Related papers: Transport maps for Beta-matrix models and Universa…
In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex,…
Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…
We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX…
We study numerically an electronic transport in strongly anisotropic weakly disorderd two-dimensional systems. We find that the conductance distribution is gaussian but the conductance fluctuations increase when anisotropy becomes stronger.…
When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions…
As cities struggle to adapt to more ``people-centered'' urbanism, transportation planning and engineering must innovate to expand the street network strategically in order to ensure efficiency but also to deter sprawl. Here, we conducted a…
We propose a matrix model which embodies the semiclassical approach to the problem of quantum transport in chaotic systems. Specifically, a matrix integral is presented whose perturbative expansion satisfies precisely the semiclassical…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
Future urban transportation concepts include a mixture of ground and air vehicles with varying degrees of autonomy in a congested environment. In such dynamic environments, occupancy maps alone are not sufficient for safe path planning.…
Statistical traffic data analysis is a hot topic in traffic management and control. In this field, current research progresses focus on analyzing traffic flows of individual links or local regions in a transportation network. Less attention…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
The ability to autonomously navigate in unknown environments is important for mobile robots. The map is the core component to achieve this. Most map representations rely on drift-free state estimation and provide a global metric map to…
We investigate some statistical and transport properties of the relativistic standard map. Through the Hamiltonian of a wave packet under an electric potential, we are able to obtain a relativistic version of the standard map, where there…
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…
Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been…
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box…
Understanding the variability of people's travel patterns is key to transport planning and policy-making. However, to what extent daily transit use displays geographic and temporal variabilities, and what are the contributing factors have…
Many applications, including climate-model analysis and stochastic weather generators, require learning or emulating the distribution of a high-dimensional and non-Gaussian spatial field based on relatively few training samples. To address…