arXiv research

A new algorithm computes elastic shape distances between curves efficiently.

Paper computes optimal matching between curves on manifolds.

The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …

Two optimization problems for Loewner energy curves and their symmetries.

The paper studies properties of optimal metrics associated to curves on surfaces.

Accelerates pulsar light curve inference with learned representations and optimization.

The term structure of interest rates or yield curve is a function relating the interest rate with its own term. Nonlinear regression models of Nelson-Siegel and Svensson were used to estimate the yield curve using a sample of historical data supplied by the National Stock Exchange of Costa Rica. The optimization proble…

Optimal thresholds ensure curves remain embedded in flows.

Optimizes the conformal capacity of linked curves in $S^3$.

ResNets learn the geodesic curve in Wasserstein space.

Optimizes shapes of curves using Möbius energy gradients.

Researchers found counterexamples to conjectures about optimal transport maps on curved spaces.

Optimizes curves on Riemannian manifolds to minimize curvature.

Estimates personalized treatment response curves using covariates.

Optimizes profit in targeted marketing across multiple markets with varying marketing expenditures.

Optimal curves minimize crossings on surfaces.

Paper estimates optimal ROC curve arc length and AUC, improving classification performance.

Optimal flat ribbons can be created from nonplanar curves with minimal energy.

The paper explores using machine learning for yield curve calibration in multiple markets.

Optimizes bond portfolios to avoid worst-case losses.

This paper aims at formulating the issue of ranking multivariate unlabeled observations depending on their degree of abnormality as an unsupervised statistical learning task. In the 1-d situation, this problem is usually tackled by means of tail estimation techniques: univariate observations are viewed as all the more …

New method saves computational budget by ranking and transferring learning curves.

We determine the asymptotic behavior of the optimal Lipschitz constant for the systole map from Teichmuller space to the curve complex.

This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associat…

Study variance-optimal hedging of forward curve derivatives under stochastic volatility.

New optimization method improves AUC for binary classification and changepoint detection.

The optimality of the integral inequality $\int\limits_γ\sqrt{k_1^2+k_2^2+k_3^2}ds>2π$ for closed curves with non-vanishing curvatures in $\mathbb R^4$ is discussed. We prove that an arbitrary closed curve of constant positive curvatures in $\mathbb R^4$ satisfies the inequality $\int\limits_γ\sqrt{k_1^2+k_2^2+k_3^2}ds…

The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an op…

Gradient flow preserves speed for integral Menger curvature curves.

Establishes a Li-Yau type inequality for curves in any codimension.

We give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest projectively invariant singularities on such curves. Our method is axiomatic and can be applied in other situations.

This paper introduces a novel monotone curve estimation framework based on convex duality.

A new FFT-based method for fast rigid alignment of 2D closed curves.

Optimizes AMM markets with a new framework reducing complex optimization to simpler root finding.

Optimal bounds on rational points on algebraic curves established.

The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new ec…

This work studies learning curves for revenue maximization algorithms.

Optimal dividend payout strategies with drawdown constraint identified.

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given pr…

3D filament plots visualize curves in datasets, avoiding visual clutter.

Of concern is the study of the space of curves in homogeneous spaces. Motivated by applications in shape analysis we identify two curves if they only differ by their parametrization and/or a rigid motion. For curves in Euclidean space the Square-Root-Velocity-Function (SRVF) allows to define and efficiently compute a d…

Study preserves planar and graphical properties of curves under elastic flow.

We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when investing in futures contracts. We study a class of futures price curve models wh…

Optimal cutoff interval for risk scores improves binary classification accuracy.

Adaptive market maker curves minimize arbitrage losses in DeFi.

Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure.…

Optimizes the crossing number for curve systems on surfaces.

This study examines abnormal geodesics in 2D-Zermelo navigation problems, revealing their role in separating time minimal and maximal curves.