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We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
We investigate the stability and robustness properties of a continuification-based strategy for the control of large-scale multiagent systems. Within continuation-based strategy, one transforms the microscopic, agent-level description of…
This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…
Coordinated movement and self-organisation of active self-driven agents is common in nature and is seen across different scales, from herds of animals to collective motion in bacteria. Often, these systems are heterogeneous in composition,…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Large-scale coherent structures are identified in turbulent pipe flow at $Re_\tau=181$ by having long lifetimes, living on large scales and travelling with a certain group velocity. A Characteristic Dynamic Mode Decomposition (CDMD) is used…
Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
Compressive sensing is the newly emerging method in information technology that could impact array beamforming and the associated engineering applications. However, practical measurements are inevitably polluted by noise from external…
The availability of empirical data that capture the structure and behavior of complex networked systems has been greatly increased in recent years, however a versatile computational toolbox for unveiling a complex system's nodal and…
We present our preliminary work on a multi-agent system involving the complex human phenomena of identity and dynamic teams. We outline our ongoing experimentation into understanding how these factors can eliminate some of the naive…
We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
Specialization and diversification are two major strategies that complex systems might exploit. Given a fixed amount of resources, the question is whether to invest this in elements that respond in a correlated manner to external…
We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…