Study Fuchsian loci in mPSLn(R)-Hitchin components of a pair of pants.
problem Understanding Fuchsian loci in mPSLn(R)-Hitchin components. method Using Bonahon-Dreyer parametrization, explicit parametrization of Fuchsian loci of a pair of pants.
result Explicit parametrization of Fuchsian loci of a pair of pants.
Let P(S) be the space of convex projective structures on a surface S with negative Euler characteristic. Goldman and Bonahon-Dreyer constructed two different sets of global coordinates for P(S), both associated to a pair of pants decomposition of the surface S. The article explicitly describes the coordinate change bet…
The paper studies properties of triangle and shearing invariants in PSL(n,R) and connects them to a slice of Hitchin components.
problem Understanding invariants of PSL(n,R)-Fuchsian representations and their relationship to Hitchin components.
method Examined triangle and shearing invariants, used Bonahon-Dreyer parameterization.
result The Fuchsian locus of Hitchin components corresponds to a slice.
The area of a convex projective surface of genus g≥2 is at least (g−1)π2/2+∥τ∥2/8 where τ=(logti) is the vector of triangle invariants of Bonahon-Dreyer and ti are the Fock-Goncharov triangle coordinates.
Using the work of Bonahon-Dreyer and Fock-Goncharov, one can construct a real-analytic parameterization for the PSL(n,R) Hitchin component of a surface S, that is explicitly analogous to the Fenchel-Nielsen coordinates on the Teichmuller space of S. Given a Hitchin representation, we give a lower bound on the "length" …
This paper connects real closed fields to Hitchin representations and their properties.
problem Understanding representations of surface groups over real closed fields.
method Tarski-Seidenberg transfer principle and multiplicative Bonahon-Dreyer coordinates.
result Hitchin representations correspond to F-positive representations over real closed fields. Over-parametrization speeds up learning a single neuron model.
problem Understanding why over-parametrization accelerates learning in neural networks.
method Studied a simple model of a single teacher neuron with quadratic activation, showing how over-parametrization can lead to faster convergence.
result Over-parametrization helps gradient descent enter the neighborhood of a global optimal solution faster.
Polynomially parametrize interesting knotted surfaces.
problem Constructing polynomial parametrizations of knotted surfaces.
method Develop polynomial parametrization methods for specific knotted surfaces.
result Examples of polynomial parametrizations for knotted spheres, tori, and planes.
FAMOS combines parametric and non-parametric methods for efficient image stylization.
problem Efficiently stylize images with limited data and compute resources.
method Fully Adversarial Mosaics (FAMOS) that integrates parametric and non-parametric approaches.
result Demonstrates the effectiveness of FAMOS in stylizing images with minimal data and compute resources.
We give a local parametric description of all holomorphic hypersurfaces in complex Euclidean and projective spaces with constant index of relative nullity, together with applications. This is a complex analogue to the parametrization for real hypersurfaces in Euclidean space known as the Gauss parametrization.
New parametrization handles sextactic points on closed curves.
problem Parametrizing closed projective plane curves with sextactic points.
method Introducing an additional scalar parameter α to define a 2π-periodic global parametrization.
result The balanced parametrization is unique up to a shift of the parameter and is a global projective invariant.
Paper solves recovery of parametrizations from Legendre data.
problem Recovering parametrizations from Legendre data.
method Systematic and widely-applicable method to recover parametrizations from Gauss mapping and height function.
result Showed how to recover parametrization from dense subset of real-analytic parametrizations.
Improves deep learning theory by reducing over-parametrization size.
problem Deep learning theory over-parametrization issues.
method Used Matrix Chernoff Bound to improve over-parametrization size.
result Improved over-parametrization size over previous results.
Parametric UMAP learns a mapping from data to embeddings.
problem Representing and learning from structured data.
method Parametric optimization over neural network weights for UMAP.
result Parametric UMAP performs comparably to non-parametric UMAP with faster online embeddings.
Proposes new conformal parametrizations for modified Einstein gravity.
problem Initial data in modified Einstein gravity theories.
method Proposes conformal parametrizations that lead to conformally covariant systems.
result Some conformal parametrizations give rise to conformally covariant systems.
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…
The study finds parametrizations for surfaces of revolution with a linear curvature ratio.
problem Deriving surfaces of revolution with a specific curvature ratio.
method Derives parametrizations for surfaces of revolution with an affine-linear relation between their curvature radii.
result Explicit parametrizations found for a countably-infinite number of surfaces.
Paper compares different models for time-to-event analysis.
problem Comparing models for time-to-event analysis.
method Experimental comparison of semi-parametric, parametric, and machine learning models.
result Models' performance evaluated using concordance index.
Proposes a parametric t-SNE without perplexity tuning.
problem Non-parametric t-SNE's perplexity parameter limits DR quality.
method Multi-scale parametric t-SNE with deep neural network.
result Produces reliable embeddings with competitive neighborhood preservation.
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, …
Proposes method for eliciting non-parametric joint priors using normalizing flows.
problem Learning complex non-parametric joint priors for model parameters.
method Expert elicitation combined with normalizing flows for generative modeling.
result Framework supports elicitation of both parametric and non-parametric priors.
Article explains and implements mean curvature flow for surface parametrization.
problem Surface parametrization challenges.
method Conformalized mean curvature flow implementation.
result Demonstrates effectiveness of mean curvature flow for surface parametrization.
The CAPM fails to explain small firm effect and proposes semi-parametric measures.
problem The CAPM fails to explain the small firm effect and is biased and inconsistent.
method Uses non-parametric and semi-parametric asset pricing models to analyze risk and performance measures.
result Semi-parametric measures are non-constant under extreme market conditions and not significantly different from the Fama-French three-factor model.
Cookbook transforms constrained statistical inference into unconstrained problems.
problem Transforming constrained statistical inference into unconstrained problems.
method Bijective and diffeomorphisms parametrizations.
result Maintains statistical inference properties like identifiability.
Teichmüller space and hyperelliptic surfaces parametrized by angles.
problem Parametrizing Teichmüller space and hyperelliptic surfaces using angles.
method Proved parametrization using 6g-5 and 4g-2 angle parameters for Teichmüller space and hyperelliptic surfaces respectively.
result Proved parametrization of Teichmüller space and hyperelliptic surfaces by angle parameters.
Parametric t-SNE improves generalization for streaming data.
problem Training neural networks for t-SNE objective function fails due to gradient exploding.
method Applied gradient clipping to solve gradient exploding problem.
result Parametric t-SNE achieves quality compatible with non-parametric t-SNE while generalizing to new data.
New defense method for non-parametric classifiers robust against adversarial attacks.
problem Lack of robustness in non-parametric classifiers against adversarial attacks.
method Adversarial pruning method to preprocess datasets and a novel attack.
result Adversarial pruning provides a robust defense for non-parametric classifiers.
Symbolic regression finds simple formulas for implied volatility.
problem Discovering accurate parametric representations for implied volatility.
method Symbolic regression to find analytic formulas from market data.
result Symbolic regression identifies compact parametrizations with competitive fitting performance.
Proposes a flexible framework for implied volatility surfaces with random parameters.
problem Inconsistent calibration of parametric implied volatility models when market volatility deviates from the model's regime.
method Introduces random coefficients for parametric implied volatility formulas, preserving analytic flexibility and efficiency.
result Demonstrates improved modeling of implied volatility curves, especially for short-term options and earnings announcements.
Semi-parametric models improve robot dynamics modeling accuracy.
problem Improving inverse dynamics model accuracy in robotics.
method Comparison of semi-parametric Gaussian process regression and a novel model-based neural network.
result Semi-parametric Gaussian process regression yields the most accurate models.
Dr. of Crosswise reduces over-parametrization in neural networks.
problem Reduction of over-parametrization in neural networks.
method Introduces a new operand for rapid computation in neural networks framework.
result Reduces over-parametrization in neural networks.
Parametric divergences are effective for generative modeling despite being non-optimal.
problem Training high-dimensional distributions with GANs.
method Generalization of GAN losses to parametric divergences, focusing on sensitivity to specific distribution moments.
result Parametric divergences are more suitable for learning high-dimensional distributions due to their sensitivity to specific aspects of the distribution.
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model …
Neural networks can learn relationships that traditional models cannot.
problem Identifying factors that differentiate neural networks from traditional models.
method Proving non-identifiability of neural networks compared to smooth parametric models.
result Neural networks can learn nontrivial relationships that traditional models cannot.
This research uses DPPs to improve semi-parametric regression models.
problem Improving comprehensibility in semi-parametric regression models without sacrificing accuracy.
method Introduced a novel representation of finite DPPs and used it to derive a key identity illustrating implicit regularization.
result Demonstrated the implicit regularization effect of determinantal sampling for semi-parametric regression.
Parametric insurance offers better risk-sharing in high-risk settings than traditional indemnity insurance.
problem High-risk environments where traditional indemnity insurance is unaffordable or ineffective.
method Comparison of excess-of-loss indemnity insurance and parametric insurance within a mean-variance framework, considering fixed costs and binding budget constraints.
result Parametric insurance yields higher welfare for risk-averse individuals, especially when indemnity insurance is impractical.
New method to parametrize infinite Riemann surfaces with bounded triangulations.
problem Parametrizing infinite Riemann surfaces with bounded triangulations.
method Introducing bounded ideal triangulations and proving real-analyticity of the parametrization.
result Real-analytic parametrization of Teichmüller spaces for infinite surfaces with bounded triangulations.
New method improves Bayesian inference for parametric models, robust to misspecification.
problem Inference can be untrustworthy when parametric models are wrong.
method Adaptive nonparametric corrections for parametric Bayesian models using generalized Bayes.
result The method achieves robustness and efficiency, converging fast when the parametric model is close to true.
PGPs handle big data uncertainty with parametric Gaussian processes.
problem Uncertainty quantification in big data.
method Parametric Gaussian processes designed for big data, avoiding stochastic variational inference.
result Demonstrated effectiveness in handling large datasets with uncertainty quantification.
New network learns non-parametric invariances from data.
problem Modeling non-parametric invariances in data.
method Introduces PRC-NPTN networks with permanent random connectomes.
result Improves generalization and outperforms existing methods.
Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It …
Generative adversarial networks improve stochastic input parametrization in subsurface flow simulations.
problem Effective parametrization of high-dimensional, correlated stochastic inputs in subsurface flow simulations.
method Training a generative adversarial network to emulate the data generating process of stochastic inputs.
result Generative adversarial networks preserve both visual realism and high-order statistics of flow responses, achieving a significant dimensionality reduction.
The article applies Lusternik-Schnirelmann theory to establish lower bounds on critical points using sequential and parametrized topological complexity.
problem Establishing lower bounds on the number of critical points of functions using topological complexity.
method Applying Lusternik-Schnirelmann theory to sequential and parametrized topological complexity.
result Established various lower bounds on the number of critical points using sequential and parametrized topological complexity.
In this article we will construct the Liouville parametrization of the triaxial ellipsoid. In the literature quadrics are given as examples of Liouville surfaces, yet no one gives such a parametrization. For this we introduce the generalized Jacobi amplitude as inverse of the elliptic integral of the third kind.
Derives Weyl law for volume spectrum using parametric inequalities.
problem Deriving the Weyl law for the volume spectrum in compact Riemannian manifolds.
method Proves parametric generalizations of isoperimetric and coarea inequalities to derive the Weyl law.
result Derives the Weyl law for 1-cycles in 3-manifolds.
Proposes extensions to semi-parametric models using BART for shared covariates.
problem Avoiding poor coverage properties and reducing bias in linear predictor estimates.
method Modifies tree-generation moves in BART to handle shared covariates between linear and non-parametric components.
result Competitive performance in modelling complex interactions and predicting student achievements.
This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equa- tion, while the latter exploits a suitable kernel function. We provide an extensive comparison …
SGD converges exponentially fast in non-convex over-parametrized learning.
problem Convergence of SGD in non-convex, over-parametrized learning.
method Analysis of SGD with constant step size for non-convex functions satisfying the PL condition.
result Exponential convergence of SGD for non-convex functions satisfying the PL condition.