Related papers: A Geometric Algebra Framework for a Multidimension…
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
This study introduces geometric algebra to decompose credit system relationships into their projective (correlation-like) and rotational (feedback-spiral) components. We represent economic states as multi-vectors in Clifford algebra, where…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
This paper extends approach of our joint paper with K\"{a}hler and recent paper of the author, published in 2021, on problems of the static Maxwell system in three dimensional inhomogeneous media. Applied pseudoanalytic function theory…
The Clifford spectrum is an elegant way to define the joint spectrum of several Hermitian operators. While it has been know that for examples as small as three $2$-by-$2$ matrices the Clifford spectrum can be a two-dimensional manifold, few…
We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…
Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on "ordinary" amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
Were investigated anisotropic metric of higher dimensional space-time with only cosmological term and scalar field. Showed, that presence of scalar field is equivalent to anisotropic metric in the multy dimensional space-time and proposed…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…
The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…
A solution to the effectiveness problem in Kohn's algorithm for generating subelliptic multipliers is provided for domains that include those given by sums of squares of holomorphic functions (also including infinite sums). These domains…
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…
The paper concerns nilpotent associative dialgebras and their corresponding diassociative Schur multipliers. Using Lie (and group) theory as a guide, we first extend a classic five-term cohomological sequence under alternative conditions in…