arXiv research

Best-choice edge grafting speeds up MRF structure learning.

We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type. The oriented graph of graftings is the graph whose vertices are the equivalence classes of marked CP^1…

Let $\mathcal{G}^*(S,ρ)$ be the graph whose vertices are marked complex projective structures with holonomy $ρ$ and whose edges are graftings from one vertex to another. If $ρ$ is quasi-Fuchsian, a theorem of Goldman implies that $\mathcal{G}^*(S,ρ)$ is connected. If $ρ(π_1(S))$ is a Schottky group Baba has shown that …

The paper introduces flat grafting to deform quadratic differentials on surfaces.

The definition of the grafting operation for quasifuchsian groups is extended by Bromberg to all $b$-groups. Although the grafting maps are not necessarily continuous at boundary groups, in this paper, we show that the grafting maps take every "standard" convergent sequence to a convergent sequence. As a consequence of…

Given a measured geodesic lamination on a hyperbolic surface, grafting the surface along multiples of the lamination defines a path in Teichmuller space, called the grafting ray. We show that every grafting ray, after reparametrization, is a Teichmuller quasi-geodesic and stays in a bounded neighborhood of a Teichmulle…

We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems f…

Real projective surfaces with Hitchin holonomy can be related via grafting.

In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmuller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmuller geodesics and lines of minima. We also sho…

The paper proves a grafting theorem for meromorphic projective structures and shows the monodromy map is a local homeomorphism.

We show that any grafting ray in Teichmüller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichmüller geodesic ray. As a consequence the projection of a generic grafting ray to moduli space is dense. We also show that the set of points in Teichmüller space obtained by integ…

Let $X$ be a closed hyperbolic surface and $λ, η$ be weighted geodesic multicurves which are short on X. We show that the iterated grafting along $λ$ and $η$ is close in the Teichmueller metric to grafting along a single multicurve which can be given explicitly in terms of $λ$ and $η$. Using this result, we study the h…

Grafting is a surgery on Riemann surfaces introduced by Thurston which connects hyperbolic geometry and the theory of projective structures on surfaces. We will discuss the space of projective structures in terms of the Thurston's geometric parametrization given by grafting. From this approach we will prove that on any…

Paper explores grafting consistent estimators to improve Random Forest consistency.

Deep learning predicts kidney graft survival better than traditional methods.

The paper proves unique foliations for hyperbolic ends and convex de Sitter spacetimes.

Grafting a measured lamination on a hyperbolic surface defines a self-map of Teichmuller space, which is a homeomorphism by a result of Scannell and Wolf. In this paper we study the large-scale behavior of pruning, which is the inverse of grafting. Specifically, for each conformal structure $X \in \T(S)$, pruning $X$ g…

Grafting is a method of obtaining new projective structures from a hyperbolic structure, basically by gluing a flat cylinder into a surface along a closed geodesic in the hyperbolic structure, or by limits of that procedure. This induces a map of Teichmuller space to itself. We prove that this map is a homeomorphism by…

The article extends Thurston's Grafting Theorem to signed spaces and defines a framed monodromy map.

Let $S$ be a closed oriented surface of genus at least two. Gallo, Kapovich, and Marden asked if 2π-graftings produce all projective structures on $S$ with arbitrarily fixed holonomy (Grafting Conjecture). In this paper, we show that the conjecture holds true "locally" in the space $GL$ of geodesic laminations on $S$ v…

We prove that a Bers slice is never algebraic, meaning that its Zariski closure in the character variety has strictly larger dimension. A corollary is that skinning maps are never constant. The proof uses grafting and the theory of complex projective structures.

Let S be an oriented closed surface of genus at least two. We show that, given a generic representation in the PSL(2,C)-character variety of S, (2π-)graftings produce all projective structures on S with the holonomy representation.

We show that any grafting ray in Teichmüller space is (strongly) asymptotic to some Teichmüller geodesic ray. As an intermediate step we introduce surfaces that arise as limits of these degenerating Riemann surfaces. Given a grafting ray, the proof involves a Teichmüller ray with a conformally equivalent limit, and bui…

Geometrically boundary of surface moduli space defined.

A framework for real-time gesture recognition in tomato grafting.

Study of lattices and subgroups in PSL2(R) with grafting continuity.

Study of hyperbolic surface laminations and their Teichmüller spaces.

The landslide flow, introduced in [5], is a smoother analog of the earthquake flow on Teichmüller space which shares some of its key properties. We show here that further properties of earthquakes apply to landslides. The landslide flow is the Hamiltonian flow of a convex function. The smooth grafting map $sgr$ taking …

This paper explores how pairs of multicurves can be realized as cylinders on translation surfaces.

Estimates Schwarzian derivative on long complex projective tubes.

Complex projective structures can be joined via simple bubbling and debubbling.

This paper investigates Shampoo's heuristics and decouples preconditioner updates.

Researchers find a method to construct projective structures on a specific surface.

Based on graphic lambda calculus, we propose a program for a new model of asynchronous distributed computing, inspired from Hewitt Actor Model, as well as several investigation paths, concerning how one may graft lambda calculus and knot diagrammatics.

Grinch efficiently clusters large datasets with complex structures.

GRAB efficiently learns combinatorial Boolean models from data.

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …

We cut a hyperbolic surface of finite area along some analytic simple closed curves, and glue in cylinders of varying moduli. We prove that as the moduli of the glued cylinders go to infinity, the Fenchel-Nielsen twist coordinates for the resulting surface around those cylinders converge.

Geometric interpretation of Fock-Goncharov positivity and disk stabilization in symmetric space.

This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the moduli space (2) Thurston's parameterization of the moduli space using grafting (3) …

A Schottky group in PSL(2, C) induces an open hyperbolic handlebody and its ideal boundary is a closed orientable surface S whose genus is equal to the rank of the Schottky group. This boundary surface is equipped with a (complex) projective structure and its holonomy representation is an epimorphism from pi_1(S) to th…

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy re…

Deep learning predicts 30-day readmissions after CABG surgery.

We survey the renormalized volume of hyperbolic 3-manifolds, as a tool for Teichmuller theory, using simple differential geometry arguments to recover results sometimes first achieved by other means. One such application is McMullen's quasifuchsian (or more generally Kleinian) reciprocity, for which different arguments…

This paper describes the resource- and system-building efforts of an eight-week Johns Hopkins University Human Language Technology Center of Excellence Summer Camp for Applied Language Exploration (SCALE-2009) on Semantically-Informed Machine Translation (SIMT). We describe a new modality/negation (MN) annotation schem…

We describe a unified and coherent syntactic framework for supporting a semantically-informed syntactic approach to statistical machine translation. Semantically enriched syntactic tags assigned to the target-language training texts improved translation quality. The resulting system significantly outperformed a linguis…

We prove that if S is a closed compact surface of negative Euler characteristic, and if R is a quasi-Fuchsian representation in PSL(2,C), then the deformation space M(k,R) of branched projective structures on S with total branching order k and holonomy R is connected, as soon as k>0. Equivalently, two branched projecti…

The space ML(F) of measured geodesic laminations on a given closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (earthquake theory) or complex projective (grafting) geometry as well as in (2+1) Lorentzian one (globally hyperbolic spacetimes of …