Related papers: Networks with complex weights: Green function and …

We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…

We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…

In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…

This work analyzes the convergence properties of signed networks with nonlinear edge functions. We consider diffusively coupled networks comprised of maximal equilibrium-independent passive (MEIP) dynamics on the nodes, and a general class…

The ability to control complex networks is of crucial importance across a wide range of applications in natural and engineering sciences. However, issues of both theoretical and numerical nature introduce fundamental limitations to…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and…

Transport properties of 2D materials especially close to their boundary has received much attention after the successful fabrication of graphene and other fascinating materials afterwards. While most previous work is devoted to the…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

I review the application of self-consistent Green's functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of…

We study questions related to critical points of the Green's function of a bounded multiply connected domain in the complex plane. The motion of critical points, their limiting positions as the pole approaches the boundary and the…

We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

Many applications in network science have recently been discovered for the "curvature" of a network, but there is no consensus on the definition for this term. A common approach in these applications is to derive from the curvature either a…

We discuss the general form of the transmission spectrum through a molec- ular junction in terms of the Green function of the isolated molecule. By introducing a tight binding method, we are able to translate the Green func- tion properties…

We propose an efficient and interpretable neural network with a novel activation function called the weighted Lehmer transform. This new activation function enables adaptive feature selection and extends to the complex domain, capturing…

Analysing and computing with Gaussian processes arising from infinitely wide neural networks has recently seen a resurgence in popularity. Despite this, many explicit covariance functions of networks with activation functions used in modern…

It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…

The development of methods to guide the design of neural networks is an important open challenge for deep learning theory. As a paradigm for principled neural architecture design, we propose the translation of high-performing kernels, which…