Related papers: AC-Feasibility on Tree Networks is NP-Hard
Designing fare systems for public transportation networks is a challenging task. A popular approach is to partition the network into fare zones (``zoning'') and fix journey prices depending on the number of traversed zones (``pricing''). In…
This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex…
A temporal graph is a graph whose edges appear at certain points in time. These graphs are temporally connected (in class TC) if all vertices can reach each other by temporal paths (traversing the edges in chronological order). Reachability…
Linear networks provide valuable insights into the workings of neural networks in general. This paper identifies conditions under which the gradient flow provably trains a linear network, in spite of the non-strict saddle points present in…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
We consider the problem of optimally compressing and caching data across a communication network. Given the data generated at edge nodes and a routing path, our goal is to determine the optimal data compression ratios and caching decisions…
Network connectedness is indispensable for the normal operation of transmission networks. However, there still remains a lack of efficient constraints that can be directly added to the problem formulation of optimal transmission switching…
With the increasing inclusion of regenerative resources in the energy mix, their intermittent character challenges power grid stability. Hence it is essential to determine which input fluctuations power grids are particularly vulnerable to.…
Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow…
This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various…
The increasing penetration of renewable energy resources, paired with the fact that load can vary significantly, introduce a high degree of uncertainty in the behavior of modern power grids. Given that classical dispatch solutions are…
Here we show that deciding whether two rooted binary phylogenetic trees on the same set of taxa permit a cherry-picking sequence, a special type of elimination order on the taxa, is NP-complete. This improves on an earlier result which…
A weakness of next-hop routing is that following a link or router failure there may be no routes between some source-destination pairs, or packets may get stuck in a routing loop as the protocol operates to establish new routes. In this…
To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits…
A major outage in the electricity distribution system may affect the operation of water and natural gas supply systems, leading to an interruption of multiple services to critical customers. Therefore, enhancing resilience of critical…
With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC…
We examine the convexity and tractability of the two-sided linear chance constraint model under Gaussian uncertainty. We show that these constraints can be applied directly to model a larger class of nonlinear chance constraints as well as…
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for…
Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC…
A complex network approach on a rough fracture is developed. In this manner, some hidden metric spaces (similarity measurements) between apertures profiles are set up and a general evolutionary network in two directions (in parallel and…