The weighted k-nearest neighbors (WkNN) algorithm is by far the most popular choice in the design of fingerprinting indoor positioning systems based on WiFi received signal strength (RSS). WkNN estimates the position of a target device by selecting k...
Traditional supervised band selection (BS) methods mainly consider reducing the spectral redundancy to improve hyperspectral imagery (HSI) classification with class labels and pairwise constraints. A key observation is that pixels spatially close to...
With the urgent demand for automatic management of large numbers of high-resolution remote sensing images, content-based high-resolution remote sensing image retrieval (CB-HRRS-IR) has attracted much research interest. Accordingly, this paper propose...
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformati...
In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are o...
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most...
This paper presents an overview of coding methods used to encode a set of covariance matrices. Starting from a Gaussian mixture model (GMM) adapted to the Log-Euclidean (LE) or affine invariant Riemannian metric, we propose a Fisher Vector (FV) descr...
The current scenario of colorimetry shows a wide variety of different metrics which do not converge in the assessment of the color rendering of light sources. The limitations of the Color Rendering Index have promoted the emergence of new metrics, su...
The polynomial affine model of gravity was proposed as an alternative to metric and metric-affine gravitational models. What, in the beginning, was thought to be a source of unpredictability—the presence of many terms in the action—turned...
We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physi...
Locally strictly convex surfaces in four-dimensional affine space are studied from a perspective of the affine structure invented by Nuño-Ballesteros and Sánchez, which is especially suitable in convex geometry. The surfaces that are embedded in loca...
We geometrically derive the explicit form of the unitary representation of the Poincaré group for vector-valued wave functions and use it to apply speed-of-light boosts to a simple polarization basis to end up with a Hawton–Baylis photon...
This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties. We show how to use parameterized Alpha-Beta (AB) and Gamma log-det divergences...
We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a “ro...
The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as “Lie group thermodynam...
We derive the full set of field equations for the metric-affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by F(R,T...
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The e...
A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space that—in...
Three-dimensional (3D) object tracking is critical in 3D computer vision. It has applications in autonomous driving, robotics, and human–computer interaction. However, methods for using multimodal information among objects to increase multi-obj...
Mapping large areas for planning and conservation is a challenge undergoing rapid transformation. For centuries, the creation of broad-extent maps was the near-exclusive domain of expert specialist cartographers, who painstakingly delineated regions...
The early cosmology, driven by a single scalar field, both massless and massive, in the context of Eddington-inspired Born-Infeld gravity, is explored. We show the existence of nonsingular solutions of bouncing and loitering type (depending on the si...
In this paper, focusing on 4-dimensional space, we extend our previous results of solving linear tensor equations. In particular, we consider a 30-parameter linear tensor equation for the unknown tensor component Nαμν in terms of the know...
In this article, we generalize Yano’s concept of a half-symmetric affine connection. With respect to this generalization, we obtain five linearly independent curvature tensors. In the following, we examine which special kinds of affine connecti...
Using a semiempirical approach, we show that modified gravity affects the internal properties of terrestrial planets, such as their physical characteristics of a core, mantle, and core–mantle boundary. We also apply these findings for modeling...
A Riemannian manifold endowed with k>2 orthogonal complementary distributions (called here an almost multi-product structure) appears in such topics as multiply twisted or warped products and the webs or nets composed of orthogonal foliations. In...
Minisuperspace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from various po...
We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern...
Palatini-like theories of gravity have a remarkable connection to models incorporating linear generalized uncertainty principles. Considering this, we delve into the thermodynamics of systems comprising both Bose and Fermi gases. Our analysis encompa...
Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral formulas for almost multi-product manifolds, foliations and multiply twisted products of Riemannian, metric-affine and sub-Riemannian manifolds,...
We present an algorithmic and visual grouping of participants and eye-tracking metrics derived from recorded eye-tracking data. Our method utilizes two well-established visualization concepts. First, parallel coordinates are used to provide an overvi...
The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of diff...
A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,∇) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection ∇* can be defined. In this wo...
The subjects of our study are affine hypersurfaces f:M→R2n+2 considered with a transversal vector field C, which is J˜-tangent. By J˜ we understand the canonical paracomplex structure on R2n+2. The vector field C induces on the hyper...
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providin...
Let Mk be a metric E4=I−manifold equipped with electromagnetic-type structure E, a pseudo-Riemannian metric g and a nondegenerate 2−form ω^. The paper deals with Codazzi couplings of an affine connection ∇ with E, g and &omega...
Finding affine parameters for null geodesics is often of considerable physical importance, especially when studying null geodesics or dealing with conservation laws and/or averaged energy conditions. But explicitly finding null affine parameters is a...
A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices. Although affine-invaria...
In this study, we introduce an innovative method for load forecasting that capitalizes on the concept of task affinity score to measure the similarity between various tasks. The task affinity score emerges as a superior technique for assessing task s...
In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply norma...
We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r0. After imposing spherical symmetry and after restriction to the Killing horizon, the metric is quantized employing the chiral currents f...
In this work, we explore a three-dimensional formulation of the polynomial affine model of gravity, which is a model that extends general relativity by relaxing the equivalence principle through the exclusion of the metric from the set of fundamental...
Canonical quantization has created many valid quantizations that require infinite-line coordinate variables. However, the half-harmonic oscillator, which is limited to the positive coordinate half, cannot receive a valid canonical quantization becaus...
We introduce the concept of quasi-semi-Weyl structure, we provide a couple of ways for constructing quasi-statistical and quasi-semi-Weyl structures by means of a pseudo-Riemannian metric, an affine connection and a tensor field on a smooth manifold,...
The judicious application of ligand or binding efficiency (LE) metrics, which quantify the molecular properties required to obtain binding affinity for a drug target, is gaining traction in the selection and optimization of fragments, hits and leads....
In this paper, we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz–Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on this Riemann...
Current state-of-the-art techniques for the solid phase synthesis of molecularly imprinted polymer (MIP) nanoparticles typically rely on amino silanes for the immobilisation of template molecules prior to polymerisation. An investigation into commonl...
We explore the information geometric structure of the statistical manifold generated by the \(\kappa\)-deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fi...
We review Pólya vector fields associated to holomorphic functions as an important pedagogical tool for making the complex integral understandable to the students, briefly mentioning its use in other dimensions. Techniques of differential geometry are...
The metric self-organization of matterspace–time implies a nonlocal correlation of its affine connections and the fulfillment of the volumetric conservation of energy–momentum under shifts in coordinate time. Geodesic forces or accelerati...
In the paper, we consider holomorphically projective mappings of n-dimensional pseudo-Riemannian Kähler and hyperbolic Kähler spaces. We refined the fundamental linear equations of the above problems for metrics of differentiability class C...
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