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. We take our steps from a recent work on Mean Field methods for the inference of the model with hidden spins and 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 calculate the log-likelihood in polynomial time, giving as output a maximum likelihood 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 like LASSO regularization or decimation. We test the performance of the algorithm on synthetic data and find interesting properties when it comes to 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

On the equivalence between the Kinetic Ising Model and discrete autoregressive processes

Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In Statistical Physics the Kinetic Ising Model has been introduced to describe the dynamics of the magnetic moments of a spin lattice, while in time series analysis discrete autoregressive processes have been designed to capture the multivariate dependence structure across binary time series. In this article we provide a rigorous proof of the equivalence between the two models in the range of a unique and invertible map unambiguously linking one model parameters set to the other. Our result finds further justification acknowledging that both models provide maximum entropy distributions of binary time series with given means, auto-correlations, and lagged cross-correlations of order one. We further show that the equivalence between the two models permits to exploit the inference methods originally developed for one model in the inference of the other

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

Heterogeneity- and homophily-induced vulnerability of a P2P network formation model: the IOTA auto-peering protocol

IOTA is a distributed ledger technology that relies on a peer-to-peer (P2P) network for communications. Recently an auto-peering algorithm was proposed to build connections among IOTA peers according to their "Mana" endowment, which is an IOTA internal reputation system. This paper's goal is to detect potential vulnerabilities and evaluate the resilience of the P2P network generated using IOTA auto-peering algorithm against eclipse attacks. In order to do so, we interpret IOTA's auto-peering algorithm as a random network formation model and employ different network metrics to identify cost-efficient partitions of the network. As a result, we present a potential strategy that an attacker can use to eclipse a significant part of the network, providing estimates of costs and potential damage caused by the attack. On the side, we provide an analysis of the properties of IOTA auto-peering network ensemble, as an interesting class of homophile random networks in between 1D lattices and regular Poisson graphs

Network-based indicators of Bitcoin bubbles

The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science. Here we analyse the evolution of the network of Bitcoin transactions between users. We achieve this by using the complete transaction history from December 5th 2011 to December 23rd 2013. This period includes three bubbles experienced by the Bitcoin price. In particular, we focus on the global and local structural properties of the user network and their variation in relation to the different period of price surge and decline. By analysing the temporal variation of the heterogeneity of the connectivity patterns we gain insights on the different mechanisms that take place during bubbles, and find that hubs (i.e., the most connected nodes) had a fundamental role in triggering the burst of the second bubble. Finally, we examine the local topological structures of interactions between users, we discover that the relative frequency of triadic interactions experiences a strong change before, during and after a bubble, and suggest that the importance of the hubs grows during the bubble. These results provide further evidence that the behaviour of the hubs during bubbles significantly increases the systemic risk of the Bitcoin network, and discuss the implications on public policy interventions

The Evolving Liaisons between the Transaction Networks of Bitcoin and Its Price Dynamics

Cryptocurrencies (the most paradigmatic blockchain-based systems) are distributed systems that allow to exchange tokens among participants. These cryptocurrencies can also be acquired in exchange markets. The availability of the historical bookkeeping of cryptocurrency transfers in a public ledger opens up the possibility of understanding the relationship between aggregate users’ behaviour and the cryptocurrency pricing in exchange markets. This paper analyses the properties of the transaction network of Bitcoin. We consider different representations over a period of nine years since its creation and involving 16 million users and 283 million transactions. Importantly, these transactions do not include orders filled in exchange markets, which are settled outside of the blockchain, and ultimately determine Bitcoin price. By analysing these networks, we show the existence of Granger causal relationships between Bitcoin price movements and changes of its transaction network topology. Our results reveal the interplay between structural quantities, indicative of the collective behaviour of Bitcoin users, and price movements, showing that, during price drops, the system is characterised by a larger heterogeneity of users’ activity

Measurement of the CKM Matrix Element ∣Vcb∣|V_{cb}| from B0→D∗−ℓ+νℓB^{0} \to D^{*-} \ell^+ \nu_\ell at Belle

We present a new measurement of the CKM matrix element $|V_{cb}|$ from $B^{0} \to D^{*-} \ell^+ \nu_\ell$ decays, reconstructed with the full Belle data set of $711 \, \rm fb^{-1}$ integrated luminosity. Two form factor parameterizations, originally conceived by the Caprini-Lellouch-Neubert (CLN) and the Boyd, Grinstein and Lebed (BGL) groups, are used to extract the product $\mathcal{F}(1)\eta_{\rm EW}|V_{cb}|$ and the decay form factors, where $\mathcal{F}(1)$ is the normalization factor and $\eta_{\rm EW}$ is a small electroweak correction. In the CLN parameterization we find $\mathcal{F}(1)\eta_{\rm EW}|V_{cb}| = (35.06 \pm 0.15 \pm 0.56) \times 10^{-3}$, $\rho^{2}=1.106 \pm 0.031 \pm 0.007$, $R_{1}(1)=1.229 \pm 0.028 \pm 0.009$, $R_{2}(1)=0.852 \pm 0.021 \pm 0.006$. For the BGL parameterization we obtain $\mathcal{F}(1)\eta_{\rm EW}|V_{cb}|= (34.93 \pm 0.23 \pm 0.59)\times 10^{-3}$, which is consistent with the World Average when correcting for $\mathcal{F}(1)\eta_{\rm EW}$. The branching fraction of $B^{0} \to D^{*-} \ell^+ \nu_\ell$ is measured to be $\mathcal{B}(B^{0}\rightarrow D^{*-}\ell^{+}\nu_{\ell}) = (4.90 \pm 0.02 \pm 0.16)\%$. We also present a new test of lepton flavor universality violation in semileptonic $B$ decays, $\frac{{\cal B }(B^0 \to D^{*-} e^+ \nu)}{{\cal B }(B^0 \to D^{*-} \mu^+ \nu)} = 1.01 \pm 0.01 \pm 0.03~$. The errors correspond to the statistical and systematic uncertainties respectively. This is the most precise measurement of $\mathcal{F}(1)\eta_{\rm EW}|V_{cb}|$ and form factors to date and the first experimental study of the BGL form factor parameterization in an experimental measurement

Measurement of B(Bs_{s} →ds_{s}X) with Bs_{s} semileptonic tagging

We report the first direct measurement of the inclusive branching fraction B(B$_{s}$ →D$_{s}$X) via B$_{s}$ tagging in e$^{+}$e$^{–}$→Υ(5S) events. Tagging is accomplished through a partial reconstruction of semileptonic decays B$_{s}$→D$_{s}$Xℓν, where X denotes unreconstructed additional hadrons or photons and ℓ is an electron or muon. With 121.4 fb$^{–1}$ of data collected at the Υ(5S) resonance by the Belle detector at the KEKB asymmetric-energy e$^{+}$e$^{–}$ collider, we obtain B(B$_{s}$ →D$_{s}$X)=(60.2±5.8±2.3)%, where the first uncertainty is statistical and the second is systematic