arXiv research

Proposes a method to improve class-conditional conformal prediction for many classes.

Infinitely many unique ways to generate a surface's mapping class group.

Accessible groups with infinitely many ends have infinitely many twisted conjugacy classes.

Paper tackles many-class few-shot learning with class hierarchy, improving accuracy.

Generating user interpretable multi-class predictions in data rich environments with many classes and explanatory covariates is a daunting task. We introduce Diagonal Orthant Latent Dirichlet Allocation (DOLDA), a supervised topic model for multi-class classification that can handle both many classes as well as many co…

Previously one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincaré duality groups for each $n\geq 4$. We strengthen these results by showing that these groups comprise uncountably many quasi-isometry classes. We deduce that for each $n\geq 4$ there are uncountably many…

Transfer-learning and meta-learning are two effective methods to apply knowledge learned from large data sources to new tasks. In few-class, few-shot target task settings (i.e. when there are only a few classes and training examples available in the target task), meta-learning approaches that optimize for future task l…

New families of hyperbolic polyhedra yield infinitely many unique reflection groups.

We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4-manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We further show that for a large class of examples that lambda(T) is actually a C-infinit…

Maps with many singularities found in complex space.

The study finds many tight contact structures on hyperbolic 3-spheres.

Study Euler class of surface bundles with nontrivial results.

Study on achiral Sol 3-manifolds with density results.

The purpose of this paper is to investigate the following problem: For a fixed 2-dimensional homology class K in a simply connected symplectic 4-manifold, up to smooth isotopy, how many connected smoothly embedded symplectic submanifolds represent K? We show that when K can be represented by a symplectic torus, there a…

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.

We prove that many normal subgroups of the extended mapping class group of a surface with punctures are geometric, that is, that their automorphism groups and abstract commensurator groups are isomorphic to the extended mapping class group. In order to apply our theorem to a normal subgroup we require that the "minimal…

Proposes a method to estimate acceptance regions for many classes, including new ones.

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how these tori can be non-isotopically embedded as homologous symplectic …

New method finds infinitely many knots in 3-manifolds.

We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with a hyperbolic structure, embedding the universal cover in the hyperbolic plane, a…

Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.

A left orderable completely metrizable topological group is exhibited containing Artin's braid group on infinitely many strands. The group is the mapping class group (rel boundary) of the closed unit disk with a sequence of interior punctures converging to the boundary. This resolves an issue suggested by work of Dehor…

This paper proposes a non-parallel many-to-many voice conversion (VC) method using a variant of the conditional variational autoencoder (VAE) called an auxiliary classifier VAE (ACVAE). The proposed method has three key features. First, it adopts fully convolutional architectures to construct the encoder and decoder ne…

We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us …

The study finds hyperbolic manifolds without spin^c structures in dimensions 5 and above.

Study on exotic smooth embeddings of surfaces in 4-manifolds, revealing different properties and complexities.

We show that there exist infinitely many commensurability classes of finite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup which is locally free but not free. The main technical tool is the fact that a collection of hyperbolic 3-manifolds of bounded volume contains infinitely many commensurab…

We construct infinitely many linearly independent quasi-homomorphisms on the mapping class group of a Riemann surface with genus at least two which vanish on a handlebody subgroup. As a corollary, we disprove a conjecture of Reznikov on bounded width in Heegaard splittings. Another corollary is that there are infinitel…

Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.

We prove that the rank problem is decidable in the class of torsion-free word-hyperbolic Kleinian groups. We also show that every group in this class has only finitely many Nielsen equivalence classes of generating sets of a given cardinality.

We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants. We prove that a large class of closed 3-manifolds (including disjoint unions of Stein fillable 3-manifo…

The study finds infinitely many different geometries for odd-dimensional manifolds with positive Ricci curvature.

We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.

Random Forest variable importance is improved by class balancing techniques.

We parametrize the commensurability classes of curves on Shimura surfaces that are totally geodesic, i.e., the commensurability classes of so-called $\mathbb{C}$-Fuchsian subgroups. In particular, if a Shimura surface contains one commensurability class of totally geodesic curves, it contains infinitely many.

Our main result is that the image of the quantum representation of a central extension of the mapping class group of the genus $g\geq 3$ closed orientable surface at a prime $p\geq 5$ is a Zariski dense discrete subgroup of some higher rank algebraic semi-simple Lie group $\mathbb G_p$ defined over $\Q$. As an applicat…

Engel manifolds show transverse tori can be made to have various formal invariants.

The study shows boundedness of certain fibered varieties in algebraic geometry.

The objective of the paper is to study accuracy of multi-class classification in high-dimensional setting, where the number of classes is also large ("large $L$, large $p$, small $n$" model). While this problem arises in many practical applications and many techniques have been recently developed for its solution, to t…

New examples of knots with infinitely many inequivalent slice disks.

The paper explores smooth equivariant rigidity and finds infinitely many exotic smooth structures.

Tautological classes, or generalised Miller-Morita-Mumford classes, are basic characteristic classes of smooth fibre bundles, and have recently been used to describe the rational cohomology of classifying spaces of diffeomorphism groups for several types of manifolds. We show that rationally tautological classes depend…

The study provides polynomial bounds for essential surfaces in various 3-manifolds.

Many Internet-of-Things (IoT) applications demand fast and accurate understanding of a few key events in their surrounding environment. Deep Convolutional Neural Networks (CNNs) have emerged as an effective approach to understand speech, images, and similar high dimensional data types. Algorithmic performance of modern…

Uncountably many fibrations found on genus 2 handlebody.

We show that the set of harmonic maps from the 2-dimensional stratified spheres with uniformly bounded energies contains only finitely many homotopy classes. We apply this result to construct infinitely many harmonic map flows and mean curvature flows of 2-sphere in the connected sum of two closed 3-dimensional manifol…

We prove that symplectic 4-manifolds with $b_1 = 0$ and $b^+ > 1$ have nonvanishing Donaldson invariants, and that the canonical class is always a basic class. We also characterize in many situations the basic classes of a Lefschetz fibration over the sphere which evaluate maximally on a generic fiber.

Proves transitivity of a specific class of quadratic polynomials.