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Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
We develop a technique to formulate quantum field theory on arbitrary network, based on different, randomly disposed sets of scattering's. We define R-matrix of the whole network as a product of R-matrices attached to each of scattering…
The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust…
Given the ever-increasing computational costs of modern machine learning models, we need to find new ways to reuse such expert models and thus tap into the resources that have been invested in their creation. Recent work suggests that the…
This overview presents a collection of results from classical electrical network theory concerning properties of the network admittance matrix, and the relationship between electrical characteristics of the network and various mathematical…
We present a general and flexible procedure which allows for the reduction (or expansion) of any dynamical network while preserving the spectrum of the network's adjacency matrix. Computationally, this process is simple and easily…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
Multilayer networks have been widely used to represent and analyze systems of interconnected entities where both the entities and their connections can be of different types. However, real multilayer networks can be difficult to analyze…
We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…
Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…
This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…
We describe modeling approaches to a "network" of connected enzyme-catalyzed reactions, with added (bio)chemical processes that introduce biochemical filtering steps into the functioning of such a biocatalytic cascade. Theoretical…
Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…
Understanding and learning the characteristics of network paths has been of particular interest for decades and has led to several successful applications. Such analysis becomes challenging for urban networks as their size and complexity…
This paper introduces a formal definition of the transfer ABCD parameters in time-varying electromagnetic systems. The formal definition comes after the rearrangement of the fields $D$ and $B$ at the inputs and outputs of the temporal…
We establish a link between quantum mechanical molecular simulations and the transfer matrix of a molecule. The transfer matrix (T-matrix) of an object provides a complete description of its electromagnetic response. Once the T-matrices of…
A system of 'telegrapher's' equations for a number of long lines joined into a network is studied. Explicit formulas for Fourier transforms of current and voltage are derived. These formulas are very suitable for computer application as…
Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…