arXiv research

Random branched covers of groups are homotopy equivalent to geometrically small cancellation complexes.

Random covers of surfaces have tangle-free monodromy and the Putman-Wieland property.

Random covers of hyperbolic surfaces have a spectral gap with polynomial rate.

Random covers of hyperbolic surfaces follow a specific probability measure.

The study finds effective lower bounds for spectra of random surfaces and bundles.

Study shows a central limit theorem for random coverings of manifolds with nilpotent groups.

Study smooth linear statistics on random covers of hyperbolic surfaces, showing central limit and variance results.

The paper studies random covers of torus knot complements and their statistical properties.

Eigenvalues of random hyperbolic surface covers converge to hyperbolic plane's.

The Dirichlet random walk on manifolds has a positive escape rate if the cover is non-amenable.

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficul…

Random square-tiled surfaces have normal genus distribution and cover all integer vectors.

Two algorithms for interpreting and boosting tree-based models using rule covering.

We prove that any two finite-area non-compact hyperbolic Riemann surfaces S and T have finite covers that are arbitrarily close in the normalized Weil-Petersson metric, where we normalize by dividing the square of the metric by the area of the surface. In the case where T is the modular surface this reduces to showing …

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…

We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth.

We study a tower of normal coverings over a compact Kähler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we deduce the equidistribution for zero currents of random holomorphic sections. Furth…

Extends spectral number variance convergence to random matrix ensembles for twisted Laplacians.

Study shows no new eigenvalues in specific finite coverings.

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Infere…

Improved cover song detection with neural networks.

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a bypr…

Let T(x,r) denote the first hitting time of the disc of radius r centered at x for Brownian motion on the two dimensional torus. We prove that sup_{x} T(x,r)/|log r|^2 --> 2/pi as r --> 0. The same applies to Brownian motion on any smooth, compact connected, two-dimensional, Riemannian manifold with unit area and no bo…

We give an asymptotic probabilistic real Riemann-Hurwitz formula computing the expected real ramification index of a random covering over the Riemann sphere. More generally, we study the asymptotic expected number and distribution of critical points of a random real Lefschetz pencil over a smooth real algebraic variety…

Study on covering probability of random balls in bounded open sets.

For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function theory.

JRFs improve semi-supervised learning by balancing generation and classification.

Random subgroups in hyperbolic spaces have full limit sets and bounded critical exponents.

The study proves optimal spectral gaps for hyperbolic surfaces.

A translation structure equips a Riemann surface with a singular flat metric. Not much is known about the shape of a random translation surface. We compute an upper bound on the expected value of the covering radius of a translation surface in any stratum H_1(kappa). The covering radius of a translation surface is the …

This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2016) on the…

Gradient boosting with randomized trees reduces discontinuities and complexity.

We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup $H$. We further assume that $H$ is not consisting only of lifts with respect to any one covering. Then w…

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…

Paper reinterprets majorizing measure theorem in terms of coding theory.

Develops an empirical likelihood framework for random forests and ensembles.

Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…

We study critera for a pair $(\{ X_n \}$, $\{ Y_n \})$ of approximating processes which guarantee closeness of moments by generalizing known results for the special case that $Y_n = Y$ for all $n$ and $X_n$ converges to $Y$ in probability. This problem especially arises when working with surrogate models, e.g. …

Semantic segmentation of land cover classes is fundamental for agricultural and economic development work, from sustainable forestry to urban planning, yet existing training datasets have significant limitations. To generate an open and comprehensive training library of high resolution Earth imagery and high quality la…

For finitely supported random walks on finitely generated groups $G$ we prove that the identity map on $G$ extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This yields new results for relatively hyperbolic groups. Our key e…

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of th…

Random harmonic maps into spheres converge to a specific metric under strong convergence of representations.

Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with statistical guarantees. In this paper, we develop a statistical theory of graph c…

Uniformly random permutations converge to regular representation on surface groups.

Graph Neural Networks struggle on random graphs without node identifiers.

The paper characterizes the geometry and topology of spin random fields.

Study uniform convergence of random walk Laplacians to diffusion Laplacian on smooth manifolds.

Quantum algorithm speeds up nested expectation estimation by nearly quadratically.