arXiv research

Study shows normal distribution in divisor counts of random sections on complex manifolds.

Study on zeros of Gaussian sections on semipositive line bundles on punctured Riemann surfaces.

The study proves a central limit theorem for Gaussian holomorphic sections on Kähler manifolds.

This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on Metropolis-Hastings algorithm. Next, by using MH algorithm, we simulate the data from Ising model…

We prove that a Gaussian ensemble of smooth random sections of a real vector bundle over compact manifold canonically defines a metric on the bundle together with a connection compatible with it. Additionally, we prove a refined Gauss-Bonnet-Chern theorem stating that if the bundle and the manifold are oriented, then t…

We extend Kac-Rice formula to compute expected intersections of random submanifolds.

The paper studies random systems of holomorphic sections on compact Kähler manifolds and proves equidistribution results.

The paper estimates variance of random sections on complex manifolds.

The paper classifies translation surfaces with constant curvature in a specific connection.

The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space of Gaussian measures inside the $L^2$-Wasserstein space, we manag…

We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact structure on a closed 3-dimensional manifold $M$ there is a metric, such that th…

Serial section electron microscopy (ssEM) is a widely used technique for obtaining volumetric information of biological tissues at nanometer scale. However, accurate 3D reconstructions of identified cellular structures and volumetric quantifications require precise estimates of section thickness and anisotropy (or stre…

Safe active learning for time-series models with Gaussian processes.

SLEIPNIR improves Gaussian process regression with derivatives, scaling up efficiently and accurately.

In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold. We then combine the notion of curvature of a Markov chain due to Joulin and Ollivier with the classical se…

The paper tackles Kakeya and Nikodym sets on curved manifolds, reducing problems to Euclidean space.

New method for unbinned, profiled unfolding in particle physics.

A surface M is called p-minimal if one of the coordinate functions is p-harmonic in the inner metric. We show that in the twodimensional case the Gaussian map of such surfaces is quasiconformal. In the case when the surface is a tube we study the geometrical structure of such surfaces. In particularly, we establish the…

The problem of missing values in multivariable time series is a key challenge in many applications such as clinical data mining. Although many imputation methods show their effectiveness in many applications, few of them are designed to accommodate clinical multivariable time series. In this work, we propose a multiple…

GPR ensemble method predicts stock returns efficiently.

A new method uses deep Gaussian processes to handle missing values in irregularly sampled healthcare data.

In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff orthogonality, we get an analogue of the Gauss map. Then we can define concepts of principa…

Grauert constructs complete Kähler metrics on complements of complex analytic sets.

We apply variational inference to learn vehicle trajectory parameters from noisy data.

Method for factor analysis in short panels without assuming sphericity or Gaussianity.

We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, …

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…

Rapidly estimating the remaining wall thickness (RWT) is paramount for the non-destructive condition assessment evaluation of large critical metallic pipelines. A robotic vehicle with embedded magnetism-based sensors has been developed to traverse the inside of a pipeline and conduct inspections at the location of a br…

This paper proposes an empirical test of financial contagion in European equity markets during the tumultuous period of 2008-2011. Our analysis shows that traditional GARCH and Gaussian stochastic-volatility models are unable to explain two key stylized features of global markets during presumptive contagion periods: s…

Researchers provide counterexamples to Pogorelov and Toponogov's questions about saddle surfaces.

In the present paper we study the structure of the cut locus of a Randers rotational 2-sphere of revolution $(M, F = α+β)$. We show that in the case when the Gaussian curvature of the Randers surface is monotone along a meridian, the cut locus of a point $q\in M$ is a point on a subarc of the opposite half bending meri…

The study proves inequalities and curvature properties for Markov chains.

Deep forecasting models show output heads significantly improve performance on fat-tailed financial returns.

In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton $(M^{n},g,f)$ with sectional curvature $K(g)<A$ and ${\rm Vol}_{f}(M)\geq v$ for some uniform constant $A,v$, there exists…

A new machine learning method handles nuisance parameters for better unfolding in particle physics.

We define the notion of special Lagrangian curvature, showing how it may be interpreted as an alternative higher dimensional generalisation of two dimensional Gaussian curvature. We obtain first a local rigidity result for this curvature when the ambiant manifold has negative sectional curvature. We then show how this …

Bayesian optimisation (BO) is widely used to optimise stochastic black box functions. While most BO approaches focus on optimising conditional expectations, many applications require risk-averse strategies and alternative criteria accounting for the distribution tails need to be considered. In this paper, we propose ne…

Survey on Bayesian inference for Gaussian mixture models.

The Chern sectional curvature of a Hermitian manifold is derived and related to Kähler metrics.

In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalar curvature of the underlying Riemannian manifold. In particular we show that the only complete expanding solitons with no…

Study Higgs sections and flat sections for nonlinear harmonic bundles.

PAGP uses physics-assisted Gaussian processes to solve and learn PDEs.

Defines basic sections of LA-groupoids for simpler modeling.

This thesis predicts the distribution of smoothed zeros of random sections on line bundles.

New proof shows holomorphic sectional curvature fully determines curvature tensor.

Introduces homotopy momentum sections on multisymplectic manifolds.

Let $P(M,G)$ be a principal fiber bundle and $E(M,N,G,P)$ be an associate fiber bundle. Our interested is to study harmonic sections of the projection $π_{E}$ of $E$ into $M$. Our first purpose is to give a stochastic characterization of harmonic section from $M$ into $E$ and a geometric characterization of harmonic se…

Classifies surfaces of section for Seifert fibrations.