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.
Paper shows geometric frequency and Lagrange derivative equivalence for electric and fluid systems.
The article derives gradient estimations for semilinear equations on geometric flows.
We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.
Introduces a new geometric framework for non-perturbative BV-theory.
Geometric AD framework simplifies derivative computation in JAX.
A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation of triangulations in a plane. We show that geometric triangulations of a compac…
Derives Lagrangian for minimal surfaces, proving tangential variations vanish.
Derives derivatives and geometric framework for functions with non-independent variables.
We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the geometric phase). We also give an approximate geometric interpretation of the geometri…
The paper derives inequalities on Finsler manifolds, influenced by their curvatures.
Study of nonlinear PDEs using derived geometry and BV formalism.
The covariant derivative of the Kähler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.
This paper develops a geometric framework for Wilson surfaces in higher gauge theory.
Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions for deriving the Dirac equation in Curved Spacetime make no mention of employin…
Geometric deformations preserve post-Lie algebra structure in regularity structures.
I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
Lower bounds for Hodge-Laplacian spectrum on orbifolds.
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about empirically supported mathematical ideas behind splitting and merging…
The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems [S. Vacaru: J. Math. Phys. \textbf{49} (2008) 043504 \& Rep. Math. Phys. \textbf{63} (2009) 95] is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometri…
The paper derives Harnack inequalities for evolving Riemannian manifolds without dimensionality restrictions.
The study examines extensions of Lie algebras with specific geometric structures.
Unified geometric framework for Brownian motion on various manifolds.
In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative cont…
This paper, sixth in a series of eight, uses the geometric calculus on manifolds developed in previous papers of the series to introduce through the concept of a metric extensor field g a metric structure for a smooth manifold M. The associated Christoffel operators, a notable decomposition of that object and the assoc…
The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and transitively on the base. Then we survey the known counting results for differential in…
This paper extends liquidity returns in geometric mean markets to time-varying weights.
Develops Riemannian geometry for optimization on manifolds with detailed derivations.
The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and derive various characterizations for both European-type and American-type geometri…
New method finds precise late-time behavior of wave equations.
Derives energy-momentum tensor from Standard Model, examines energy conditions.
Study of generalized vector bundles and their geometric tools.
Paper finds conditions for special geometric structures on certain spaces.
Novel approach to financial derivatives pricing using rough path theory.
We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, althou…
The paper shows bounds for a geometric flow related to Type IIB string theory.
In this paper, we examine a geometrical projection algorithm for statistical inference. The algorithm is based on Pythagorean relation and it is derivative-free as well as representation-free that is useful in nonparametric cases. We derive a bound of learning rate to guarantee local convergence. In special cases of m-…
An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Carta-Maxwell-Dirac fields based on "minimal geometric data": all the needed underlying structure is geometrical…
Geometric QCD framework establishes stable vacuum for quark confinement.
We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U of M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection ext…
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…
New inequalities for convex curves with multiple geometric factors.
The paper proves geometric inequalities in sphere using locally constrained flows.
We consider the gradient flow of hypersurfaces immersed in the Euclidean space associated to geometric energy functionals. We show that for particular functionals depending by higher covariant derivatives of the curvature, singularities in finite time cannot occur during the evolution. Such geometric functionals are re…
New proof of Willmore inequality using geometric divergence inequality.
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave equations satisfied by the curvatures are derived. The relation of hypergeometric flo…
Automatically explores geometric loci of curves using software networking.
New method speeds up Bayesian inverse problem solving with neural operators.
The paper proves geometric inequalities for pinched convex hypersurfaces in de Sitter space.