Related papers: Uncertainty, trajectories, and duality
The observation of duality by Mukherji and Mishra in one dimensional transport problems has been used to develop a general approach to classify and characterize the steady state phase diagrams. The phase diagrams are determined by the zeros…
Linear trajectory models provide mathematical advantages to autonomous driving applications such as motion prediction. However, linear models' expressive power and bias for real-world trajectories have not been thoroughly analyzed. We…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
Neural networks used for multi-interaction trajectory reconstruction lack the ability to estimate the uncertainty in their outputs, which would be useful to better analyse and understand the systems they model. In this paper we extend the…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility V of the fringes measured at the output port of the interferometer. A hierarchy of…
We show that dimensional theoretical properties of dynamical systems can considerably change because of number theoretical peculiarities of some parameter values
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
Accurately estimating uncertainties in neural network predictions is of great importance in building trusted DNNs-based models, and there is an increasing interest in providing accurate uncertainty estimation on many tasks, such as security…
Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex…
We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer…
We examine the transport behaviour of non-interacting particles in a simple channel billiard, at equilibrium and in the presence of an external field. The channel walls are constructed from straight line-segments. We observe a sensitive…
We show within a statistical model of quantization reported in the previous work based on Hamilton-Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in…
Large deviation functions of configurations exhibit very different behaviors in and out of thermal equilibrium. In particular, they exhibit singularities in a broad range of non-equilibrium models, which are absent in equilibrium. These…
We derive a semiclassical scheme for the conductance through a rectangular cavity. The transmission amplitudes are expressed as a sum over families of trajectories rather than a sum over isolated trajectories. The contributing families are…
We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…