Related papers: Spectral Dependence
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
Effective multivariate time series forecasting often benefits from accurately modeling complex inter-variable dependencies. However, existing attention- or graph-based methods face three key issues: (a) strong temporal self-dependencies are…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models…
Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…
Parametric copula families have been known to flexibly capture various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. In this paper, our objective is to…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We discuss Bayesian forecasting of increasingly high-dimensional time series, a key area of application of stochastic dynamic models in the financial industry and allied areas of business. Novel state-space models characterizing sparse…
Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
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…
Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
We present a general approach for studying autoregressive categorical time series models with dependence of infinite order and defined conditional on an exogenous covariate process. To this end, we adapt a coupling approach, developed in…
The purpose of this paper to analyze in some detail the arguably simplest case of diversity-induced reseonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…