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A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
The beta distribution serves as a canonical tool for modeling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent…
Congestion in transport networks is a topic of theoretical interest and practical importance. In this paper we study the flow of vehicles in urban street networks. In particular, we use a cellular automata model to simulate the motion of…
We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic…
This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell^{1}$. We also point…
The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of topological nature; more specifically, we show that convexity follows if the map is open onto…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
Bayes additive regression trees(BART) is a nonparametric regression model which has gained wide -spread popularity in recent years due to its flexibility and high accuracy of estimation .In spatio-temporal related model,the spatio or…
We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions…
We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…
Resolving a conjecture of von Neumann, Ogata's theorem in arXiv:1111.5933 showed the highly nontrivial result that arbitrarily many matrices corresponding to macroscopic observables with $N$ sites and a fixed site dimension $d$ are…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Algorithms for motion planning in unknown environments are generally limited in their ability to reason about the structure of the unobserved environment. As such, current methods generally navigate unknown environments by relying on…
Epidemics are emergent phenomena depending on the epidemiological characteristics of pathogens and the interaction and movement of people. Public transit systems have provided much important information about the movement of people, but…
We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
Traffic prediction is a crucial topic because of its broad scope of applications in the transportation domain. Recently, various studies have achieved promising results. However, most studies assume the prediction locations have complete or…