Modelling time-varying interactions in complex systems: the Score Driven Kinetic Ising Model.

A common issue when analyzing real-world complex systems is that the interactions between their elements often change over time. Here we propose a new modeling approach for time-varying interactions generalising the well-known Kinetic Ising Model, a minimalistic pairwise constant interactions model which has found applications in several scientific disciplines. Keeping arbitrary choices of dynamics to a minimum and seeking information theoretical optimality, the Score-Driven methodology allows to extract from data and interpret the presence of temporal patterns describing time-varying interactions. We identify a parameter whose value at a given time can be directly associated with the local predictability of the dynamics and we introduce a method to dynamically learn its value from the data, without specifying parametrically the system's dynamics. We extend our framework to disentangle different sources (e.g. endogenous vs exogenous) of predictability in real time, and show how our methodology applies to a variety of complex systems such as financial markets, temporal (social) networks, and neuronal populations.

Information dynamics of price and liquidity around the 2017 Bitcoin markets crash.

We study information dynamics between the largest Bitcoin exchange markets during the bubble in 2017-2018. By analyzing high-frequency market microstructure observables with different information-theoretic measures for dynamical systems, we find temporal changes in information sharing across markets. In particular, we study time-varying components of predictability, memory, and (a)synchronous coupling, measured by transfer entropy, active information storage, and multi-information. By comparing these empirical findings with several models, we argue that some results could relate to intra-market and inter-market regime shifts and changes in the direction of information flow between different market observables.

Non-Markovian temporal networks with auto- and cross-correlated link dynamics.

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often observed to be non-Markovian, and the dynamics of their links are often correlated. Hence, to accurately model these networks, predict their evolution, and understand how information and other relevant quantities propagate over them, the inclusion of both memory and dynamical dependencies between links is key. In this article we introduce a general class of models of temporal networks based on discrete autoregressive processes for link dynamics. As a concrete and useful case study, we then concentrate on a specific model within this class, which allows to generate temporal networks with a specified underlying structural backbone, and with precise control over the dynamical dependencies between links and the strength and length of their memories. In this network model the presence of each link is influenced not only by its past activity, but also by the past activities of other links, as specified by a coupling matrix, which directly controls the causal relations, and hence the correlations, among links. We propose a maximum likelihood method for estimating the model's parameters from data, showing how the model allows a more realistic description of real-world temporal networks and also to predict their evolution. Due to the flexibility of maximum likelihood inference, we illustrate how to deal with heterogeneity and time-varying patterns, possibly including also nonstationary network dynamics. We then use our network model to investigate the role that, both the features of memory and the type of correlations in the dynamics of links have on the properties of processes occurring over a temporal network. Namely, we study the speed of a spreading process, as measured by the time it takes for diffusion to reach equilibrium. Through both numerical simulations and analytical results, we are able to separate the roles of autocorrelations and neighborhood correlations in link dynamics, showing that not only is the speed of diffusion nonmonotonically dependent on the memory length, but also that correlations among neighboring links help to speed up the spreading process, while autocorrelations slow it back down. Our results have implications in the study of opinion formation, the modeling of social networks, and the spreading of epidemics through mobile populations.

Betweenness centrality for temporal multiplexes.

Betweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of [Formula: see text]k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.

Knowledge and social relatedness shape research portfolio diversification.

Scientific discovery is shaped by scientists' choices and thus by their career patterns. The increasing knowledge required to work at the frontier of science makes it harder for an individual to embark on unexplored paths. Yet collaborations can reduce learning costs-albeit at the expense of increased coordination costs. In this article, we use data on the publication histories of a very large sample of physicists to measure the effects of knowledge and social relatedness on their diversification strategies. Using bipartite networks, we compute a measure of topic similarity and a measure of social proximity. We find that scientists' strategies are not random, and that they are significantly affected by both. Knowledge relatedness across topics explains [Formula: see text] of logistic regression deviances and social relatedness as much as [Formula: see text], suggesting that science is an eminently social enterprise: when scientists move out of their core specialization, they do so through collaborations. Interestingly, we also find a significant negative interaction between knowledge and social relatedness, suggesting that the farther scientists move from their specialization, the more they rely on collaborations. Our results provide a starting point for broader quantitative analyses of scientific diversification strategies, which could also be extended to the domain of technological innovation-offering insights from a comparative and policy perspective.

Trip Centrality: walking on a temporal multiplex with non-instantaneous link travel time.

In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their presence depends on time, and travelling between two nodes requires a non-vanishing time. Additionally, many networks are structured on several layers, representing, e.g., different transportation modes or service providers. Temporal generalisations of centrality metrics based on walk-counting, like Katz centrality, exist, however they do not account for non-zero link travel times and for the multiplex structure. We propose a generalisation of Katz centrality, termed Trip Centrality, counting only the walks that can be travelled according to the network temporal structure, i.e. "trips", while also differentiating the contributions of inter- and intra-layer walks to centrality. We show an application to the US air transport system, specifically computing airports' centrality losses due to delays in the flight network.

Inference of the kinetic Ising model with heterogeneous missing data.

We consider the problem of inferring a causality structure from multiple binary time series by using the kinetic Ising model in datasets where a fraction of observations is missing. Inspired by recent work on mean field methods for the inference of the model with hidden spins, we develop a pseudo-expectation-maximization algorithm that is able to work even in conditions of severe data sparsity. The methodology relies on the Martin-Siggia-Rose path integral method with second-order saddle-point solution to make it possible to approximate the log-likelihood in polynomial time, giving as output an estimate of the couplings matrix and of the missing observations. We also propose a recursive version of the algorithm, where at every iteration some missing values are substituted by their maximum-likelihood estimate, showing that the method can be used together with sparsification schemes such as lasso regularization or decimation. We test the performance of the algorithm on synthetic data and find interesting properties regarding the dependency on heterogeneity of the observation frequency of spins and when some of the hypotheses that are necessary to the saddle-point approximation are violated, such as the small couplings limit and the assumption of statistical independence between couplings.

Detectability of macroscopic structures in directed asymmetric stochastic block model.

We study the problem of identifying macroscopic structures in networks, characterizing the impact of introducing link directions on the detectability phase transition. To this end, building on the stochastic block model, we construct a class of nontrivially detectable directed networks. We find closed-form solutions by using the belief propagation method, showing how the transition line depends on the assortativity and the asymmetry of the network. Finally, we numerically identify the existence of a hard phase for detection close to the transition point.

Crossover from Linear to Square-Root Market Impact.

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order. Our empirical results are remarkably well explained by a recently proposed dynamical theory of liquidity that makes specific predictions about the scaling function describing this crossover. Allowing at least two characteristic timescales for the liquidity ("fast" and "slow") enables one to reach quantitative agreement with the data.

Detection of intensity bursts using Hawkes processes: An application to high-frequency financial data.

Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local nonstationarity or the presence of an external perturbation to the system. In this paper we propose a procedure for the detection of intensity bursts within the Hawkes process framework. By using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown. Moreover, the initial time of the burst can be determined with a precision given by the typical interevent time. We apply our methodology to the midprice change in foreign exchange (FX) markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival. We show lead-lag relations in intensity burst occurrence across different FX rates and we discuss their relation with price jumps.

Resolution of ranking hierarchies in directed networks.

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.

Optimal information diffusion in stochastic block models.

We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two-community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e., those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative. We then look for minimal cost structures, i.e., those for which a minimal fraction of initially informed nodes is needed to trigger a global cascade. We find that the optimal networks are assortative but with a structure very close to a core-periphery graph, i.e., a very dense community linked to a much more sparsely connected periphery.

Coupling News Sentiment with Web Browsing Data Improves Prediction of Intra-Day Price Dynamics.

The new digital revolution of big data is deeply changing our capability of understanding society and forecasting the outcome of many social and economic systems. Unfortunately, information can be very heterogeneous in the importance, relevance, and surprise it conveys, affecting severely the predictive power of semantic and statistical methods. Here we show that the aggregation of web users' behavior can be elicited to overcome this problem in a hard to predict complex system, namely the financial market. Specifically, our in-sample analysis shows that the combined use of sentiment analysis of news and browsing activity of users of Yahoo! Finance greatly helps forecasting intra-day and daily price changes of a set of 100 highly capitalized US stocks traded in the period 2012-2013. Sentiment analysis or browsing activity when taken alone have very small or no predictive power. Conversely, when considering a news signal where in a given time interval we compute the average sentiment of the clicked news, weighted by the number of clicks, we show that for nearly 50% of the companies such signal Granger-causes hourly price returns. Our result indicates a "wisdom-of-the-crowd" effect that allows to exploit users' activity to identify and weigh properly the relevant and surprising news, enhancing considerably the forecasting power of the news sentiment.

Modeling foreign exchange market activity around macroeconomic news: Hawkes-process approach.

We present a Hawkes-model approach to the foreign exchange market in which the high-frequency price dynamics is affected by a self-exciting mechanism and an exogenous component, generated by the pre-announced arrival of macroeconomic news. By focusing on time windows around the news announcement, we find that the model is able to capture the increase of trading activity after the news, both when the news has a sizable effect on volatility and when this effect is negligible, either because the news in not important or because the announcement is in line with the forecast by analysts. We extend the model by considering noncausal effects, due to the fact that the existence of the news (but not its content) is known by the market before the announcement.

Multi-scale analysis of the European airspace using network community detection.

We show that the European airspace can be represented as a multi-scale traffic network whose nodes are airports, sectors, or navigation points and links are defined and weighted according to the traffic of flights between the nodes. By using a unique database of the air traffic in the European airspace, we investigate the architecture of these networks with a special emphasis on their community structure. We propose that unsupervised network community detection algorithms can be used to monitor the current use of the airspace and improve it by guiding the design of new ones. Specifically, we compare the performance of several community detection algorithms, both with fixed and variable resolution, and also by using a null model which takes into account the spatial distance between nodes, and we discuss their ability to find communities that could be used to define new control units of the airspace.

Statistically validated networks in bipartite complex systems.

Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting system's heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved.

Market reaction to a bid-ask spread change: a power-law relaxation dynamics.

We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of prices and times of submitted orders, which affect the decay of the spread.

Market impact and trading profile of hidden orders in stock markets.

We empirically study the market impact of trading orders. We are specifically interested in large trading orders that are executed incrementally, which we call hidden orders. These are statistically reconstructed based on information about market member codes using data from the Spanish Stock Market and the London Stock Exchange. We find that market impact is strongly concave, approximately increasing as the square root of order size. Furthermore, as a given order is executed, the impact grows in time according to a power law; after the order is finished, it reverts to a level of about 0.5-0.7 of its value at its peak. We observe that hidden orders are executed at a rate that more or less matches trading in the overall market, except for small deviations at the beginning and end of the order.

Scaling laws of strategic behavior and size heterogeneity in agent dynamics.

We consider the financial market as a model system and study empirically how agents strategically adjust the properties of large orders in order to meet their preference and minimize their impact. We quantify this strategic behavior by detecting scaling relations between the variables characterizing the trading activity of different institutions. We also observe power-law distributions in the investment time horizon, in the number of transactions needed to execute a large order, and in the traded value exchanged by large institutions, and we show that heterogeneity of agents is a key ingredient for the emergence of some aggregate properties characterizing this complex system.

Inverted and mirror repeats in model nucleotide sequences.

We analytically and numerically study the probabilistic properties of inverted and mirror repeats in model sequences of nucleic acids. We consider both perfect and nonperfect repeats, i.e., repeats with mismatches and gaps. The considered sequence models are independent identically distributed (i.i.d.) sequences, Markov processes and long-range sequences. We show that the number of repeats in correlated sequences is significantly larger than in i.i.d. sequences and that this discrepancy increases exponentially with the repeat length for long-range sequences.