相关论文: Variational Analysis of Landscape Elevation and Dr…
The onset of life is often framed around membrane bound compartments and encoded metabolism, leaving unresolved how spatial organization arose before stable boundaries. In this context, environmental gradients are usually treated as…
We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a non-equilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of…
Landslides, movement of soil and rock under the influence of gravity, are common phenomena that cause significant human and economic losses every year. Experts use heterogeneous features such as slope, elevation, land cover, lithology, rock…
Surfacic networks are structures built upon a two-dimensional manifold. Many systems, including transportation networks and various urban networks, fall into this category. The fluctuations of node elevations imply significant deviations…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…
We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has…
It has previously been shown that the network of connected minima on a potential energy landscape is scale-free, and that this reflects a power-law distribution for the areas of the basins of attraction surrounding the minima. Here, we set…
A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $\phi$ where $\phi=0$ and $1$ represent a regular lattice and a random network respectively. In the…
An integro-differential equation on a tree graph is used to model the evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an…
In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. We consider a two-component…
We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid is governed by the incompressible quasi-steady Stokes…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…
We report a Lagrangian study on the evolution of material surfaces in the K-type temporal transitional channel flow. Based on the Eulerian velocity field from the DNS, a backward-particle-tracking method is applied to solve the transport…