Bayesian topology identification of linear dynamic networks

In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying the connectivity of networks of transfer functions, without the need to estimate the dynamics. The algorithm employs a Bayesian measure and a forward-backward search algorithm. To obtain the Bayesian measure, the impulse responses of network modules are modeled as Gaussian processes and the hyperparameters are estimated by marginal likelihood maximization using the expectation-maximization algorithm. Numerical results demonstrate the effectiveness of this method

Online Machine Learning for Inference from Multivariate Time-series

Inference and data analysis over networks have become significant areas of research due to the increasing prevalence of interconnected systems and the growing volume of data they produce. Many of these systems generate data in the form of multivariate time series, which are collections of time series data that are observed simultaneously across multiple variables. For example, EEG measurements of the brain produce multivariate time series data that record the electrical activity of different brain regions over time. Cyber-physical systems generate multivariate time series that capture the behaviour of physical systems in response to cybernetic inputs. Similarly, financial time series reflect the dynamics of multiple financial instruments or market indices over time. Through the analysis of these time series, one can uncover important details about the behavior of the system, detect patterns, and make predictions. Therefore, designing effective methods for data analysis and inference over networks of multivariate time series is a crucial area of research with numerous applications across various fields. In this Ph.D. Thesis, our focus is on identifying the directed relationships between time series and leveraging this information to design algorithms for data prediction as well as missing data imputation. This Ph.D. thesis is organized as a compendium of papers, which consists of seven chapters and appendices. The first chapter is dedicated to motivation and literature survey, whereas in the second chapter, we present the fundamental concepts that readers should understand to grasp the material presented in the dissertation with ease. In the third chapter, we present three online nonlinear topology identification algorithms, namely NL-TISO, RFNL-TISO, and RFNL-TIRSO. In this chapter, we assume the data is generated from a sparse nonlinear vector autoregressive model (VAR), and propose online data-driven solutions for identifying nonlinear VAR topology. We also provide convergence guarantees in terms of dynamic regret for the proposed algorithm RFNL-TIRSO. Chapters four and five of the dissertation delve into the issue of missing data and explore how the learned topology can be leveraged to address this challenge. Chapter five is distinct from other chapters in its exclusive focus on edge flow data and introduces an online imputation strategy based on a simplicial complex framework that leverages the known network structure in addition to the learned topology. Chapter six of the dissertation takes a different approach, assuming that the data is generated from nonlinear structural equation models. In this chapter, we propose an online topology identification algorithm using a time-structured approach, incorporating information from both the data and the model evolution. The algorithm is shown to have convergence guarantees achieved by bounding the dynamic regret. Finally, chapter seven of the dissertation provides concluding remarks and outlines potential future research directions.publishedVersio

An introduction to spectral distances in networks (extended version)

Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an overview of the spectral distances, highlighting their behavior in some basic cases of static and dynamic synthetic and real networks

A generative model for protein contact networks

In this paper we present a generative model for protein contact networks. The soundness of the proposed model is investigated by focusing primarily on mesoscopic properties elaborated from the spectra of the graph Laplacian. To complement the analysis, we study also classical topological descriptors, such as statistics of the shortest paths and the important feature of modularity. Our experiments show that the proposed model results in a considerable improvement with respect to two suitably chosen generative mechanisms, mimicking with better approximation real protein contact networks in terms of diffusion properties elaborated from the Laplacian spectra. However, as well as the other considered models, it does not reproduce with sufficient accuracy the shortest paths structure. To compensate this drawback, we designed a second step involving a targeted edge reconfiguration process. The ensemble of reconfigured networks denotes improvements that are statistically significant. As a byproduct of our study, we demonstrate that modularity, a well-known property of proteins, does not entirely explain the actual network architecture characterizing protein contact networks. In fact, we conclude that modularity, intended as a quantification of an underlying community structure, should be considered as an emergent property of the structural organization of proteins. Interestingly, such a property is suitably optimized in protein contact networks together with the feature of path efficiency.Comment: 18 pages, 67 reference

Institutional paraconsciousness and its pathologies

This analysis extends a recent mathematical treatment of the Baars consciousness model to analogous, but far more complicated, phenomena of institutional cognition. Individual consciousness is limited to a single, tunable, giant component of interacting cognitive modules, instantiating a Global Workspace. Human institutions, by contrast, support several, sometimes many, such giant components simultaneously, although their behavior remains constrained to a topology generated by cultural context and by the path-dependence inherent to organizational history. Such highly parallel multitasking - institutional paraconsciousness - while clearly limiting inattentional blindness and the consequences of failures within individual workspaces, does not eliminate them, and introduces new characteristic dysfunctions involving the distortion of information sent between global workspaces. Consequently, organizations (or machines designed along these principles), while highly efficient at certain kinds of tasks, remain subject to canonical and idiosyncratic failure patterns similar to, but more complicated than, those afflicting individuals. Remediation is complicated by the manner in which pathogenic externalities can write images of themselves on both institutional function and therapeutic intervention, in the context of relentless market selection pressures. The approach is broadly consonant with recent work on collective efficacy, collective consciousness, and distributed cognition