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Following the works of Newelski we continue the study of the relations between abstract topological dynamics and generalized stable group theory. We show that the Ellis theory, applied to the action of G(M) on its type space, for G an fsg…
Physics-based models are computationally time-consuming and infeasible for real-time scenarios of urban drainage networks, and a surrogate model is needed to accelerate the online predictive modelling. Fully-connected neural networks (NNs)…
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…
Under suitable conditions a flow on a torus $C^{(p)}$--close, with $p$ large enough, to a quasi periodic diophantine rotation is shown to be conjugated to the quasi periodic rotation by a map that is analytic in the perturbation size. This…
We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and…
The increasing complexity of energy systems due to sector coupling and decarbonization calls for unified modeling frameworks that capture the physical and structural interactions between electricity, gas, and heat networks. This paper…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
We use the framework of "props" to study electrical circuits, signal-flow diagrams, and bond graphs. A prop is a strict symmetric monoidal category where the objects are natural numbers, with the tensor product of objects given by addition.…
Given any possibly unbounded, locally finite link, we show that there exists a smooth diffeomorphism transforming this link into a set of stream (or vortex) lines of a vector field that solves the steady incompressible Euler equation in…
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…
The landslide flow, introduced in [5], is a smoother analog of the earthquake flow on Teichm\"uller space which shares some of its key properties. We show here that further properties of earthquakes apply to landslides. The landslide flow…
We derive a class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels, with several sources and sinks, and adaptive conductivities. The flow is controlled by…
In this paper, we establish three Arnold-type stability theorems for steady or rotating solutions of the incompressible Euler equation on a sphere. Specifically, we prove that if the stream function of a flow solves a semilinear elliptic…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.
For $p,q\ge2$ the $\{p,q\}$-tiling graph is the (finite or infinite) planar graph $T_{p,q}$ where all faces are cycles of length $p$ and all vertices have degree $q$. We give algorithms for the problem of recognizing (induced) subgraphs of…
It is well known, due to Lindstr\"om, that the minors of a (real or complex) matrix can be expressed in terms of weights of flows in a planar directed graph. Another classical fact is that there are plenty of homogeneous quadratic relations…
In this second part of the work, we correct the flaw which was left in the proof of the main Theorem in the first part. This affects only a small part of the text in this first part and two consecutive papers. Yet, some additional arguments…
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…