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Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, {\em but also} by directly…
Wildfires pose an increasing threat to the safety and reliability of power systems, particularly in distribution networks located in fire-prone regions. To mitigate ignition risk from electrical infrastructure, utilities often employ safety…
The global financial system can be represented as a large complex network in which banks, hedge funds and other financial institutions are interconnected to each other through visible and invisible financial linkages. Recently, a lot of…
Combustion reaction kinetics models are used for the description of a special class of bursty Financial Time Series. The small number of parameters they depend upon enable financial analysts to predict the time as well as the magnitude of…
We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…
We present a financial market model, characterized by self-organized criticality, that is able to generate endogenously a realistic price dynamics and to reproduce well-known stylized facts. We consider a community of heterogeneous traders,…
Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of…
Fire is an indissoluble component of ecosystems, however quantifying the effects of fire on vegetation is challenging task as fire lies outside the typical experimental design attributes. A recent simulation study showed that under…
Our planet is facing increasingly frequent extreme events, which pose major risks to human lives and ecosystems. Recent advances in machine learning (ML), especially with foundation models (FMs) trained on extensive datasets, excel in…
The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network…
As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and…
The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…
The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
The scope of this work is to serve as a guiding tool against subjective estimations on real pandemic situations (mainly due to the inability to acquire objective real data over whole populations). The previously introduced model of closed…
Risks threatening modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about how risk materializations in distinct domains influence each other. Here we present an approach…
This paper develops the Jungle model in a credit portfolio framework. The Jungle model is able to model credit contagion, produce doubly-peaked probability distributions for the total default loss and endogenously generate quasi phase…
Why do capitalist economies recurrently generate crises whose severity is disproportionate to the size of the triggering shock? This paper proposes a structural answer grounded in the evolutionary geometry of production networks. As…