arXiv research

New inequality for odd-degree flexible curves using surface doubling.

Study on choosing points on cubic curves, answering some questions about their flexibility.

New method for comparing curves with flexible matching constraints.

Curves with constant curvature are flexible and can be deformed.

Maximizing energy on flexible curves yields regular or convex polygons.

Flexible metrics found on a genus 2 surface.

Geodesic curves improve flexibility in covariance estimation.

Characterizes rigid and flexible hyperbolic cone metrics and billiards.

Tool for contracting subcurves of hyperelliptic curves, proving differential implications.

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…

Identifies smooth curves for financial models.

We present a new mixture model-based discriminant analysis approach for functional data using a specific hidden process regression model. The approach allows for fitting flexible curve-models to each class of complex-shaped curves presenting regime changes. The model parameters are learned by maximizing the observed-da…

Riemannian flows model curved spaces better.

Flexible model captures commodity skews with maturity effects.

Study presents a twistor correspondence for specific geometric structures.

Congealing is a flexible nonparametric data-driven framework for the joint alignment of data. It has been successfully applied to the joint alignment of binary images of digits, binary images of object silhouettes, grayscale MRI images, color images of cars and faces, and 3D brain volumes. This research enhances congea…

Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time. Further, the outcome variable may not be measured at a regular frequency. Our propos…

Adma proposes a flexible loss function for neural networks.

Unified framework identifies nonlinear systems using characteristic curves and neural networks.

New method analyzes knots and links using multiscale Gauss link integral.

We study closed smooth convex plane curves $Γ$ enjoying the following property: a pair of points $x,y$ can traverse $Γ$ so that the distances between $x$ and $y$ along the curve and in the ambient plane do not change; such curves are called {\it bicycle curves}. Motivation for this study comes from the problem how to d…

A new method models individual survival curves using conditional normalizing flows.

We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJ…

We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In ge…

By adopting the polynomial interpolation method, we propose an approach to hedge against the interest-rate risk of the default-free bonds by measuring the nonparallel movement of the yield-curve, such as the translation, the rotation and the twist. The empirical analysis shows that our hedging strategies are comparable…

WDL models density curves using Wasserstein distance and flexible mixture models.

Let $\mathcal{R}$ be an open Riemann surface. In this paper we prove that every continuous function $M \to \mathbb{R}^n$, $n\ge 3$, defined on a divergent Jordan arc $M \subset \mathcal{R}$ can be approximated in the Carleman sense by conformal minimal immersions; thus providing a new generalization of Carleman's theor…

We consider the results of combining two approaches developed for the design of Riemannian metrics on curves and surfaces, namely parametrization-invariant metrics of the Sobolev type on spaces of immersions, and metrics derived through Riemannian submersions from right-invariant Sobolev metrics on groups of diffeomorp…

Estimates personalized treatment response curves using covariates.

The process of designing neural architectures requires expert knowledge and extensive trial and error. While automated architecture search may simplify these requirements, the recurrent neural network (RNN) architectures generated by existing methods are limited in both flexibility and components. We propose a domain-s…

We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of "extremal" tight contact structures. Specifically, there is exactly one contact s…

We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the …

Statistical approaches for Functional Data Analysis concern the paradigm for which the individuals are functions or curves rather than finite dimensional vectors. In this paper, we particularly focus on the modeling and the classification of functional data which are temporal curves presenting regime changes over time.…

We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved Kähler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex surfaces may share the rigidity of quaternionic/octionic hyperbolic manifolds, ou…

Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previou…

Empirical Gaussian Processes learn flexible priors from data.

Consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ with a hyperbolic metric $σ$ of total area $A$. In this article, we study the behavior of geometric and dynamical characteristics (e.g., diameter, Laplace spectrum, Gaussian curvature and entropies) of nonpositively curved smooth metrics with total area …

ContiVAE estimates individual dose-response curves from unobserved confounders using observational data.

Neural network models improve ROC curve evaluation of biomarkers, focusing on age's role in physical activity-mortality association.

Develops ML tool for macroeconomic forecasting with clear interpretations.

Functional BART adds shape priors to Bayesian tree regression for better curve fitting.

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed total area in a fixed conformal class. Moreover, we obtain a collar lemma, a th…

In this paper we introduce a flexible HJM-type framework that allows for consistent modelling of intraday, spot, futures, and option prices. This framework is based on stochastic processes with economic interpretations and consistent with the initial term structure given in the form of a price forward curve. Furthermor…

We study the problem of estimating the continuous response over time to interventions using observational time series---a retrospective dataset where the policy by which the data are generated is unknown to the learner. We are motivated by applications where response varies by individuals and therefore, estimating resp…

The paper explores how complex models can improve system identification beyond traditional limits.

We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are tractable…

In this paper we define and study flexible links and flexible isotopy in projective space. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholms interpretation of Viros encomplexed writhe.

The authors characterize flexibility in power and energy markets considering time, spatiality, resource, and risk.