with interacting self-avoiding walks is constructed for isotropic percolation.

cond-mat.stat-mech↗