Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data.

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

Interplay between past market correlation structure changes and future volatility outbursts.

We report significant relations between past changes in the market correlation structure and future changes in the market volatility. This relation is made evident by using a measure of "correlation structure persistence" on correlation-based information filtering networks that quantifies the rate of change of the market dependence structure. We also measured changes in the correlation structure by means of a "metacorrelation" that measures a lagged correlation between correlation matrices computed over different time windows. Both methods show a deep interplay between past changes in correlation structure and future changes in volatility and we demonstrate they can anticipate market risk variations and this can be used to better forecast portfolio risk. Notably, these methods overcome the curse of dimensionality that limits the applicability of traditional econometric tools to portfolios made of a large number of assets. We report on forecasting performances and statistical significance of both methods for two different equity datasets. We also identify an optimal region of parameters in terms of True Positive and False Positive trade-off, through a ROC curve analysis. We find that this forecasting method is robust and it outperforms logistic regression predictors based on past volatility only. Moreover the temporal analysis indicates that methods based on correlation structural persistence are able to adapt to abrupt changes in the market, such as financial crises, more rapidly than methods based on past volatility.

Parsimonious modeling with information filtering networks.

We introduce a methodology to construct parsimonious probabilistic models. This method makes use of information filtering networks to produce a robust estimate of the global sparse inverse covariance from a simple sum of local inverse covariances computed on small subparts of the network. Being based on local and low-dimensional inversions, this method is computationally very efficient and statistically robust, even for the estimation of inverse covariance of high-dimensional, noisy, and short time series. Applied to financial data our method results are computationally more efficient than state-of-the-art methodologies such as Glasso producing, in a fraction of the computation time, models that can have equivalent or better performances but with a sparser inference structure. We also discuss performances with sparse factor models where we notice that relative performances decrease with the number of factors. The local nature of this approach allows us to perform computations in parallel and provides a tool for dynamical adaptation by partial updating when the properties of some variables change without the need of recomputing the whole model. This makes this approach particularly suitable to handle big data sets with large numbers of variables. Examples of practical application for forecasting, stress testing, and risk allocation in financial systems are also provided.

Relation between financial market structure and the real economy: comparison between clustering methods.

We quantify the amount of information filtered by different hierarchical clustering methods on correlations between stock returns comparing the clustering structure with the underlying industrial activity classification. We apply, for the first time to financial data, a novel hierarchical clustering approach, the Directed Bubble Hierarchical Tree and we compare it with other methods including the Linkage and k-medoids. By taking the industrial sector classification of stocks as a benchmark partition, we evaluate how the different methods retrieve this classification. The results show that the Directed Bubble Hierarchical Tree can outperform other methods, being able to retrieve more information with fewer clusters. Moreover,we show that the economic information is hidden at different levels of the hierarchical structures depending on the clustering method. The dynamical analysis on a rolling window also reveals that the different methods show different degrees of sensitivity to events affecting financial markets, like crises. These results can be of interest for all the applications of clustering methods to portfolio optimization and risk hedging [corrected].

Dependency structure and scaling properties of financial time series are related.

We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose a dynamical model that reproduces this observation along with an array of other empirical properties. The structure of this model is such that the hierarchical structure of heterogeneous risks plays a crucial role in the time evolution of the correlation matrix, providing an interpretation to the mechanism behind the interplay between cross-correlation and multifractality in financial markets, where the degree of multifractality of stocks is associated to their hierarchical positioning in the cross-correlation structure. Empirical observations reported in this paper present a new perspective towards the merging of univariate multi scaling and multivariate cross-correlation properties of financial time series.

Graph theory enables drug repurposing--how a mathematical model can drive the discovery of hidden mechanisms of action.

We introduce a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational Linguistics and Graph Theory, a methodology is defined to build a graph representation of knowledge, which is automatically analysed to discover hidden relations between any drug and any disease: these relations are specific paths among the biomedical entities of the graph, representing possible Modes of Action for any given pharmacological compound. We propose a measure for the likeliness of these paths based on a stochastic process on the graph. This measure depends on the abundance of indirect paths between a peptide and a disease, rather than solely on the strength of the shortest path connecting them. We provide real-world examples, showing how the method successfully retrieves known pathophysiological Mode of Action and finds new ones by meaningfully selecting and aggregating contributions from known bio-molecular interactions. Applications of this methodology are presented, and prove the efficacy of the method for selecting drugs as treatment options for rare diseases.

Spread of risk across financial markets: better to invest in the peripheries.

Risk is not uniformly spread across financial markets and this fact can be exploited to reduce investment risk contributing to improve global financial stability. We discuss how, by extracting the dependency structure of financial equities, a network approach can be used to build a well-diversified portfolio that effectively reduces investment risk. We find that investments in stocks that occupy peripheral, poorly connected regions in financial filtered networks, namely Minimum Spanning Trees and Planar Maximally Filtered Graphs, are most successful in diversifying, improving the ratio between returns' average and standard deviation, reducing the likelihood of negative returns, while keeping profits in line with the general market average even for small baskets of stocks. On the contrary, investments in subsets of central, highly connected stocks are characterized by greater risk and worse performance. This methodology has the added advantage of visualizing portfolio choices directly over the graphic layout of the network.

Exploring complex networks via topological embedding on surfaces.

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, to characterize, and to simulate networks with a broad range of properties. Any network can be embedded on a surface with sufficiently high genus and therefore the study of topologically embedded graphs is non-restrictive. We show that the local properties of the network are affected by the surface genus which determines the average degree, which influences the degree distribution, and which controls the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwovenness, changing the scaling properties of the network from large-world kind (small genus) to small- and ultrasmall-world kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description for these networks. Within such a framework, we study the properties of topologically embedded graphs which dynamically tend to lower their energy towards a ground state with a given reference degree distribution. We show that the cooling dynamics between high and low "temperatures" is strongly affected by the surface genus with the manifestation of a glass-like transition occurring when the distance from the reference distribution is low. We prove, with examples, that topologically embedded graphs can be built in a way to contain arbitrary complex networks as subgraphs. This method opens a new avenue to build geometrically embedded networks on hyperbolic manifolds.

Building complex networks with Platonic solids.

We propose a unified model to build planar graphs with diverse topological characteristics which are of relevance in real applications. Here convex regular polyhedra (Platonic solids) are used as the building blocks for the construction of a variety of complex planar networks. These networks are obtained by merging polyhedra face by face on a tree-structure leading to planar graphs. We investigate two different constructions: (1) a fully deterministic construction where a self-similar fractal structure is built by using a single kind of polyhedron which is iteratively attached to every face and (2) a stochastic construction where at each step a polyhedron is attached to a randomly chosen face. These networks are scale-free, small-world, clustered, and sparse, sharing several characteristics of real-world complex networks. We derive analytical expressions for the degree distribution, the clustering coefficient, and the mean degree of nearest neighbors showing that these networks have power-law degree distributions with tunable exponents associated with the building polyhedron, and they possess a hierarchical organization that is determined by planarity.

Hierarchical information clustering by means of topologically embedded graphs.

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded networks containing the subset of most significant links and analyzing the network structure. For a planar embedding, this method provides both the intra-cluster hierarchy, which describes the way clusters are composed, and the inter-cluster hierarchy which describes how clusters gather together. We discuss performance, robustness and reliability of this method by first investigating several artificial data-sets, finding that it can outperform significantly other established approaches. Then we show that our method can successfully differentiate meaningful clusters and hierarchies in a variety of real data-sets. In particular, we find that the application to gene expression patterns of lymphoma samples uncovers biologically significant groups of genes which play key-roles in diagnosis, prognosis and treatment of some of the most relevant human lymphoid malignancies.

Emergence of Gamma distributions in granular materials and packing models.

We study the distribution of volume fluctuations in experiments and numerical simulations concerning equal-sized sphere packings prepared with different techniques. We show that the distribution of the local volumes (Voronoï cells) and also the distributions of the global volumes (whole samples) follow remarkably well a shifted and rescaled Gamma distribution that we name a k-Gamma distribution. Such agreement is robust over a broad range of packing fractions and it is observed for several distinct systems. This distribution is characterized by the average packing fraction and a shape parameter "k" which is very sensitive to changes in the structural organization. A statistical mechanics approach predicts such k-Gamma distribution at statistical equilibrium and it links the parameter k with the number of elementary cells which are exchanging volume during the system preparation. The thermodynamical equivalent of k and its relation with the "granular temperature" are also discussed.

Correlations and aggregate statistics in granular packs.

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Voronoï cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.

A tool for filtering information in complex systems.

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.

Hard X-Ray Emission from Elliptical Galaxies and Its Contribution to the X-Ray Background.

We explore the implications of the discovery of hard, power-law X-ray sources in the spectra of nearby elliptical galaxies for the origin of the X-ray background (XRB). The spectra of these sources are consistent with models of thermal bremsstrahlung emission from low radiative efficiency accretion flows around central supermassive black holes and are unique in that they approximately match the spectrum of the hard XRB. If such sources, with luminosities consistent with those observed in nearby elliptical galaxies, are present in most early-type galaxies, then their integrated emission may contribute significantly to the XRB. These sources may also contribute to the hard source counts detected in deep X-ray surveys.

Quasi-Periodic Variability and the Inner Radii of Thin Accretion Disks in Galactic Black Hole Systems.

We calculate upper bounds on the inner radii of geometrically thin accretion disks in galactic black hole systems by relating their rapid variability properties to those of neutron stars. We infer that the inner disk radii do not exhibit large excursions between different spectral states, in contrast with the concept that the disk retreats significantly during the soft-to-hard-state transition. We find that, in the hard state, the accretion disks extend down to radii less, similar6-25 GM/c2 and discuss the implications of our results for models of black hole X-ray spectra.

Possible Evidence for Truncated Thin Disks in the Low-Luminosity Active Galactic Nuclei M81 and NGC 4579.

M81 and NGC 4579 are two of the few low-luminosity active galactic nuclei that have an estimated mass for the central black hole, detected hard X-ray emission, and detected optical/UV emission. In contrast to the canonical "big blue bump," both have optical/UV spectra that decrease with increasing frequency in a nuLnu plot. Barring significant reddening by dust and/or large errors in the black hole mass estimates, the optical/UV spectra of these systems require that the inner edge of a geometrically thin, optically thick accretion disk lies at approximately 100 Schwarzschild radii. The observed X-ray radiation can be explained by an optically thin, two-temperature, advection-dominated accretion flow at smaller radii.