Related papers: Functionalising the wavefunction
The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…
A recurring task in image processing, approximation theory, and the numerical solution of partial differential equations is to reconstruct a piecewise-smooth real-valued function f(x) in multiple dimensions from its truncated Fourier…
In Information Retrieval (IR), whether implicitly or explicitly, queries and documents are often represented as vectors. However, it may be more beneficial to consider documents and/or queries as multidimensional objects. Our belief is this…
A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are…
The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
Among the various attempts to formulate a theory of quantum gravity, a class of approaches suggests that spacetime, as modeled by general relativity, is destined to fade away. A major issue becomes then to identify which structures may…
The precise definition of causality is currently an open problem in philosophy and statistics. We believe causality should be defined as functions (in mathematics) that map causes to effects. We propose a reductive definition of causality…
Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…
The structure function is a useful quantity to characterize wavefront distortions. We derive expressions for the structure functions of the averaged wavefront phase and slopes. The expressions are valid within the inertial range of…
Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…
This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…
A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
Functional epistemology is about ways to access functional objects by using varieties of methods and procedures. Not all such means are equally capable of reproducing these functions in the desired consistency and resolution. Dyson's…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
In representation learning, a disentangled representation is highly desirable as it encodes generative factors of data in a separable and compact pattern. Researchers have advocated leveraging disentangled representations to complete…