We propose a network-filtering method, the Triangulated Maximally Filtered Graph (TMFG), that provides an approximate solution to the Weighted Maximal Planar Graph problem. The underlying idea of TMFG consists in building a triangulation that maximizes a score function associated with the amount of information retained by the network. TMFG uses as weights any arbitrary similarity measure to arrange data into a meaningful network structure that can be used for clustering, community detection and modelling. The method is fast, adaptable and scalable to very large datasets; it allows online updating and learning as new data can be inserted and deleted with combinations of local and non-local moves. Further, TMFG permits readjustments of the network in consequence of changes in the strength of the similarity measure. The method is based on local topological moves and can therefore take advantage of parallel and GPUs computing. We discuss how this network-filtering method can be used intuitively and efficiently for big data studies and its significance from an information-theoretic perspective.

We investigate how efficiently a known underlying sparse causality structure of a simulated multivariate linear process can be retrieved from the analysis of time series of short lengths. Causality is quantified from conditional transfer entropy and the network is constructed by retaining only the statistically validated contributions. We compare results from three methodologies: two commonly used regularization methods, Glasso and ridge, and a newly introduced technique, LoGo, based on the combination of information filtering network and graphical modelling. For these three methodologies we explore the regions of time series lengths and model-parameters where a significant fraction of true causality links is retrieved. We conclude that when time series are short, with their lengths shorter than the number of variables, sparse models are better suited to uncover true causality links with LoGo retrieving the true causality network more accurately than Glasso and ridge.

Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using empirical mode decomposition (EMD), a method which separates time series into a set of cyclical components at different time-scales. By applying the EMD to fBm, we retrieve a scaling law that relates the variance of the components to a power law of the oscillating period. In contrast, when analysing 22 different stock market indices, we observe deviations from the fBm and Brownian motion scaling behaviour. We discuss and quantify these deviations, associating them to the characteristics of financial markets, with larger deviations corresponding to less developed markets. (C) 2015 Elsevier B.V. All rights reserved.

We perform an extensive empirical analysis of scaling properties of equity returns, suggesting that financial data show time varying multifractal properties. This is obtained by comparing empirical observations of the weighted generalised Hurst exponent (wGHE) with time series simulated via Multifractal Random Walk (MRW) by Bacry et al. [E. Bacry, J. Delour, J.-F. Muzy, Multifractal random walk, Physical Review E 64 (2) (2001) 026103]. While dynamical wGHE computed on synthetic MRW series is consistent with a scenario where multifractality is constant over time, fluctuations in the dynamical wGHE observed in empirical data are not in agreement with a MRW with constant intermittency parameter. We test these hypotheses of constant multifractality considering different specifications of MRW model with fatter tails: in all cases considered, although the thickness of the tails accounts for most of the anomalous fluctuations of multifractality, it still cannot fully explain the observed fluctuations. (C) 2013 Elsevier B.V. All rights reserved.

Triangulations of complex surfaces with different genera are studied within a statistical mechanics framework where an energy is associated to deviations from an ideal, ordered ground state. We observe that the complexity of the embedding surface strongly affects the properties of the triangulations. At high temperatures the 'random states' have degree distributions that broaden with the surface genus. At low temperatures the 'frozen states' can reach a higher degree of order with increasing genus. The dynamics between disordered and ordered states is also affected by the surface genus. High genus triangulations start from more disordered states at high temperatures but they quench faster into more ordered states than the low genus counterparts. However, the ground state is never reached because at low temperatures the relaxation dynamics slows down into a glassy kind of behavior. Topological frustration can also play a very important role when the surface genus forces the average degree to be a fractional number.

Di Matteo, T.
Khandai, N.
DeGraf, C.
Feng, Y.
Croft, R. A. C.
Lopez, J.
Springel, V.

Observations of the most distant bright quasars imply that billion solar mass supermassive black holes (SMBHs) have to be assembled within the first 800 million years. Under our standard galaxy formation scenario such fast growth implies large gas densities providing sustained accretion at critical or supercritical rates onto an initial black hole seed. It has been a long standing question whether and how such high black hole accretion rates can be achieved and sustained at the centers of early galaxies. Here we use our new MassiveBlack cosmological hydrodynamic simulation covering a volume (0.75 Gpc)(3) appropriate for studying the rare first quasars to show that steady high density cold gas flows responsible for assembling the first galaxies produce the high gas densities that lead to sustained critical accretion rates and hence rapid growth commensurate with the existence of similar to 10(9) M-circle dot black holes as early as z similar to 7. We find that under these conditions quasar feedback is not effective at stopping the cold gas from penetrating the central regions and hence cannot quench the accretion until the host galaxy reaches M-halo greater than or similar to 10(12) M-circle dot. This cold-flow-driven scenario for the formation of quasars implies that they should be ubiquitous in galaxies in the early universe and that major (proto) galaxy mergers are not a requirement for efficient fuel supply and growth, particularly for the earliest SMBHs.

In this paper, we use the generalized Hurst exponent approach to study the multi-scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multi-scaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal model, autoregressive fractionally integrated moving average processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality. [All rights reserved Elsevier].

Di Matteo, T.
Khandai, N.
DeGraf, C.
Feng, Y.
Croft, R. A. C.
Lopez, J.
Springel, V.

Observations of the most distant bright quasars imply that billion solar mass supermassive black holes (SMBHs) have to be assembled within the first 800 million years. Under our standard galaxy formation scenario such fast growth implies large gas densities providing sustained accretion at critical or supercritical rates onto an initial black hole seed. It has been a long standing question whether and how such high black hole accretion rates can be achieved and sustained at the centers of early galaxies. Here we use our new MassiveBlack cosmological hydrodynamic simulation covering a volume (0.75 Gpc)(3) appropriate for studying the rare first quasars to show that steady high density cold gas flows responsible for assembling the first galaxies produce the high gas densities that lead to sustained critical accretion rates and hence rapid growth commensurate with the existence of similar to 10(9) M-circle dot black holes as early as z similar to 7. We find that under these conditions quasar feedback is not effective at stopping the cold gas from penetrating the central regions and hence cannot quench the accretion until the host galaxy reaches M-halo greater than or similar to 10(12) M-circle dot. This cold-flow-driven scenario for the formation of quasars implies that they should be ubiquitous in galaxies in the early universe and that major (proto) galaxy mergers are not a requirement for efficient fuel supply and growth, particularly for the earliest SMBHs.

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.

It has been recently pointed out that local volume fluctuations in granular packings follow remarkably well a shifted and rescaled Gamma distribution named the kGamma distribution [T. Aste, T. Di Matteo, Phys. Rev. E 77 (2008) 021309]. In this paper we confirm, extend and discuss this finding by supporting it with additional experimental and simulation data.

In this paper, we examine the effect of X-ray and Ly alpha photons on the intergalactic medium (IGM) temperature. We calculate the photon production from a population of stars and microquasars in a set of cosmological hydrodynamic simulations which self-consistently follow the dark matter dynamics, radiative processes as well as star formation, black hole (BH) growth and associated feedback processes. We find that (i) IGM heating is always dominated by X-rays unless the Ly alpha photon contribution from stars in objects with mass M < 10(8) M(circle dot) becomes significantly enhanced with respect to the X-ray contribution from BHs in the same halo (which we do not directly model). (ii) Without overproducing the unresolved X-ray background, the gas temperature becomes larger than the CMB temperature, and thus an associated 21-cm signal should be expected in emission, at z less than or similar to 11.5. We discuss how in such a scenario the transition redshift between a 21-cm signal in absorption and in emission could be used to constraint BHs accretion and associated feedback processes.

We combine X-ray computed tomography data from real experimental samples with discrete element method simulations to investigate the limiting packing fraction for the loosest mechanically-stable disordered packing. We establish a possible lower bound at packing fraction ~53%.

Chatterjee, S.
Di Matteo, T.
Kosowsky, A.
Pelupessy, I.

Quasar feedback has most likely a substantial but only partially understood impact on the formation of structure in the universe. A potential direct probe of this feedback mechanism is the Sunyaev-Zel'dovich (SZ) effect: energy emitted from quasar heats the surrounding intergalactic medium and induces a distortion in the microwave background radiation passing through the region. Here, we examine the formation of such hot quasar bubbles using a cosmological hydrodynamic simulation which includes a self-consistent treatment of black hole growth and associated feedback, along with radiative gas cooling and star formation. From this simulation, we construct microwave maps of the resulting SZ effect around black holes with a range of masses and redshifts. The size of the temperature distortion scales approximately with black hole mass and accretion rate, with a typical amplitude up to a few micro-Kelvin on angular scales around 10 arcsec. We discuss prospects for the direct detection of this signal with current and future single-dish and interferometric observations, including Atacama Large Millimetre Array (ALMA) and Cornell Caltech Atacama Telescope (CCAT). These measurements will be challenging, but will allow us to characterize the evolution and growth of supermassive black holes and the role of their energy feedback on galaxy formation.

One of the main goals in the field of complex systems is the selection and extraction of relevant and meaningful information about the properties of the underlying system from large datasets. In the last years different methods have been proposed for filtering financial data by extracting a structure of interactions from cross-correlation matrices where only few entries are selected by means of criteria borrowed from network theory. We discuss and compare the stability and robustness of two methods: the Minimum Spanning Tree and the Planar Maximally Filtered Graph. We construct such graphs dynamically by considering running windows of the whole dataset. We study their stability and their edges's persistence and we come to the conclusion that the Planar Maximally Filtered Graph offers a richer and more signi.cant structure with respect to the Minimum Spanning Tree, showing also a stronger stability in the long run.

The most suitable paradigms and tools for investigating the scaling structure of financial time series are reviewed and discussed in the light of some recent empirical results. Different types of scaling are distinguished and several definitions of scaling exponents, scaling and multi-scaling processes are given. Methods to estimate such exponents from empirical financial data are reviewed. A detailed description of the generalized Hurst exponent approach is presented and substantiated with an empirical analysis across different markets and assets