AQFC method estimates mesh curvatures using quadratic surfaces.
problem Estimating curvatures for irregular polygonal meshes.
method Local approximation of vertices and normals by quadratic surfaces, computed as implicit surfaces.
result AQFC provides robust curvature estimation for irregular meshes.
We smooth out the math of fitting surfaces into 3D space.
problem Fitting surfaces into 3D space isometrically.
method Introduce elliptic regularization to the PDE system.
result The regularization leads to a natural variational interpretation.
The method constructs arbitrage-free option surfaces from noisy quotes using Chebyshev bases and a fog post-fit layer.
problem Constructing arbitrage-free option price surfaces from noisy bid-ask quotes.
method Chebyshev tensor bases, linear sampling, no-arbitrage operators, quadratic objective, OSQP solvers, fog post-fit layer, Hamiltonian energy.
result High inside-spread coverage (98-99%) and low no-arbitrage violations (below 1%) in stable periods, controlled leakage in stressed periods.
Study uses shape and surface fitting to classify Parkinson's disease accurately.
problem Early identification of Parkinson's disease from non-degenerative variants.
method Processed SPECT images to compute shape- and surface fitting-based features for classification.
result Support Vector Machine (SVM) classifier achieved 97.29% accuracy.
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
We show that for each aspherical compact complex surface X whose fundamental group π fits into a short exact sequence 1→K→π→π1(S)→1 where S is a compact hyperbolic Riemann surface and the group K is finitely-presentable, there is a complex structure on S and a nonsingular holomorphic fibr…
The special isothermic surfaces, discovered by Darboux in connection with deformations of quadrics, admit a simple explanation via the gauge-theoretic approach to isothermic surfaces. We find that they fit into a heirarchy of special classes of isothermic surface and extend the theory to arbitrary codimension.
Neural networks fit fewer samples than their parameters suggest in practice.
problem Understanding the practical limitations of neural network flexibility.
method Examination of neural network optimization, parameter efficiency, and loss surfaces.
result Neural networks can only fit training sets with significantly fewer samples than their parameters suggest.
CTEF fits ellipsoids to noisy data in any dimension.
problem Fitting ellipsoids to noisy data in arbitrary dimensions.
method Uses the Cayley transform to fit ellipsoids.
result CTEF outperforms other methods, especially when data are not uniformly distributed.
This study examines how neural network architecture parameters affect loss surface modality.
problem Understanding the relationship between neural architecture parameters and loss surface modality.
method Fitness landscape analysis of neural network loss surfaces under various architecture settings.
result An increase in problem dimensionality, hidden layer width, and architecture depth affects the modality of loss surfaces.
A hybrid Convolutional VAE predicts crypto volatility surfaces, outperforming single-symbol approaches.
problem Predicting crypto volatility surfaces
method Convolutional VAE with hybrid predictor
result Model achieves 0.94-1.56 vol-point RMSE across BTC and ETH markets
Tropical geometry and weighted lattices improve curve and surface fitting.
problem Fitting max-⋆ tropical curves and surfaces to data. method Max-⋆ algebra, weighted lattices, morphological adjunctions. result Optimal piecewise-linear regression for max-⋆ curves and surfaces. Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules. They fit into the structure of a 2-category of bundle gerbes, and lead to natural d…
We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied volatilities which demonstrate smile or skew. An arbitrage-free calibration algorithm i…
Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on surface meshes is important and challenging, and some existing methods often produce …
Constructs currents and heights on K3 surfaces.
problem Understanding the geometry and arithmetic of K3 surfaces.
method Constructs canonical positive currents and heights on K3 surfaces, equivariant for automorphism group.
result Continuous family of currents and heights defined over an enlarged boundary of the ample cone.
Paper uses DRL to improve volatility fitting in equity derivatives.
problem Improving volatility fitting in equity derivatives markets.
method Apply Deep Reinforcement Learning (DRL) to solve the fitting problem.
result DRL algorithms achieve at least as good as standard fitting methods.
In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the h…
New method calibrates eSSVI volatility surfaces without arbitrage.
problem Sequential calibration of eSSVI surfaces lacks global view and guarantees no arbitrage.
method Global and arbitrage-free parametrization of eSSVI surfaces.
result Faster calibration always guarantees an arbitrage-free fit.
A new framework forecasts implied volatility surfaces by separating learning and refinement stages.
problem Forecasting implied volatility surfaces is challenging due to stochastic future surfaces and static no-arbitrage constraints.
method Decoupled generative refinement framework using a conditional diffusion model and SAAM for surface refinement.
result The framework improves forecasting accuracy and reduces static no-arbitrage violations.
Automated neural network potentials achieve coupled cluster accuracy for protonated water clusters.
problem Creating highly accurate potential energy surfaces for chemical systems.
method Automated fitting of neural network potentials to ab initio reference calculations.
result Single potential energy surface for H3O+ to H9O4+ clusters at essentially converged coupled cluster accuracy.
Improves cardiac simulator fit to real patient ECG data.
problem Intractable inference over non-differentiable cardiac simulators.
method Variational inference combined with Bayesian optimization.
result Significant improvement in simulator fit to real patient ECG data.
Special Lagrangian submanifolds emerge from K3 surface collapse.
problem Understanding special Lagrangian submanifolds in K3 surface collapse.
method Lifting affine lines to degenerating sequences of special Lagrangian submanifolds.
result Constructing special Lagrangian two-spheres connecting Taub-NUT bubbles.
We introduce a metric notion of Ricci curvature for PL manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers Theorem, for surfaces as well as for a large class of higher dimensional manifolds.
A new method for signal processing using piecewise convex fitting.
problem Nonparametric function estimation in signal processing.
method Two-stage adaptive estimate with strong smoothing and constrained smoothing spline fit.
result Piecewise convex fitting reduces MSE and accurately estimates change points.
The paper proposes a new method to calibrate option pricing models that accurately match both volatility surfaces and variance term structures.
problem Calibrated models often produce inaccurate variance term structures relative to market observations.
method The paper introduces a joint calibration framework that augments the conventional objective function with a penalty term for variance term structure deviations, using a hyperparameter to balance volatility surface and variance term structure weights.
result The proposed method accurately fits observed option prices while delivering realistic term structures of variance.
We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We then use these results to study the minimal entropy problem for compact complex surfaces. For instance we prove that compact Kahler surfaces o…
Two methods monitor high-dimensional processes via manifold fitting or learning.
problem Monitoring high-dimensional, dynamic industrial processes.
method Manifold fitting and learning approaches for online SPC.
result Manifold-fitting approach achieves performance competitive with classical methods.
New families of twisted torus knots found with essential surfaces.
problem Whether all twisted torus knots have essential tori.
method Analyzing sequences of twists on torus knots.
result Found two new families of toroidal twisted torus knots.
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on how to further improve the calibration procedure.
Exact LAD line fitting via PALB with linear scaling and speed.
problem Robust line fitting for data with outliers.
method Piecewise Affine Lower-Bounding (PALB) method using supporting lines and subdivision scheme.
result Empirical log-linear scaling and significantly faster than LP and IRLS methods.
A new pricing model from game theory fits financial data well.
problem Financial models lack economic justification and randomness assumptions.
method CMMV pricing model based on game theory and information asymmetry.
result The CMMV model predicts option prices and volatility surface well.
WamOL uses PINNs to efficiently calibrate IVS from sparse data.
problem Calibrating time-dependent IVS from sparse market data.
method Physics-Informed Neural Networks (PINNs) with adaptive reweighting.
result WamOL outperforms in calibrating intraday IVS from uneven data.
Veering branched surfaces help construct geodesic flows on curved surfaces.
problem Constructing geodesic flows on negatively curved surfaces.
method Introduce veering branched surfaces and surgeries, then use them to construct veering triangulations that correspond to geodesic flows.
result Explicit constructions of veering branched surfaces corresponding to geodesic flows on negatively curved surfaces.
New method characterizes surface quadrilateral layouts as special immersions.
problem Characterize surface quadrilateral layouts mathematically.
method Characterizes quadrilateral layouts as special immersions of a cut representation of the surface into the Euclidean plane.
result Mathematically describes and generalizes integer grid maps.
This paper is devoted to the application of an l1 -minimisation technique to construct an arbitrage-free call-option surface. We propose a nononparametric approach to obtaining model-free call option surfaces that are perfectly consistent with market quotes and free of static arbitrage. The approach is inspired from…
Outfittery uses machine learning to help stylists choose appropriate fashion items.
problem Selecting appropriate fashion items and ensuring relevance to customers.
method Combining machine learning with human expertise to recommend items by style fit and relevance.
result The method successfully recommends fashion items by style fit and relevance.
Characterizes transverse surfaces for pseudo-Anosov flows in 3-manifolds.
problem Characterizing surfaces transverse to pseudo-Anosov flows.
method Correspondence between surfaces and veering triangulations, Thurston norm minimization.
result Thurston-norm minimizing surfaces are almost transverse to pseudo-Anosov flows.
Study Kähler geometry on Hurwitz spaces of Riemann surfaces.
problem Curvature of Kähler metric on Hurwitz spaces.
method Generalized Weil-Petersson metric and Horikawa's deformation theory.
result Investigate curvature of Kähler metric on Hurwitz spaces.
Non-spanning identification of scheduled event risk in option pricing.
problem Separating continuous surface from scheduled jump in option pricing.
method Modeling FOMC decisions, CPI releases, and NFP reports as deterministic-time jumps in risk-neutral option pricing.
result Improves held-out event-spanning pricing with Gaussian and two-component mixture jumps.
A new method constructs smooth, arbitrage-free option surfaces efficiently.
problem Creating smooth, arbitrage-free option surfaces efficiently.
method Non-parametric approach using strictly positive 'discrete local volatility' variables.
result First construction of smooth, strictly arbitrage-free option price surfaces.
We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection phase in which we pick the tree splits, followed by a model fitting phase where we f…
A new method to estimate local volatility from high-frequency data.
problem Quantitative trading risk management needs a better way to estimate volatility.
method Realized local volatility surface estimated via high-frequency data and Bayesian nonparametric estimation.
result The method can capture counterfactual volatility and improve risk management.
Variational autoencoders help estimate missing volatility data.
problem Estimating missing points on partially observed volatility surfaces.
method Derive latent variables, construct synthetic surfaces fitting available data.
result Synthetic volatility surfaces can be used for stress testing and exotic option valuation.
A new model fits SPX and VIX volatility surfaces and term structures efficiently.
problem Calibrating SPX and VIX volatility models to market data.
method Gaussian polynomial volatility models, joint calibration, functional quantization, Neural Networks.
result A conventional one-factor Markovian model outperforms rough and non-rough models.
Chinchilla Approach 2 biases neural scaling law estimates, leading to unnecessary compute costs.
problem Systematic biases in Chinchilla Approach 2's parabolic fits of neural scaling laws.
method Analyzes three sources of error: IsoFLOP sampling grid width, uncentered sampling, and loss surface asymmetry.
result Chinchilla Approach 3 largely eliminates these biases, offering a more convenient or scalable alternative.
Constructs parallel transport in higher gauge theory using principal 2-bundles.
problem Higher gauge theory and parallel transport in categorified principal bundles.
method Explicit construction of parallel transport for connections on principal 2-bundles.
result Proves constructions fit into axiomatic framework for categorified parallel transport.
The abstract introduces a method to compute surface invariants in 4-manifolds.
problem Computing invariants of surfaces embedded in 4-manifolds.
method Using a nested pair of ribbon fusion categories and banded-link presentations.
result The method provides an invariant sensitive to both genus and knotting.