Related papers: Perfectly normal type-2 fuzzy interpolation B-spli…
In this contribution, we propose a detailed study of interpolation-based data-driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer…
Classical machine learning classifiers tend to be overconfident can be unreliable outside of the laboratory benchmarks. Properly assessing the reliability of the output of the model per sample is instrumental for real-life scenarios where…
We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Previous methods focus on learning point weights to fit neighborhoods into a geometric…
Shape-Text matching is an important task of high-level shape understanding. Current methods mainly represent a 3D shape as multiple 2D rendered views, which obviously can not be understood well due to the structural ambiguity caused by…
Fuzziness in databases is used to denote uncertain or incomplete data. Relational Databases stress on the nature of the data to be certain. This certainty based data is used as the basis of the normalization approach designed for…
In this work, we tackle the task of point cloud denoising through a novel framework that adapts Diffusion Schr\"odinger bridges to points clouds. Unlike previous approaches that predict point-wise displacements from point features or…
Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point…
Berezinskii-Kosterlitz-Thouless transition of the classical XY model is re-investigated, combining the Tensor Network Renormalization (TNR) and the Level Spectroscopy method based on the finite-size scaling of the Conformal Field Theory. By…
We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve…
We consider a RG flow in certain 2D coset models perturbed by the least relevant field. In the case of the symmetric su(2) coset model we show, up to second order of the perturbation theory, that there exists a nontrivial IR fixed point.We…
The fuzzy supersphere $S_F^{(2,2)}$ is a finite-dimensional matrix approximation to the supersphere $S^{(2,2)}$ incorporating supersymmetry exactly. Here the star-product of functions on $S_F^{(2,2)}$ is obtained by utilizing the OSp(2,1)…
Real-world data contain uncertainty and variations that can be correlated to external variables, known as randomness. An alternative cause of randomness is chaos, which can be an important component of chaotic time series. One of the…
Generating continuous surfaces from discrete point cloud data is a fundamental task in several 3D vision applications. Real-world point clouds are inherently noisy due to various technical and environmental factors. Existing data-driven…
The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Tzung thus proposed deals with the problem of producing a…
We use the theory of p-curvature of connections to analyze stable vector bundles of rank 2 on curves of genus 2 which pull back to unstable bundles under the Frobenius morphism. We take two approaches, first using explicit formulas for…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
In Type-2 rule-based fuzzy systems (T2 RFSs), triangular norms on complete lattice $(\mathbf{L},\sqsubseteq)$ or $(\mathbf{L_u},\sqsubseteq)$ can be used to model the compositional rule of inference, where $\textbf{L}$ is the set of all…
Point cloud upsampling aims to generate dense point clouds from given sparse ones, which is a challenging task due to the irregular and unordered nature of point sets. To address this issue, we present a novel deep learning-based model,…
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…