Related papers: Nonlinear Statistical Modelling and Model Discover…

Non-invasive measurement of the arterial blood speed gives rise to important healthinformation such as cardio output and blood supplies to vital organs. The magnitude andchange in arterial blood speed are key indicators of the health…

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal…

This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian…

Mathematical models of the human heart are increasingly playing a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The aim is to aid medical practitioners diagnose and treat…

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…

Predictive modeling of blood flow and pressure have numerous applications ranging from non-invasive assessment of functional significance of disease to planning invasive procedures. While several such predictive modeling techniques have…

The dynamics of time-reversible systems are statistically indistinguishable when observed forward or backward in time. A rich literature of statistical methods to distinguish irreversible dynamics from the reversible dynamics of linear,…

Estimation of cardiovascular model parameters from electronic health records (EHR) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is…

The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…

Cardiopulmonary resuscitation (CPR) is alongside electrical defibrillation the most crucial countermeasure for sudden cardiac arrest, which affects thousands of individuals every year. In this paper, we present a novel approach including…

We consider the task of data-driven identification of dynamical systems, specifically for systems whose behavior at large frequencies is non-standard, as encoded by a non-trivial relative degree of the transfer function or, alternatively, a…

Using a three-compartment model of blood pressure dynamics, we analyze theoretically the short term cardiovascular variability: how the respiratory-related blood pressure fluctuations are buffered by appropriate heart rate changes: i.e. the…

In this work we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the random component, conditioned on the past information, follows…

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…

In this paper, we investigate induced and nonlinear fiber topological pressure for random dynamical systems. We define a non-averaged induced fiber pressure via spanning and separated sets, characterize it as the pseudo-inverse of the…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…