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We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\mu$, admits a density over $\mathbb{R}^d$. For a semi-concave cost function…

Optimization and Control · Mathematics 2025-07-21 Lénaïc Chizat , Alex Delalande , Tomas Vaškevičius

We study the optimal distance in networks, $\ell_{\scriptsize opt}$, defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For…

Soft Condensed Matter · Physics 2007-05-23 Lidia A. Braunstein , Sergey V. Buldyrev , Reuven Cohen , Shlomo Havlin , H. Eugene Stanley

This paper considers the jointly optimal pilot and data power allocation in single-cell uplink massive multiple-input-multiple-output (MIMO) systems. Using the spectral efficiency (SE) as performance metric and setting a total energy budget…

Information Theory · Computer Science 2026-04-28 Hei Victor Cheng , Emil Björnson , Erik G. Larsson

Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$…

Physics and Society · Physics 2016-01-20 A. J. E. M. Janssen , Johan S. H. van Leeuwaarden

We consider navigation or search schemes on networks which have a degree distribution of the form $P(k) \propto \exp(-k^\gamma)$. In addition, the linking probability is taken to be dependent on social distances and is governed by a…

Physics and Society · Physics 2009-11-13 Parongama Sen

We consider a model for complex networks that was recently proposed as a model for complex networks by Krioukov et al. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at…

Probability · Mathematics 2026-01-14 Tobias Müller , Merlijn Staps

Using deep neural networks to predict the solutions of AC optimal power flow (ACOPF) problems has been an active direction of research. However, because the ACOPF is nonconvex, it is difficult to construct a good data set that contains…

Systems and Control · Electrical Eng. & Systems 2021-10-06 Ling Zhang , Baosen Zhang

The scaling laws guiding modern model training were calibrated for a single regime: data-rich, single-epoch pretraining. The dominant such scaling law form, Chinchilla's $L = E + A/N^\alpha + B/D^\beta$, has three structural limitations…

Machine Learning · Computer Science 2026-05-12 Christopher M. Bryant , Hao Liu

In the last three decades, researchers have tried to establish universal patterns about the structure of food webs. Recently was proposed that the exponent $\eta$ characterizing the efficiency of the energy transportation of the food web…

Statistical Mechanics · Physics 2007-05-23 L. A. Barbosa , A. Castro e Silva , J. Kamphorst Leal da Silva

We study an NP-hard problem motivated by energy-efficiently maintaining the connectivity of a symmetric wireless communication network: Given an edge-weighted $n$-vertex graph, find a connected spanning subgraph of minimum cost, where the…

Data Structures and Algorithms · Computer Science 2022-03-23 Matthias Bentert , René van Bevern , André Nichterlein , Rolf Niedermeier , Pavel V. Smirnov

We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are…

Probability · Mathematics 2016-09-05 Nikolaos Fountoulakis , Tobias Müller

This article generalizes the study of branched/ramified optimal transportation to those with capacity constraints. Each admissible transport network studied here is represented by a transport multi-path between measures, with a capacity…

Optimization and Control · Mathematics 2024-02-13 Qinglan Xia , Haotian Sun

Despite its importance for practical applications, not much is known about the optimal shape of a network that connects in an efficient way a set of points. This problem can be formulated in terms of a multiplex network with a fast layer…

Physics and Society · Physics 2023-11-13 Siddharth Patwardhan , Marc Barthelemy , Sirag Erkol , Santo Fortunato , Filippo Radicchi

The work of Avestimehr et al. '07 has recently proposed a deterministic model for wireless networks and characterized the unicast capacity C of such networks as the minimum rank of the adjacency matrices describing all possible…

Information Theory · Computer Science 2010-10-08 Cuizhu Shi , Aditya Ramamoorthy

For a random walk on a network, the mean first-passage time from a node $i$ to another node $j$ chosen stochastically according to the equilibrium distribution of Markov chain representing the random walk is called Kemeny constant, which is…

Statistical Mechanics · Physics 2013-01-17 Zhongzhi Zhang , Yibin Sheng , Zhengyi Hu , Guanrong Chen

The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved…

Systems and Control · Electrical Eng. & Systems 2022-11-15 Shravan Mohan

The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is…

Differential Geometry · Mathematics 2018-08-15 Martin Kell , Stefan Suhr

We consider a variety of NP-Complete network connectivity problems. We introduce a novel dual-based approach to approximating network design problems with cut-based linear programming relaxations. This approach gives a $3/2$-approximation…

Data Structures and Algorithms · Computer Science 2017-07-24 Benjamin Grimmer

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…

Other Condensed Matter · Physics 2009-11-10 G. Paul , T. Tanizawa , S. Havlin , H. E. Stanley

We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest…

Optimization and Control · Mathematics 2025-04-01 Quang Minh Bui , Bernard Gendron , Margarida Carvalho