arXiv research

We show that if X is a minimal length carrier graph in a hyperbolic 3-manifold, M, then if X contains a sufficiently short edge, it must contain a short circuit, as well. The meaning of "short" depends only on the rank of the fundamental group of M. We also expand the class of manifolds which are known to have minimal …

The study finds at least two short, simple geodesic chords on a disk with convex boundary.

Meta-learning framework improves short utterance speaker recognition.

In this paper, we use Floer theory to study the Hofer length functional for paths of Hamiltonian diffeomorphisms which are sufficiently short. In particular, the length minimizing properties of a short Hamiltonian path are related to the properties and number of its periodic orbits.

Proposes a differentiable STFT for more efficient optimization of hop length.

3D spheres can't be swept by short curves, complicating geodesic length estimates.

Short geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers' theorem gives a global bound on the length of the first $3g-3$ geodesics. We use the construction of Brooks and Makover of random Riemann surfaces to investigate the distribution of short ($< \log (g)$) geodesics on a …

Characterizes curves with short representatives on hyperbolic surfaces.

Shorter adversarial prompts help protect LLMs from jailbreak attacks.

Short proof for ideal polygons with near optimal orthogeodesic decomposition.

Withdrawn by first author.

New method uses short geodesics to approximate marked length spectrum.

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…

We investigate the maximal solid tubes around short simple geodesics in hyperbolic three-manifolds and how complex length of curves relate to closed, incompressible, least area minimal surfaces. As applications, we prove, there are some closed hyperbolic three-manifolds fibering over the circle which are not foliated b…

Study of lengths of cycles in large genus random maps converging to Poisson process.

In this paper we examine the relationship between the length spectrum and the geometric genus spectrum of an arithmetic hyperbolic 3-orbifold M. In particular we analyze the extent to which the geometry of M is determined by the closed geodesics coming from finite area totally geodesic surfaces. Using a variety of tech…

We give a lower bound for the widths of the collars of certain short partial pants decomposition of the surface. Then we apply this to obtain upper bounds of the renormalized volume of certain Schottky manifolds in terms of the hyperbolic length of compressible curves.

For two measured laminations $ν^+$ and $ν^-$ that fill up a hyperbolizable surface $S$ and for $t \in (-\infty, \infty)$, let $L_t$ be the unique hyperbolic surface that minimizes the length function $e^t l(ν^+) + e^{-t} l(ν^-)$ on Teichmuller space. We characterize the curves that are short in $L_t$ and estimate their…

In response to Sanki-Vadnere, we present a short proof of the following theorem: a pair of simple curves on a hyperbolic surface whose complementary regions are disks has length at least half the perimeter of the regular right-angled $(8g-4)$-gon.

Short text classi cation is a method for classifying short sentence with prede ned labels. However, short text is limited in shortness in text length that leads to a challenging problem of sparse features. Most of existing methods treat each short sentences as independently and identically distributed (IID), local cont…

Study curves evolving on hypersurfaces with free boundaries, preserving length.

This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive e there is a positive d depending only on n and on e such that an element of pi_1(M) with stable commutator length less than d is represented by a geodesic with leng…

A rope is a non-singular embedding of a closed interval into R^3, which sends the ends of the interval to some fixed points A and B such that |AB|=1. A rope is short if its length is less than 3. The main result of the paper is that the fundamental group of the space of short ropes is naturally isomorphic to the group …

New phenomenon found in Gothen components' boundary.

Given a geometrically finite hyperbolic cone-manifold, with the cone singularity sufficiently short, we construct a one parameter family of cone-manifolds decreasing the cone angle to zero. We also control the geometry of this one parameter family via the Schwarzian derivative of the projective boundary and the length …

Model learns brevity by exposing to easy problems, improving efficiency without explicit length penalties.

Lower bounds on geodesic lengths for spheres with Willmore energy.

Adaptive TFTs improve cryptocurrency price prediction accuracy.

In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurabiltiy classes by analyzing their cusp sha…

New lattice extensions of Schottky groups in hyperbolic space.

It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in ge…

3D manifold with positive curvature has a short geodesic.

We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives …

Given a surface of infinite topological type, there are several Teichmüller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the comparison between the quasiconformal Teichmüller space and the length-spectrum Teichm…

A new isoperimetric estimate is proved for embedded closed curves evolving by curve shortening flow, normalized to have total length $2π$. The estimate bounds the length of any chord from below in terms of the arc length between its endpoints and elapsed time. Applying the estimate to short segments we deduce directly …

A closed Teichmuller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L > 0, there exist e_2 > e_1 > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the e_1-thick part and the e_2-thin part. We …

Formula for projecting geodesics in hyperbolic 3-manifolds, relating lengths to subsurface projections.

The paper calculates the volume growth of hyperbolic surfaces with short geodesics.

Paper introduces a differentiable STFT for continuous window length optimization.

Study finds phase transition in context-sensitive language model with short-range interactions.

New insights into attention mechanisms reveal dramatic trade-offs between rank and heads.

We give a complete classification of complex hyperbolic $(n_1, n_2, n_3)$-triangle groups by types defined according to the ellipticity of two particular words of short length. This improves the Schwartz conjecture proved by Grossi.

Study on ordering geodesics on hyperbolic surfaces.

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic…

The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono- and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of t…

We consider closed simplicial and cubical $n$-complexes in terms of link of their $(n-2)$-faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2)$-face is contained in 3 or 4 $n$-faces. Such simplicial complexes with {\em short} (i.e. of length 3 or 4) links are completely classified…

In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of the fixed global extrema in the Floer complex of the generating Hamiltonian. Our…

Wolpert's cosine formula on Teichmüller space gives the Weil-Petersson Poisson bracket $\{l_α, l_β\}$ for geodesic length functions $l_α,l_β$ of closed curves $α,β$ as the sum of the cosines of the angle of intersection of the associated geodesics. This was recently generalized to Hitchin representations by Labourie. I…