Related papers: Generalised Modal Analysis with the Pad\'e-Laplace…
We consider the k-th order statistic from unit exponential distribution and show that it can be represented as a sum of independent exponential random variables. Our proof is simple and different. It readily proves that the standardized…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
A numerical procedure and its MAPLE implementation capable of rigorously, albeit in a brute-force manner, proving specific strict one-variable inequalities in specific finite intervals is described. The procedure is useful, for instance, to…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However,…
Existing methods for multi-modal time series representation learning aim to disentangle the modality-shared and modality-specific latent variables. Although achieving notable performances on downstream tasks, they usually assume an…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families…
The Bopp's shifts will be generalized through symplectic formalism. A special procedure, like a "diagonalization", which drives the completely deformed symplectic matrix to the standard symplectic form was found as suggested by…
A new class of distributions, called Generalized One Parameter Polynomial Exponential-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented.…
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…
We present an algorithm using transformation groups and their irreducible representations to generate an orthogonal basis for a signal in the vector space of the signal. It is shown that multiresolution analysis can be done with amplitudes…
Modelling longitudinal data is an important yet challenging task. These datasets can be high-dimensional, contain non-linear effects and time-varying covariates. Gaussian process (GP) prior-based variational autoencoders (VAEs) have emerged…
PDDSparse is a new hybrid parallelisation scheme for solving large-scale elliptic boundary value problems on supercomputers, which can be described as a Feynman-Kac formula for domain decomposition. At its core lies a stochastic linear,…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
Many modern causal questions ask how treatments affect complex outcomes that are measured using wearable devices and sensors. Current analysis approaches require summarizing these data into scalar statistics (e.g., the mean), but these…
We offer a groupoid-theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand-MacPherson correspondence and the Gale transform as well as giving Zariski-local descriptions of the moduli space of…
Finance is heavily influenced by data-driven decision-making. Meanwhile, our ability to comprehend the full informational content of data sets remains impeded by the tools we apply in analysis, especially where the data is high-dimensional.…
This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…