Related papers: Holography, Pade Approximants and Deconstruction
Despite a recent flurry of applications of the broadly defined ('non-AdS/non-CFT') holographic correspondence to a variety of condensed matter problems, the status of this intriguing, yet speculative, approach remains largely undetermined.…
We provide a concrete link between celestial amplitudes and cosmological correlators. We first construct a map from quantum field theories (QFTs) in $(D+2)$-dimensional Euclidean space to theories on the $(D+1)$-dimensional sphere, through…
This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are…
This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…
The Runge approximation theorem for holomorphic maps (U -> C) is a fundamental result in complex analysis. The aim of this article is to prove such a result for (pseudo-)holomorphic maps from a compact Riemann surface to a compact…
Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…
In this paper, we compute a conservative approximation of the path-connected components of the free space of a rigid object in a 2D workspace in order to solve two closely related problems: to determine whether there exists a collision-free…
Digital holography numerically restores three-dimensional image information using optically captured diffractive waves. The required bandwidth is larger than that of hologram pixel at a closer distance in the Fresnel diffraction regime,…
This dissertation represents work on three different subjects relating to quantum gravity and the AdS/CFT correspondence. First, we review a holographic computation of the one-loop corrections to the Weyl anomaly on Ricci flat backgrounds…
Learning in hyperbolic spaces has attracted increasing attention due to its superior ability to model hierarchical structures of data. Most existing hyperbolic learning methods use fixed distance measures for all data, assuming a uniform…
In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean…
The holographic mutual information for the small separation of two circles and two strips in 2+1 dimensional space-time is considered based on the known exact minimal surfaces spanning the boundaries on AdS4. The results suggest a…
This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
3D model retrieval techniques can be classified as histogram-based, view-based and graph-based approaches. We propose a hybrid shape descriptor which combines the global and local radial distance features by utilizing the histogram-based…
Capturing the 3D geometry of transparent objects is a challenging task, ill-suited for general-purpose scanning and reconstruction techniques, since these cannot handle specular light transport phenomena. Existing state-of-the-art methods,…
We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in Anti-de…
Monocular 3D human pose estimation (HPE) often encounters challenges such as depth ambiguity and occlusion during the 2D-to-3D lifting process. Additionally, traditional methods may overlook multi-scale skeleton features when utilizing…
We consider the simplicial de Rham complex and the \v{C}ech-de Rham complex, two bigraded Hilbert complexes whose Hodge-Laplace problems govern spatially coupled problems in mixed dimension and homogeneous dimension, respectively. The…