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.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
The paper concerns a simple model of bicycle kinematics: a bicycle is represented by an oriented segment of constant length in n-dimensional space that can move in such a way that the velocity of its rear end is aligned with the segment (the rear wheel is fixed on the bicycle frame). Starting with a closed trajectory o…
Model predicts multi-agent trajectories using a differentiable simulator.
New conditions found for hyperbolic bicycle tracks.
Bicycle paths form geodesics in 3D subspaces, related to Kirchhoff rods.
We study closed smooth convex plane curves enjoying the following property: a pair of points can traverse so that the distances between and along the curve and in the ambient plane do not change; such curves are called {\it bicycle curves}. Motivation for this study comes from the problem how to d…
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transform…
Dataset of 4500 bicycle designs aids in design analysis and synthesis.
New model for visual cortex border completion using bicycle wheel motions.
We study a simple model of bicycle motion: a segment of fixed length in multi-dimensional Euclidean space, moving so that the velocity of the rear end is always aligned with the segment. If the front track is prescribed, the trajectory of the rear wheel is uniquely determined via a certain first order differential equa…
Paper presents LSTMMDN for hourly bike flow estimation in Copenhagen.
We prove generalizations of the isoperimetric inequality for both spherical and hyperbolic wave fronts (i.e. piecewise smooth curves which may have cusps). We then discuss "bicycle curves" using the generalized isoperimetric inequalities. The euclidean model of a bicycle is a unit segment AB that can move so that it re…
Sub-Riemannian geometry connects bike paths to mathematical curves.
The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its…
Geometry of the tracks left by a bicycle is closely related with the so-called Prytz planimeter and with linear fractional transformations of the complex plane. We describe these relations, along with the history of the problem, and give a proof of a conjecture made by Menzin in 1906.
The paper studies self-Bäcklund curves in centroaffine geometry using elliptic functions.
New method linearizes Darboux transformations of discrete curves.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
The space C of conservative vertex colorings (over a field F) of a countable, locally finite graph G is introduced. The subspace of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Z^d-action by automorphisms, C is a finitely generated module over the polynomial ring…
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.
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.
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.
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…
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.
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 prove that if is a rational number between zero and one, then there is no integer such that This has interpretations both in the theory of bicycle curves and that of mathematical billiards.
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.
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 generates synthetic radar signatures for motion classification.
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.
A spiral unibike track emerges from a mathematical construction.
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.