Related papers: Kleinberg navigation on anisotropic lattices
We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…
Navigation in complex and noisy environments is a key issue in diverse fields from biology to engineering. Despite extensive progress in numerical optimization methods for computing navigation policies, insights into how disorder reshapes…
We study the non-equilibrium transport properties of a highly anisotropic two-dimensional lattice of spin-1/2 particles governed by a Heisenberg XXZ Hamiltonian. The anisotropy of the lattice allows us to approximate the system at finite…
We consider the Ginzburg-Landau energy for a type-I superconductor in the shape of an infinite three-dimensional slab, with two-dimensional periodicity, with an applied magnetic field which is uniform and perpendicular to the slab. We…
Lattice gauge theory's discretization of spacetime suffers from a drawback in that Lorentz covariance is lost because the axes of the lattice create preferred directions in spacetime. Smaller and smaller lattice spacings decrease the effect…
We present and study lattice and off-lattice microscopic models in which particles interact via a local anisotropic rule. The rule induces preferential hopping along one direction, so that a net current sets in if allowed by boundary…
We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $\tilde\Omega (L \cdot r \cdot d_{\mathrm{out}} \cdot \kappa^3 )$, where $r$ and $\kappa$ are the rank and the condition number of…
In this work, we initiate the study of controlling nonlinear Klein-Gordon chains and lattices through their emergent collective flocking behavior. By constructing appropriate feedback control mechanisms, we demonstrate that any physically…
We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…
One of the key features of small-worlds is the ability to route messages with few hops only using local knowledge of the topology. In 2000, Kleinberg proposed a model based on an augmented grid that asymptotically exhibits such property. In…
Continuing in the steps of Jon Kleinberg's and others celebrated work on decentralized search in small-world networks, we conduct an experimental analysis of a dynamic algorithm that produces small-world networks. We find that the algorithm…
We consider the adaptive routing problem in multihop wireless networks. The link states are assumed to be random variables drawn from unknown distributions, independent and identically distributed across links and time. This model has…
In this paper we consider a nonlocal energy $I_\alpha$ whose kernel is obtained by adding to the Coulomb potential an anisotropic term weighted by a parameter $\alpha\in \R$. The case $\alpha=0$ corresponds to purely logarithmic…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
The throughput of submarine transport cables is approaching fundamental limits imposed by amplifier noise and Kerr nonlinearity. Energy constraints in ultra-long submarine links exacerbate this problem, as the throughput per fiber is…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
We consider nontrivial finite energy traveling waves for the Landau-Lifshitz equation with easy-plane anisotropy. Our main result is the existence of a minimal energy for these traveling waves, in dimensions two, three and four. The proof…
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…
Network infrastructures are essential for the distribution of resources such as electricity and water. Typical strategies to assess their resilience focus on the impact of a sequence of random or targeted failures of network nodes or links.…