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.
New method characterizes surface quadrilateral layouts as special immersions.
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significan…
The paper classifies surfaces formed by quadrilateral gluings.
We interpret a normal surface in a (singular) three-manifold in terms of the homology of a chain complex. This allows us to study the relation between normal surfaces and their quadrilateral co-ordinates. Specifically, we give a proof of an (unpublished) observation independently given by Casson and Rubinstein saying t…
Constructs minimal surfaces over Pitot quadrilaterals using harmonic diffeomorphisms.
Constructs constant mean curvature surfaces using geometric flow.
We investigate the relationship between stability and the existence of extremal Kähler metrics on certain toric surfaces. In particular, we consider how log stability depends on weights for toric surfaces whose moment polytope is a quadrilateral. We introduce a space of symplectic potentials for toric manifolds, which …
Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension …
Let be a compact 3-manifold with a triangulation . We give an inequality relating the Euler characteristic of a surface normally embedded in with the number of normal quadrilaterals in . This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial …
We discuss discretization of Koenigs nets (conjugate nets with equal Laplace invariants) and of isothermic surfaces. Our discretization is based on the notion of dual quadrilaterals: two planar quadrilaterals are called dual, if their corresponding sides are parallel, and their non-corresponding diagonals are parallel.…
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary quadrilaterals are skew. We classify the simply connected affine A-nets that can be ext…
The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds up this operation by using a much smaller space (quadrilateral coord…
We determine all the Q-fundamental surfaces in -lens spaces and -lens spaces with respect to natural triangulations with tetrahedra. For general -lens spaces, we give an upper bound for elements of vectors which represent Q-fundamental surfaces with no quadrilateral normal disks disjoint from t…
For a manifold with an affine connection, we prove formulas which infinitesimally quantify the gap in a certain naturally defined open geodesic quadrilateral associated to a pair of tangent vectors , at a point of the manifold. We show that the 1st order infinitesimal obstruction to the quadrilateral to close is…
Approximates surfaces using Laguerre geometry with spherical faces.
Approximates smooth surfaces using Laguerre geometry meshes.
We provide an explicit resolution of the Abreu equation on convex labeled quadrilaterals. This confirms a conjecture of Donaldson in this particular case and implies a complete classification of the explicit toric Kähler-Einstein and toric Sasaki-Einstein metrics constructed in [6,22,14]. As a byproduct, we obtain a we…
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles. For discrete planar quadrilateral nets, circular nets, -nets and conical…
Paper introduces quadrilateral labyrinth fractals and their properties.
Different layouts can characterize different aspects of the same graph. Finding a "good" layout of a graph is thus an important task for graph visualization. In practice, users often visualize a graph in multiple layouts by using different methods and varying parameter settings until they find a layout that best suits …
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on di…
Spherical quadrilaterals classified based on geometric properties.
We prove that any cyclic quadrilateral can be inscribed in any closed convex -curve. The smoothness condition is not required if the quadrilateral is a rectangle.
Similarity maps cyclic quadrilaterals onto smooth curves.
We show that a topologically minimal disk in a tetrahedron with index is either a normal triangle, a normal quadrilateral, or a normal helicoid with boundary length 4(n+1). This mirrors geometric results of Colding and Minicozzi.
Paper shows any link can be diagrammed with only triangles and quadrilaterals.
A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that every Margulis spacetime is orientable, even though S may be nonorientable. We classify Margulis spacetimes when S is homeomorphic…
Despite remarkable recent progress on both unconditional and conditional image synthesis, it remains a long-standing problem to learn generative models that are capable of synthesizing realistic and sharp images from reconfigurable spatial layout (i.e., bounding boxes + class labels in an image lattice) and style (i.e.…
The study classifies tilings of the sphere by congruent quadrilaterals.
OLALA automates document layout annotation by selecting ambiguous regions for labeling.
The paper explores discrete isothermic nets using checkerboard patterns in quadrilateral nets.
Machine learning-based lithography hotspot detection has been deeply studied recently, from varies feature extraction techniques to efficient learning models. It has been observed that such machine learning-based frameworks are providing satisfactory metal layer hotspot prediction results on known public metal layer be…
A new lower bound on the complexity of a 3-manifold is given using the Z2-Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characterised using normal surfaces consisting entirely of quadrilateral discs.
A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pieces of this normal form are triangles, quadrilaterals, and helicoids. Helical pieces can have any number of positive or negative twists. We…
We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of discrete nets on the smooth surface one can obtain second-order approximation g…
Stochastic gradient descent outperforms traditional force-directed methods.
This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface or triangulation. Two applications of these bounds are given. First, the minima…
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isoth…
We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. A focus is given to dimension 3 where slicings are normal surfaces. In the case of 2-neighborly 3-manifolds and quadrangulated slicings, a lower bound on the number of quadrilaterals of normal surfaces depending on the …
The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a boundary curve map which takes a spun-normal surface to an element of the direct sum of the first homology groups of the v…
Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to se…
Square-like quadrilaterals inscribed in space curves proven for finite total curvature.
Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used. Suppose is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In Q-theory, if contains an essential surface, then the projective solution space has an e…
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the quadrilateral conditions. This yields normal surfaces that are no longer embedded. We …
AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.
Study examines Hilbert area of inscribed polygons in projective geometry.
Researchers describe isometric deformations of T-hedra and T-surfaces.