Related papers: A multivariate phase distribution and its estimati…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
Multivariate phase relationships are important to characterize and understand numerous physical, biological, and chemical systems, from electromagnetic waves to neural oscillations. These systems exhibit complex spatiotemporal dynamics and…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Objective. We identify two linked problems related to estimating the phase of the alpha rhythm when the signal after a specific event is unknown (real-time case), or corrupted (offline analysis). We propose methods to estimate the phase…
Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
Assume that we observe a large number of curves, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective…
Correlating neural communication in brain networks with behavior and cognition can provide fundamental insights into the functionality of both healthy and diseased brains. We demonstrate how communication in the brain can be estimated from…
Many real-world systems are often regarded as weakly coupled limit-cycle oscillators, in which each oscillator corresponds to a dynamical system with many degrees of freedom that have collective oscillations. One of the most practical…
In this paper, we consider the relationship between phase-type distributions and positive systems through practical examples. Phase-type distributions, commonly used in modelling dynamic systems, represent the temporal evolution of a set of…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al.…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
The major sources of abundant data are constantly expanding with the available data collection methodologies in various applications - medical, insurance, scientific, bio-informatics and business. These data sets may be distributed…
The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…