arXiv research

EVI-MMD approximates target distributions via MMD minimization with adaptive kernel.

A new EVI framework improves ParVI methods by maintaining variational structure and reducing KL-divergence.

Variational inference (VI) is a widely used framework in Bayesian estimation. For most of the non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimate the posterior distributions of the parameters. Recently, an improved framework, namely the extended variational inference…

This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the structural properties of solutions to the $\mathrm{EVI}$ formulation, such as co…

New method accelerates energetic variational inference using particle dynamics.

We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying space as a super Ricci flow as previously introduced by the second author. Our ma…

The goal of this paper is twofold: we study metric measure spaces $(X,d,m)$ with variable lower bounds for the Ricci curvature and we study pathwise coupling of Brownian motions. Given any lower semicontinuous function $k:X\to \mathbb R$ we introduce the curvature-dimension condition $CD(k,\infty)$ which canonically ex…

New rule reduces exploration regret to logarithmic, improving bad episode handling.

Extends graph factor system to quasi-median graphs.

Survey of tools for studying hierarchical hyperbolic spaces.

Study K-theory of homogeneous spaces of Lie groups.

The article constructs differential operators for parabolic geometries.

Unified approach to analysis on Ricci nonnegative manifolds and flows using optimal transport.

Paper presents a data preprocessing method for PHM models.

The ability to generalize is an important feature of any intelligent agent. Not only because it may allow the agent to cope with large amounts of data, but also because in some environments, an agent with no generalization capabilities cannot learn. In this work we outline several criteria for generalization, and prese…

This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set of algebraic invariants -- the homotopy groups, and (2) an analog o…

Paper shows mapping class groups are not extremely amenable except for specific cases.

New method connects CAT(0) spaces to hyperbolic spaces.

We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.

This article presents an empirical study of thirteen derivative markets for commodity and financial assets. It compares the statistical properties of futures contracts's daily returns at different maturities, from 1998 to 2010 and for delivery dates up to 120 months. The analysis of the fourth first moments of the dist…

New theory proves representability of PDE solutions without complex machinery.

Abstract machinery finds obstructions to uniform positive scalar curvature.

Keywords: corporate finance, Wrocław University of Economics, net profit margin lub net sales profitability

Accurately estimating the remaining useful life (RUL) of industrial machinery is beneficial in many real-world applications. Estimation techniques have mainly utilized linear models or neural network based approaches with a focus on short term time dependencies. This paper, introduces a system model that incorporates t…

For a real or complex semisimple Lie group $G$ and two nested parabolic subgroups $Q\subset P\subset G$, we study parabolic geometries of type $(G,Q)$. Associated to the group $P$, we introduce a class of relative natural bundles and relative tractor bundles and construct some basic invariant differential operators on …

We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on various special types…

New method detects bearing faults using multivariate statistical process control.

In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently proposed extended variational inference (EVI) framework is adopted to derive an a…

We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns $Y(t), Z(t), K(t,\cdot)$. The driver of …

The study finds that the export shares of machinery and food/crude materials are significantly correlated with GDP.

Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.

We prove the Chern-Gauss-Bonnet Theorem using sigma models whose source supermanifolds have super dimension 0|2. Along the way we develop machinery for understanding manifold invariants encoded by families of 0|n-dimensional Euclidean field theories and their quantization.

Recent trends focusing on Industry 4.0 concept and smart manufacturing arise a data-driven fault diagnosis as key topic in condition-based maintenance. Fault diagnosis is considered as an essential task in rotary machinery since possibility of an early detection and diagnosis of the faulty condition can save both time …

The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to …

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of …

Instantons on various spaces can be constructed via a generalization of the Fourier transform called the ADHM-Nahm transform. An explicit use of this construction, however, involves rather tedious calculations. Here we derive a simple formula for instantons on a space with one periodic direction. It simplifies the ADHM…

We prove a version of the Tits alternative for groups acting on complete, finite rank median spaces. This shows that group actions on finite rank median spaces are much more restricted than actions on general median spaces. Along the way, we extend to median spaces the Caprace-Sageev machinery and part of Hagen's theor…

We study minimal graphs in the homogeneous Riemannian 3-manifold $\widetilde{PSL_2(\mathbb{R})}$ and we give examples of invariant surfaces. We derive a gradient estimate for solutions of the minimal surface equation in this space and develop the machinery necessary to prove a Jenkins-Serrin type theorem for solutions …

We give a global version of the Bryant representation of surfaces of constant mean curvature one (cmc-1) in hyperbolic space. This allows to set the associated non-abelian period problem in the framework of flat unitary vector bundles on Riemann surfaces. We use this machinery to prove the existence of certain cmc-1 su…

Systematic prolongation for Killing two-tensors in symmetric spaces.

We study Hamiltonian stationary Lagrangian surfaces in C^2, i.e. Lagrangian surfaces in C^2 which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representatio…

In this paper, we present a probability one convergence proof, under suitable conditions, of a certain class of actor-critic algorithms for finding approximate solutions to entropy-regularized MDPs using the machinery of stochastic approximation. To obtain this overall result, we prove the convergence of policy evaluat…

Categorifies Jones polynomial using Lie theory.

Harmonic maps pull convex functions on metric spaces to subharmonic ones.

New method improves anomaly detection in acoustic signals.

We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey products in de Rham, singular, and Deligne cohomology. The setting and the algebraic m…

Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.

Study shows symplectic mapping groups of K3 surfaces are infinitely generated.