Related papers: Towards an Algebra for Cascade Effects
We investigate the abrupt breakdown behavior of coupled distribution grids under load growth. This scenario mimics the ever-increasing customer demand and the foreseen introduction of energy hubs interconnecting the different energy…
Cascading failures, wherein the failure of one component triggers subsequent failures in complex interconnected systems, pose a significant risk of disruptions and emerge across various domains. Understanding and mitigating the risk of such…
Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…
The increasing complexity and interdependency of today's networks highlight the importance of studying network robustness to failure and attacks. Many large-scale networks are prone to cascading effects where a limited number of initial…
Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding the universal aspects of these phenomena is of fundamental interest, yet typically bound to numerical observations in ad-hoc models…
We present a framework to formally describe probabilistic system behavior and symbolically reason about it. In particular we aim at reasoning about possible failures and fault tolerance. We regard systems which are composed of different…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
We introduce a family of particle systems on sparse graphs where local interactions occur via hitting times, providing a dynamic and tractable model for default cascades in large sparsely-connected financial networks. Building on the…
Threshold rules of spreading in binary-state networks lead to cascades. We study persistent cascade-recovery dynamics on quasi-robust networks, i.e., networks which are robust against small trigger but may collapse for larger one. It is…
A universal framework is proposed, where all laws are regularities of relations between things or agents. Parts of the world at one or all times are modeled as networks called SYSTEMS with a minimum of axiomatic properties. A notion of…
The central problem of fully developed turbulence is the energy cascading process. It has revisited all attempts at a full physical understanding or mathematical formulation. The main reason for this failure are related to the large…
Distributed systems often exhibit emergent behaviors that impact their resilience (Franz-Kaiser et al., 2020; Adilson E. Motter, 2002; Jianxi Gao, 2016). This paper presents a theoretical framework combining attributed graph models,…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\kappa$…
Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
In this paper I conceptualise a novel approach for capturing coincidences between events that have not necessarily an observed causal relationship. Building on the Transcendental Information Cascades approach I outline a tensor theory of…
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional…
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only…
Cascading failure of a power transmission system are initiated by an exogenous event that disable a set of elements (e.g., lines) followed by a sequence of interrelated failures (or more precisely, trips) of overloaded elements caused by…