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.
Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.
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…
Study caustics of an elliptical paraboloid and extend Apollonius problem solution.
WeLa-VAE learns interpretable disentangled representations with weak supervision.
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.
Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.
The study finds conditions for certain surfaces to have a specific type of metric.
The center of mass in General Relativity is hard to define due to coordinate freedom.
For particles constrained on a curved surface, how to perform quantization within Dirac's canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance in passing from the classical Hamiltonian to its quantum mechanical form while p…
In this paper we form relations for the determination of the elements of the Eötvös matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the normal equipotential surface and the Gauss curvature of the actual equipotential surface both passing through the point P is presented…
Locally symplectic structure found on Kerr space-time.
Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide with the foci of conics, 3) the net of tangents to a conic of the confocal family…
Given a bounded domain in with a conformally Euclidean metric , in this paper we consider the inverse problem of recovering a semigeodesic neighborhood of a domain and the conformal factor in the neighborhood from the travel time data (defined below) and the Carte…
Researchers found new functions for spherical clothoids using special functions.
Study examines Hilbert area of inscribed polygons in projective geometry.
The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.
Robot learns to manipulate objects using multiple geometric representations.
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.
The paper proves foliation of area-minimizing hypersurfaces in asymptotically flat manifolds.
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…
Study proper sampling for X-ray transforms on simple surfaces.
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.
New neural network improves MRI reconstruction for non-Cartesian data.
We establish the equivalence of the Tuynman midpoint area formula for a spherical triangle to the classical area formulas of Euler and of Cagnoli. The derivation also yields a variant of the Cagnoli formula in terms of the medial triangle. We introduce the three barycentric coordinates of a point within the spherical t…
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…
Few ideas have enjoyed as large an impact on deep learning as convolution. For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample to this intuition via the seemingly trivial coordinate tra…
We consider solutions to the complex Trkalian equation,~$ \vec{\nabla} \times \vc = \vc ,$ where~$\vc$ is a 3 component vector function with each component in the complex field, and may be expressed in the form~$ \vc = e^{ig} \vec{\nabla} F, $ with~ real and~ complex. We find, there are precisely two classes of s…
The goal of cross-domain object matching (CDOM) is to find correspondence between two sets of objects in different domains in an unsupervised way. Photo album summarization is a typical application of CDOM, where photos are automatically aligned into a designed frame expressed in the Cartesian coordinate system. CDOM i…
A new method speeds up sampling of Boltzmann distribution in high-dimensional systems.
This work proposes a geometric approach to equivariant message passing on Riemannian manifolds.
Automating molecular design using deep reinforcement learning (RL) holds the promise of accelerating the discovery of new chemical compounds. Existing approaches work with molecular graphs and thus ignore the location of atoms in space, which restricts them to 1) generating single organic molecules and 2) heuristic rew…
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.
Discover equations of motion from distorted video frames.
Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
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…
Modified proof constructs holomorphic quilts on closed surfaces.
The leaf space of a Killing Riemannian foliation is a diffeological quasifold.