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.
Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal -equivariant triangulations of -dimensional small covers. We discuss vertex minimal equilibrium triangulations of $\mathbb{R…
This paper shows GNNs can learn good approximations for graph problems.
Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.
This paper shows semi-equivelar toroidal maps are vertex-transitive covers.
The L1 loss landscape of neural nets near local minima behaves differently, revealing exponential decay and increased vertex density.
The study finds the bounds of vertex orbits in maps derived from specific lattices.
Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path…
A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the core. Interactions between pairs of nodes in the fringe, however, are not recor…
Paper shows minimum 10 vertices for hyperbolic origami 2-torus.
A Seifert surgery is an integral surgery on a knot in S^3 producing a Seifert fiber space which may contain an exceptional fiber of index 0. The Seifert Surgery Network is a 1-dimensional complex whose vertices correspond to Seifert surgeries; its edges correspond to single twistings along "seiferters" or "annular pair…
Optimal Reeb graphs identified for polygon decomposition.
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the algorithms instead? In many real-world applications, it is typically the case t…
We give three constructions of a vertex-minimal triangulation of -dimensional real projective space . The first construction describes a -dimensional sphere on vertices, which is a double cover of a triangulated and has a large amount of symmetry. The second and third construct…
We study several properties of $\ZZ_2^n$-equivariant triangulations of $\RR P^n$. We show that a $\ZZ_2^n$-equivariant triangulation of $\RR P^n$ induces a triangulated subdivision of the orbit space . We show that any vertex minimum $\ZZ_2^3$-equivariant triangulation of $\RR P^3$ contains verti…
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface , including the minimum number of self-intersections, the minimum length of the words representing them in a geometric presentation of , and the minimum degree of the coverings of to which …
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…
Given a flag in each of the vertex-transitive tessellations of the Euclidean plane by regular polygons, we determine the flag stabilizer under the action of the automorphism group of a regular cover. In so doing we give a presentation of these tilings as quotients of regular (infinite) polyhedra.
Tiny complexes share 3-5 triangles in common coverings.
We find the minimum dilatation of pseudo-Anosov braids on n-punctured discs for 3 <= n <= 8. This covers the results of Song-Ko-Los (n=4) and Ham-Song (n=5). The proof is elementary, and uses the Lefschetz formula.
The article studies crystallizations of small covers over simple polytopes and finds unique crystallizations for the -simplex.
The 4-dimensional abstract Kummer variety K^4 with 16 nodes leads to the K3 surface by resolving the 16 singularities. Here we present a simplicial realization of this minimal resolution. Starting with a minimal 16-vertex triangulation of K^4 we resolve its 16 isolated singularities - step by step - by simplicial blowu…
Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination w…
New algorithm finds corrupted vertices in graphs with few queries.
We employ random geometric digraphs to construct semi-parametric classifiers. These data-random digraphs are from parametrized random digraph families called proximity catch digraphs (PCDs). A related geometric digraph family, class cover catch digraph (CCCD), has been used to solve the class cover problem by using its…
Every open Riemann surface can be triangulated with equilateral triangles.
Approximates cycles in planar and bounded-genus graphs.
Study optimal adjustment sets for causal policies with hidden variables.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that none of these are vertex transitive. We establish existence of 12-covered triangula…
Ensemble methods have been shown to be an effective tool for solving multi-label classification tasks. In the RAndom k-labELsets (RAKEL) algorithm, each member of the ensemble is associated with a small randomly-selected subset of k labels. Then, a single label classifier is trained according to each combination of ele…
The study shows how nonnegative Ricci curvature and metric cones imply the existence of abelian subgroups in the fundamental group of open manifolds.
The paper constructs simplicial maps of any degree on spheres, solving a long-standing problem.
The Four Vertex Theorem, one of the earliest results in global differential geometry, says that a simple closed curve in the plane, other than a circle, must have at least four "vertices", that is, at least four points where the curvature has a local maximum or local minimum. In 1909 Syamadas Mukhopadhyaya proved this …
The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex homotopy equivalent…
Study efficient algorithms for identifying minimum interventional sets to learn causal relationships.
The study explores maps of 2- and 3-uniform tilings on the torus.
With the -family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic -equivelar triangulations of orientable and non-orientable surfaces for every , , and every , . Series of cy…
Study classifies graphs with positive curvature without quadrilaterals.
Paper proves ribbonlength grows linearly with knot complexity.
The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.
Mathematical framework for minimum enclosing ball problem.
In 2004, Sormani and Wei introduced the covering spectrum: a geometric invariant that isolates part of the length spectrum of a Riemannian manifold. In their paper they observed that certain Sunada isospectral manifolds share the same covering spectrum, thus raising the question of whether the covering spectrum is a sp…
A new algorithm optimizes graph problems faster and more accurately.
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum number of such 1-handles is called the unknotting number or the triple point cancelling number, respectively. In this paper,…
The study connects triangulated surfaces to complex projective structures and circle patterns.
Paper offers a method for finding the smallest sphere enclosing a set in d-dimensional space.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
Optimizes minimum-volume prediction sets for multivariate regression.