Covariance matrix filtering with bootstrapped hierarchies.

Cleaning covariance matrices is a highly non-trivial problem, yet of central importance in the statistical inference of dependence between objects. We propose here a probabilistic hierarchical clustering method, named Bootstrapped Average Hierarchical Clustering (BAHC), that is particularly effective in the high-dimensional case, i.e.

Statistically validated network of portfolio overlaps and systemic risk.

Common asset holding by financial institutions (portfolio overlap) is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and severe losses at the systemic level. We propose a method to assess the statistical significance of the overlap between heterogeneously diversified portfolios, which we use to build a validated network of financial institutions where links indicate potential contagion channels. The method is implemented on a historical database of institutional holdings ranging from 1999 to the end of 2013, but can be applied to any bipartite network.

Emergence of heterogeneity in a noncompetitive resource allocation problem.

Tuning one's shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite number of possible tap positions, identical agents are unlikely to reach even approximately their favorite water temperature.

Bug propagation and debugging in asymmetric software structures.

We address the issue of how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Because of the functional form of the incoming link distribution of software dependence network, software is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failure only affects its nearest neighbors, while it is hard if it propagates further.

Criticality and market efficiency in a simple realistic model of the 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. Stylized facts arise only close to a line of critical points with nontrivial properties, marking the transition to an unpredictable market.

Optimal combinations of imperfect objects.

We consider how to make best use of imperfect objects, such as defective analog and digital components. We show that perfect, or near-perfect, devices can be constructed by taking combinations of such defects. Any remaining objects can be recycled efficiently.