arXiv research

We explore xor function using copula representations and error surface projections.

Estimates surface count with prescribed foliations.

The aim here is to continue the investigation in \cite{AB} of Jacobians of a Klein surface and also to correct an error in \cite{AB}.

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

We explain an error in our paper "A smooth foliation of the 5-sphere by complex surfaces", Ann. Math 156 (2002), p.915-930.

Estimates the number of closed curves on surfaces with power-saving error terms.

Geometrically, spherical 3-manifolds emerge from flat SU(2)-bundles over hyperbolic surfaces.

Improved method for numerical conformal mappings on complex domains.

Study compares machine learning algorithms for predicting SST in the Great Barrier Reef.

Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order $o(\log\log g)$ with $g$…

This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account perturbations of the surfaces, in particular when the surfaces are approximated by spl…

This paper has been withdrawn by the author due to serious error found in main argument.

We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichmüller geodesic flow.

Discrete approximation solves Björling's minimal surface problem.

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

The paper improves bounds on geodesic lengths and their simplicity on hyperbolic surfaces.

We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the underlying surface. We use this to give an effective proof of a result regarding maps between curve complexes of surfaces induced by finite…

Random covers of hyperbolic surfaces have a spectral gap with polynomial rate.

A hybrid Convolutional VAE predicts crypto volatility surfaces, outperforming single-symbol approaches.

Classifies orientation-reversing homeomorphisms of even periods on surfaces.

This article was originally published in Topology 31 (1992). The present hyperTeXed redaction corrects a few typographical errors and updates the references.

In this paper, we treat the problem of evaluating the asymptotic error in a numerical integration scheme as one with inherent uncertainty. Adding to the growing field of probabilistic numerics, we show that Gaussian process regression (GPR) can be embedded into a numerical integration scheme to allow for (i) robust sel…

Non-spanning identification of scheduled event risk in option pricing.

Algorithm classifies surface homeomorphisms with polynomial time complexity.

Derivative-informed models improve financial surrogates for accurate hedging and risk management.

The paper proposes a new method to calibrate option pricing models that accurately match both volatility surfaces and variance term structures.

CNN improves medium-range temperature forecasts with limited resources.

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points…

Meta-learning extends supervised learning to tasks with varying numbers of examples, revealing conditions for successful learning.

For a sequence of coupled fields $\{(φ_n,ψ_n)\}$ from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up pr…

We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it $I_0$) and solenoidal vector fields on surfaces with negative curvature and strictly convex boundary. These formulas generalize the Pestov-Uhlmann formulas in [Pestov-Uhlmann, IMRN '04] (established for simple surfaces) to ca…

Fast ML framework for derivative valuation from volatility surfaces.

In this paper, we develop new techniques for understanding surfaces in $\mathbb{CP}^2$ via bridge trisections. Trisections are a novel approach to smooth 4-manifold topology, introduced by Gay and Kirby, that provide an avenue to apply 3-dimensional tools to 4-dimensional problems. Meier and Zupan subsequently develope…

Spotlight method finds hidden errors in deep learning models.

Let F be a surface and suppose that φ: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_φis hyperbolic and contains a maximal cusp C about the puncture p. We show that the area (and height) of the cusp torus bounding C is equal to the stable translation distance of φacting on th…

Study on RL on volatility surfaces, proving no free lunch for law-seeking methods.

Deep learning models reconstruct volatility surfaces from noisy data under no-arbitrage constraints.

Corrects a 1-off error in Harer's spine dimension calculation for decorated Teichmüller spaces.

Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may suffer from difficulties when representing higher dimensional surfaces. Motivated by…

A fast Monte Carlo method for additive processes and option pricing.

The paper extends a method for numerical conformal mappings to surfaces using Laplace-Beltrami equations.

Eigenvalues of random hyperbolic surface covers converge to hyperbolic plane's.

Due to a significant error in the main result (pointed out by J. Wahl), the paper has been withdrawn by the authors. A corrected and expanded version is 'Rational blow-downs and smoothings of surface singularities' by A. Stipsicz, Z. Szabo and J. Wahl.

Study determines minimal surfaces from boundary data, proving topological and conformal recoverability.

We consider the first non-zero eigenvalue $λ_1$ of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that $8π\nabla\log(λ_1)$ essentially agrees with the dual of the differential of the degenerating Fenchel-Nielsen length coordinate. As a consequence, we can improve previous …

In this work, we design a machine learning based method, online adaptive primal support vector regression (SVR), to model the implied volatility surface (IVS). The algorithm proposed is the first derivation and implementation of an online primal kernel SVR. It features enhancements that allow efficient online adaptive …

Framework predicts implied volatility surface without arbitrage.