Related papers: The Optimal Form of Distribution Networks Applied …
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi, and animals. By combining machine-learning techniques with new theory that relates vascular form to…
We present a systematic theoretical framework that interprets masked diffusion models (MDMs) as solutions to energy minimization problems in discrete optimal transport. Specifically, we prove that three distinct energy…
We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized.…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing…
Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
Endowing brain anatomy, dynamics, and function with a network structure is becoming standard in neuroscience. In its simplest form, a network is a collection of units and relationships between them. The pattern of relations among the units…
For the problem of efficiently supplying material to a spatial region from a single source, we present a simple scaling argument based on branching network volume minimization that identifies limits to the scaling of sink density. We…
Metabolic allometry, a common pattern in nature, is a close-to-3/4-power scaling law between metabolic rate and body mass in organisms, across and within species. An analogous relationship between metabolic rate and water volume in river…
We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of…
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
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…
The efficient computation of shortest paths in complex networks is essential to face new challenges related to critical infrastructures such as a near real-time monitoring and control and the management of big size systems. In particular,…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…