arXiv research

Poisson CNN solves Poisson equations on Cartesian grids efficiently.

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher acc…

We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found using a Nystrom approximation from a dense Cartesian product grid of inducing points. B…

Scalable Gaussian processes with latent Kronecker structure for large datasets.

The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.

Study on balanced Hermitian structures on Lie algebras twisted by representations.

Paper learns Cartesian product graphs with Laplacian constraints.

Study benchmarks methods for learning non-Cartesian k-space trajectories and reconstruction.

In compressed sensing MRI (CS-MRI), k-space measurements are under-sampled to achieve accelerated scan times. CS-MRI presents two fundamental problems: (1) where to sample and (2) how to reconstruct an under-sampled scan. In this paper, we tackle both problems simultaneously for the specific case of 2D Cartesian sampli…

TACE unifies scalar and tensorial modeling in Cartesian space for accurate, stable, and efficient atomistic predictions.

Examines how irreducibility and rigidity affect digital images.

It is well known that the category of Frolicher spaces and smooth mappings is Cartesian closed. The principal objective in this paper is to show that the full subcategory of Frolicher spaces that believe in fantasy that every Weil functor is really an exponentiation by the corresponding infinitesimal object is also Car…

We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.

Given a complete and (locally) cartesian closed category U, it is shown that the category of functors from the category of Weil algebras to the category U is (locally, resp.) cartesian closed. The corresponding axiomatization for differential geometry based upon Weil functors is then given.

Paper proves model structures equal for smooth manifolds and Cartesian spaces.

With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized U-net architecture, and evaluate a large number of trained neural networks with respect to their accuracy for the calculation of pressure and velocity distribution…

New neural network improves MRI reconstruction for non-Cartesian data.

Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is cartesian closed. By emancipating microlinearity from within a well-adapted model …

Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.

Improved computational efficiency for estimating Wasserstein distance.

The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we show that similar analogs do not exist unless one imposes further restrictions such…

Generative model learns shape drift for quantifying domain uncertainty in hemodynamics.

For any n>1 we give an explicit example of an n-axially symmetric Cartesian current in B^3 x S^2 with non-trivial vertical part and non-constant graph part minimizing the relaxed Dirichlet energy among the n-axially symmetric Cartesian currents with the same boundary. This stands in sharp contrast with a results of Har…

New proof shows how to fill a square with Fibonacci curve.

New method for manifold topological learning avoids remeshing issues.

We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.

Let B be a fiber bundle with compact fiber F over a compact Riemannian n-manifold M. There is a natural Riemannian metric on the total space B consistent with the metric on M. With respect to that metric, the volume of a rectifiable section s:M--> B is the mass of the image s(M) as a rectifiable n-current in B. Theorem…

We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.

Modified proof constructs holomorphic quilts on closed surfaces.

The leaf space of a Killing Riemannian foliation is a diffeological quasifold.

The abstract discusses maximal rank 4-webs formed by confocal conics and their properties.

We prove that if a compact nilmanifold $Γ\backslash G$ is endowed with a Vaisman structure, then $G$ is isomorphic to the Cartesian product of the Heisenberg group with $\mathbb{R}$.

We show that the maximal orbit dimension of a simultaneous Lie group action on n copies of a manifold does not pseudo-stabilize when n increases. We also show that if a Lie group action is (locally) effective on subsets of a manifold, then the induced Cartesian action is locally free on an open subset of a sufficiently…

We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…

In this paper, we establish the rigidity result for local holomorphic volume preserving maps from an irreducible Hermitian manifold of compact type into its Cartesian products.

New limits of minimal surface systems have surprising large interior parts.

This paper focuses on Bayesian Optimization (BO) for objectives on combinatorial search spaces, including ordinal and categorical variables. Despite the abundance of potential applications of Combinatorial BO, including chipset configuration search and neural architecture search, only a handful of methods have been pro…

Using standard analysis only, we present an extension ${^\bullet\R}$ of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesim…

WeLa-VAE learns interpretable disentangled representations with weak supervision.

The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.

Study caustics of an elliptical paraboloid and extend Apollonius problem solution.

The study bounds the effective diameter of graphs with positive Ollivier curvature.

Half grid diagrams prove every link can be represented by a special type of grid diagram.

Grid homology confirms the Upsilon invariant in knot theory.

GridPyM handles grid diagrams for knot theory.

Grid homology theory for spatial graphs extends skein sequence.

Extends knot invariant to filtered grid complexes.

New method finds grid diagrams for many fibered knots.