Related papers: Spectral Dependence

In the past few years, time series foundation models have achieved superior predicting accuracy. However, real-world time series often exhibit significant diversity in their temporal patterns across different time spans and domains, making…

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the…

Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…

The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…

The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…

In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the…

Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by…

In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…

Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…

This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…

We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…

Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…

Machine learning approaches to modelling analog audio effects have seen intensive investigation in recent years, particularly in the context of non-linear time-invariant effects such as guitar amplifiers. For modulation effects such as…

Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different…

With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…

While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent…

We develop a framework to uncover and analyze dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive data sets to eliminate erroneous data segments,…

We introduce a framework for the study of multiparty entanglement by analyzing the behavior of collective variables. Throughout the manuscript, we explore a specific type of multiparty entanglement which can be detected through the…