Related papers: Packing Meets Topology
Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…
How does the topological space of science emerge? Inspired by the concept of maps of science, i.e. mapping scientific topics to a scientific space, we ask which topological structure a dynamical process of authors collaborating and…
The homotopy type of the complement manifold of a complexified toric arrangement has been investigated by d'Antonio and Delucchi in a paper that shows the minimality of such topological space. In this work we associate to a given toric…
For any given natural number $k$, this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by $k$ equal-radius disks in terms of the surface's topology. We show that the bounds given here are…
We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric…
We study the relationship between local and global density for sphere packings, and in particular the convergence of packing densities in large, compact regions to the Euclidean limit. We axiomatize key properties of sphere packing bounds…
The aim of the present dissertation is to analyze the meaning of the entropy bounds of the holographic sector once tested for statistical ensembles of particles, in order to deeper investigate the nature of these constraints and their…
Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…
In this work, we develop a systematic formalism to evaluate the upper bound of a large family of holographic entanglement entropy combinations when fixing $n$ subsystems and fine-tuning one other subsystem. The upper bound configurations…
We establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…
We prove tight upper bounds for the number of vertices of a simple polygon that is the union or the intersection of two simple polygons with given numbers of convex and concave vertices. The similar question on graphs of the lower (or…
In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…
We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological…
Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…
Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external…
We present first results of our study on the Euclidean topological charge density correlation function. In order to get a well defined topological charge density and to improve the signal of the correlation function at large separations we…
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship…
Optical links and knots have attracted growing attention owing to their exotic topologic features and promising applications in next-generation information transfer and storage. However, current protocols for optical topology realization…