Related papers: Conversions between Electrical Network Representat…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data.…
For a network consisting of a graph with edge weights prescribed by a given conductance function $c$, we consider the effects of replacing these weights with a new function $b$ that satisfies $b \leq c$ on each edge. In particular, we…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
Regulatory interactions between genes show a large amount of cross-species variability, even when the underlying functions are conserved: There are many ways to achieve the same function. Here we investigate the ability of regulatory…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
In power system dynamic simulation, up to 90% of the computational time is devoted to solve the network equations, i.e., a set of linear equations. Traditional approaches are based on sparse LU factorization, which is inherently sequential.…
The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…
In this letter, we consider a typical scenario where the transmitter employs different power adaption methods, including the optimal rate and power algorithm, optimal rate adaption, channel inversion and truncated channel inversion, to…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…
We provide an overview of methods for designing and implementing experiments (field, lab, hybrid, and natural) when there are networks of interactions between subjects.
Power cables have complex geometries in order to reduce their ac resistance. Although there are many different cable designs, most have in common that their inner conductors' cross-section is divided into several electrically insulated…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…
How can we effectively find the best structures in tree models? Tree models have been favored over complex black box models in domains where interpretability is crucial for making irreversible decisions. However, searching for a tree…
Social network position confers power and social capital. In the setting of online social networks that have massive reach, creating mathematical representations of social capital is an important step towards understanding how network…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and…