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We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…
We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
When it comes to clinical survival trials, regulatory restrictions usually require the application of methods that solely utilize baseline covariates and the intention-to-treat principle. Thereby a lot of potentially useful information is…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
This thesis presents the theoretical, conceptual and methodological aspects that support the modeling of dynamical systems (DS) by using several agents. The modeling approach permits the assessment of properties representing order, change,…
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…
When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction, and…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
The paper deals with the estimation of a signal model in the form of the output of a continuous linear time-invariant system driven by a sequence of instantaneous impulses, i.e. an impulsive time series. This modeling concept arises in,…
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…
The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with…
The main objective of this paper is the construction of the solution of an impulsive stochastic differential equation, subject to control conditions in the pulse-times and give sufficient conditions for them to be random variables with…
The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations…
Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data…
Athletic training is characterized by physiological systems responding to repeated exercise-induced stress, resulting in gradual alterations in the functional properties of these systems. The adaptive response leading to improved…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…