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.
Extends Euler calculus to continuous integrands using curvature.
Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the geometrical setting. The constrained Euler-Lagrange equations are derived for ana…
Extends calculus of variations to generalized functions.
Paper derives invariantised Euler-Lagrange equations for Herglotz problems.
Proves Euler-Lagrange equations for complex functionals on Fréchet manifolds.
Study characteristic classes of a specific type of determinantal varieties.
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of the first--order variational integrals related to the second--order Euler--Lagra…
We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms between our bundles of smooth maps, we introduce the concept of fiberwise -j…
New techniques analyze steady fluid flows on non-compact manifolds.
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler-Lagrange equatio…
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
Develops a graphical calculus for stable curvature invariants.
New frame method simplifies solving variational problems with Euclidean symmetry.
It is shown that the Euler-Lagrange equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of reduction and the relation with Lagrange multiplier method are also studied.
Study of curves in Lie sphere geometry using moving frames and variational principles.
Generalizes beam models to include curvature and torsion.
The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w …
New proof of Dutertre and Fukui's theorem on Morin singularities.
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from inherent misuse of objects and for finding natural formulations of various objects…
Euler explored spherical geometry using trigonometric formulae and solid geometry methods.
We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables, together with higher order derivatives. In particular, we show that the second varia…
A new algorithm solves high-dimensional nonlinear BSDEs efficiently.
We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an introduction of the classical Poincare-Cartan form in the context of EDS, follow…
Non-trivial obstructions found for topological solitons in Yang-Mills-Chern-Simons theories.
Investors benefit from long horizons in a market with mean-reverting equity returns.
Develops tensor calculus for submanifolds of arbitrary codimension.
Geometric integrator preserves coadjoint orbits in dissipative systems.
Study Dirichlet problem for convex functionals on Riemannian manifolds.
The rational homology balls appeared in Fintushel and Stern's rational blow-down construction [FS] and were subsequently used (e.g. Fintushel-Stern[FS4], Park[Pa2]) to construct exotic smooth manifolds with small Euler numbers. We show that a large class of smooth 4-manifolds have all of the 's for odd $n \g…
Infinitesimal variation of Action functional in classical (non-quantum) field theory with higher derivatives is presented in terms of well-defined intrinsic geometric objects independent of the particular field which varies. 'Integration by parts' procedure for this variation is then described in purely formal language…
Derives energy and momentum conservation laws for Vlasov-Maxwell systems using Euler-Poincaré formulation.
Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim of this paper is to explain the mathematical structure of both the Euler…
This article is a standalone introduction to sutured Floer homology for graduate students in geometry and topology. It is divided into three parts. The first part is an introductory level exposition of Lagrangian Floer homology. The second part is a construction of Heegaard Floer homology as a special, and slightly mod…
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important featu…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian. This problem in the general version remains unsolved. Here, we contribute to it w…
The paper interprets a graph's Alexander polynomial topologically.
Develops strategies to minimize trading costs in volatile markets.
In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of , the manifold of dependent and independent variables underlying a given proble…
We establish the equivalence of the Tuynman midpoint area formula for a spherical triangle to the classical area formulas of Euler and of Cagnoli. The derivation also yields a variant of the Cagnoli formula in terms of the medial triangle. We introduce the three barycentric coordinates of a point within the spherical t…
Develops an L^p theory for Dolbeault-Dirac operators on compact Kähler manifolds.
A method to derive Lagrangians from field equations in metric-affine theories of gravity.
We identify the Variational Principle governing inifinity-Harmonic maps, that is solutions to the Infinity-Laplacian. The system was first derived in the limit of the p-Laplacian as p->inifinity in [K2] and is recently studied in [K3]. Here we show that it is the "Euler-Lagrange PDE" of vector-valued Calculus of Variat…
Lie Calculus connects differential and Lie theory using groupoids.
New calculus extends noncommutative geometry to higher N.
Study embedding calculus and link invariants using functor calculus.
Develops a new higher-order calculus using cubic algebra.
Study of Einstein-Hilbert action on metric-affine spaces with connections.