arXiv subjects

Matteo Marsili

Publications and source records attributed to Matteo Marsili.

At least 109 records · Page 6Linked to original sources

arXiv2005

On the rise and fall of networked societies

We review recent results on the dynamics of social networks which suggest that the interplay between the network formation process and volatility may lead to the occurrence of discontinuous phase transitions and phase coexistence in a large class of models. We then investigate the effects of negative links -- links inhibiting local growth of the network -- and of a geographical distribution of the agents in such models. We show, by extensive numerical simulations, that both effects enhance this phenomenology, i.e. it increases the size of the coexistence region.

physics.soc-ph↗

arXiv2005

Emergence and resilience of social networks: a general theoretical framework

We introduce and study a general model of social network formation and evolution based on the concept of preferential link formation between similar nodes and increased similarity between connected nodes. The model is studied numerically and analytically for three definitions of similarity. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence. We suggest that the positive feedback between linking and similarity which is responsible for the model's behaviour is also an important mechanism in real social networks.

physics.soc-ph↗

arXiv2005

A statistical mechanics model for the emergence of consensus

The statistical properties of pairwise majority voting over S alternatives is analyzed in an infinite random population. We first compute the probability that the majority is transitive (i.e. that if it prefers A to B to C, then it prefers A to C) and then study the case of an interacting population. This is described by a constrained multi-component random field Ising model whose ferromagnetic phase describes the emergence of a strong transitive majority. We derive the phase diagram, which is characterized by a tri-critical point and show that, contrary to intuition, it may be more likely for an interacting population to reach consensus on a number S of alternatives when S increases. This effect is due to the constraint imposed by transitivity on voting behavior. Indeed if agents are allowed to express non transitive votes, the agents' interaction may decrease considerably the probability of a transitive majority.

cond-mat.stat-mech↗

arXiv2005

On the interplay between fluctuations and efficiency in a model economy with heterogeneous adaptive consumers

We discuss the stationary states of a model economy in which $N$ heterogeneous adaptive consumers purchase commodity bundles repeatedly from $P$ sellers. The system undergoes a transition from an inefficient to an efficient state as the number of consumers increases. In the latter phase, however, price fluctuations may be much larger than in the inefficient regime. Results from dynamical mean-field theory obtained for $N\to\infty$ compare fairly well with computer simulations.

cond-mat.dis-nn↗

arXiv2005

Loops of any size and Hamilton cycles in random scale-free networks

Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free networks valid at fixed number of nodes N and for any length L of the loops. We bring evidence that the most frequent loop size in a scale-free network of N nodes is of the order of N like in random regular graphs while small loops are more frequent when the second moment of the degree distribution diverges. In particular, we find that finite loops of sizes larger than a critical one almost surely pass from any node, thus casting some doubts on the validity of the random tree approximation for the solution of lattice models on these graphs. Moreover we show that Hamiltonian cycles are rare in random scale-free networks and may fail to appear if the power-law exponent of the degree distribution is close to 2 even for minimal connectivity grater than 3.

cond-mat.dis-nn↗

arXiv2004

Minority games with finite score memory

We analyze grand-canonical minority games with infinite and finite score memory and different updating timescales (from `on-line' games to `batch' games) in detail with various complementary methods, both analytical and numerical. We focus on the emergence of `stylized facts' and on the production of exploitable information, as well as on the dynamic behaviour of the models. We find that with finite score memory no agent can be frozen, and that all the current analytical methods fail to provide satisfactory explanation of the observed behaviours.

cond-mat.dis-nn↗

arXiv2004

Stylized facts in minority games with memory: a new challenge

A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in grand-canonical models for very large times. Current analytical methods are inadequate to solve this simple and natural extension.

cond-mat.stat-mech↗

arXiv2003

Self-organized critical network dynamics

We propose a simple model that aims at describing, in a stylized manner, how local breakdowns due unbalances or congestion propagate in real dynamical networks. The model converges to a self-organized critical stationary state in which the network shapes itself as a consequence of avalanches of rewiring processes. Depending on the model's specification, we obtain either single scale or scale-free networks. We characterize in detail the relation between the statistical properties of the network and the nature of the critical state, by computing the critical exponents. The model also displays a non-trivial, sudden, collapse to a complete network.

cond-mat.stat-mech↗

arXiv2003

The Rise and Fall of a Networked Society

We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a feedback loop which results in a first-order phase transition between a very sparse network regime and a highly-connected phase. Phase coexistence and hysteresis take place for intermediate value of parameters. We derive a mean-field theory which correctly reproduces this behavior, including the distribution of degree connectivity and the non-trivial clustering properties.

cond-mat.stat-mech↗

arXiv2003

Shedding light on El Farol

We mathematize El Farol bar problem and transform it into a workable model. In general, the average convergence to optimality at the collective level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies yields a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.

cond-mat.stat-mech↗

arXiv2002

Criticality and finite size effects in a simple realistic model of stock market

We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple argument, we show that, in Minority Games, the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets as critical systems.

cond-mat.stat-mech↗

arXiv2002

Dissecting financial markets: Sectors and states

By analyzing a large data set of daily returns with data clustering technique, we identify economic sectors as clusters of assets with a similar economic dynamics. The sector size distribution follows Zipf's law. Secondly, we find that patterns of daily market-wide economic activity cluster into classes that can be identified with market states. The distribution of frequencies of market states shows scale-free properties and the memory of the market state process extends to long times ($\sim 50$ days). Assets in the same sector behave similarly across states. We characterize market efficiency by analyzing market's predictability and find that indeed the market is close to being efficient. We find evidence of the existence of a dynamic pattern after market's crashes.

cond-mat.stat-mech↗

arXiv2002

Diffusion, peer pressure and tailed distributions

We present a general, physically motivated non-linear and non-local advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an integrable dynamical system, that on varying a parameter, the steady state behaviour undergoes a transition from the standard diffusive behavior to a localized stationary state characterized by a tailed distribution. Finally, we show that recent empirical laws on economic growth can be explained as a collective phenomenon due to peer pressure interaction.

cond-mat.stat-mech↗

arXiv2002

Algorithms of maximum likelihood data clustering with applications

We address the problem of data clustering by introducing an unsupervised, parameter free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information, we construct an expression for the likelihood of any possible cluster structure. The likelihood in turn depends only on the Pearson's coefficient of the data. We discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations. Compared to standard clustering methods, our approach has the advantages that i) it is parameter free, ii) the number of clusters need not be fixed in advance and iii) the interpretation of the results is transparent. In order to test our approach and compare it with standard clustering algorithms, we analyze two very different data sets: Time series of financial market returns and gene expression data. We find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability.

cond-mat.stat-mech↗

arXiv2002

Colored minority games

We study the behavior of simple models for financial markets with widely spread frequency either in the trading activity of agents or in the occurrence of basic events. The generic picture of a phase transition between information efficient and inefficient markets still persists even when agents trade on widely spread time-scales. We derive analytically the dependence of the critical threshold on the distribution of time-scales. We also address the issue of market efficiency as a function of frequency. In an inefficient market we find that the size of arbitrage opportunities is inversely proportional to the frequency of the events on which they occur. Greatest asymmetries in market outcomes are concentrated on the most rare events. The practical limits of the applications of these ideas to real markets are discussed in a specific example.

cond-mat.stat-mech↗

arXiv2001

Statistical mechanics of asset markets with private information

Traders in a market typically have widely different, private information on the return of an asset. The equilibrium price of the asset may reflect this information more accurately if the number of traders is large enough compared to the number of the states of the world that determine the return of the asset. We study the transition from markets where prices do not reflect the information accurately into markets where it does. In competitive markets, this transition takes place suddenly, at a critical value of the ratio between number of states and number of traders. The Nash equilibrium market behaves quite differently from a competitive market even in the limit of large economies.

cond-mat.stat-mech↗

arXiv2001

Stylized facts of financial markets and market crashes in Minority Games

We present and study a Minority Game based model of a financial market where adaptive agents -- the speculators -- interact with deterministic agents -- called producers. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of active speculators grows with the amount of information that producers inject into the market. Transitions between equilibrium and out of equilibrium behavior are observed when the relative number of speculators to the complexity of information or to the number of producers are changed. When the system is out of equilibrium, stylized facts arise, such as fat tailed distribution of returns and volatility clustering. Without speculators, the price follows a random walk; this implies that stylized facts arise because of the presence of speculators. Furthermore, if speculators abandon price taking behavior, stylized facts disappear.

cond-mat.stat-mech↗

arXiv2001

Data clustering and noise undressing for correlation matrices

We discuss a new approach to data clustering. We find that maximum likelihood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation structure of the data. For random, uncorrelated data sets no correlation structure emerges. On the other hand for data sets with a built-in cluster structure, the method is able to detect and recover efficiently that structure. Finally we apply the method to financial time series, where the low temperature behavior reveals a non trivial clustering.

cond-mat.stat-mech↗