arXiv subjects

Matteo Marsili

Publications and source records attributed to Matteo Marsili.

At least 91 records · Page 5Linked to original sources

arXiv2008

Ising model with memory: coarsening and persistence properties

We consider the coarsening properties of a kinetic Ising model with a memory field. The probability of a spin-flip depends on the persistence time of the spin in a state. The more a spin has been in a given state, the less the spin-flip probability is. We numerically studied the growth and persistence properties of such a system on a two dimensional square lattice. The memory introduces energy barriers which freeze the system at zero temperature. At finite temperature we can observe an apparent arrest of coarsening for low temperature and long memory length. However, since the energy barriers introduced by memory are due to local effects, there exists a timescale on which coarsening takes place as for the Ising model. Moreover the two point correlation functions of the Ising model with and without memory are the same, indicating that they belong to the same universality class.

cond-mat.stat-mech↗

arXiv2008

On the role of volatility in the evolution of social networks

We study how the volatility, node- or link-based, affects the evolution of social networks in simple models. The model describes the competition between order -- promoted by the efforts of agents to coordinate -- and disorder induced by volatility in the underlying social network. We find that when volatility affects mostly the decay of links, the model exhibit a sharp transition between an ordered phase with a dense network and a disordered phase with a sparse network. When volatility is mostly node-based, instead, only the symmetric (disordered) phase exists These two regimes are separated by a second order phase transition of unusual type, characterized by an order parameter critical exponent $β=0^+$. We argue that node volatility has the same effect in a broader class of models, and provide numerical evidence in this direction.

physics.soc-ph↗

arXiv2008

Dynamical instabilities in a simple minority game with discounting

We explore the effect of discounting and experimentation in a simple model of interacting adaptive agents. Agents belong to either of two types and each has to decide whether to participate a game or not, the game being profitable when there is an excess of players of the other type. We find the emergence of large fluctuations as a result of the onset of a dynamical instability which may arise discontinuously (increasing the discount factor) or continuously (decreasing the experimentation rate). The phase diagram is characterized in detail and noise amplification close to a bifurcation point is identified as the physical mechanism behind the instability.

physics.soc-ph↗

arXiv2007

Statistical physics of the Schelling model of segregation

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics methods shed light on the rich phenomenology of this simple model, exhibiting static phase transitions typical of kinetic constrained models, nontrivial coarsening like in driven-particle systems and percolation-related phenomena.

physics.soc-ph↗

arXiv2007

Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode

We investigate the emergence of a structure in the correlation matrix of assets' returns as the time-horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. Result crucially depends on whether the data is restricted to the ``internal'' dynamics of the market, where the ``center of mass'' motion (the market mode) is removed or not. If the market mode is not removed, we find that the structure emerges, as the time-horizon increases, from splitting a single large cluster. In NYSE we find that when the market mode is removed, the structure of correlation at the daily scale is already well defined at the 5 minutes time-horizon, and this structure accounts for 80 % of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.

physics.soc-ph↗

arXiv2006

Statistical mechanics of combinatorial auctions

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.

cond-mat.stat-mech↗

arXiv2006

Effect of degree correlations on the loop structure of scale-free networks

In this paper we study the impact of degree correlations in the subgraphs statistics of scale-free networks. In particular we consider loops: a simple case of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the eigenvector of the correlation matrix associated with the maximal eigenvalue and we show that correlations affect in a relevant way the average number of Hamiltonian paths in a 3-core of real world networks. We prove our results in the two point correlated hidden variable ensemble and we check the results with exact counting of small loops in real graphs.

cond-mat.dis-nn↗

arXiv2006

Statistical mechanics of socio-economic systems with heterogeneous agents

We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and traffic modeling. We then focus on the analysis of the optimal properties of large random resource-allocation problems and on Minority Games and related models of speculative trading in financial markets, discussing a number of extensions including multi-asset models, Majority Games and models with asymmetric information. Finally, we summarize the main conclusions and outline the major open problems and limitations of the approach.

physics.soc-ph↗

arXiv2006

Number of cliques in random scale-free network ensembles

In this paper we calculate the average number of cliques in random scale-free networks. We consider first the hidden variable ensemble and subsequently the Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected subgraphs, appear also when the average degree is finite. This is in contrast to what happens in Erdös and Renyi graphs in which diverging average degree is required to observe cliques of size $c>3$. Moreover we show that in random scale-free networks the clique number, i.e. the size of the largest clique present in the network diverges with the system size.

cond-mat.stat-mech↗

arXiv2006

Dynamic instability in a phenomenological model of correlated assets

We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affected by investment based on it. We show that such a feedback on correlations gives rise to an instability when the volume of investment exceeds a critical value. Close to the critical point the model exhibits dynamical correlations very similar to those observed in real markets. Maximum likelihood estimates of the model's parameter for empirical data indeed confirm this conclusion, thus suggesting that real markets operate close to a dynamically unstable point.

physics.soc-ph↗

arXiv2006

Phenomenological Models of Socio-Economic Network Dynamics

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.

physics.soc-ph↗

arXiv2006

Multi-asset minority games

We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given asset depends on the relative amount of information available in that market. More specifically, in the canonical game players play preferentially in the stock with less information. The same holds in the grand canonical game when agents have positive incentives to trade, whereas when agents payoff are solely related to their speculative ability they display a larger propensity to invest in the information-rich asset. Furthermore, in this model one finds a globally predictable phase with broken ergodicity.

physics.soc-ph↗

arXiv2006

Effects of Tobin Taxes in Minority Game markets

We show that the introduction of Tobin taxes in agent-based models of currency markets can lead to a reduction of speculative trading and reduce the magnitude of exchange rate fluctuations at intermediate tax rates. In this regime revenues for the market maker obtained from speculators are maximal. We here focus on Minority Game models of markets, which are accessible by exact techniques from statistical mechanics. Results are supported by computer simulations. Our findings suggest that at finite systems sizes the effect is most pronounced in a critical region around the phase transition of the infinite system, but much weaker if the market is operating far from criticality and does not exhibit anomalous fluctuations.

cond-mat.dis-nn↗

arXiv2006

Phase coexistence in a forecasting game

Individual choices are either based on personal experience or on information provided by peers. The latter case, causes individuals to conform to the majority in their neighborhood. Such herding behavior may be very efficient in aggregating disperse private information, thereby revealing the optimal choice. However if the majority relies on herding, this mechanism may dramatically fail to aggregate correctly the information, causing the majority adopting the wrong choice. We address these issues in a simple model of interacting agents who aim at giving a correct forecast of a public variable, either seeking private information or resorting to herding. As the fraction of herders increases, the model features a phase transition beyond which a state where most agents make the correct forecast coexists with one where most of them are wrong. Simple strategic considerations suggest that indeed such a system of agents self-organizes deep in the coexistence region. There, agents tend to agree much more among themselves than with what they aim at forecasting, as found in recent empirical studies.

physics.soc-ph↗

arXiv2005

Scale-free networks with an exponent less than two

We study scale free simple graphs with an exponent of the degree distribution $γ$ less than two. Generically one expects such extremely skewed networks -- which occur very frequently in systems of virtually or logically connected units -- to have different properties than those of scale free networks with $γ>2$: The number of links grows faster than the number of nodes and they naturally posses the small world property, because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite. We discuss a simple prototype model of such networks, inspired by real world phenomena, which exhibits these properties and allows for a detailed analytical investigation.

cond-mat.stat-mech↗

arXiv2005

Emergence of large cliques in random scale-free network

In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c>3 are present in random Erdos and Renyi graphs only in the limit of diverging average connectivity. Starting from the finding that real scale free graphs have large cliques, we study the clique number in uncorrelated scale-free networks finding both upper and lower bounds. Interesting we find that in scale-free networks large cliques appear also when the average degree is finite, i.e. even for networks with power-law degree distribution exponents gamma in the interval (2,3). Moreover as long as gamma<3 scale-free networks have a maximal clique which diverges with the system size.

cond-mat.dis-nn↗

arXiv2005

Critical threshold and dynamics of a general rumor model on complex networks

We derive mean-field equations that describe the dynamics of a general model of rumor spreading on complex networks, and use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model on random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumor spreading rate below which a rumor cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumor spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumor, however, depends on the interplay between network topology and the rumor spreading rate. Our results show that scale-free networks are prone to the spreading of rumors, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale data dissemination algorithms on the Internet, the so-called gossip protocols.

physics.soc-ph↗

arXiv2005

Typical properties of optimal growth in the Von Neumann expanding model for large random economies

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ increases beyond $P$. The solution is characterized by a universal behavior, independent of the parameters of the disorder statistics. Associating technological innovation to an increase of $N$, we find that while such an increase has a large positive impact on long term growth when $N\ll P$, its effect on technologically advanced economies ($N\gg P$) is very weak.

physics.soc-ph↗