arXiv research

Defines finite type Multivalued Shape using hyperspaces.

We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally defined variational equations.

Paper constructs multivalued harmonic functions on R^3 using twistor methods.

Bayesian method models multivalued power data from wind farms.

We extend the work of Simon and Wickramasekera, who constructed a large class of $C^{1,μ}$ multivalued solutions to the minimal surface equation, to produce $C^{1,μ}$ multivalued solutions to more general classes of elliptic equations and systems, including the minimal surface system with small boundary data and the La…

We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deformations of the data. The proof is an application of a version of the Na…

Generalization is one of the most important issues in machine learning problems. In this study, we consider generalization in restricted Boltzmann machines (RBMs). We propose an RBM with multivalued hidden variables, which is a simple extension of conventional RBMs. We demonstrate that the proposed model is better than…

This article is a survey of the Novikov problem of the structure of leaves of the foliations induced by a collection of closed 1-forms in a compact manifold $M$. Equivalently, this is to the study of the level sets of multivalued functions on $M$. To date, this problem was thoroughly investigated only for $M=\Bbb T^n$ …

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our…

Two accelerated extragradient methods converge at $O(1/k)$ rate for co-hypomonotone inclusions.

Framework for universal graph function approximators outperforms existing methods.

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.

The Gauss Image Measure uniquely identifies dual convex bodies up to dilation.

New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.

The paper explores eigenfunctions of spherical conical metrics using harmonic maps to spheres.

In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the Normal- Hedge bound, which mainly depends on the effective number of experts but also weakly depends on the nominal…

Let M be a closed n-dimensional manifold, n > 2, whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form $α$ on M , closed but non-exact, and a pseudo-gradient X such that the differential $\partial$ X of the Novikov complex of the pair ($α$, X) has at leas…

Extends holomorphic functions on complex manifolds to larger spaces.

We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold $Σ$ of a Riemannian manifold $\mathcal{M}$. We define the multiple valued counterpart of the classical Jacobi fields as the minimizers of the second variation functional defined on a Sobolev space of …

Machine learning finds Z/2 eigenfunctions on a sphere.

We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm. We use the mathematical concept of fiber bundle to characterize the multivalued …

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found using mean-shift algorithms. We describe the theory and practice behind clustering…

The purpose of the paper is to introduce some conjectures regarding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and 3-manifolds into two power series of type P and NP, convergent in …

EDML is a recently proposed algorithm for learning MAP parameters in Bayesian networks. In this paper, we present a number of new advances and insights on the EDML algorithm. First, we provide the multivalued extension of EDML, originally proposed for Bayesian networks over binary variables. Next, we identify a simplif…

We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued ''Darboux'' case). We specify normal forms in e…

Cieliebak, Mundet i Riera and Salamon recently formulated a definition of branched submanifold of Euclidean space in connection with their discussion of multivalued sections and the Euler class. This note proposes an intrinsic definition of a weighted branched manifold Z that is obtained from the usual definition of or…

Proves resurgent nature of a series solution to deformed Painlevé I equation.

Geomstats introduces shape module for analyzing shapes of objects.

Study on eigenfunctions on sphere configurations, proving non-existence and construction of critical eigensections.

A new shape space allows optimization of non-smooth shapes in fluid mechanics.

Introduces Star-Shaped deviation measures for risk analysis.

Optimizes shapes in uncertain Navier-Stokes flow problems.

New method reconstructs 3D shapes from 2D images using Kendall's shape space.

A novel method predicts shape development using Riemannian shape spaces.

This paper tackles shape denoising in computer vision and medical imaging.

The paper proves a conjecture about the positivity of the Euler characteristic for complex projective manifolds.

In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…

Paper analyzes shapes of brain arterial networks using statistical methods.

Develops new shape metrics for high-dimensional objects.

Paper tackles shape graph registration using neural networks.

In this paper, we describe a novel shape classification method which is embedded in the Bayesian paradigm. We discuss the modelling and the resulting shape classification algorithm for two and three dimensional data shapes. We conclude by evaluating the efficiency and efficacy of the proposed algorithm on the Kimia sha…

The paper explores three methods to assign a metric to shape spaces.

The paper proves inequalities for star-shaped and $F$-mean convex hypersurfaces in $\mathbb{R}^{n+1}$.

PointGMM learns hGMMs from point clouds for 3D shape representation.

New star-shaped acceptability indexes generalize existing methods.

New method learns shape correspondences robustly from raw geometry.

Generative modeling of 3D shapes has become an important problem due to its relevance to many applications across Computer Vision, Graphics, and VR. In this paper we build upon recently introduced 3D mesh-convolutional Variational AutoEncoders which have shown great promise for learning rich representations of deformab…

We introduce and develop fine shape, which has a very simple definition and aims to supersede all previously known shape theories for metrizable spaces. The problem with known shape theories of metrizable spaces is illustrated by the following bizarre situation. Čech cohomology is an invariant of shape, and a fortiori …