Related papers: Fluctuations and redundancy in optimal transport n…
Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade…
We investigate the optimal design of networks for a general transport system. Our network is built from a regular two-dimensional ($d=2$) square lattice to be improved by adding long-range connections (shortcuts) with probability $P_{ij}…
This mini-course was given in the First Yaroslavl Summer School on Discrete and Computational Geometry in August 2012, organized by International Delaunay Laboratory "Discrete and Computational Geometry" of Demidov Yaroslavl State…
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore,…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
River networks exhibit a complex ramified structure that has inspired decades of studies. Yet, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
Ensuring robustness and resilience in intermodal transportation systems is essential for the continuity and reliability of global logistics. These systems are vulnerable to various disruptions, including natural disasters and technical…
Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media…
We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the model, we derive exact expressions for all…
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…
The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to…
Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a…
A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…
We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…
Networks are designed to satisfy given objectives under specific requirements. While the static connectivity of networks is normally analyzed and corresponding design principles for static robustness are proposed, the challenge still…