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Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…
We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…
Estimating causal effects from observational data informs us about which factors are important in an autonomous system, and enables us to take better decisions. This is important because it has applications in selecting a treatment in…
Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…
Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…
Distributed aggregation allows the derivation of a given global aggregate property from many individual local values in nodes of an interconnected network system. Simple aggregates such as minima/maxima, counts, sums and averages have been…
Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…
Distributed systems have been widely used in practice to accomplish data analysis tasks of huge scales. In this work, we target on the estimation problem of generalized linear models on a distributed system with nonrandomly distributed…
Design of experiments and estimation of treatment effects in large-scale networks, in the presence of strong interference, is a challenging and important problem. Most existing methods' performance deteriorates as the density of the network…
Analyzing and controlling spreading processes are challenging problems due to the involved non-linear node (subsystem) dynamics, unknown disturbances, complex interconnections, and the large-scale and multi-level nature of the problems. The…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract…
Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is…