Related papers: Noisy-chaotic time series and the forbidden/missin…

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…

We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…

On time-series data, most causal discovery methods fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information which is lost when following this approach.…

Quantifying relationships between components of a complex system is critical to understanding the rich network of interactions that characterize the behavior of the system. Traditional methods for detecting pairwise dependence of time…

Using the Bak-Sneppen model of biological evolution as our paradigm, we investigate in which cases noise can be substituted with a deterministic signal without destroying Self-Organized Criticality (SOC). If the deterministic signal is…

This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…

This paper considers how to classify the effects of interventions in causal models for outcomes and exposures observed over time. First, we demonstrate the limitations of the most common uses of potential outcomes and causal directed…

Irregular multivariate time series with missing values present significant challenges for predictive modeling in domains such as healthcare. While deep learning approaches often focus on temporal interpolation or complex architectures to…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

Quantum graphs with leads to infinity serve as convenient models for studying various aspects of systems which are usually attributed to chaotic scattering. They are also studied in several experimental systems and practical applications.…

We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time…

We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…

Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to…

We investigate Turing pattern formation in a stochastic reaction-diffusion model defined on $N$ lattice sites, where each lattice site is associated with a reaction vessel of volume $\Omega$. We focus on a regime where spatial discreteness…

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…

We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear. randomly. Using a constructive transition approach that predicts large outbreaks, prior to their occurrence, we derive an adaptive control.…

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used…

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…