arXiv research

Deep learning diagnoses rotary machine faults without expert input.

New method detects bearing faults using multivariate statistical process control.

Paper proposes new methods for improving interatomic potentials.

Improved fault diagnosis for bearings using mRMR and transfer learning.

STRING improves 2D and 3D position encodings for better performance.

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. I…

Innovative ball bearing converts rotary to reciprocating motion.

DRFormer uses dynamic tokenization and multi-scale transformer to forecast long time series.

ElasTST improves time-series forecasting across varying horizons.

Extends graph factor system to quasi-median graphs.

An energy based approach for stabilizing a mechanical system has offered a simple yet powerful control scheme. However, since it does not impose such strong constraints on parameter space of the controller, finding appropriate parameter values for an optimal controller is known to be hard. This paper intends to generat…

Survey of tools for studying hierarchical hyperbolic spaces.

The article constructs differential operators for parabolic geometries.

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.

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…

This paper studies an intelligent ultimate technique for health-monitoring and prognostic of common rotary machine components, particularly bearings. During a run-to-failure experiment, rich unsupervised features from vibration sensory data are extracted by a trained sparse auto-encoder. Then, the correlation of the ex…

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…

A new method combines EMD and diffusion maps for protein shape analysis.

This paper introduces a new task to better understand Transformers in quantitative contexts.

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.

Unified framework analyzes and compares RFF and RoPE PEs for music generation.

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…

Categorifies Jones polynomial using Lie theory.

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.

New complexes refine multicomplexes for subRiemannian geometry.

We unify $\textit{kernel density estimation}$ and $\textit{empirical Bayes}$ and address a set of problems in unsupervised learning with a geometric interpretation of those methods, rooted in the $\textit{concentration of measure}$ phenomenon. Kernel density is viewed symbolically as $X\rightharpoonup Y$ where the rand…

This article serves a few purposes. First of all, it reviews polyfold--Kuranishi correspondence I (http://arxiv.org/abs/1402.7008) and previews and samples some results from four papers I have been preparing. It is also a written-up and expanded version of a talk I gave at a symplectic conference in Chengdu on June 28,…