New formulas for measuring geometric properties of definable sets.
problem Measuring geometric properties of definable sets in a non-standard setting.
method Proved two kinematic formulas integrating on SO(n)imesSn−1. result Generalized Cauchy-Crofton and infinitesimal linear kinematic formulas.
Study rigid motions in 3D-Heisenberg group to define and relate geometric probabilities.
problem Define geometric quantities and probabilities in the 3D-Heisenberg group.
method Define density and measure for horizontal lines, use integral geometry.
result Show relationship between geometric probability and natural geometric quantity.
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, wa…
ANNs solve complex inverse kinematics of a Tricept parallel robot.
problem Solving inverse kinematics for a Tricept parallel robot.
method Developed kinematic equations, used ANNs (MLP and RBF) for solving.
result ANNs provided proper accuracy and speed in solving complex inverse kinematics.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
Proposes KStar Diffuser for kinematics-aware bimanual robotic manipulation.
problem Challenges in applying imitation learning to bimanual robotic tasks.
method Integrates physical robot structure into action prediction using a dynamic spatial-temporal graph and differentiable kinematics.
result Effective generation of kinematics-aware actions in both simulation and real-world environments.
Study kinematic formulas for quaternionic plane valuations.
problem Kinematic formulas for quaternionic plane valuations.
method Introduced different bases and determined kinematic formulas.
result Complete set of kinematic formulas for quaternionic plane valuations.
Study kinematics of Ricci Solitons in various fluid spacetimes.
problem Understanding the motion of Ricci Solitons in different fluid spacetimes.
method Examined specific fluid spacetimes including string cloud, string fluid, etc., and analyzed kinematics.
result Obtained results and discussed physical aspects of these spacetimes.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
problem Simplifying complex problems in plane differential geometry and kinematics.
method Consistent use of complex-valued functions of a real variable.
result Derives results in a particularly simple, uniform, and transparent way.
Convex optimisation solves inverse kinematics problems more reliably.
problem Finding the best parameters of a kinematic skeleton from observed joint locations.
method Convex optimisation using semidefinite programming.
result The proposed method significantly outperforms local optimisation methods.
Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.
problem Improper neck postures lead to musculoskeletal disorders requiring therapy and rehabilitation.
method Integrated use of kinematic and kinetic data with machine learning algorithms.
result 100% accuracy in predicting neck postures using the proposed platform.
The paper analyzes defects on structured surfaces and calculates stress and shape.
problem Analyzing defects on structured surfaces and their effects on stress and shape.
method Classified and quantified defects, derived strain incompatibility relations, and applied to shells.
result Determined internal stress field and deformed shape for shells with defects.
Revisits contact measures in isotropic spaces, linking kinematic formulas to curved spaces.
problem Understanding contact measures in isotropic spaces.
method Using the theory of valuations on manifolds and integral geometry.
result Explicit kinematic formula for surface area measure in hermitian space.
The thesis explores kinematical symmetries beyond Lorentzian spacetime.
problem Exploring symmetries beyond standard Lorentzian spacetime.
method Algebraic and geometric classification of kinematical, super-kinematical, and super-Bargmann symmetries.
result Classification of kinematical Lie algebras and superalgebras in 3D spacetime.
This work improves vehicle trajectory prediction for safer self-driving cars.
problem Improving trajectory predictions for safer self-driving cars.
method Deep-learning-based method combining AI and physically grounded models.
result Proposes a method that outperforms existing state-of-the-art.
Explains non-lorentzian theories and their dynamics.
problem Understanding non-lorentzian kinematics and dynamics.
method Review of kinematical spacetimes, construction of particle dynamics actions, discussion of gravity theories and field theories.
result Introduction and analysis of non-lorentzian gravity and field theories.
Surveying hermitian integral geometry, the paper describes new kinematic formulas for complex space forms.
problem Understanding curvature measures and valuations on complex spaces.
method Analyzing valuations and curvature measures on complex space forms, deriving kinematic formulas.
result New local kinematic formulas for hermitian geometry, containing more information than global formulas.
Classifies kinematical and aristotelian Lie superalgebras and their superspaces.
problem Classifying Lie superalgebras and their associated superspaces.
method Quaternionic formalism to simplify calculations, classification via isomorphism and central extensions, geometric limits to explore relationships.
result 27 homogeneous superspaces classified, some with parameters.
New formulas for geometric measures in vector spaces.
problem Local additive kinematic formulas for vector spaces.
method Introducing dual area measures and proving their convolution product.
result Local additive kinematic formulas in hermitian vector spaces.
Study explores kinematics of surfaces under metric restrictions.
problem Understanding the kinematics of surfaces under metric constraints.
method Analyzed three energy contents: stretching, drilling, and bending.
result Metric restrictions can hinder the elastic response of a shell.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
Researchers prove formulas for flag area measures, extending previous work.
problem Proving additive kinematic formulas for flag area measures.
method Introducing an algebraic framework to compute these formulas explicitly.
result Existence and explicit computation of additive kinematic formulas for flag area measures.
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…
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.
problem Control and planning of an underactuated sphere on a plane.
method Darboux frame transformation to fully-actuated model.
result Underactuated sphere model transformed into fully-actuated model.
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.
The paper proposes a method to align surgical videos using kinematic data.
problem Difficulty in learning from comparing novice to expert surgical videos due to variability in gesture duration and execution.
method A novel technique using Dynamic Time Warping to synchronize videos of the same gesture at different speeds.
result The proposed approach allows for the alignment of surgical videos, enabling better learning for novice trainees.
Paper generates synthetic radar signatures for motion classification.
problem Lack of large training datasets for radar-based human activity recognition.
method Adversarial learning for synthetic data generation, kinematic sifting for consistency.
result 93% overall accuracy achieved on diverse aspect angles.
Paper learns robot's end-effector position without prior info.
problem Lack of prior robot structure or sensor info.
method Generates internal end-effector config from raw data.
result Can control robot without prior kinematic info.
Generalizes kinematical Lie algebras for isotropic spacetimes.
problem Classifying relativity algebras in isotropic spacetimes.
method Elementary proof and Lie group analysis.
result Symplectic involutive Lie algebras always exist.
Extends Double Field Theory with new kinematical structure.
problem Formalizing Double Field Theory on para-Hermitian manifolds.
method Constructing a canonical connection and generalised Lie derivative for a Leibniz algebroid.
result Integrability conditions for symmetry algebra closure under non-flat and non-constant η and ω. ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
New proof confirms operations on constructible functions match theory.
problem Matching operations on constructible functions with generalized valuations theory.
method Comparison with characteristic cycles approach.
result Operations on constructible functions match generalized valuations theory under mild assumptions.
A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.
problem Ambiguity in viscous operator choice for Navier-Stokes equations on Riemannian manifolds.
method Kinematic construction of strain rate from Lie-dragged vectors, excluding Hodge Laplacian due to antisymmetric part.
result Kinematic selection uniquely identifies the deformation Laplacian, resolving analytical obstructions.
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…
Study examines how body segments respond to random vibrations.
problem Understanding human body responses to random vibrations.
method 35 participants were tested with random noise signals. Multiple linear regression models were created to determine influential predictors of peak translational gains.
result Multiple predictors, including motion direction and body segment, significantly influence peak translational gains.
This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.
problem Understanding the kinematics and nonlinear phenomena of Spidron units.
method Analysis of single unit cell kinematics and recursive construction of multiple cells.
result Non-periodic folding restricts isotropic folding as the number of unit cells increases.
Unified theory for curved shell deformations with elastic and inelastic components.
problem Coupled nonlinear elastic and inelastic deformations of curved thin shells.
method Multiplicative decomposition of surface deformation gradient, detailed kinematics analysis, surface balance laws, constitutive relations derived from thermodynamics.
result Unified constitutive relations for growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells.
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 …
A neural network model mimics body functions for movement tasks.
problem Solving inverse and forward kinematics, dynamics for a redundant manipulator.
method Recurrent neural network with Mean of Multiple Computations principle, dynamic extension.
result Neural network solves inverse tasks and shows prototypical population-coding.
Alternative discrete Dirac mechanics using Dirac structures.
problem Developing a new framework for discrete mechanics.
method Introducing 'continuous Dirac system' and proposing a definition of 'discrete Dirac system'.
result It is possible to recover discrete Lagrangian and Hamiltonian systems.
Study of rigid body displacements in a projective space over dual numbers with geometric interpretations.
problem Understanding rigid body displacements in a novel geometric space.
method Projective differential geometry over the ring of dual numbers.
result Existence of non-straight curves with multiple osculating tangents.
Extends particle classification to curved space-times using groupoids.
problem Classifying elementary particles in curved space-time.
method Developed a new definition of elementary particles as irreducible projective representations of kinematical groupoids, extending Wigner's program.
result Classification of elementary particles valid for a wide range of space-times, including new massless particles in magnetic-like backgrounds.
Improved sensitivity to Higgs potential through neural simulation-based inference for di-Higgs events.
problem Improving sensitivity to physics beyond the Standard Model through di-Higgs events.
method Simulation-based inference using neural networks to estimate per-event likelihood ratios.
result Adding kinematic observables improves experimental sensitivity to Higgs self-coupling.
In this note we show that the configuration spaces of the kinematic system constructed in [4] and [12] gives rise to a natural tower of sphere bundles. Moreover, we prove that, each tower of projective bundles associated to special multi- flags (cf [1], [13], [2], [3]), we can associate such a tower of sphere bundles w…
Using results on the topology of moduli space of polygons [Jaggi, 92; Kapovich and Millson, 94], it can be shown that for a planar robot arm with n segments there are some values of the base-length, z, at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected com…
Study of homogeneous spacetimes with isotropic symmetry and their symmetries.
problem Classifying and analyzing the geometry and symmetries of homogeneous spacetimes.
method Detailed calculation of symmetries, soldering form, vielbein, and invariant connections for spatially isotropic homogeneous spacetimes.
result Boosts act with generic non-compact orbits and determine infinite-dimensional symmetries reminiscent of BMS Lie algebras.