arXiv research

TSVQR captures heterogeneous and asymmetric data using quantile regression.

In this paper we describe the notion of an annular end of a Riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the harmonic function. We then apply these results to understand and cha…

A-StarGAN improves nonparallel voice conversion speed and realism.

Although voice conversion (VC) algorithms have achieved remarkable success along with the development of machine learning, superior performance is still difficult to achieve when using nonparallel data. In this paper, we propose using a cycle-consistent adversarial network (CycleGAN) for nonparallel data-based VC train…

We propose a nonparallel data-driven emotional speech conversion method. It enables the transfer of emotion-related characteristics of a speech signal while preserving the speaker's identity and linguistic content. Most existing approaches require parallel data and time alignment, which is not available in most real ap…

An immersion of a smooth $n$-dimensional manifold $M \to \mathbb{R}^q$ is called totally nonparallel if, for every distinct $x, y \in M$, the tangent spaces at $f(x)$ and $f(y)$ contain no parallel lines. Given a manifold $M$, we seek the minimum dimension $TN(M)$ such that there exists a totally nonparallel immersion …

Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. The first type constructs the hyperplanes separately. It solves a series of small optimization problems to obtain a series of hyperplanes, but is hard to measure the …

New NHCAs improve multi-category classification efficiency.

Embeddings of pairs of disjoint nonparallel primitive simple closed curves in the boundary of a genus two handlebody are classified. Briefly, two disjoint primitives either lie on opposite ends of a product $F \boldsymbol{\times} I$, or they lie on opposite ends of a kind of "twisted" product $F \widetilde{\boldsymbol{…

The complete local classification and geometric description of n-dimensional submanifolds F with recurrent nonparallel second fundamental form in the spaces of constant curvature M(c) are obtained in this article.

Develops NPSVC++ to improve NPSVC performance through representation learning.

It is shown that for given positive integers g and b, there is a number C(g,b), such that any orientable compact irreducible 3-manifold of Heegaard genus g has at most C(g,b) disjoint, nonparallel incompressible surfaces with first Betti number b_1 < b.

In this paper, we analyze the geometric structure of an Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very …

By adopting the polynomial interpolation method, we propose an approach to hedge against the interest-rate risk of the default-free bonds by measuring the nonparallel movement of the yield-curve, such as the translation, the rotation and the twist. The empirical analysis shows that our hedging strategies are comparable…

We develop a parallel variational inference (VI) procedure for use in data-distributed settings, where each machine only has access to a subset of data and runs VI independently, without communicating with other machines. This type of "embarrassingly parallel" procedure has recently been developed for MCMC inference al…

In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds with nonpositive Ricci curvature, thus generalizing a theorem of T. K. Pan. Then…

Ordinal regression (OR) is a special multiclass classification problem where an order relation exists among the labels. Recent years, people share their opinions and sentimental judgments conveniently with social networks and E-Commerce so that plentiful large-scale OR problems arise. However, few studies have focused …

We present the Voice Conversion Challenge 2018, designed as a follow up to the 2016 edition with the aim of providing a common framework for evaluating and comparing different state-of-the-art voice conversion (VC) systems. The objective of the challenge was to perform speaker conversion (i.e. transform the vocal ident…

Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to $\mathbb{CP}^2$. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plan…

We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.

The study classifies semiaffine stable planes into affine, projective, or punctured projective planes.

Stable planes are locally isomorphic to classical projective planes.

Only vertical planes are asymptotic to other planes in 3D space.

Study of elementary planes in Apollonian orbifold with unusual equidistribution.

Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…

Criteria for sharksfin and deltoid singularities from plane to plane, with applications.

We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…

The study explores conformal planes with finite areas.

For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…

We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.

This thesis explores bifoliated planes and their group actions from Anosov flows.

We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…

Two proofs show that removing a loop from a plane circuit splits the plane.

The paper classifies singularities of plane congruences and affine distance functions.

Computed distortion coefficients for the α-Grushin plane.

New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.

New harmonic maps to hyperbolic plane via Bäcklund transformation.

Study compact plane waves, showing they are essentially standard.

The paper examines asymptotic lines of plane fields in 3D space.

A 6-regular triangulation for hyperbolic plane created.

Study local and global aspects of complex plane curve embeddings.

A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and by considering the complexifications of these four projective planes.

A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that the diffeomorphism is conformal (when the condition is fulfilled for weakly degene…

We study a moduli stratum of A-orbits of plane-to-plane germs of corank 2 with codimension 3. We describe explicitly the bifurcation diagram of its topologically A-versal unfolding. Two geometric applications to parabolic objects are presented.

We shall give useful criteria of lips, beaks and swallowtail singularities of smooth map from the plane into the plane. As an application of criteria, we will discuss the singularities of Cauchy problem of single conservation law.

Proves conjecture about geodesic foliations in Riemannian planes.

Stochastic cutting planes improve data-driven optimization speed.

The paper characterizes coverings over the projective plane with minimal defect.