Related papers: Functionalising the wavefunction
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
We propose world value functions (WVFs), a type of goal-oriented general value function that represents how to solve not just a given task, but any other goal-reaching task in an agent's environment. This is achieved by equipping an agent…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a…
Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the $3\mathbf{n}$-dimensional configuration space rather than on the $3$-dimensional space has seemed uncanny to many, including Schr\"odinger, Lorentz,…
We propose a scheme to connect the wave functions on different one-dimensional branches of a three-leg junction (Y-junction). Our scheme differs from that due to Griffith [Trans. Faraday Soc. 49, 345 (1953)] in the respect that ours can…
The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
In this work we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly…
Rovelli's relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute, but it is relative to the observer itself. The interpretation goes further and…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
The purpose of this paper is to present new classes of function systems as part of multiresolution analyses. Our approach is representation theoretic, and it makes use of generalized multiresolution function systems (MRSs). It further…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…
We discuss the concept of a mesoscopic wavefunction, first in a general context, as the concept of wavefunction has evolved, and then in a more specific context of modeling. The paper concentrates on a simple, abstract one-dimensional…