Related papers: Global Symplectic Uncertainty Propagation on SO(3)
In this paper we aim at addressing the globalization problem of Hamilton-DeDonder-Weyl equations on a local $k$-symplectic framework and we introduce the notion of {\it locally conformal $k$-symplectic (l.c.k-s.) manifolds}. This formalism…
Multisymplectic variational integrators are structure preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and…
In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power,…
The existence of global nonnegative martingale solutions to a stochastic cross-diffusion system for an arbitrary but finite number of interacting population species is shown. The random influence of the environment is modeled by a…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
An accurate characterization of pose uncertainty is essential for safe autonomous navigation. Early pose uncertainty characterization methods proposed by Smith, Self, and Cheeseman (SCC), used coordinate-based first-order methods to…
ICME approaches provide decision support for materials design by establishing quantitative process-structure-property relations. Confidence in the decision support, however, must be achieved by establishing uncertainty bounds in ICME model…
This article describes the use of symplectic cut-and-paste methods to compute Gromov-Witten invariants. Our focus is on recent advances extending these methods to Kahler surfaces with geometric genus p_g>0, for which the usual GW invariants…
A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
The ground energy level of an oscillator cannot be zero because of Heisenberg's uncertainty principle. We use methods from symplectic topology (Gromov's non-squeezing theorem, and the existence of symplectic capacities) to analyze and…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We show that the massive noncommutative U(1) theory is embedded in a gauge theory using an alternative systematic way, which is based on the symplectic framework. The embedded Hamiltonian density is obtained after a finite number of steps…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…
In this work, we show that it is possible to define a classical system associated with a Generalized Uncertainty Principle (GUP) theory via the implementation of a consistent symplectic structure. This provides a solid framework for the…