Janos Kertesz

Budapest University of Technology and Economics, Institute of Physics, Faculty Member

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Fluctuation scaling in complex systems

Page 1. Fluctuation scaling in complex systems Zoltán Eisler1,2, János Kertész2 1Capital Fund Man... more

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Tunneling and Universality in the Integer Quantum Hall Effect

Abstract: We show analytically and numerically that omission of quantum interference from the Cha... more Abstract: We show analytically and numerically that omission of quantum interference from the Chalker-Coddington model of the integer quantum Hall effect gives a localization length exponent nu= 4/3 as in ordinary two-dimensional percolation. Thus, contrary to semi-classical scaling arguments, tunneling alone does not lead to nu= 7/3.

Noise and Stochastics in Complex Systems and Finance (Proceedings Volume)

We study the statistical properties of community dynamics in large social networks, where the evo... more We study the statistical properties of community dynamics in large social networks, where the evolving communities are obtained from subsequent snapshots of the modular structure. Such cohesive groups of people can grow by recruiting new members, or contract by loosing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear.

Value production in a collaborative environment

Abstract: We review some recent endeavors and add some new results to characterize and understand... more Abstract: We review some recent endeavors and add some new results to characterize and understand underlying mechanisms in Wikipedia (WP), the paradigmatic example of collaborative value production. We analyzed the statistics of editorial activity in different languages and observe typical circadian and weekly patterns, which enabled us to estimate the geographical origins of contributions to WPs in languages spoken in several time zones.

Modelling power-law distributed interevent times

Abstract: Many human-related activities show power-law decaying interevent time distribution with... more Abstract: Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model which can reproduce this property and we show exact results for the asymptotic behaviour of the model. The model satisfies a scaling law between the exponents of interevent time distribution (\ beta) and autocorrelation function (\ alpha):\ alpha+\ beta= 2.

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Computer simulation of three dimensional shearing of granular materials: Formation of shear bands

ABSTRACT: We used computer simulations to study spontaneous strain localization in granular mater... more ABSTRACT: We used computer simulations to study spontaneous strain localization in granular materials, as a result of symmetry breaking non-homogeneous deformations. Axisymmetric tnaxial shear tests were simulated by means of standard three-dimensional Distinct Element Method (DEM) with spherical grains. Carefully prepared dense specimens were compressed between two platens and, in order to mimic the experimental conditions, stress controlled (initially) axisymmetric boundary conditions were constructed.

Non-trivial scaling of fluctuations in the trading activity of NYSE

Complex systems comprise a large number of interacting elements, whose dynamics is not always a p... more Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases—in order to uncover their key features—we have to turn to empirical methods, one of which was recently introduced by Menezes and Barabási. It is based on the observation that for the activity fi (t) of the constituents there is a power law relationship between the standard deviation and the mean value: σ i∝< fi> α.

Dynamic asset trees and Black Monday

Abstract: The minimum spanning tree, based on the concept of ultrametricity, is constructed from ... more Abstract: The minimum spanning tree, based on the concept of ultrametricity, is constructed from the correlation matrix of stock returns. The dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer, as measured from an appropriately chosen centre called thecentral node'. We show how the tree length shrinks during a stock market crisis, Black Monday in this case, and how a strong reconfiguration takes place, resulting in topological shrinking of the tree.

Phase change in an opinion-dynamics model with separation of time scales

How are opinions formed? In sociology this is one of the basic questions, but it is also highly r... more How are opinions formed? In sociology this is one of the basic questions, but it is also highly relevant for politics, innovation spreading, decision making, and the general good feeling of people [1–3]. This complex process depends on various factors or components such as confidence, attitudes, communities, or media effects [4]. Recently much effort has been invested in modeling different aspects of opinion dynamics, and these models are in many ways related to those of physics [5, 6].

Modeling the Epps effect of cross correlations in asset prices

Abstract: We review the decomposition method of stock return cross-correlations, presented previo... more Abstract: We review the decomposition method of stock return cross-correlations, presented previously for studying the dependence of the correlation coefficient on the resolution of data (Epps effect). Through a toy model of random walk/Brownian motion and memoryless renewal process (ie Poisson point process) of observation times we show that in case of analytical treatability, by decomposing the correlations we get the exact result for the frequency dependence.

Unjamming due to local perturbations in granular packings with and without gravity

Many systems including granular materials, foams, and emulsions can flow like fluids when a high ... more Many systems including granular materials, foams, and emulsions can flow like fluids when a high external stress is applied but jam into a solidlike state below a certain threshold of stress. In a jammed state 1–4 the many-body system is trapped in a metastable configuration far from equilibrium where the constituent particles block each other's motion.

Multiscale analysis of spreading in a large communication network

Abstract In temporal networks, both the topology of the underlying network and the timings of int... more Abstract In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how a dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and a susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network.

Extent of force indeterminacy in packings of frictional rigid disks

Static packings of frictional rigid particles are investigated by means of discrete element simul... more Static packings of frictional rigid particles are investigated by means of discrete element simulations. We explore the ensemble of allowed force realizations in the space of contact forces for a given packing structure. We estimate the extent of force indeterminacy with different methods. The indeterminacy exhibits a nonmonotonic dependence on the interparticle friction coefficient. We verify directly that larger force indeterminacy is accompanied by a more robust behavior against local perturbations.

Order flow dynamics around extreme price changes on an emerging stock market

Abstract. We study the dynamics of order flows around large intraday price changes using ultra-hi... more Abstract. We study the dynamics of order flows around large intraday price changes using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a significant reversal of price for both intraday price decreases and increases with a permanent price impact. The volatility, the volume of different types of orders, the bid–ask spread and the volume imbalance increase before the extreme events and decay slowly as a power law, which forms a well-established peak.

Spectrum, intensity and coherence in weighted networks of a financial market

We construct a correlation matrix based financial network for a set of New York Stock Exchange (N... more We construct a correlation matrix based financial network for a set of New York Stock Exchange (NYSE) traded stocks with stocks corresponding to nodes and the links between them added one after the other, according to the strength of the correlation between the nodes. The eigenvalue spectrum of the correlation matrix reflects the structure of the market, which also shows in the cluster structure of the emergent network.

Self-organized criticality in the Kardar-Parisi-Zhang equation

Abstract Kardar-Parisi-Zhang interface depinning with quenched noise is studied in an ensemble th... more Abstract Kardar-Parisi-Zhang interface depinning with quenched noise is studied in an ensemble that leads to self-organized criticality in the quenched Edwards-Wilkinson (QEW) universality class and related sandpile models. An interface is pinned at the boundaries, and a slowly increasing external drive is added to compensate for the pinning. The ensuing interface behavior describes the integrated toppling activity history of a QKPZ cellular automaton.

Communities and beyond: mesoscopic analysis of a large social network with complementary methods

Large complex networks have different levels of organization. On the microscopic level networks a... more Large complex networks have different levels of organization. On the microscopic level networks are composed of pairwise interactions, but it is the macroscopic level that has received most attention in recent years. We now know that diverse networks exhibit similarities, for example, in degree distribution, average path length, and clustering coefficient.

The dynamics of traded value revisited

We conclude from an analysis of high resolution NYSE data that the distribution of the traded val... more We conclude from an analysis of high resolution NYSE data that the distribution of the traded value fi (or volume) has a finite variance σi for the very large majority of stocks i, and the distribution itself is non-universal across stocks. The Hurst exponent of the same time series displays a crossover from weakly to strongly correlated behavior around the time scale of 1 day. The persistence in the strongly correlated regime increases with the average trading activity〈 fi〉 as Hi= H0+ γlog〈 fi〉, which is another sign of non-universal behavior.

Phase diagram of optimal paths

We show that by choosing appropriate distributions of the randomness the search for optimal paths... more We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O N1 df= d steps, where df is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the directed polymer universality class.

Spectral methods and cluster structure in correlation-based networks

We investigate how in complex systems the eigenpairs of the matrices derived from the correlation... more We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and focus specifically on the spectral properties of weight Wij=| C| ij− δij and diffusion matrices Dij= Wij/sj− δij, where Cij is the correlation matrix and si=∑ jWij the strength of node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix are ranked in descending order.

Janos Kertesz

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