Related papers: Integrable discretizations of the SIR model
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…
In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning…
An ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals based on theire hierarchical clustering relativly to the average time of infectious contact is…
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved…
Consider the macroscale modelling of microscale spatiotemporal dynamics. Here we develop a new approach to ensure coarse scale discrete models preserve important self-adjoint properties of the fine scale dynamics. The first part explores…
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
Structural and practical parameter non-identifiability issues are common when mathematical models are used to interpret data. Such issues motivate model reparameterisation and reduction methods. Here, we consider Invariant Image…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
We introduce conservative curved systems over multiply connected domains and study relationships of such systems with related notions of functional model, characteristic function, and transfer function. In contrast to standard theory for…
Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our…
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…
Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…