Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.
problem Separate Earth's magnetic field from vehicle's magnetic field for accurate magnetic navigation.
method Use machine learning (ML) and integrate physics of magnetic navigation (SciML) to remove aircraft magnetic field from total magnetic field.
result A model can be constructed to effectively remove aircraft magnetic field from the dataset.
We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We …
We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of th…
Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by…
In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of differential twisted String- and differential twisted Fivebrane-structures that generalize the notion of Spin-structure…
PPC detects anomalies in high-dimensional data efficiently.
problem Scalability issues and reduced performance with high-dimensional data.
method Probabilistic Predictive Coding (PPC) learns latent representations and predicts uncertainties.
result PPC achieves linear time complexity and high adaptability.
Improved detection of brain tumours in MRIs using latent space dissimilarities.
problem Detecting tumours in brain MRIs using unsupervised learning.
method Slice-wise semi-supervised method based on dissimilarity between latent representations of images and their reconstructions.
result Improved detection results with higher resolution images and better reconstructions.
Extends E. Hopf's theorem to magnetic systems without conjugate points.
problem Proving magnetic curvature non-positive for magnetic systems without conjugate points.
method Using magnetic curvature introduced by the first author, proving magnetic flatness conditions.
result Magnetic flatness is a rigid condition with specific metric and curvature properties.
A magnetic field is defined by the property that its divergence is zero in a three dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to studies the magnetic flow asociated wit…
Compatibility equations adapted to magnetic geometry.
problem No specific problem stated; magnetic geometry is the setting.
method Established compatibility equations in magnetic geometry.
result Analogues of Gauss, Ricci, and Codazzi-Mainardi equations in magnetic geometry.
This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.
problem Understanding dynamics of magnetic systems with geometric constraints.
method Developed Hamilton-Jacobi equations for magnetic systems with nonholonomic constraints.
result Revealed relationships between magnetic structures, constraints, and dynamics.
Magnetic Brunn-Minkowski inequalities on Riemannian manifolds
problem Establishing equivalence between Brunn-Minkowski inequalities and magnetic Ricci curvature
method Using magnetic geodesics
result Proving a sharp, undistorted Brunn-Minkowski inequality
Study shows finiteness of magnetic hypersurfaces on closed manifolds.
problem Understanding the finiteness of magnetic hypersurfaces on closed manifolds.
method Introduced a dynamical version of the second fundamental form to generalize a previous result.
result Real-analytic negatively s-curved magnetic systems on closed real-analytic manifolds have only finitely many closed totally s-magnetic hypersurfaces. The paper studies magnetic curves in C-manifolds and their properties.
problem Understanding magnetic trajectories in C-manifolds. method Proving magnetic trajectories are θα-slant curves and providing parametrizations. result Normal magnetic curves in C-manifolds are θα-slant curves with specific curvature functions. New tensors help solve magnetic flow integrability.
problem Integrability of magnetic flows on specific manifolds.
method Introduced magnetic Killing symmetric tensors to construct first integrals.
result Proved integrability of invariant magnetic flows on 2-step nilmanifolds.
Study magnetic geodesics on Heisenberg groups and manifolds.
problem Dynamics of magnetic flows on Heisenberg groups.
method Explicit description of magnetic geodesics, determination of lengths.
result Density of periodic magnetic geodesics and marked magnetic length spectrum rigidity.
Paper introduces magnetic Hodge Laplacian for differential forms.
problem No specific problem stated; general spectral analysis of differential forms.
method Introduced magnetic Hodge Laplacian, discussed spectral results.
result Similarities and differences with magnetic Laplacian on functions.
We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space.
Study on Yang-Mills equations on conformally compact manifolds, finding obstructions and asymptotics.
problem Obstructing higher conformal Yang-Mills equations on conformally compact manifolds.
method Formal asymptotics, Dirichlet-to-Neumann maps, higher transverse derivative boundary operators.
result Obstructing current is the variation of a conformally invariant coefficient in the interior Yang-Mills energy expansion.
Study of magnetic geodesics on Heisenberg nilmanifolds.
problem Existence and properties of closed magnetic geodesics on Heisenberg nilmanifolds.
method Analyzing conditions for the existence of closed magnetic geodesics on compact quotients of Heisenberg nilmanifolds.
result Existence of contractible closed magnetic geodesics for any energy level below the Mañé critical value.
Study magnetic Steklov eigenvalues on manifolds with boundary.
problem Eigenvalue problem for magnetic Steklov operators on compact manifolds.
method Equivalent characterizations, bounds, comparison results.
result Established bounds for the smallest eigenvalue of magnetic Steklov operators.
Study magnetic potentials on Anosov manifolds using spectral data.
problem Recover magnetic potentials from spectral data on Anosov manifolds.
method Utilize principal wave trace invariants and magnetic Schrödinger operator.
result Spectral data uniquely determines magnetic and electric potentials on Anosov manifolds.
Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curva…
Study magnetic curvature on Lie groups, extending Milnor's work.
problem Exploring magnetic curvatures on Lie groups.
method Computing magnetic curvatures and analyzing algebraic properties.
result Extending results from Milnor's classic paper on left-invariant metrics.
In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic systems such that the associated Hamiltonian flow is Zoll, i.e. every orbit is clos…
Study shows magnetic trajectories in Berger spheres are homogeneous.
problem Homogeneity of contact magnetic trajectories in Berger spheres.
method Proved every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.
result Contact magnetic trajectories in Berger spheres are homogeneous.
Extends magnetic flow theory results to higher dimensions.
problem Magnetic flows on manifolds of arbitrary dimension.
method New Pestov identities and adapted Riemannian geometry concepts.
result Established tensor tomography and ergodicity results for magnetic flows.
The paper explores how magnetic systems' spectra can identify metrics and 1-forms.
problem Can the marked magnetic action spectrum of magnetic systems with Anosov flow determine the metric and 1-form?
method The paper addresses this question in two settings: locally for systems with close metrics and 1-forms, and for metrics in the same conformal class.
result The paper answers the question affirmatively in both settings.
Study magnetic flows on 3D contact sub-Riemannian manifolds using Rumin complex.
problem Understanding magnetic flows on 3D contact sub-Riemannian manifolds.
method Introducing horizontal magnetic flows via closed Rumin differential two-forms and analyzing the lifted sub-Riemannian structure.
result Horizontal magnetic flows can be interpreted as geodesic flows on a suitably lifted structure, which is of Engel type when the magnetic field is non-vanishing.
Metrics are isometric for certain Anosov magnetic systems.
problem Isometry of metrics for Anosov magnetic systems.
method Conjugacy isotopic to the identity, volume-preserving conjugacy, cohomology class.
result Isometric metrics for conjugate Anosov magnetic systems.
Study on magnetic Dirac operators and their spectrum.
problem Understanding the spectrum of magnetic Dirac operators.
method Analysis of magnetic Dirac operators over complete Riemannian manifolds.
result Find sufficient conditions for maximal or discrete spectrum.
In a three-dimensional Riemannian manifold M that admits a unit Killing vector field ξ, we regard ξ as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with ξ. Then we characterize Sasakian structure on M from magnetic Hopf surfaces. That is, we show that i…
A quasiclassical method approximates magnetic monopole eigenvalues.
problem Describing eigenvalues of magnetic Laplacian in non-exact magnetic fields.
method Applying multidimensional WKB method to nontrivial line bundles.
result Demonstrated for Dirac magnetic monopole on a sphere.
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.
Homogeneous magnetic trajectories in a special linear group proven.
problem Proving homogeneity of magnetic trajectories in a specific group.
method Using contact magnetic curves and geodesics.
result Every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.
Study on Killing magnetic curves in Heisenberg group geometry.
problem Understanding Killing magnetic curves in Heisenberg group.
method Presentation of Heisenberg group geometry and geodesics, study of Killing magnetic curves with explicit formulas.
result Explicit formulas for Killing magnetic curves in Heisenberg group.
We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence equals angle of reflection" are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. Thi…
Homogeneous magnetic paths found in Heisenberg space.
problem Understanding magnetic geodesics in the Heisenberg group.
method Proving homogeneity of magnetic geodesics derived from the canonical contact structure.
result Magnetic geodesics in the Heisenberg group are homogeneous.
This study explores magnetic trajectories on the Heisenberg group, finding symmetries and solutions.
problem Understanding magnetic geodesics on the Heisenberg group with invariant Lorentz force.
method Analyzing the Heisenberg Lie group with a non-commutative product, deriving magnetic equations, identifying symmetries, and solving variational problems.
result Magnetic trajectories are solutions to a variational problem, providing explicit examples of Lagrangians.
Study magnetic curves in Sasakian manifolds, classifying and parametrizing them.
problem Classify and parameterize pseudo-Hermitian magnetic curves in Sasakian manifolds.
method Define and classify pseudo-Hermitian magnetic curves, construct parametrizations.
result Complete classification theorem for pseudo-Hermitian magnetic curves in Sasakian manifolds.
Study magnetic geodesics on Kähler potentials using variational methods.
problem Understanding magnetic geodesics on Kähler potentials.
method Variational method for a generalized Landau-Hall functional.
result Magnetic geodesic equation and its relation to a perturbed complex Monge-Ampère equation.
The article studies eigenvalues and spectrum of magnetic Dirac operators.
problem Fundamental mathematical properties of magnetic Dirac operators remain unexplored.
method Eigenvalue estimates and explicit spectrum computation for specific cases.
result Explicit computation of spectrum for magnetic fields on specific manifolds.
We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece γ of the boundary must be algebraic and eith…
Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …
Combines geometric hydrodynamics with magnetic systems to derive new equations and prove well-posedness.
problem Deriving new equations for magnetic systems and proving their well-posedness.
method Introducing the magnetic Euler-Arnold equation and proving well-posedness for specific equations.
result Local and global well-posedness results for the magnetic Euler-Arnold equation associated with the global quasi-geostrophic equations.
Anosov magnetic flows on surfaces are characterized.
problem Characterizing Anosov magnetic flows on surfaces.
method Using Wojtkowski's quotient bundle, necessary and sufficient conditions are derived.
result Necessary and sufficient conditions for Anosov magnetic flows on surfaces are established.
Study magnetic geodesics on odd spheres, computing critical energy values.
problem Understanding magnetic geodesics on odd-dimensional spheres.
method Explicit computation and analysis of submanifolds and symmetries.
result Energy values determine magnetic geodesic connectivity on spheres.
Researchers prove integrability of magnetic systems on spheres up to dimension 6.
problem Integrability of magnetic systems on spheres restricted to their surface.
method Proved complete integrability for n ≤ 6, noncommutative integrability for n ≥ 7, conjectured integrability for all n.
result Complete integrability of magnetic flows on spheres for n ≤ 6, noncommutative integrability for n ≥ 7.