arXiv research

Paper translates train track concepts to cluster algebras for pseudo-Anosov mapping classes.

Study of endperiodic maps on infinite graphs, proving homotopy and eigenvalue properties.

The paper defines and proves the existence of train track maps on graphs of groups.

We prove that for every P there is a bound B depending only on P so that the mapping torus of every P--small irreducible train-track map can be obtained by surgery from one of B mapping tori. We show that given an integer P>0 there is a bound $M$ depending only on P, so that there exists a presentation of the fundament…

The study of pseudo-Anosov maps with minimum expansion factor using train tracks.

New train tracks for complex homeomorphisms found.

This note gives a brief survey of the minimum dilatation problem for pseudo-Anosov mapping classes, and the first explicit train track description of an infinite family of pseudo-Anosov mapping classes with orientable stable foliations and the conjectural minimum dilatation for closed surfaces of even genus $g \ge 2$.

The thesis shows how automorphisms of hyperbolic groups can be represented by train track maps.

Study Agol cycles on 2-punctured torus and 5-punctured sphere, finding new dilatation formula.

In this paper we develop the metric theory for the outer space of a free product of groups. This generalizes the theory of the outer space of a free group, and includes its relative versions. The outer space of a free product is made of $G$-trees with possibly non-trivial vertex stabilisers. The strategies are the same…

Study Agol cycles in pseudo-Anosov 3-braids.

Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train track map inducing an endomorphism of the fundamental group gives rise to an expa…

The study examines the stretch factors of outer automorphisms and their latent symmetry.

We investigate the structure of the characteristic polynomial det(xI-T) of a transition matrix T that is associated to a train track representative of a pseudo-Anosov map [F] acting on a surface. As a result we obtain three new polynomial invariants of [F], one of them being the product of the other two, and all three …

A new method computes Teichmüller polynomials from integer permutations.

Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in a previous paper, which claims that forcing organizes al…

Let $φ\in \mbox{Out}(F_n)$ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism $φ$ determines a free-by-cyclic group $Γ=F_n \rtimes_φ\mathbb Z,$ and a homomorphism $α\in H^1(Γ; \mathbb Z)$. By work of Neumann, Bieri-Neumann-Strebel and Dowdall-Kapovi…

Train track automata for fully irreducible elements in Out(F_r).

We show that the subsurface projection of a train track splitting sequence is an unparameterized quasi-geodesic in the curve complex of the subsurface. For the proof we introduce induced tracks, efficient position, and wide curves. This result is an important step in the proof that the disk complex is Gromov hyperbolic…

The Long Short-Term Memory (LSTM) neural network based data association algorithm named as DeepDA for multi-target tracking in clutters is proposed to deal with the NP-hard combinatorial optimization problem in this paper. Different from the classical data association methods involving complex models and accurate prior…

Detects handlebodies and mapping class extensions using bordered Floer homology.

NBF combines deep learning with classical filtering for better belief tracking.

This work uses SVM to identify track component failures in AC Track Circuits.

In \cite{Ka14} we produced an algorithm for deciding whether or not an element $φ\in Out(F_N)$ is an iwip ("fully irreducible") automorphism. At several points that algorithm was rather inefficient as it involved some general enumeration procedures as well as running several abstract processes in parallel. In this pape…

Study quotients of curve complex actions by mapping class group.

Classifies knots in the Poincaré sphere, using fixed points and folding automata.

Using Lipschitz distance on Outer space we give another proof of the train track theorem.

Let $X$ be an infinite Riemann surface equipped with its conformal hyperbolic metric such that the action of the covering group $π_1(X)$ on $\tilde{X}$ is of the first kind-i.e., the surface $X$ is equal to its convex core. We first prove that any geodesic lamination on $X$ is nowhere dense. Given a fixed geodesic pant…

Outer automorphisms of free products are represented by CTs.

Noninjective monodromy found in polynomial critical point tracking.

In this paper, we present a reverberation removal approach for speaker verification, utilizing dual-label deep neural networks (DNNs). The networks perform feature mapping between the spectral features of reverberant and clean speech. Long short term memory recurrent neural networks (LSTMs) are trained to map corrupted…

In this thesis we describe how to estimate the distance spanned in the pants graph by a train track splitting sequence on a surface, up to multiplicative and additive constants. If some moderate assumptions on a splitting sequence are satisfied, each vertex set of a train track in it will represent a vertex of a graph …

Quadratic-time algorithm computes stretch factors and foliations for pseudo-Anosov mapping classes.

We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.

Let $S_{g,p}$ denote the genus $g$ orientable surface with $p$ punctures. We show that nested train track sequences constitute $O((g,p)^{2})$-quasiconvex subsets of the curve graph, effectivizing a theorem of Masur and Minsky. As a consequence, the genus $g$ disk set is $O(g^{2})$-quasiconvex. We also show that splitti…

An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by the invariant foliations is described, and is shown to make S into a complex sp…

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

Given a free-by-cyclic group $G = F_N \rtimes_\varphi \mathbb{Z}$ determined by any outer automorphism $\varphi \in \mathrm{Out}(F_N)$ which is represented by an expanding irreducible train-track map $f$, we construct a $K(G,1)$ $2$-complex $X$ called the folded mapping torus of $f$, and equip it with a semiflow. We sh…

Masked LARk prevents cross-site tracking while training models.

We describe a machine-learning approach to pitch correcting a solo singing performance in a karaoke setting, where the solo voice and accompaniment are on separate tracks. The proposed approach addresses the situation where no musical score of the vocals nor the accompaniment exists: It predicts the amount of correctio…

New architecture tracks objects in cluttered scenes without supervision.

The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its…

Mapping class group dynamics tracked through Teichmüller space.

BootsTAP uses real-world data to improve TAP tracking performance.

BusTr predicts bus travel times from real-time traffic forecasts.

Adaptive ML learns complex time-varying systems without new data.

Paper introduces TAP-Vid, a benchmark for tracking any point in videos.

New data-driven Cartan connection tracks complex vascular structures.