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This study introduces an efficient workflow for functional data analysis in classification problems, utilizing advanced orthogonal spline bases. The methodology is based on the flexible Splinets package, featuring a novel spline…

The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…

Delicate cloth simulations have long been desired in computer graphics. Various methods were proposed to improve engaged force interactions, collision handling, and numerical integrations. Deep learning has the potential to achieve fast and…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves.…

The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…

This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…

We present a flexible illustrative line style model for the visualization of streamline data. Our model partitions view-oriented line strips into parallel bands whose basic visual properties can be controlled independently. We thus extend…

This is the first report on Working Paper WP-RFM-14-01. The potential and capability of sparse representations is well-known. However, their (multivariate variable) vectorial form, which is completely fine in many fields and disciplines,…

In the field of volumetric data processing and analysis, extracting mid-surfaces from thinly bounded compartments is crucial for tasks such as surface area estimation and accurate modeling of biological structures, yet it has lacked a…

Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…

This research proposes an effective vertical clustering strategy of 3D data in an elliptical helical shape based on 2D geometry. The clustering object is an elliptical cross-sectioned metal pipe which is been bended in to an elliptical…

This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of time interpolation of such data. Current models in use…

To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…

The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…

In this paper, we propose a new flexible family of distributions for data that consist of three angles, two angles and one linear component, or one angle and two linear components. To achieve this, we equip the recently proposed trivariate…

Dense suspensions of particles dispersed in liquids are central to industrial and geophysical processes and serve as model systems for out-of-equilibrium soft matter. At high particle concentrations, they exhibit stress-dependent rheology,…

We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construction of provably stable discretizations of arbitrary order…

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…

A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…