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Cascading failures are one of the main reasons for blackouts in power transmission grids. The topology of a power grid, together with its operative state determine, for the most part, the robustness of the power grid against cascading…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…
We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
This article introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents…
Electrical power grids are vulnerable to cascading failures that can lead to large blackouts. Detection and prevention of cascading failures in power grids is impor- tant. Currently, grid operators mainly monitor the state (loading level)…
Feedback dynamic routing is a commonly used control strategy in transportation systems. This class of control strategies relies on real-time information about the traffic state in each link. However, such information may not always be…
To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…
Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures the…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…
Power grids vulnerability is a key issue in society. A component failure may trigger cascades of failures across the grid and lead to a large blackout. Complex network approaches have shown a direction to study some of the problems faced by…
Resilience is emerging as a key requirement for next-generation wireless communication systems, requiring the ability to assess and control rare, path-dependent failure events arising from sequential degradation and delayed recovery. In…
In this paper a stochastic model of a large distributed system where users' files are duplicated on unreliable data servers is investigated. Due to a server breakdown, a copy of a file can be lost, it can be retrieved if another copy of the…
This paper concerns the resilience of systems with wind power upon wind reduction by evaluating the potential of corrective actions, such as generation and load dispatch, on minimizing the effects of transmission line failures. Three…