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Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions…
In this paper, we consider the optimal power flow (OPF) problem which consists in determining the power production at each bus of an electric network by minimizing the production cost. Our contribution is an exact solution algorithm for the…
We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…
In this paper, we focus our attention on the large capacities unsplittable flow problem in a game theoretic setting. In this setting, there are selfish agents, which control some of the requests characteristics, and may be dishonest about…
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…
We develop a general approach for designing scheduling policies for real-time traffic over wireless channels. We extend prior work, which characterizes a real-time flow by its traffic pattern, delay bound, timely-throughput requirement, and…
The prediction non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network…
Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…
We study a variant of Min Cost Flow in which the flow needs to be connected. Specifically, in the Connected Flow problem one is given a directed graph $G$, along with a set of demand vertices $D \subseteq V(G)$ with demands $\mathsf{dem}: D…
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…
In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice…
We present a theory for slicing probabilistic imperative programs -- containing random assignments, and ``observe'' statements (for conditioning) -- represented as probabilistic control-flow graphs (pCFGs) whose nodes modify probability…
The support of a flow $x$ in a network is the subdigraph induced by the arcs $uv$ for which $x(uv)>0$. We discuss a number of results on flows in networks where we put certain restrictions on structure of the support of the flow. Many of…