Related papers: Wave propagation phenomena in nonlinear hierarchic…

We study signal propagation in linear recurrent models at finite width. While existing signal propagation theory relies predominantly on the infinite-width limit, it remains unclear for how long that approximation remains accurate when…

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a…

Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave…

In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in…

We develop a computing framework that leverages wave propagation within an interconnected network, where nodes and edges possess wave manipulation capabilities, such as frequency mixing or time delay. This computing paradigm can not only…

We present a novel approach to achieve adaptable band structures and non-reciprocal wave propagation by exploring and exploiting the concept of metastable modular metastructures. Through studying the dynamics of wave propagation in a chain…

This paper studies the problem of learning message propagation strategies for graph neural networks (GNNs). One of the challenges for graph neural networks is that of defining the propagation strategy. For instance, the choices of…

The Linear Threshold Model is a widely used model that describes how information diffuses through a social network. According to this model, an individual adopts an idea or product after the proportion of their neighbors who have adopted it…

For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…

Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…

Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the…

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social…

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable,…

We study the problems of estimating the past and future evolutions of two diffusion processes that spread concurrently on a network. Specifically, given a known network $G=(V, \overrightarrow{E})$ and a (possibly noisy) snapshot…