Related papers: Geometric Constrained Variational Calculus. I. - P…
Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…
We prove that autoparallel curves associated with a torsion-free but not necessarily metric-compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational…
We introduce a notion of geometric tempering using exponentially-dampened Mittag-Leffler tempering functions and closely investigate the univariate case. Characteristic exponents and cumulants are calculated, as well as spectral densities.…
We look at the covariant techniques and the ideas on constraints and gauge-invariance, which were recently employed in [gr-qc/0702104] to support earlier work by the same authors. That work was criticised in [gr-qc/0503042]. Using very…
We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal case and is not restricted to plane curves, encompassing curves…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
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.…
Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are…
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
The class of effective actions exactly reproducing the conformal anomaly in 4D is considered. It is demonstrated that the freedom within this class can be fixed by the choice of the conformal gauge. The conformal invariant part of the…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is a type of moving incidence relation. The characterisation is used to provide…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…