相关论文: Freezing Sets for Arbitrary Digital Dimension
We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional dual conformal field theories through the $AdS/CFT$ correspondence. The holographic…
Recently, a new method for encoding data sets in the form of "Density Codes" was proposed in the literature (Courrieu, 2006). This method allows to compare sets of points belonging to every multidimensional space, and to build shape spaces…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
There are many papers studying properties of point sets in the Euclidean space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the…
We prove that instantaneous gelation (i.e., instantaneous loss of mass) occurs for coagulation equations with sum-type kernels of homogeneity greater than one which vanish on the diagonal. Our proof includes solutions that are Radon…
State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs)…
Image prediction methods often struggle on tasks that require changing the positions of objects, such as video prediction, producing blurry images that average over the many positions that objects might occupy. In this paper, we propose a…
We show that for any positive forward density subset N \subset Z, there exists an integer m>0, such that, for all n>m, N contains almost perfect n-scaled reproductions of any previously chosen finite set of integers.
The aim of this paper is to provide a coherent framework for transforming boundary pairs of digital images from one resolution to another without knowledge of the full images. It is intended to facilitate the simultaneous usage of…
Cold atomic ensembles can mediate the generation of entanglement between pairs of photons. Photons with specific directions of propagation are detected, and the entanglement can reside in any of the degrees of freedom that describe the…
We show that abelian bosonization of 1+1 dimensional fermion systems can be interpreted as duality transformation and, as a conseguence, it can be generalized to arbitrary dimensions in terms of gauge forms of rank $d-1$, where $d$ is the…
We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.
What makes images similar? To measure the similarity between images, they are typically embedded in a feature-vector space, in which their distance preserve the relative dissimilarity. However, when learning such similarity embeddings the…
We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set, we also study the Assouad dimensions of Cantor-like sets.
In this article, we investigate some properties of the coincidence point set of digitally continuous maps. Following the Rosenfeld graphical model which seems more combinatorial than topological, we expect to achieve results that might not…
We study the accretion of cold and hot dark matter onto a cosmic string wake using a high-resolution numerical simulation. We verify previous analytical calculations predicting the radius of bound matter around wakes and inflow velocities…
Using first-principles calculations, we identify "magic-zero" optical wavelengths, \lambda_zero, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic…
We propose a generic ansatz for the extension of parton distributions of the real photon to those of the virtual photon. Alternatives and approximations are studied that allow closed-form parametrizations.
We use optical tweezers based on time-multiplexed acousto-optic deflectors to trap ultra-cold cesium atoms in one-dimensional arrays of atomic ensembles. For temperatures between 2.5 $\mu$K and 50 nK we study the maximal time between…
We introduce Zernike polynomials as a novel degree of freedom for encoding quantum information in the spatial structure of photons. Building on their orthogonality and completeness over the unit disc, we develop a framework for generating,…