Related papers: Maximizing the algebraic connectivity in multilaye…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…
Large-scale low-Earth-orbit satellite constellations offer a promising platform for global low-latency networking, aided by faster propagation in free space than in fiber and copper. In such systems, end-to-end latency is largely determined…
We investigate the optimization of synchronizability in multiplex networks and demonstrate that the interlayer coupling strength is the deciding factor for the efficiency of optimization. The optimized networks have homogeneity in the…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
The largest eigenvalue of a network provides understanding to various dynamical as well as stability properties of the underlying system. We investigate an interplay of inhibition and multiplexing on the largest eigenvalue statistics of…
The empirical results suggest that the learnability of a neural network is directly related to its size. To mathematically prove this, we borrow a tool in topological algebra: Betti numbers to measure the topological geometric complexity of…
This paper considers a mobile edge computing-enabled cell-free massive MIMO wireless network. An optimization problem for the joint allocation of uplink powers and remote computational resources is formulated, aimed at minimizing the total…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
An overarching objective in contemporary statistical network analysis is extracting salient information from datasets consisting of multiple networks. To date, considerable attention has been devoted to node and network clustering, while…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
Adding edges between layers of interconnected networks is an important way to optimize the spreading dynamics. While previous studies mostly focus on the case of adding a single edge, the theoretical optimal strategy for adding multiple…
In this work, we address the problem of multi-domain image-to-image translation with particular attention paid to computational cost. In particular, current state of the art models require a large and deep model in order to handle the…
Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…
A class of graphs is bridge-addable if given a graph $G$ in the class, any graph obtained by adding an edge between two connected components of $G$ is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, that says that…
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…
This correspondence considers the resource allocation problem in wireless interference channel (IC) under link outage constraints. Since the optimization problem is non-convex in nature, existing approaches to find the optimal power…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…