arXiv research

New tree-structured Markov fields with Poisson marginals for counting variables.

Reconstructing signature features from randomized vector fields in differential equations.

In this note, we consider a fixed vector field $V$ on $S^2$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ is also tangent. We show that the expected value of the corresponding counting function is asymptotic to the eigenvalue with a leading coefficient that i…

High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical me…

Detects anomalies in vector fields without distributional assumptions.

Logistic regression for brain imaging without p-values.

Let $(M,g)$ be a smooth compact Riemannian surface with no boundary. Given a smooth vector field $V$ with finitely many zeroes on $M$, we study the distribution of the number of tangencies to $V$ of the nodal components of random band-limited functions. It is determined that in the high-energy limit, these obey a unive…

In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient messa…

MLDL preserves manifold geometry in vector transformations.

We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued kernels, whose equilibria are placed exactly at a desired set of locations and whose …

Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…

Study a risk model with tree-structured Poisson-Markov random field for rainfall events.

Based on the Aristotelian concept of potentiality vs. actuality allowing for the study of energy and dynamics in language, we propose a field approach to lexical analysis. Falling back on the distributional hypothesis to statistically model word meaning, we used evolving fields as a metaphor to express time-dependent c…

Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an algorithm to generate complex dynamics for parameters and (both visible and hidde…

We introduce a stochastic model for noisy vector fields on manifolds.

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class o…

The paper develops sampling methods for ocean phenomena based on temperature and salinity measurements.

Estimates binary labels from dependent data using Markov Random Fields.

A new method uses SPDEs to efficiently model random fields on complex domains.

DeformRS certifies deep networks against various input deformations.

Optimized sampling scheme for compressed sensing combining randomness and determinism.

Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert space…

Independent Component Analysis (ICA) is a statistical tool that decomposes an observed random vector into components that are as statistically independent as possible. ICA over finite fields is a special case of ICA, in which both the observations and the decomposed components take values over a finite alphabet. This p…

Paper transforms torse-forming vector fields into simpler forms.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

Conformal vector fields on LCP manifolds are orthogonal and Killing.

For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth famil…

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

Study on generalized derivations in polynomial vector fields Lie algebras.

Study on Einstein solitons with specific vector fields and their properties.

Investigates point spectra of vector fields and their properties.

We consider four dimensional lie groups equipped with left invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields de…

Examining singularities of commuting vector fields on submanifolds.

Vector fields invariant under Lie group action are finitely generated by polynomial fields.

The paper proves non-existence of torqued and anti-torqued vector fields on hyperbolic spaces.

We introduce G_2-vector fields, Rochesterian 1-forms and Rochesterian vector fields on manifolds with a closed G_2-structure as analogues of symplectic vector fields, Hamiltonian functions and Hamiltonian vector fields respectively, and we show that the spaces of G_2-vector fields and of Rochesterian vector fields are …

Enhances Hamiltonian systems stability through generalized double bracket vector fields.

Study classifies harmonic vector fields on 3-manifolds.

Machine Learning (ML) algorithms, like Convolutional Neural Networks (CNN), Support Vector Machines (SVM), etc. have become widespread and can achieve high statistical performance. However their accuracy decreases significantly in energy-constrained mobile and embedded systems space, where all computations need to be c…

Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology -- the entanglement of its field lines -- is non-trivial,…

Study proves conformal vector fields on certain Finsler manifolds are Killing fields.

Indices of vector fields and 1-forms studied for singular varieties and actions.

Harmonic basis vector fields on surfaces

The paper explores how vector fields relate to volume in geometric contexts.