A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Simple constructions of semi-discrete and discrete surfaces using Jacobi elliptic functions.
We establish what semi-discrete linear Weingarten surfaces with Weierstrass-type representations in -dimensional Riemannian and Lorentzian spaceforms are, confirming their required properties regarding curvatures and parallel surfaces, and then classify them. We then define and analyze their singularities. In partic…
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves in the conformal n-sphere and their transformation theory is studied. Semi-discre…
We give a Weierstrass type representation for semi-discrete minimal surfaces in Euclidean 3-space. We then give explicit parametrizations of various smooth, semi-discrete and fully-discrete catenoids, determined from either variational or integrable systems principles. Finally, we state the shared properties that those…
New method for flexible tubes and structures, enabling rigid-foldability.
New geometric transformations link discrete and continuous curve motions.
Proves hardness of semi-discrete optimal transport and proposes regularization methods.
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the po…
Stochastic optimization improves semi-discrete OT map estimation with a minimax rate.
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
DRAG decreases regularization to accelerate semi-discrete OT convergence.
On compact surfaces, a Green-Wasserstein inequality cannot be improved without the sqrt(log n) factor.
Framework uses optimal transport for neural architecture search.
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer…
New algorithm improves OT map estimation for semi-discrete settings.
AlignFlow improves FGMs by optimizing noise and data alignment.
Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.
Paper explores folding patterns of curved creases preserving their geometric properties.
Two new algorithms improve neural architecture search efficiency.
Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution. A possible way of dealing with this problem is to use an ensemble of GANs, wher…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed numerical scheme and underlying computational cost. Solution of a such problem i…
We discuss results for the Ribaucour transformation of curves or of higher dimensional smooth and discrete submanifolds. In particular, a result for the reduction of the ambient dimension of a submanifold is proved and the notion of Ribaucour coordinates is derived using a Bianchi permutability result. Further, we disc…
Paper variates Navier-Stokes-Fourier system for thermodynamic consistency.
New methods create full discretized isothermic tori in Euclidean spaces.
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic sp…
This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source randomness of the network is a continuous distribution (the "semi-discrete" setting), th…
Estimates discontinuous optimal transport maps between a discrete and continuous distribution.
New method for pricing options in stochastic volatility models.
The paper analyzes rates of convergence for optimal transport map estimators using barycentric projections.
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations wi…
SVD-based methods reduce computational cost for stochastic systems.
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
Optimal transport reformulates multiple quantile hedging problem.
A new method learns quantization boundaries in continuous space using tessellation.
We solve integrable systems to describe the motion of Kaleidocycles.
A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of -copies of a rigid body joined together by hinges to form…
WGANs use optimal 1-Wasserstein distance to generate distributions.
This paper tackles co-design of neural hardware and software to improve efficiency.
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various probability measures, as in the Wasserstein barycenter problem, or to carry out param…
Deep neural networks can approximate any target probability distribution given certain conditions.
Enhances CEV model pricing with high-order scheme and adaptive time stepping.
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons: sensors in a sensor network may be placed far apart, affecting their individual meas…
Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.
Optimal transport simplifies machine learning by comparing probability measures.
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction …
Wasserstein archetypal analysis finds optimal data summaries using Wasserstein metric.
New scalable methods for unbalanced optimal transport improve efficiency and applicability.