A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Generalizes beam models to include curvature and torsion.
In this paper, we carry a detailed study of mechanical systems with configuration space for which the base variables are being controlled. The overall system's motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the…
In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie algebroid.
Study geodesics on nested non-holonomic systems.
Study of motion constraints and path-following on 3D space.
A Lie groupoid, called \textit{second-order non-holonomic material Lie groupoid}, is associated in a natural way to any Cosserat media. This groupoid is used to give a new definition of homogeneity which does not depend on a reference crystal. The corresponding Lie algebroid, called \textit{second-order non-holonomic m…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied to linear as well as to non-linear constraints. Only the basic notions of vecto…
Rolling systems limit to billiard models with no-slip collisions.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Us…
Proposes KStar Diffuser for kinematics-aware bimanual robotic manipulation.
We construct a co-dimension completely non-holonomic sub-bundle on the Gromoll-Meyer exotic sphere based on its realization as a base space of a Sp(2)-principal bundle with the structure group Sp(1). The same method is valid for constructing a co-dimension 3 completely non-holonomic sub-bundle on the standard 7…
A multisymplectic setting for classical field theories subjected to non-holonomic constraints is presented. The infinite dimensional setting in the space of Cauchy data is also given.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
New formulas for measuring geometric properties of definable sets.
Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.
We provide a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that we show is canonically available, given a choice of complement to the distribution. We also describe conditions which, if satisfied, mean that even this choice of complement is determined canonic…
The thesis explores kinematical symmetries beyond Lorentzian spacetime.
Explains non-lorentzian theories and their dynamics.
We introduce different bases for the vector space of -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.
Self-driving vehicles (SDVs) hold great potential for improving traffic safety and are poised to positively affect the quality of life of millions of people. To unlock this potential one of the critical aspects of the autonomous technology is understanding and predicting future movement of vehicles surrounding the SDV.…
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…
A framework for computing holonomy groups of hybrid systems to achieve forward motion.
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.
Geometrical properties of holonomic and non holonomic varieties defined by the Pfaff equations connected with a first order systems of differential equations are studied. The Riemann extensions of affine connected spaces for investigation of geodesics and asymptotic lines are used.
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.
New kinematic model for a spin-rolling sphere using Darboux frame.
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.
Modified Gibbs-Helmholtz equation geometric models for thermodynamics.
Dancing polygons and rolling balls linked via a special geometric distribution.
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…
We give definition of a holonomy flag in subRiemannian geometry --- a generalization of a Riemannian holonomy algebra --- and calculate it for the 3D subRiemannian Lie groups. We rewrite and give new interpretation for the Codazzi equations for the -distributions on the and the Heisenberg group.
Generalizes kinematical Lie algebras for isotropic spacetimes.
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to a…
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…
New proof confirms operations on constructible functions match theory.
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…
Study examines how body segments respond to random vibrations.
This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.
Deep neural networks (DNNs) have recently received vast attention in applications requiring classification of radar returns, including radar-based human activity recognition for security, smart homes, assisted living, and biomedicine. However,acquiring a sufficiently large training dataset remains a daunting task due t…
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…
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 …
We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman's functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. W…