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Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these…
Learning, inference, and emergence in biological and artificial systems are often studied within disparate theoretical frameworks, ranging from energy-based models to recurrent and attention-based architectures. Here we develop a unified…
Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and…
We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…
Uncertainties arising in various control systems, such as robots that are subject to unknown disturbances or environmental variations, pose significant challenges for ensuring system safety, such as collision avoidance. At the same time,…
In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems…
Bursty dynamics characterizes systems that evolve through short active periods of several events, which are separated by long periods of inactivity. Systems with such temporal heterogeneities are not only found in nature but also include…
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…
We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Modern learning systems increasingly interact with data that evolve over time and depend on hidden internal state. We ask a basic question: when is such a dynamical system learnable from observations alone? This paper proposes a research…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…
One of the primary drivers for self-adaptation is ensuring that systems achieve their goals regardless of the uncertainties they face during operation. Nevertheless, the concept of uncertainty in self-adaptive systems is still…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
Self-adaptive robots adjust their behaviors in response to unpredictable environmental changes. These robots often incorporate deep learning (DL) components into their software to support functionality such as perception, decision-making,…
The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical system, indecision is modeled by a discrete-state Markov process determined by…