arXiv research

New formulas for measuring geometric properties of definable sets.

Researchers prove formulas for flag area measures, extending previous work.

The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is shown to have the structure of a co-product. In the case of the unitary group the…

We revisit the contact measures introduced by Firey, and further developed by Schneider and Teufel, from the perspective of the theory of valuations on manifolds. This reveals a link between the kinematic formulas for area measures studied by Wannerer and the integral geometry of curved isotropic spaces. As an applicat…

We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natu…

Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ of dual unitarily invariant curvature measures. Building on the recent results from integral geometry in complex space forms, we describe this algebra structure explicitly as a…

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local kinematic formulas on such spaces were recently obtained. While the local and global k…

New proof confirms operations on constructible functions match theory.

The paper proposes a method to align surgical videos using kinematic data.

ANNs solve complex inverse kinematics of a Tricept parallel robot.

Proves a special case of the Gaussian kinematic formula using large sphere limits.

Proposes KStar Diffuser for kinematics-aware bimanual robotic manipulation.

Study examines how body segments respond to random vibrations.

The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic quantity and quality of objects of transactions is introduced. It has been shown…

We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…

The paper uses complex-valued functions to simplify plane differential geometry and kinematics.

Convex optimisation solves inverse kinematics problems more reliably.

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and com…

By studying the group of rigid motions, $PSH(1)$, in the 3D-Heisenberg group $H_1$, we define the density and the measure for the sets of horizontal lines. We show that the volume of a convex domain $D\subset H_1$ is equal to the integral of length of chord over all horizontal lines intersecting $D$. As the classical r…

A computer vision approach improves neutral particle detection in particle flow algorithms.

The thesis explores kinematical symmetries beyond Lorentzian spacetime.

This work improves vehicle trajectory prediction for safer self-driving cars.

Study uses ANN with LM for ASD screening.

Explains non-lorentzian theories and their dynamics.

Classifies kinematical and aristotelian Lie superalgebras and their superspaces.

We introduce different bases for the vector space of $\mathrm{Sp}(2)\mathrm{Sp}(1)$-invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.

Study explores kinematics of surfaces under metric restrictions.

Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.

In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.

New kinematic model for a spin-rolling sphere using Darboux frame.

A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.

We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.

Two of the authors have defined the class $WDC(M)$ as the class of all subsets of a smooth manifold $M$ that may be expressed in local coordinates as certain sublevel sets of DC (differences of convex) functions. If $M$ is Riemanian and $G$ is a group of isometries acting transitively on the sphere bundle $SM$, we def…

Paper generates synthetic radar signatures for motion classification.

Paper learns robot's end-effector position without prior info.

Generalizes kinematical Lie algebras for isotropic spacetimes.

MadMiner uses machine learning to analyze high-dimensional particle physics data.

A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.

We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric…

This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.

We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other …

We give in explicit form the principal kinematic formula for the action of the affine unitary group on $\C^n$, together with a straightforward algebraic method for computing the full array of unitary kinematic formulas, expressed in terms of certain convex valuations introduced, essentially, by H. Tasaki. We introduce …

Unified theory for curved shell deformations with elastic and inelastic components.

A neural network model mimics body functions for movement tasks.

On curved spaces, viscous fluids reach equilibrium quickly.

We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},η,ω)$ where the $O(d,d)$ metric $η$ is supplemented by an almost symplectic two-form $ω$. Together $η$ and $ω$ define an almost bi-Lagrangian structure $K$ which provides a splitting of the tangent bu…