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Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
We study the dynamics of the Bak-Sneppen model on small-world networks. For each site in the network, we define a ``connectance,'' which measures the distance to all other sites. We find radically different patterns of activity for…
In order to better understand the impact of environmental stochastic fluctuations on the evolution of animal behavior, we introduce the concept of a stochastic Nash equilibrium (SNE) that extends the classical concept of a Nash equilibrium…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically…
Approximate message passing algorithms proved to be extremely effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately…
Software-defined networking (SDN) programs must simultaneously describe static forwarding behavior and dynamic updates in response to events. Event-driven updates are critical to get right, but difficult to implement correctly due to the…
Topological Data Analysis (TDA) provides a toolkit for the study of the shape of high dimensional and complex data. While operating on a space of persistence diagrams is cumbersome, persistence norms provide a simple real value measure of…
This article addresses the problem of state observer design for continuous-time linear positive networked systems. Considering the bandwidth constraint in the communication network, an event-measurement-based positive observer design is…
We introduce a simple network model that is inspired by social information networks such as twitter. Agents are nodes, connecting to another agent by building a directed edge has a cost, and reaching other agents via short directed paths…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition…
In this paper we provide a set of stability conditions for linear time-invariant networked control systems with arbitrary topology, using a Lyapunov direct approach. We then use these stability conditions to provide a novel low-complexity…
Information can evolve as a physical consequence of non-equilibrium dynamics, even in the absence of genes, replication, or predefined fitness functions. We present Stability-Driven Assembly (SDA), a framework in which stochastic assembly…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
This paper presents a practical approach for detecting non-stationarity in time series prediction. This method is called SAFE and works by monitoring the evolution of the spectral contents of time series through a distance function. This…
Online incremental clustering of sequentially incoming data without prior knowledge suffers from changing cluster numbers and tends to fall into local extrema according to given data order. To overcome these limitations, we propose a…