arXiv research

Develops an analytical method for filtering point process observations.

In this study, we investigate the locus of the centers of the Meusnier spheres. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a principal line, the locus of the …

Study centro-affine invariants on ellipses using canonical Lorentz metric.

We show that the center of the Goldman algebra associated to a closed oriented hyperbolic surface is trivial. For a hyperbolic surface of finite type with nonempty boundary, the center consists of closed curves which are homotopic to boundary components or punctures.

Characterizes curves for minimal surfaces in de Sitter space.

We show that some of centeral fibers of degenerations of hyperelliptic curves are realized as those trigonal curves. In particular, any hyperelliptic curve can be the central fiber of a degeneration of trigonal curves.

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord $AB$ on the parabola, let us denote by $P$ the point on the parabola where the tangent is parallel to $AB$ and by $V$ the point where the line through $P$ parallel to the axis of the p…

Confidence bands for tuning curves improve hyperparameter comparison in NLP.

We prove that curves indicated in the title exist. This results answers to a question posed by A.G.Vitushkin about 30 years ago. We also discuss the minimal number of boundary components of a curve in the unit ball passing through the center, under the condition that all these components are shorter than a given number…

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscien…

In this paper we study properties of the area evolute (AE) and the center symmetry set (CSS) of a convex planar curve $γ$. The main tool is to define a Minkowski plane where $γ$ becomes a constant width curve. In this Minkowski plane, the CSS is the evolute of $γ$ and the AE is an involute of the CSS. We prove that the…

Paper centers Koebe polyhedra using Möbius transformations.

Study shows how torsion in fundamental groups is related to fiber bundles.

New method ranks multivariate distributions in SMOOP using q-dominance.

Refined estimates for surfaces in curved spaces based on Willmore functional.

The paper studies a flow of spacelike curves in a Lorentz-Minkowski plane, showing convergence to a constant function.

Effective methods compute equivariant harmonic maps from surfaces to nonpositively curved spaces.

Spirals are not shortest paths in certain sub-Riemannian geometries.

A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also lines of curvature. Last of all, for special spine curves we obtain the radius …

Improved neural population modeling using shared features and ensemble detection.

Explains curves and surfaces in differential geometry.

Loewner inequality proven for curved surfaces.

We consider two types of $p$-centro affine flows on smooth, centrally symmetric, closed convex planar curves, $p$-contracting, respectively, $p$-expanding. Here $p$ is an arbitrary real number greater than 1. We show that, under any $p$-contracting flow, the evolving curves shrink to a point in finite time and the only…

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For …

New method classifies geodesics on cones.

Sharp inequalities for curved surfaces and cones.

These notes introduce key techniques in differential geometry for curves and surfaces.

We prove that the only compact, origin-symmetric, strictly convex ancient solutions of the planar $p$ centro-affine normal flows are contracting origin-centered ellipses.

Study of evolutes of polygons and curves in higher dimensions.

The study explores isoptic curves of cycloids and their applications.

Develops a method to approximate surfaces with intrinsically flat ribbons for topological inspection.

Study characterizes involutes and evolutes of curves in n-dimensional space.

Spheres in curve graphs are connected, proving Gromov boundary linearity.

In this paper, we deals with isoperimetric-type inequalities for closed convex curves in the Euclidean plane R^2. We derive a family of parametric inequalities involving the following geometric functionals associated to a given convex curve with a simple Fourier series proof: length, area of the region included by the …

New geometric definition of Lie bracket for undirected curves.

Covariance is shown as a commutator in random variable calculus.

Deep learning identifies unique walking patterns from pressure data.

The paper studies the center of the Goldman Lie algebra and its properties.

HAMLET optimizes algorithm selection for machine learning tasks.

LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.

Study geodesic curvature of logarithmic spirals on curved surfaces.

We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these curves being centered at a point of a regular curve and contained in its normal p…

Paper analyzes CKRR for large data, showing risks converge to deterministic values.

In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is $0$ or $1$ and that the surface is ruled. If the generating curve is a Lorentzian ci…

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

Optimizes variational autoencoder for detecting missing data in Mars rover transmissions.

There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this paper, we show that both constructions can be generalized to arbitrary even dime…

Unified method visualizes curvature on curves and surfaces.