相关论文: A mathematical approach to resilience

Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…

Health-policy planning requires evidence on the burden that epidemics place on healthcare systems. Multiple, often dependent, datasets provide a noisy and fragmented signal from the unobserved epidemic process including transmission and…

We address the issue of resilience of the Atlantic Meridional Overturning Circulation (AMOC) given the many indications that this dynamical system is in a multi-stable regime. A novel approach to resilience based on rare event techniques is…

At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…

We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as…

Numeracy is the ability to understand and work with numbers. It is a necessary skill for composing and understanding documents in clinical, scientific, and other technical domains. In this paper, we explore different strategies for…

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems,…

A full accounting of biological robustness remains elusive; both in terms of the mechanisms by which robustness is achieved and the forces that have caused robustness to grow over evolutionary time. Although its importance to topics such as…

Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…

Desirable system performance in the face of threats and disruptions has been characterized by various management concepts. Through semi-structured interviews with editors of journals in the fields of emergency response and systems…

Robustness analysis is an emerging field in the domain of uncertainty quantification. It consists of analysing the response of a computer model with uncertain inputs to the perturbation of one or several of its input distributions. Thus, a…

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…

We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding…

We investigate the minimal number of failures that can partition a system where processes communicate both through shared memory and by message passing. We prove that this number precisely captures the resilience that can be achieved by…

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…

We address the problem of distributed state estimation of a linear dynamical process in an attack-prone environment. Recent attempts to solve this problem impose stringent redundancy requirements on the measurement and communication…

Statistics experiences a storm around the perceived misuse and possible abuse of its methods in the context of the so-called reproducibility crisis. The methods and styles of quantification practiced in mathematical modelling rarely make it…

Resilience has emerged as a crucial concept for evaluating structural performance under disasters because of its ability to extend beyond traditional risk assessments, accounting for a system's ability to minimize disruptions and maintain…

The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…

There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…