Related papers: A geometric analysis of nonlinear dynamics and its…
We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore…
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
This article is devoted to the mathematical study of a new Navier-Stokes-alpha model with a nonlinear filter equation. For a given indicator function, this filter equation was first considered by W. Layton, G. Rebholz, and C. Trenchea to…
The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…
We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to…
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the…
We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of…
The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
We consider a stochastic perturbation of the phase field alpha-Navier-Stokes model with vesicle-fluid interaction. It consists in a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction…
Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
We consider set of functions on Poisson manifold related by continues one-parameter group of transformations. Class of vector fields that produce involutive families of functions is investigated and relationship between these vector fields…
A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of…
Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow…
The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…
We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…