A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper solves the existence problem of sphere packings in higher dimensions.
Paper proves circle packings converge to Riemann mapping for Jordan domains.
The paper studies circle packings using renormalization and subdivision rules.
Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.
We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study th…
Analyzes packing of circles in bounded and unbounded planes using mathematical formulas.
Paper studies degenerated circle packings in hyperbolic geometry and finds conditions for their existence.
Kernel sparsity ("dying ReLUs") and lack of diversity are commonly observed in CNN kernels, which decreases model capacity. Drawing inspiration from information theory and wireless communications, we demonstrate the intersection of coding theory and deep learning through the Grassmannian subspace packing problem in CNN…
Solves online 3D bin packing with deep reinforcement learning under constraints.
A 3D flexible bin packing problem (3D-FBPP) arises from the process of warehouse packing in e-commerce. An online customer's order usually contains several items and needs to be packed as a whole before shipping. In particular, 5% of tens of millions of packages are using plastic wrapping as outer packaging every day, …
CLAMP uses neural manifold packing to improve self-supervised learning.
The paper solves circle packings on surfaces with boundaries.
We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in $\sp^3$ and . We prove the thickness of a nontrivial knot or link in $\sp^3$ is no more than , the thickness of a Hopf link. We also give arguments and evidence supporting the conject…
Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate solutions. Specifically, for the 1D variable sized bin packing problem, the two ke…
We show that any subgroup of a (virtually) nilpotent-by-polycyclic group satisfies the bounded packing property of Hruska-Wise. In particular, the same is true about metabelian groups and linear solvable groups. However, we find an example of a finitely generated solvable group of derived length 3 which admits a finite…
Develops Kleinian Sphere Packings and Bugs, proving their arithmetic origins.
Proves rigidity of circle packings in the plane, generalizing previous work.
The paper studies rigidity of sphere packings on 3D manifolds with boundary.
Improved algorithms solve multi-period multi-class packing problems with bandit feedback.
Study generates infinite circle packings with a specific property.
Paper introduces new flows to find circle packings with specific curvature.
We give an overview of various counting problems for Apollonian circle packings, which turn out to be related to problems in dynamics and number theory for thin groups. This survey article is an expanded version of my lecture notes prepared for the 13th Takagi lectures given at RIMS, Kyoto in the fall of 2013.
The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.
Projective rigidity of circle packings on complex surfaces proved.
The paper studies rigid sphere packings on 3D manifolds with boundary.
New method finds metrics on surfaces with prescribed curvatures using circle packings and surgery.
This paper optimizes neural network training by packing multiple models on a single GPU.
Thurston's sphere packing on a 3-dimensional manifold is a generalization of Thusrton's circle packing on a surface, the rigidity of which has been open for many years. In this paper, we prove that Thurston's Euclidean sphere packing is locally determined by combinatorial scalar curvature up to scaling, which generaliz…
The paper studies circle packings on surfaces with boundary and their total geodesic curvatures.
Study of rod packings in 3-torus using 3-manifold geometry.
Thurston's circle packing approximation of the Riemann Mapping (proven to give the Riemann Mapping in the limit by Rodin-Sullivan) is largely based on the theorem that any topological disk with a circle packing metric can be deformed into a circle packing metric in the disk with boundary circles internally tangent to t…
We completely solve the symplectic packing problem with equally sized balls for any rational, ruled, symplectic 4-manifolds. We give explicit formulae for the packing numbers, the generalized Gromov widths, the stability numbers, and the corresponding obstructing exceptional classes. As a corollary, we give explicit va…
Paper constructs hyperbolic metrics using circle packings and curvature parameters.
Study on packing links with geometric constraints.
Confirms unique eigenfunction in hyperbolic packing has maximal spectral gap.
Paper calculates ball number of links using Lorentz geometry and circle packing.
The traditional Riemann Mapping Theorem can be proved with circle packing techniques. We prove the Combinatorial Riemann Mapping Theorem for tilings of bounded size using circle packings.
New theorem proves rigidity of circle packings in hyperbolic geometry.
The paper connects Apollonian packings to knot theory and improves link representations.
Paper proves rigidity of Doyle spirals in hexagonal lattice circle packings.
After having investigated the regular prisms and prism tilings in the $\SLR$ space in the previous work \cite{Sz13-1} of the second author, we consider the problem of geodesic ball packings related to those tilings and their symmetry groups . $\SLR$ is one of the eight Thurston geometries that can be de…
The paper finds circle packings with specific curvatures in hyperbolic geometry.
From the geometric study of the elementary cell of hexagonal circle packings --- a flower of 7 circles --- the class of conformally symmetric circle packings is defined. Up to Moebius transformations, this class is a three parameter family, that contains the famous Doyle spirals as a special case. The solutions are giv…
An extremal -packing is a collection of mutually disjoint metric discs, embedded in a surface, whose radius is maximal for the given topology. We study compact non-orientable surfaces of genus containing extremal -packings.
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternati…
Inversive distance circle packing metric was introduced by P Bowers and K Stephenson \cite{BS} as a generalization of Thurston's circle packing metric \cite{T1}. They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo \cite{Guo} proved the infinitesimal rigidity a…
The Andreev-Thurston theorem states that for any triangulation of a closed orientable surface Σ_g of genus g which is covered by a simple graph in the universal cover, there exists a unique metric of curvature 1, 0 or -1 on the surface depending on whether g=0, 1 or \ge 2 such that the surface with this metric admits a…
Recently, Freedman [arXiv:2301.00295] introduced the idea of packing a maximal number of links into a bounded region subject to geometric constraints, and produced upper bounds on the packing number in some cases, while commenting that these bounds seemed far too large. We show that the smallest of these "extravagantly…