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We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
Emergent behavior in complex systems arises from nonlinear interactions among components, yet the intricate nature of self-organization often obscures the underlying causal relationships, long regarded as the "holy grail" of complexity…
It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…
Reinforcement learning is a general methodology of adaptive optimal control that has attracted much attention in various fields ranging from video game industry to robot manipulators. Despite its remarkable performance demonstrations, plain…
Reinforcement learning (RL) approaches based on Markov Decision Processes (MDPs) are predominantly applied in the robot joint space, often relying on limited task-specific information and partial awareness of the 3D environment. In…
This study is aimed at addressing the problem of fault tolerance of quadruped robots to actuator failure, which is critical for robots operating in remote or extreme environments. In particular, an adaptive curriculum reinforcement learning…
Real-world autonomous decision-making systems, from robots to recommendation engines, must operate in environments that change over time. While deep reinforcement learning (RL) has shown an impressive ability to learn optimal policies in…
Reinforcement learning (RL) has attracted increasing interest for adaptive traffic signal control due to its model-free ability to learn control policies directly from interaction with the traffic environment. However, several challenges…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
Interacting-Particle Reaction Dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enable a wide range of…
The Activated Random Walk (ARW) model is a promising candidate for demonstrating self-organized criticality due to its potential for universality. Recent studies have shown that the ARW model exhibits a well-defined critical density in one…
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems.…
Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to…
Adaptive cruise control systems are fundamental components of the automation of the driving. At upper control level, ACC systems are based on car-following models determining the acceleration rate of a vehicle according to the distance gap…
The "ratchet principle" asserts that non-equilibrium systems which violate parity symmetry generically exhibit steady-state currents. As recently shown, there are exceptions to this principle, due to the existence of hidden time-reversal…
Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation.…
High Power Laser (HPL) systems operate in the attoseconds regime -- the shortest timescale ever created by humanity. HPL systems are instrumental in high-energy physics, leveraging ultra-short impulse durations to yield extremely high…
Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…
We present some aspects of the rheology of field-responsive suspensions, a class of field-responsive liquid matter systems possessing the ability to undergo significant changes in their strength upon application of an external field. Both…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…