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Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
Motivated by studies of stochastic systems describing non-equilibrium dynamics of (real-valued) spins of an infinite particle system in $\mathbb{R}^n$ we consider a row-finite system of stochastic differential equations with dissipative…
Many dynamic applications are built upon large network infrastructures, such as social networks, communication networks, biological networks and the Web. Such applications create data that can be naturally modeled as graph streams, in which…
We study exact solutions for the slow viscous flow of an infinite liquid caused by two rigid spheres approaching each either along or parallel to their line of centres, valid at all separations. This goes beyond the applicable range of…
In this paper we introduce the concept of Direct Statistical Simulation (DSS) for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous…
Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
The usual explicit finite-difference method of solving partial differential equations is limited in stability because it approximates the exact amplification factor by power-series. By adapting the same exponential-splitting method of…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
Finding image correspondences remains a challenging problem in the presence of intra-class variations and large changes in scene layout.~Semantic flow methods are designed to handle images depicting different instances of the same object or…
After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two methods to deal with the existence of solutions for this…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
Diffusion models achieve high-quality image generation but are limited by slow iterative sampling. Distillation methods alleviate this by enabling one- or few-step generation. Flow matching, originally introduced as a distinct framework,…
While studying gradient dynamical systems (DSs), Morse introduced the idea of encoding the qualitative behavior of a DS into a graph. Smale later refined Morse's idea and extended it to Axiom-A diffeomorphisms on manifolds. In Smale's…