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We study the statistics of growing networks in which each link carries a weight (k_i k_j)^theta, where k_i and k_j are the node degrees at the endpoints of link ij. Network growth is governed by preferential attachment in which a…
This article generalizes the study of ramified optimal transport with capacity constraint in transport multi-paths by generalizing the $\mathbf{M}_{\alpha}$ cost to $\mathbf{M}_{\alpha,c}$, which incorporates capacity constraints into the…
Recently, the interpretability of deep learning has attracted a lot of attention. A plethora of methods have attempted to explain neural networks by feature visualization, saliency maps, model distillation, and so on. However, it is hard…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
To make machine learning (ML) sustainable and apt to run on the diverse devices where relevant data is, it is essential to compress ML models as needed, while still meeting the required learning quality and time performance. However, how…
Networks created and maintained by social processes, such as the human friendship network and the World Wide Web, appear to exhibit the property of navigability: namely, not only do short paths exist between any pair of nodes, but such…
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness…
We present a unified analytical framework within which power control, rate allocation, routing, and congestion control for wireless networks can be optimized in a coherent and integrated manner. We consider a multi-commodity flow model with…
Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…
We consider the optimal paths in a $d$-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential.…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the…
We study a network design problem (NDP) where the planner aims at selecting the optimal single-link intervention on a transportation network to minimize the travel time under Wardrop equilibrium flows. Our first result is that, if the delay…
Energy saving is becoming an important issue in the design and use of computer networks. In this work we propose a problem that considers the use of rate adaptation as the energy saving strategy in networks. The problem is modeled as an…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges.…
Motivated by potential applications in power systems, we study a problem of optimizing a sum of $n$ convex functions on dynamic networks of $n$ nodes when each function is known to only a single node. The nodes' variables, while satisfy…
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…
This paper presents a new method for finding the node-disjoint paths with maximum combined bandwidth in communication networks. This problem is an NP-complete problem which can be optimally solved in exponential time using integer linear…