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

Dark Sector first results at Belle II

Understanding the nature of dark matter is one of the most exciting challenges in fundamental physics nowadays, requiring the synergy of different search techniques, as well as theoretical inputs. An interesting opportunity for the investigation of dark matter is the one offered by the \textit{B}-factories. The Belle~II experiment, located at the interaction point of the SuperKEKB asymmetric energy $e^+e^-$ collider, is a new generation \textit{B}-factory experiment operating at the Japanese KEK laboratory. With a machine design luminosity of $6\times10^{35}\,\rm{cm}^{-2}s^{-1}$, Belle II aims to record 50 ab$^{-1}$ of data within the next decade. Thanks to this large data-sample and by using dedicated triggers, Belle~II is expected to explore dark sector candidates with unprecedented sensitivity in the mass range up to 10 GeV$/c^2$. During 2018, the experiment concluded a commissioning run, collecting a data-sample corresponding to an integrated luminosity of about 0.5 fb$^{-1}$, while main operations started on March 2019 with an almost complete detector. So far the experiment collected an integrated luminosity of $\sim90\, \rm{fb}^{-1}$. With these data-sets Belle~II has already shown the possibility to search for a large variety of dark sector candidates in the GeV mass range. This paper reviews the status of the dark sector searches performed at the Belle~II experiment, with a focus on the first obtained results and the discovery potential with the data-set available in the short term.Comment: This is an author-created, un-copyedited version of an article accepted for publication/published in Physica Scripta. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://iopscience.iop.org/article/10.1088/1402-4896/abfef

Searches for an invisible Z' and for the dark Higgsstrahlung A'h' process in μ⁺μ⁻ plus missing energy final states at Belle II

The work presented in this thesis concerns two searches for dark sector mediators in e^+e^- annihilations at the center-of-mass energy of 10.58 GeV with the Belle II experiment. Two different processes have been investigated in the same final state, consisting of two muons plus missing energy, by using the first data collected by the experiment so far. The first search presented in this work investigates an invisibly decaying Z' boson (in the framework of a L_µ - L_τ symmetry) produced radiatively by muons in the process e^+e^- → μ^+μ^-Z'; Z'→ invisible. The only previous measurements in the same theoretical framework have been performed by the BaBar and CMS experiments for a Z' decaying to muons, while no results for an invisible decay have been reported before. For this measure, the data-set collected by Belle II during the so-called Phase 2 commissioning run in 2018 has been used, corresponding to an integrated luminosity of 276 pb^-1. No anomalies have been observed in data, and upper limits on the coupling constant g' in the range [5 × 10^2 − 1] have been placed for a Z' mass less than 6 GeV/c^2. As an extension of the above search, the existence of a LFV Z' boson has been investigated in the process e^+e^- → e^±μ^∓Z'; Z'→ invisible. Even in that case, no anomalies have been observed, and model independent upper limits on the cross section (times efficiency) have been computed. The search for a different process is also presented, consisting in the simultaneous production of a dark photon A' and a dark Higgs h' boson via the so-called dark Higgstrahlung process e^+e^- → A'h'; A'→ μ^+μ^-, h'→ invisible. The only similar measurement was performed by the KLOE experiment, for A' masses up to ~ 1 GeV/c^2. Therefore, Belle II would be able to produce a sizeable enlargement of the explored region. The analysis flow, optimized for the data collected by the experiment during 2019, corresponding to an integrated luminosity of ~ 9 fb^-1, is described and the expected upper limits on the cross section and in terms of the coupling constants product є × α_D are provided

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

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

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

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

Radiation Damage in Polyethylene Naphthalate Thin-Film Scintillators.

This paper describes the scintillation features and the radiation damage in polyethylene naphthalate 100 µm-thick scintillators irradiated with an 11 MeV proton beam and with a 1 MeV electron beam at doses up to 15 and 85 Mrad, respectively. The scintillator emission spectrum, optical transmission, light yield loss, and scintillation pulse decay times were investigated before and after the irradiation. A deep blue emission spectrum peaked at 422 nm, and fast and slow scintillation decay time constants of the order of 1-2 ns and 25-30 nm, respectively, were measured. After irradiation, transmittance showed a loss of transparency for wavelengths between 380 and 420 nm, and a light yield reduction of ~40% was measured at the maximum dose of 85 Mrad