Related papers: Critical branching processes in digital memcomputi…

Machine Learning has become a pervasive tool in climate science applications. However, current models fail to address nonstationarity induced by anthropogenic alterations in greenhouse emissions and do not routinely quantify the uncertainty…

In this article, we present the potential benefits of incorporating jumps into the dynamics of digital memcomputing machines (DMMs), which have been developed to address complex optimization problems. We illustrate the potential speed…

Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and…

This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…

We study the well-motivated problem of online distribution shift in which the data arrive in batches and the distribution of each batch can change arbitrarily over time. Since the shifts can be large or small, abrupt or gradual, the length…

We investigate the synaptic noise as a novel mechanism for creating critical avalanches in the activity of neural networks. We model neurons and chemical synapses by dynamical maps with a uniform noise term in the synaptic coupling. An…

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations…

We revisit the problem of deriving the mean-field values of avalanche critical exponents in systems with absorbing states. These are well-known to coincide with those of an un-biased branching process. Here, we show that for at least 4…

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system…

Disordered systems are characterized by the existence of many sample- dependent local energy minima, that cause a stepwise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods…

Markov chain Monte Carlo (MCMC) is a widely used sampling method in modern artificial intelligence and probabilistic computing systems. It involves repetitive random number generations and thus often dominates the latency of probabilistic…

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…

Dynamic contingency screening is a challenging task in dynamic security assessment, when traditional numerical approaches are computationally intensive and often not able to repeatedly solve full AC power flow for all possible contingencies…

In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes,…