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 learns better branching policies for MILP problems.
Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect recent development in spherical conic metrics to this old problem, and give a new m…
Paper finds new realizable data for maps with three branch points.
Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0. This …
Course on knots using branched coverings.
The paper studies which branched covers can be lifted to braided embeddings.
Study on minimal disks in metric spaces, focusing on branch set structure.
We discuss the issue of branching in quasiregular mapping, and in particular the relation between branching and the problem of finding geometric parametrizations for topological manifolds. Other recent progress and open problems of a more function theoretic nature are also presented.
Solve arc diagrams on surfaces via branched covers.
Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a branching heuristic inspired from reinforcement learning with a goal of reaching…
The paper explores rational functions with 3 branching points on the Riemann sphere.
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs…
Quantum algorithm speeds up MIP solving by a near-quadratic factor.
For the existence of a branched covering Sigma~ --> Sigma between closed surfaces there are easy necessary conditions in terms of chi(Sigma~), chi(Sigma), orientability, the total degree, and the local degrees at the branching points. A classical problem dating back to Hurwitz asks whether these conditions are also suf…
Explains how group representations behave under subgroup restrictions.
A new Branch-and-Bound solver tackles L0-penalized problems with flexible loss functions.
To a branched cover f between orientable surfaces one can associate a certain branch datum D(f), that encodes the combinatorics of the cover. This D(f) satisfies a compatibility condition called the Riemann-Hurwitz relation. The old but still partly unsolved Hurwitz problem asks whether for a given abstract compatible …
New partial solution to Hurwitz problem for surface branched covers.
Given two closed orientable surfaces, the Hurwitz existence problem asks whether there exists a branched cover between them having prescribed global degree and local degrees over the branching points. The Riemann-Hurwitz formula gives a necessary condition, which was shown to be also sufficient when the base surface ha…
Improved phylogenetic tree reconstruction using flexible branch length distributions.
Paper uses RL to optimize branching strategy in B&B algorithms.
The paper introduces branched α-flows on surfaces with negative Euler characteristic and proves their long-term existence and convergence.
Efficiently models tree-like data with coupled branches using HMMs.
New hybrid model reduces MILP solver time by up to 26%.
The paper proposes modern computational methods for optimizing reinsurance contracts.
Study on moduli spaces of branched projective structures on surfaces.
Simply-connected 4-manifolds are covered by products with a 2-torus.
We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…
Extends branch and bound for probabilistic neural network verification.
New criterion for branched covers between 2-spheres.
Paper solves the Hurwitz existence problem using fiber products.
We associate to a parametrized family of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index is derived from the index bundle of the linearization of the …
Uniformly branching trees are equivalent to certain metric spaces.
To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate su…
We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b) enhances T to a Delta-complex. Branched triangulations of (M, V ) are considered up to…
We present the Integrated Size and Price Optimization Problem (ISPO) for a fashion discounter with many branches. Based on a two-stage stochastic programming model with recourse, we develop an exact algorithm and a production-compliant heuristic that produces small optimality gaps. In a field study we show that a distr…
The paper details folding of branched covers of the 3-sphere over knots.
In this work we characterize branch data of branched coverings of even degree over the projective plane which are realizable by indecomposable branched coverings.
For a given branched covering between closed connected surfaces, there are several easy relations one can establish between the Euler characteristics of the surfaces, their orientability, the total degree, and the local degrees at the branching points, including the classical Riemann-Hurwitz formula. These necessary re…
A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot , where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of . We can simplify a branched cover…
Techniques for constructing codimension 2 embeddings and immersions of the 2 and 3-fold branched covers of the 3 and 4-dimensional spheres are presented. These covers are in braided form, and it is in this sense that they are folded. More precisely the composition of the embedding (or immersion) and the canonical proje…
Formula compares metrics on branched coverings of line bundles.
A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.
New findings on convexity of special Lagrangian geodesics.
New examples show transverse knots are determined by their branched covers.
We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.
New method solves matrix completion problems to certifiable optimality.
Improved phylogenetic inference with normalizing flows.