arXiv research

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…

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

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…

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

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

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.

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.

Digital trees have approximate fixed point property, and conditions for products are explored.

Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star, Lie derivative, pullback and interior product. Partitions of unity exist in thi…

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 …

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…

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

The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first geometrical application, every surface that admits a conformal polynomic paramet…

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

Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired during an US scan to parameterize the spatio-temporal stress-strain behavior. Curr…

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.

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…

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.

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.

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

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

We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, $G$, over the rows and columns. Our main results shows that for …

In our previous papers [Far East Journal of Mathematical Sciences, 35 (2009), 211-223] and [International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have developed the theory of Weil prolongation, Weil exponentiability and microlinearity for Frolicher spaces. In this paper we will relativize it so as…

We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii)…

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …

New method detects non-product domains using squeezing function.

We prove a modified version of Turbiner's conjecture in three dimensions and we give a counter-example to the original conjecture. The Lie algebraic Schrödinger operators corresponding to flat metrics of a certain restricted type are shown to separate partially in either Cartesian, cylindrical or spherical coordinates.

Constructs special Kähler structures on Lie groups.

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a conjecture of Lewis made in 1968.

Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat spacetime due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived, which are particularly unusual as they involve second derivatives of the coordin…

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…

The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lame type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transf…

New Calabi-Yau metrics constructed with detailed geometry at infinity.

CAN approximates explicit feature interactions for CTR prediction.

Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case and the case when the map's domain is a Cartesian product of two sets. Also cons…